2010-2011 Bulletin – PDF - SEAS Bulletin - Columbia University

A MESSAGE FROM THE DEANAs students of The Fu FoundationSchool of Engineering and AppliedScience at Columbia University, you arepart of a long line of engineering and appliedscience leaders who have studied at Columbia.From John Stevens (Class of 1768), inventorof the steamboat, and William Barclay Parsons(Class of 1882), chief engineer of New York’sfirst subway line, to Robert C. Merton (Classof 1965), Nobel laureate in economics, andMichael J. Massimino (Class of 1984), theNASA astronaut who twice repaired the HubbleSpace Telescope and was the first person totweet from space, our alumni exemplify theexcellence, leadership, and impact that defineColumbia Engineering.You are among the select few who havejoined our community for an education that willenable you to become the next generation ofsocially responsible engineering and appliedscience leaders whose work results in thebetterment of the human condition. You, too,will become part of the history of this school,which is inextricably entwined with ColumbiaUniversity’s and with the City of New York.We foster an engineering educationparadigm that is symbolized by the Greekletter π. The first support column of the πis the depth of knowledge you gain in yourengineering or applied science major. Thesecond is the knowledge you acquire througha minor, or your involvement in entrepreneurshipinitiatives, research opportunities, andcommunity-based service-learning. The overarchingconnector of these two foundations,the crossbeam of the π, is Columbia’s famedliberal arts Core Curriculum, the umbrella thatpositions engineering and applied sciencewithin the context of the larger society, for thebetterment of the human condition and thesustainability of our planet.Some of you will choose to make an impactby bringing together your knowledge andleadership in pandisciplinary research, perhapsin an area that I call “CyberBioPhysicalSystems,” where the biological, physical, anddigital worlds intersect and fuse. These areasbring together our knowledge of sensors,materials, nanotechnology, and biological systems,and hold promise as a frontier for thedevelopment of innovative solutions to the mostchallenging problems of modern society.You are part of a school that offers greatopportunities for learning and advancement,within a premier research university that is situatedin the vibrant and cosmopolitan City ofNew York. I encourage you to take full advantageof these opportunities.Feniosky Peña-MoraDeanSEAS 2010–2011

TABLE OF CONTENTSAbout the School and 1UniversityHISTORY OF THE SCHOOL 2RESOURCES AND FACILITIES 5Undergraduate Studies 9UNDERGRADUATE PROGRAMS 10Policy on Degree Requirements 10The First Year/Sophomore Program 10Study Abroad 14Combined Plan Programs 16The Junior-Senior Programs 17Programs in Preparation for 18Other ProfessionsJoint Programs 19Registered Programs 19UNDERGRADUATE ADMISSIONS 21Admission as a First-Year Student 21Applicants with Advanced Standings 22Campus Visits and Interviews 23UNDERGRADUATE TUITION, 24FEES, AND PAYMENTSFINANCIAL AID FOR 26UNDERGRADUATE STUDYDetermining Eligibility 26Financial Aid Awards 27How to Apply for Financial Aid 28Tax Withholding for Nonresident 30Alien Scholarship andFellowship RecipientsGraduate Studies 31THE GRADUATE PROGRAMS 32The Master of Science Degree 32The Professional Degree 34Doctoral Degrees: Eng.Sc.D. 34and Ph.D.Special Nondegree Students 35COLUMBIA VIDEO NETWORK 36GRADUATE ADMISSIONS 37GRADUATE TUITION, FEES, 39AND PAYMENTSFINANCIAL AID FOR GRADUATE 41STUDYFinancing Graduate Education 41Instructions for Financial Aid 41ApplicantsGraduate School Departmental 42FundingAlternative Funding Sources 42O ther Financial Aid—Federal, 43State, and Private ProgramsEmployment 44Contact Information 44Faculty and Administration 45Departments and Academic 55ProgramsKEY TO COURSE LISTINGS 56APPLIED PHYSICS AND 58APPLIED MATHEMATICSBIOMEDICAL ENGINEERING 71CHEMICAL ENGINEERING 83CIVIL ENGINEERING AND 94ENGINEERING MECHANICSCOMPUTER ENGINEERING 105PROGRAMCOMPUTER SCIENCE 110EARTH AND ENVIRONMENTAL 123ENGINEERINGELECTRICAL ENGINEERING 137INDUSTRIAL ENGINEERING 155AND OPERATIONS RESEARCHMATERIALS SCIENCE AND 171ENGINEERING PROGRAMMECHANICAL ENGINEERING 179Undergraduate Minors 193Interdisciplinary Courses 201and Courses in OtherDivisions of the UniversityINTERDISCIPLINARY 202ENGINEERING COURSESCOURSES IN OTHER DIVISIONS 203OF THE UNIVERSITYBiological Sciences 203Business 203Chemistry 203Earth and Environmental Sciences 204Humanities and Social Sciences 206Mathematics 207Physics 207Statistics 209Campus and Student Life 211CAMPUS LIFE 212STUDENT SERVICES 217Scholarships, Fellowships, 221Awards, and PrizesUniversity and School 233Policies, Procedures, andRegulationsACADEMIC PROCEDURES 234AND STANDARDSACADEMIC STANDING 238POLICY ON CONDUCT AND 241DISCIPLINEESSENTIAL POLICIES FOR THECOLUMBIA COMMUNITY 244STUDENT GRIEVANCES, 245ACADEMIC CONCERNS, ANDCOMPLAINTSDirectory of University 247ResourcesCOLUMBIA UNIVERSITY 248RESOURCE LISTMAPS 252INDEX 254Academic Calendar (see inside backcover)

About the School and University

2HISTORY OF THE SCHOOLA COLONIAL CHARTERSince its founding in 1754, as King’sCollege, Columbia University has alwaysbeen an institution both of and for theCity of New York. And with an originalcharter directing it to teach, amongother things, “the arts of Number andMeasuring, of Surveying and Navigation,. . . the knowledge of . . . various kindsof Meteors, Stones, Mines and Minerals,Plants and Animals, and everything usefulfor the Comfort, the Convenienceand Elegance of Life,” it has also alwaysbeen an institution of and for engineers.ENGINEERS FOR ANINDUSTRIAL REVOLUTIONAn early and influential graduate from theschool was John Stevens, Class of 1768.Instrumental in the establishment of U.S.patent law, Stevens procured manypatents in early steamboat technology,operated the first steam ferry betweenNew York and New Jersey, received thefirst railroad charter in the U.S., built apioneer locomotive, and amassed a fortune,which allowed his sons to found theStevens Institute of Technology.THE GILDED AGEAs the city grew, so did the school.King’s College was rechartered asColumbia College in 1784, and relocatedfrom the Wall Street area to what isnow Midtown in 1857. Students beganentering the new School of Mines in1864. Trained in mining, mineralogy, andengineering, Columbia graduates continuedto make their mark both at homeand abroad.Working around the globe, WilliamBarclay Parsons, Class of 1882, wasan engineer on the Chinese railway andthe Cape Cod and Panama Canals,and, most importantly for New York,chief engineer of the city’s first subway.Opened in 1904, the subway’s electriccars took passengers from City Hallto Brooklyn, the Bronx, and the newlyrenamed and relocated ColumbiaUniversity in Morningside Heights, itspresent location on the Upper West Sideof Manhattan.A MODERN SCHOOL FOR THEMODERN ERAThe School of Mines became the Schoolof Mines, Engineering, and Chemistry in1896, and its professors—now calledthe Faculty of Engineering and AppliedScience—included Michael IdvorskyPupin, a graduate of the Class of 1883.As a professor at Columbia, Pupin didpioneering work in carrier-wave detectionand current analysis, with importantapplications in radio broadcasting; inventedthe “Pupin coil,” which extended therange of long-distance telephones; andtaught classes in electromechanics.An early student of Pupin’s was IrvingLangmuir. Graduating in the Class of1903, Langmuir enjoyed a long career atthe General Electric research laboratory,where he invented a gas-filled tungstenlamp; contributed to the development ofthe radio vacuum tube; extended GilbertLewis’s work on electron bonding andatomic structure; and did research inmonolayering and surface chemistry,which led to a Nobel Prize in chemistryin 1932.But early work on radio vacuumtubes was not restricted to privateindustry. Working with Pupin, an engineeringstudent named Edwin HowardArmstrong was conducting experimentswith the Audion tube in the basementof Philosophy Hall when he discoveredhow to amplify radio signals throughregenerative circuits. Graduating a yearlater, in the Class of 1913, Armstrongwas stationed in France during theFirst World War, where he inventedthe superheterodyne circuit to tune inand detect the frequencies of enemyaircraft ignition systems. After the warArmstrong improved his method of frequencymodulation (FM) and by 1931had both eliminated the static andimproved the fidelity of radio broadcastingforever. The historic significance ofArmstrong’s contributions was recognizedby the U.S. government when thePhilosophy Hall laboratory was designateda National Historic Landmark in2003.THE NUCLEAR AGEAs the United States evolved into amajor twentieth-century political power,the University continued to build ontoits undergraduate curriculum the broadrange of influential graduate and professionalschools that define it today.Renamed once again in 1926, theSchool of Engineering prepared studentsfor careers not only as engineersof nuclear-age technology, but as engineersof the far-reaching political implicationsof that technology as well.After receiving a master’s degreefrom the School in 1929, AdmiralSEAS 2010–2011

4remains an institution of manageablesize within a great university. Committedto the educational philosophy that abroad, rigorous exposure to the liberalarts provides the surest chart with whichan engineer can navigate the future,all undergraduates must complete amodified but equally rigorous versionof Columbia College’s celebrated CoreCurriculum. It is these selected coursesin contemporary civilization in the Westand other global cultures that bestprepare a student for advanced coursework; a wide range of eventual professions;and a continuing, life-long pursuitof knowledge, understanding, and socialperspective. It is also these Core coursesthat most closely tie today’s studentto the alumni of centuries past. Througha shared exposure to the nontechnicalareas, all Columbia engineering students—past,present, and future—gainthe humanistic tools needed to buildlives not solely as technical innovators,but as social and political ones as well.SEAS 2010–2011

RESOURCES AND FACILITIES5A COLLEGE WITHIN THEUNIVERSITYA unique educational opportunity, TheFu Foundation School of Engineeringand Applied Science at ColumbiaUniversity offers programs to bothundergraduate and graduate studentswho undertake a course of study leadingto the bachelor’s, master’s, or doctoraldegree in engineering and appliedscience. Combining the advantagesof a small college with the extensiveresources of a major research university,students at the School pursue their academicinterests under the guidance ofoutstanding senior faculty members whoteach both undergraduate and graduatelevel courses. Encouraged by the facultyto undertake research at all levels, studentsat the School receive the kind ofpersonal attention that only Columbia’sexceptionally high faculty-student ratioaffords.THE NEW YORK ADVANTAGEBesides the faculty, the single greatestfacility at a Columbia student’s disposalis without doubt the City of New York.Within easy reach by walking, bus, subway,or taxi, New York’s broad range ofsocial, cultural, and business communitiesoffer an unparalleled opportunityfor students to expand their horizons ordeepen their understanding of almostany human endeavor imaginable. Withart from small SoHo galleries to majorUptown museums; music from Harlemjazz clubs to the Metropolitan Opera;theatre from performance art in the EastVillage to musicals on Broadway; foodfrom French on the Upper East Side toAsian in Chinatown; and sports teamsfrom the Jets to the Yankees, New Yorkis the crossroads of the world.New York is fast becoming a majorplayer in high-tech research and development,where Fortune 500 companiestraded on Wall Street seek partnershipswith high-tech start-up venturesin Tribeca. As part of the researchcommunity themselves, Columbia studentshave exceptional opportunitiesfor contact with industry both on andoff campus. Senior representatives ofthese companies often visit Columbia tolecture as adjunct faculty members oras special speakers, and undergraduateand graduate students frequently undertakeresearch or internships with theseand other companies, oftentimes leadingto offers of full-time employment aftergraduation.In addition to its ties to privateindustry, Columbia also has a historicallyclose relationship with the publicsector of New York, stretching back tothe eighteenth century. No other cityin the world offers as many impressiveexamples of the built environment—theworld’s most famous collection of skyscrapers,long-span bridges, road andrailroad tunnels, and one of the world’slargest subway and water supply systems.Involved in all aspects of the city’sgrowth and capital improvements overthe years, Columbia engineers havebeen responsible for the design, analysis,and maintenance of New York’senormous infrastructure of municipalservices and communications links, aswell as its great buildings, bridges, tunnels,and monuments.THE UNIVERSITY AT LARGEColumbia University occupies two majorcampuses, as well as additional specialpurposefacilities throughout the area.Besides the main campus located onthe Upper West Side in MorningsideHeights, further uptown in WashingtonHeights is the Health Sciences campus,which includes Columbia’s medicalschool (the College of Physicians andSurgeons), the Mailman School of PublicHealth, the New York State PsychiatricInstitute, and other health professionsprograms. The Health Sciences Divisionis an equal partner with NewYork-Presbyterian Hospital in the ColumbiaMedical Center, the world’s first academicmedical center. The medicalcenter opened in 1928 when Columbia’shealth-related schools and PresbyterianHospital (which has since mergedwith New York Hospital to becomeNewYork-Presbyterian Hospital) movedto the Washington Heights location. TheEngineering School’s new BiomedicalEngineering Department has officeson both the Morningside and HealthSciences campuses.Beyond its schools and programs,the measure of Columbia’s true breadthand depth must take into account itsseventy-odd internationally recognizedcenters and institutions for specializedresearch, which study everything fromhuman rights to molecular recognition,as well as the close affiliations it holdswith Teachers and Barnard Colleges, theJuilliard School, the American Museumof Natural History, and both the Jewishand Union Theological Seminaries.Columbia also maintains major off-SEAS 2010–2011

6campus facilities such as the Lamont-Doherty Earth Observatory in Palisades,N.Y., and the Nevis Laboratories inIrvington, N.Y. Involved in many cooperativeventures, Columbia also conductsongoing research at such facilitiesas Brookhaven National Laboratory inUpton, N.Y., and the NASA GoddardInstitute for Space Studies located justoff the Morningside campus.THE MORNINGSIDE HEIGHTSCAMPUSThe Fu Foundation School ofEngineering and Applied Science islocated on Columbia’s Morningsidecampus. One of the handsomest urbaninstitutions in the country, the thirtytwoacres of the Morningside campuscomprise over sixty buildings of housing;recreation and research facilities; centersfor the humanities and social and puresciences; and professional schools inarchitecture, business, the fine arts, journalism,law, and other fields.THE FU FOUNDATION SCHOOLOF ENGINEERING AND APPLIEDSCIENCEThe Fu Foundation School ofEngineering and Applied Scienceoccupies three laboratory and classroombuildings at the north end of thecampus, including the Schapiro Centerfor Engineering and Physical ScienceResearch. In September 2010 theInterdisciplinary Science and EngineeringBuilding currently under constructionis scheduled to open and will houseSEAS laboratories in nanotechnologyand biomedical imaging. Because ofthe School’s close proximity to theother Morningside facilities and programs,Columbia engineering studentshave ready access to the whole of theUniversity’s resources.Comprising multiple programs ofstudy, with facilities specifically designedand equipped to meet the laboratoryand research needs of both undergraduateand graduate students, the Schoolis the site of an almost overwhelmingarray of basic and advanced researchinstallations, from the Columbia GenomeCenter and Nanoscale Science andEngineering Center to the School’s newestmajor center, the Energy FrontierResearch Center, which will examinenew and more efficient ways to extractsolar energy. Details about specificprograms’ laboratories and equipmentcan be found in the sections describingthose programs.SEAS COMPUTING FACILITIESThe Botwinick Multimedia LearningLaboratory at Columbia University haschanged the way engineers are educatedhere.Created with both education andinteraction in mind, the lab providesstudents and instructors with fifty stateof-the-artApple MacPro workstations, afull set of professional-grade engineeringsoftware tools, and a collaborativeclassroom learning environment to helpthem engage in real-world interactionswith community clients, SEAS faculty,and professional practitioners. It is hometo the School’s introductory first-yearengineering course, as well as advancedclasses in 3-D modeling and animation,technology and society, and entrepreneurship.The classroom features a widescreenSMART Board, two highdefinitionLCD projectors, and a SonyEVI-HD1 PTZ camera with direct-to-diskrecording via HD-SDI using a Kona3video capture card.CENTRAL COMPUTINGRESOURCESColumbia University InformationTechnology (CUIT)www.columbia.eduContact the CUIT Helpdesk forTechnical Support:askCUIT@columbia. edu or visitwww.columbia.edu/acis/support/By phone: 212-854-1919Monday–Thursday: 8:00 a.m.–11:00 p.m.Friday: 8:00 a.m.–7:00 p.m.Saturday: 10:00 a.m.–6:00 p.m.Sunday: 3:00 p.m.–11:00 p.m.In person (some consultations mayrequire an appointment):CUIT Helpdesk Support Center202 Philosophy HallMonday–Friday: 10:00 a.m.–6:00 p.m.Columbia University InformationTechnology (CUIT) provides ColumbiaUniversity students, faculty, and staffwith a myriad of central computing andcommunications services, includingColumbia’s wireless and high-speedcampus Ethernet network, available toall students in residence hall rooms.CUIT also manages an array of computerlabs, terminal clusters, ColumbiaNetkiosk stations, electronic classrooms,and provides a variety of technical supportservices via the CUIT Helpdesk.CUIT services include the following: E-mail accounts and CubMail, aWeb-based program for accessingColumbia e-mail. It provides a secureand convenient way to send andreceive mail from anywhere, using anyWeb browser.Computer account IDs provide accessto Columbia’s secure online informationresources, campus computerlabs, and printing on CUIT printers. AllColumbia students, faculty, and staffare assigned an ID account (calledUniversity Network ID or UNI).Columbia’s Web site provides accessto hundreds of online services andresources, including extensive academic,scholarly, and administrativeresources, a myriad of library catalogsand references, the Directory ofClasses, registration information, campuspublications, and events listings.Technical support is available throughthe CUIT Helpdesk, which providestechnical assistance to students onthe Morningside campus online, byphone, or in person. (See beginningof this section for hours and contactinformation.)CourseWorks is the University coursemanagement system. It allows instructorsto easily develop and maintaincourse Web sites, distribute classmaterials, link to online reserves,administer quizzes and tests, communicatewith students, and promoteonline discussions.Electronic classrooms are equippedwith multimedia capabilities such ascomputer and projection systems,DVD and CD-ROM players, VCRs, andaudio systems.Public computer kiosks are availablein various locations around theMorningside campus for accessingColumbia’s web resources and e-mail.Computer labs and clusters providestudents, faculty, and researchers withSEAS 2010–2011

access to a range of software. Somelocations have consultants to providelab help.Printing facilities are available throughoutthe Morningside campus andBarnard College. These high-speed,high-volume printers are located inCUIT computer labs, libraries, residencehalls, and other computer clustersand electronic classrooms.Computer security is extremely importantat Columbia and CUIT providesseveral resources online, includinglinks to download antivirus and antispywaresoftware. The site also providesinformation on how to protectyour system, data, and privacy whenworking online.Electronic Data Service run jointly byCUIT and the Libraries, provides computingsupport for researchers withdata-intensive applications, includingstatistical software, and finding andselecting appropriate data.Telephone and cable TV service isavailable to students living in Universityresidence halls.THE COLUMBIA UNIVERSITYLIBRARIESColumbia University Libraries/InformationServices is one of the top five academicresearch library systems in NorthAmerica. The collections include over10 million volumes, over 100,000 journalsand serials, as well as extensiveelectronic resources, manuscripts, rarebooks, microforms, maps, graphic andaudio-visual materials. The services andcollections are organized into 22 librariesand various academic technologycenters. The Libraries employ more than550 professional and support staff. TheWeb site of the Libraries at www.columbia.edu/cu/lwebis the gateway to itsservices and resources.The Ambrose Monell EngineeringLibrary, located in 422 Mudd, containsmore than 70,000 print volumes pertainingto biomedical, chemical, civil, electrical,industrial, mechanical, and materialsengineering as well as applied physics,applied mathematics and computerscience. Online, LibraryWeb providesaccess to extensive collections of electronicjournals, ebooks (including handbooks),standards, patents and societypublications (ACM, ACS, ASCE, ASME,IEEE, MRS, SPIE, etc.) Databasessuch as Compendex, INSPEC, Scopusand Web of Science help patrons topinpoint relevant engineering and scienceresearch. Assistance is availablein person, by telephone (212-854-2976)or by e-mail (engineering@libraries.cul.columbia.edu.)CENTER FOR CAREEREDUCATIONCenter for Career EducationColumbia UniversityEast Campus, Lower LevelMail Code 57272960 BroadwayNew York, NY 1002770-74 Morningside DrivePhone: 212-854-5609Fax: 212-854-5640E-mail: cce@columbia.eduThe Columbia University Center forCareer Education (CCE) helps studentsand alumni develop the key competenciesnecessary to make informed decisionsand take the necessary steps toachieve their career goals. CCE establishesconnections and facilitates interactionamong undergraduate students, graduatestudents, alumni, employers, andorganizations to generate opportunitiesthat help students pursue their personaland professional career objectives.CCE encourages students andalumni to visit the Center and to registerto use Columbia’s job and internshipdatabase, LionSHARE, to maximize thelevel of resources and assistance theycan receive. CCE’s Web site (www.careereducation.columbia.edu) containsinformation on career search strategiesand tools, a calendar of events, careerfairs, and access to LionSHARE.CCE provides career developmentopportunities for students beginning intheir first year at Columbia, offering aseries of coordinated programs, workshops,seminars, and individual one-toonecounseling. Career development isa lifelong process that may include selfassessment,competency development,networking, informational interviewing,internships, summer work experience,study abroad, preparation for the jobsearch or for the graduate/professionalschool application process. Above allelse, it is a process of discovery andlearning, which provides a foundationfor achieving goals throughout life. CCEpartners with students on all of theseaspects of the career search.CCE manages full-time andinternship opportunities for studentsthroughout the year in two capacities.On-campus recruiting is conductedthroughout the academic year andallows students to submit their resumesand cover letters online to the opportunitiesfrom employers who have chosen torecruit on campus. These opportunitiesare listed in LionSHARE. LionSHAREalso hosts full-time, part-time, and temporaryon- and off-campus employmentopportunities advertised year round.While at Columbia, students are encouragedto take advantage of internships,which offer opportunities to gain firsthandknowledge of a career field.CCE also offers Columbia studentshigh-quality domestic and internationalinternship experiences through alumniand employer partnerships in a diversearray of industries, including engineeringand technology. The internship programsinclude the Science, Technology,Engineering Program (STEP), CU InCalifornia, the Virtual Internship Program(VIP) and Columbia Experience Overseas(CEO), which offers internships inLondon, Hong Kong, Beijing, Shanghai,and Singapore. CCE also offers twoNew York–based internship programs,the Columbia Arts Experience and acivic engagement program, ColumbiaCommunities in Action.CCE fosters entrepreneurshipthrough Columbia Student Enterprises(CSE). The Columbia StudentEnterprises program is a unique opportunityto learn about and develop valuableentrepreneurship and leadershipskills through managing and working forstudent-run enterprises. The programconsists of student-managed businessessuch as the Columbia BartendingAgency and School of Mixology, InsideNY (a distinctive tourist guide to NewYork), and the Columbia UniversityTutoring and Translation Agency. Theparticipants of the program receive trainingand develop transferable businessskills applicable to all industries. Theprogram also promotes student initiativesin business and increases serviceson campus, enhancing the quality ofstudent life and creating job opportuni-7SEAS 2010–2011

8ties for Columbia University students.In addition, CCE recognizes thespecial interests of graduate studentswith programs, workshops, and one-toonecounseling opportunities that focuson both academic and nonacademiccareers. On-campus recruiting andLionSHARE are, of course, available tograduate students. CCE also maintainsa dossier service, managed by Interfolio,for graduate students and alumni whohold graduate degrees. A dossier consistsof letters of reference and othercredentials that speak to a candidate’sscholarship, research interests, andteaching experience. It is typically usedin applying for teaching positions ateither the secondary school or the collegelevel and for graduate/professionalschool and fellowship applications.Students can register online (www.interfolio.com) for the service. It is recommendedthat candidates for teachingpositions open a credentials file in thelate summer or early autumn of the yearpreceding their availability for employment.Undergraduate students or alumniwith undergraduate degrees from SEASshould contact the Center for StudentAdvising for dossier management.To gain a complete understandingof all Center for Career Educationprograms and resources, please visitthe Center in the lower level of EastCampus. For additional information andquestions, please call 212-854-5609.THE INTERNATIONALSTUDENTS AND SCHOLARSOFFICEInternational Students and ScholarsOfficeColumbia UniversityMail Code 57242960 BroadwayNew York, NY 10027Phone: 212-854-3587E-mail: isso@columbia.eduThe International Students and ScholarsOffice (ISSO) offers many servicesfor international students as well asAmerican citizens and permanentresidents who have received theireducation in another country. Servicesfor international students include preadmissioncounseling, document andother immigration-related services, theInternational Orientation program, socialand cultural activities, and a program forthe spouses of students. The ISSO alsoprovides credential analysis services tothe admissions offices of the University.The ISSO is open year-round, and internationalstudents are urged to make useof its services during their stay at theUniversity and are also invited to visit theISSO Web site at www.columbia.edu/cu/isso, with comprehensive informationfor both prospective and currentstudents.The staff of the International Studentsand Scholars Office is available for personaladvisement and for help in learningabout the campus and New YorkCity. The ISSO is an essential source ofinformation regarding immigration andDepartment of State regulations thataffect students studying in the UnitedStates. The staff can also assist withmany other non-academic matters. TheISSO provides information about culturalactivities in the New York area and hasreduced-rate tickets for plays, concerts,and other events.Students are required to check inwith the ISSO within a week of theirarrival at Columbia. The office’s streetaddress is 524 Riverside Drive inInternational House North, just north of122nd Street. The orientation programfor new international students arrivingfor the September term takes placeduring orientation week, usually thelast week in August or the first weekin September. For further information,consult the International Students andScholars Office using the contact informationabove.SEAS 2010–2011

Undergraduate Studies

10THE UNDERGRADUATE PROGRAMSThe undergraduate programs atThe Fu Foundation School ofEngineering and Applied Science(SEAS) not only are academically excitingand technically innovative but alsolead into a wide range of career pathsfor the educated citizen of the twentyfirstcentury. Whether you want tobecome a professional engineer, work inindustry or government, or plan to pursuea career in the physical and socialsciences, medicine, law, business, oreducation, SEAS will provide you withan unparalleled education.SEAS firmly believes that studentsgain the most when engineering isbrought up front, early in the four-yearcurriculum. Therefore, first-year studentsuse the networked, high-performanceworkstations and multimedia softwareof the Botwinick Multimedia LearningLaboratory as part of their technicalcore requirements. Here students applyfundamental principles of engineeringdesign to modeling advanced engineeringand applied science problems. Laterin the four-year program, students oftenuse the Laboratory’s symbolic, numeric,and graphical computing power in everdeepening integration with classroom,laboratory, and research work of theirchosen engineering program.While pursuing their own interests,undergraduate students are encouragedto participate in a broad range of ongoingfaculty research projects encompassed bythe Undergraduate Research InvolvementProgram (URIP). An annual URIP publicationsent to students describes facultyprojects in which students may participate,lists necessary qualifications, anddetails whether the student’s participationwill be voluntary, for academic credit, orfor monetary compensation.In addition to in-depth exploration ofengineering and applied science, SEASundergraduates explore the humanitiesand social sciences with ColumbiaCollege students through intellectuallychallenging Core Curriculum coursestaught by the Faculty of Arts andSciences. These courses in art, literature,music, major cultures, and economics,among others, provide studentswith a broad, intellectually disciplined,cultural perspective on the times theylive in and the work they do.POLICY ON DEGREEREQUIREMENTSThe Committee on Instruction andfaculty of The Fu Foundation School ofEngineering and Applied Science reviewdegree requirements and curricula matterseach year, and the bulletin reflectsthese faculty recommendations andcurricular changes in its yearly reprinting.School policy requires students tofulfill all general degree requirementsas stated in the bulletin of the first yearof their matriculation into the School.Students declare their major during thefirst semester of their sophomore year.Requirements for the major or minor arein accordance with the bulletin duringthe year in which the student declaresthe major or minor.THE FIRST YEAR/SOPHOMOREPROGRAMStudents entering The Fu FoundationSchool of Engineering and AppliedScience are encouraged to consider thewide range of possibilities open to them,both academically and professionally.To this end, the first and second yearsof the four-year undergraduate programcomprise approximately 66 semesterpoints of credit that expose students toa cross-fertilization of ideas from differentdisciplines within the University. Thesequence of study proceeds from anengagement with engineering and scientificfundamentals, along with humanitiesand social sciences, toward an increasinglyfocused training in the third andfourth years designed to give studentsmastery of certain principles and artscentral to engineering and applied science.Liberal Arts Core for SEAS Students:27-Point Nontechnical RequirementThis requirement provides a broad liberalarts component that enhances theSEAS professional curriculum to helpstudents meet the challenges of thetwenty-first century. Our students aredestined to be leaders in their professionsand will require sophisticatedcommunication, planning, and managementskills. The SEAS Committee onInstruction established the school’s nontechnicalrequirement so that studentswould learn perspectives and principlesof the humanities and social sciencesas part of a well-rounded and multiperspectiveeducation. Through discussion,debate, and writing, students improvetheir ability to engage in ethical, analytic,discursive, and imaginative thinking thatwill prove indispensable later in life.SEAS 2010–2011

11points of credit of required coursesin list A and 9 to 11 elective pointschosen from the approved coursesin list B. The total combined numberof nontechnical points (fromlists A and B, below) must add upto at least 27. Neither list can bemodified by advising deans or facultyadvisers.appropriate subject areas can beapplied toward the 9-point electivenontechnical requirement.If electing Global Core, students musttake two courses from the List ofApproved Courses (www.college.columbia.edu/bulletin/core/mc.php) for aletter grade.A. Required Nontechnical Courses(16–18 points of credit)These courses must be taken atColumbia.1. ENGL C1010: University writing (3 points)2. One of the following two-semester sequences:HUMA C1001-C1002: Masterpieces ofWestern literature and philosophy (All studentsregistering for this course should be preparedto discuss books 1–12 of the Iliad on the firstday of class.) orCOCI C1101-C1102: Introduction to contemporarycivilization in the West or Global Core (any2 courses from approved list) (6–8 points)3. One of the following two courses: HUMAW1121: Masterpieces of Western art, orHUMA W1123: Masterpieces of Westernmusic (3 points)4. ECON W1105: Principles of economics. (Thiscourse can be satisfied through AdvancedPlacement; see the Advanced Placementchart on page 14.) Note: SEAS students maynot take BC1003: Introduction to economicreasoning as a substitute for ECON W1105.(4 points)B. Elective Nontechnical Courses (9–11points of credit)The following course listing by departmentspecifies the Columbia College,Barnard, or SEAS courses that eitherfulfill or do not fulfill the nontechnicalrequirement.(Professional, workshop, lab, project,scientific, studio, music instruction, andmaster’s-level professional courses donot satisfy the 27-point nontechnicalrequirement.)AFRICAN-AMERICAN STUDIES: All coursesAMERICAN STUDIES: All coursesANCIENT STUDIES: All coursesANTHROPOLOGY: All courses in socioculturalanthropologyAll courses in archaeology except field workNo courses in biological/physical anthropology[V1010, V1011, W3204, V3940, G4147-G4148,W4200, G4700]ARCHITECTURE: No coursesART HISTORY AND ARCHEOLOGY: AllcoursesASIAN AMERICAN STUDIES: All coursesASTRONOMY: No coursesBIOLOGICAL SCIENCES: No coursesBUSINESS: No coursesCHEMISTRY: No coursesCLASSICS: All coursesCOLLOQUIA: All coursesCOMPARATIVE ETHNIC STUDIES: All coursesCOMPARATIVE LITERATURE AND SOCIETY:All coursesCOMPUTER SCIENCE: No coursesCREATIVE WRITING: All courses (This is anexception to the workshop rule.)DANCE: All courses except performance classesDRAMA AND THEATRE ARTS: All coursesexcept workshops, rehearsal, or performanceclasses, THTR BC2120 Technical production,THTR BC3135 Set design, and THTR BC3134Lighting designEARTH AND ENVIRONMENTAL SCIENCES:No coursesEAST ASIAN LANGUAGES AND CULTURE:All coursesECOLOGY, EVOLUTION ANDENVIRONMENTAL BIOLOGY: No coursesexcept EEEB W4700ECONOMICS: All courses except:W3211 Intermediate microeconomicsW3213 Intermediate macroeconomicsW3412 Introduction to econometricsW3025 Financial economicsW4020 Economics of uncertainty and informationW4211 Advanced microeconomicsW4213 Advanced macroeconomicsW4251 Industrial OrganizationW4280 Corporate financeW4412 Advanced econometricsW4415 Game theoryW4911 Seminar in microeconomicsW4913 Seminar in macroeconomicsW4918 Seminar in applied econometricsBC1003 Introduction to economic reasoning(equivalent to ECON W1105)BC1007 Mathematical methods for economicsBC2411 Statistics for economicsBC3014 EntrepreneurshipBC3018 EconometricsBC3033 Intermediate macroeconomic theoryBC3035 Intermediate microeconomic theorySEAS 2010–2011

12BC3038 International money and financeBC2411 Statistics for economicsEDUCATION: All coursesENGLISH AND COMPARATIVE LITERATURE:All coursesFILM STUDIES: All courses except: lab courses,andW3850: Senior seminar in screenwritingW4005: The film medium: script analysisFRENCH AND ROMANCE PHILOLOGY: AllcoursesGERMANIC LANGUAGES: All coursesGREEK: All coursesHISTORY: All coursesHISTORY AND PHILOSOPHY OF SCIENCE:All coursesHUMAN RIGHTS: All coursesITALIAN: All coursesJAZZ STUDIES: All coursesLATIN: All coursesLATINO STUDIES: All coursesLINGUISTICS: All courses except CLLN W4202MATHEMATICS: No coursesMEDIEVAL AND RENAISSANCE STUDIES: AllcoursesMIDDLE EASTERN AND ASIAN LANGUAGEAND CULTURES: All coursesMUSIC: All courses except performance courses,instrument instruction courses, and workshopsPHILOSOPHY: All courses except:F1401 Elementary logicV3411 Introduction to symbolic logicW4137 Non-classical logicG4431 Introduction to set theoryG4424 Modal logicCSPH W4801 Mathematical logic, ICSPH G4802 Incompleteness results in logicCourses in logicPHYSICAL EDUCATION: No coursesPHYSICS: No coursesPOLITICAL SCIENCE: All courses exceptW4209 Game theoryW4291 Advanced topics in quantitative researchW4292 Advanced topics in quantitative researchW4360 Math methods for political scienceW4910 Principles of quantitative politicalresearchW4911 Analysis of political dataW4912 Multivariate political analysisPSYCHOLOGY: Only:W1001 The science of psychologyW2235 Thinking and decision makingW2240 Human communicationW2280 Introduction to developmental psychologyW2610 Introduction to personalityW2620 Abnormal behaviorW2630 Social psychologyW2640 Introduction to social cognitionV2680 Social and personality developmentW3615 Children at riskW3630 Seminar in social cognitionRELIGION: All coursesSEAS: Only:SCNC W3010 Science, technology and societyBMEN E4010 Ethics for biomedical engineersEEHS E3900 History of telecommunicationsSLAVIC LANGUAGES: All coursesSOCIOLOGY: All courses exceptSOCI V3212: Statistics and methodsSPANISH AND PORTUGUESE: All coursesSPEECH: No coursesSTATISTICS: No coursesSUSTAINABLE DEVELOPMENT: No coursesURBAN STUDIES: All coursesVISUAL ARTS: No more than one course, whichmust be at the 3000-level or higher (This is anexception to the workshop rule.)WOMEN AND GENDER STUDIES: All coursesTechnical Course RequirementsThe prescribed First Year-SophomoreProgram curriculum requires students tocomplete a program of technical coursework introducing them to five majorareas of technical inquiry: engineering,mathematics, physics, chemistry, andcomputer science.All first-year SEAS undergraduatestudents take ENGI E1102: Designfundamentals using the advancedcomputer technologies (4 points), inthe Botwinick Multimedia LearningLaboratory. In this course, studentslearn the basics of engineering designalong with professional and teamworkskills through participation in communityservice projects for real clients in localcommunities.While students need not officiallycommit to a particular branch of engineeringuntil the third semester, mostprograms recommend, and in somecases may require, that particularcourses be taken earlier for maximumefficiency in program planning. For informationconcerning these requirements,students should turn to the individualprogram sections in this bulletin.Professional-Level Courses for FirstandSecond-Year StudentsFirst- and second-year students arerequired to take at least one professional-levelcourse chosen from thelist below. The faculty strongly encouragesstudents to schedule two of thesecourses. (The Botwinick MultimediaLearning Laboratory course in computerand engineering design technology,ENGI E1102, which is required of everyfirst-year student, is not included in thislist.)Each course is designed to acquaintSEAS students with rigorous intellectualeffort in engineering and applied scienceearly in their academic careers. Ifa student chooses to take the secondprofessional-level course, such a 1000-level course may, at the discretion ofeach department, be used as an upperleveltechnical elective normally satisfiedby 3000-level or higher courses.The courses stipulate minimal prerequisites.Each course serves as anintroduction to the area of study in additionto teaching the subject matter. Eachcourse is taught by regular departmentfaculty and thus provides a double introductionto both subject area and faculty.The courses are:APPH E1300y Physics of the human bodyThe human body analyzed from the basic principlesof physics: energy balance in the body,mechanics of motion, fluid dynamics of the heartand circulation, vibrations in speaking and hearing,muscle mechanics, vision, gas exchangeand transport in the lungs, structural propertiesand limits, and other topics.APAM E1601y Introduction to computationalmathematics and physicsMathematics and physics problems solved byusing computers. Topics include elementaryinterpolation of functions, solution of nonlinearalgebraic equations, curve-fitting and hypothesistesting, wave propagation, fluid motion, gravitationaland celestial mechanics, and chaoticdynamics.BMEN E1001x Engineering in medicineThe present and historical role of engineering inmedicine and health care delivery. Engineeringapproaches to understanding organismic andcellular function in living systems. Engineering inthe diagnosis and treatment of disease. Medicalimaging, medical devices: diagnostic and surgi-SEAS 2010–2011

cal instruments, drug delivery systems, prostheses,artificial organs.CHEN E1040y Molecular engineering andproduct designExamines the ways in which chemical andbiological sciences are interpreted throughanalytical design and engineering frameworksto generate products that enhance humanendeavor. Culture of chemical engineering andthe wide variety of chemical engineering practices,through lectures by department faculty andpracticing chemical engineers, trips to industrialfacilities, reverse engineering of chemical products,and a chemical design competition.CIEN E1201y Design of buildings, bridges,and spacecraftBasic principles according to which many structuresare designed, constructed, and maintainedin service. How strength and safety are treatedand the role of the computer at this design stage.Performance requirements, such as noise andmotion limitations. Classic and new materials ofconstruction, their important features, and laboratorydemonstration of properties. Managementof both design and construction projects, andfollow-up assessment monitoring and control.EAEE E1100y A better planet by designSustainable development and managementof Earth resources (water, minerals, energy,and land) are now recognized globally as anessential goal. A “systems analytic” approachto understanding feedbacks and interactionsbetween human activity and the environment isintroduced. Elements of integrated assessment,modeling, forecasting and decision analysis areillustrated by means of case studies of currentresource and environment concerns.ELEN E1201x and y Introduction to electricalengineering, with laboratory in circuit designExploration of selected topics and their application.Electrical variables, circuit laws, nonlinearand linear elements, ideal and real sources,transducers, operational amplifiers in simple circuits,external behavior of diodes and transistors,first order RC and RL circuits. Digital representationof a signal, digital logic gates, flip-flops.GRAP E1115x and y Engineering graphicsVisualization and simulation in virtual environments;computer graphics methods for presentationof data. 3D modeling; animation; rendering;image editing; technical drawing.MECE E1001x Mechanical engineering: micromachinesto jumbo jetsThe role of mechanical engineering in developingmany of the fundamental technological advanceson which today’s society depends. Topics includeairplanes, automobiles, robots, and modernmanufacturing methods, as well as the emergingfields of micro-electro-mechanical machines(MEMS) and nanotechnology. The physicalconcepts that govern the operation of these technologieswill be developed from basic principlesand then applied in simple design problems.Students will also be exposed to state-of-the artinnovations in each case study.MSAE E1001y Atomic-scale engineering ofnew materialsAn introduction to the nanoscale science andengineering of new materials. The control andmanipulation of atomic structure can create newsolids with unprecedented properties. Computerhard drives, compact disc players, and liquidcrystal displays (LCDs) are explored to understandthe role of new materials in enabling technologies.Group problem-solving sessions areused to develop understanding.Physical EducationTwo terms of physical education(C1001-C1002) are a degree requirementfor students in The Fu FoundationSchool of Engineering and AppliedScience. No more than 4 points of physicaleducation courses may be countedtoward the degree. A student whointends to participate in an intercollegiatesport should register for the appropriatesection of C1005: Intercollegiateathletics. Intercollegiate athletes whoattend regularly receive 1 point of creditup to the maximum of 4. Those whoare advised to follow a restricted oradapted activity program should contactProfessor Torrey in the Department ofPhysical Education and IntercollegiateAthletics. The physical education programoffers a variety of activities in theareas of aquatics, fitness, martial arts,individual and dual lifetime sports, teamsports, and outdoor education. Mostactivities are designed for the beginner/intermediate levels. Advanced coursesare indicated on the schedule. Themajority of the activities are offered inten time preferences. However, thereare early-morning conditioning activities,Friday-only classes at Baker Field, andspecial courses that utilize off-campusfacilities during weekends and vacationperiods. The courses offered by thedepartment for each term are includedin the online Department of PhysicalEducation and Intercollegiate AthleticsDirectory of Classes, and a descriptionof the scheduled activities for each timepreference is posted in the PhysicalEducation Office, 336 Dodge PhysicalFitness Center, and is included on thewww.gocolumbialions.com Web site.Students may register for only one sectionof physical education each term.Music Instruction CoursesMusic instruction and performancecourses do not count toward the 128points of credit required for a B.S.degree. Please note that this includescourses taken at Teachers College,Columbia College, and the School ofthe Arts.Visual Arts CoursesStudents are allowed to take coursesin the Visual Arts Department for generalcredit to be applied toward theB.S. degree. However, no more thanone visual arts course, which must betaken at the 3000 level or higher, maycount toward the nontechnical electiverequirement. This 3000 course is anexception to the rule that no workshopclasses can fulfill the non-tech electiverequirement.Advanced PlacementPrior to entering Columbia, studentsmay have taken the College EntranceExamination Board’s Advanced PlacementExaminations in a number of technicaland nontechnical areas. Studentsmay be assigned to an advanced-levelcourse in mathematics, chemistry, orphysics. A maximum of 16 points maybe applied.In the required pure science areas,the number of advanced placementacademic credits awarded to studentsof engineering and applied science variesfrom the levels awarded for liberalarts programs, notably in mathematics,physics, chemistry, and computer science.The benefit of advanced placementis acceleration through certain FirstYear–Sophomore Program requirementsand thus the opportunity of taking specializedcourses earlier.Each year the school reviews theCEEB advanced placement curriculumand makes determinations as toappropriate placements, credit, and/orexemption. Please see the AdvancedPlacement Credit Chart.International Baccalaureate (IB)Entering students may be granted 6points of credit for each score of 6 or 7on IB Higher Level Examinations if taken13SEAS 2010–2011

14Advanced Placement Credit ChartIn order to receive AP credit, students must be in possession of appropriate transcripts or scores.Subject AP Advanced Requirements or Placement StatusScore CreditArt history 5 3* No exemption from HUMA W1121Biology 4 or 5 3 No exemptionChemistry 4 or 5 3 Requires completion of CHEM C1604 withgrade of C or better.4 or 5 6 Requires completion of CHEM C3045-C3046with grade of C or better.Computer 4 or 5 3* Exemption from COMS W1004science A or ABEnglishLanguage and 5 3* No exemptioncompositionLiterature and 5 3* No exemptioncompositionEconomicsMicro & macro 5 & 4 4* Exemption from ECON W1105 (Test must be inboth with a score of 5 in one and at least 4 inthe other.)FrenchLanguage 4 or 5 3*Literature 4 or 5 3*German 4 or 5 3*languageGovernmentand politicsUnited States 5 3*Comparative 5 3*HistoryEuropean 5 3*United States 5 3*Italian language 4 or 5 3*Latin literature 4 or 5 3*MathematicsCalculus AB 4 or 5 3** Requires completion of MATH V1102 with agrade of C or better.Calculus BC 4 3** Requires completion of MATH V1102 with agrade of C or better.Calculus BC 5 6 Requires completion of MATH V1201 (orV1207) with a grade of C or better.Music theory 5 3* Exemption from MUSI V1002. MUSIV2318-V2319 determined by department.Physics (6 credits maximum)C-MECH 4 or 5 3 Credit reduced to 0 if PHYS 1401 or 1601 istaken. Credit reduced to 0 if PHYS C2801 istaken and the final grade is C– or lower.C-E&M 4 or 5 3 Credit reduced to 0 if PHYS 1402 or 1602 istaken. Credit reduced to 0 if PHYS C2801 istaken and the final grade is C– or lower.Physics B 4 or 5 3* No exemption.SpanishLanguage 4 or 5 3*Literature 4 or 5 3**Up to 3 AP credits may be applied toward minor requirements.** SEAS students with a 4 or 5 on Calculus AB or a 4 on Calculus BC must begin withCalculus II. If a SEAS student with these scores goes directly into Calculus III, he or she willnot be awarded credit and may have to go back and complete Calculus II. Students withA-level or IB calculus credit must start with Calculus II.in disciplines offered as undergraduateprograms at Columbia. Students shouldconsult their adviser for further clarification.British Advanced Level ExaminationsPending review by the appropriatedepartment at Columbia, students withgrades of A or B on British AdvancedLevel examinations are granted 6 pointsof credit if the examinations were takenin disciplines offered as undergraduateprograms at Columbia College. Theappropriate transcript should be submittedto the Center for Student Advising,403 Lerner.Other National SystemsPending review by the appropriatedepartment at Columbia, studentswhose secondary school work was inother national systems may be grantedcredit in certain disciplines for sufficientlyhigh scores. The appropriate transcriptshould be submitted to the Center forStudent Advising, 403 Lerner.STUDY ABROADEngineering today is a global profession.Engineers are increasingly being calledupon to work with other engineers fromacross the world or they may even findthemselves living abroad on an overseasassignment. Learning problem-solvingskills in a foreign context will helpengineering students to expand theirhorizons, and their adaptability to crossculturalcommunication will make them avaluable addition to a team of engineers.Study abroad allows engineering studentsto discover the field through theperspective of engineers working in adifferent language and culture, enablingthem to learn the relationship of cultureto science and develop the range oftransferable skills that employers areseeking today. Study abroad will helpstudents develop intellectually, emotionally,culturally, and socially.SEAS undergraduate students canstudy abroad for either a semester (fall,spring or summer) or, exceptionally,for a full academic year. Students fromevery engineering major have studiedabroad without adding any time to theircourse of study at Columbia. Most doso in the spring semester of their sophomoreyear or in their junior year.SEAS 2010–2011

SEAS students have two study abroadoptions:1) the option of studying engineeringat one of SEAS’ partner universitiesUniversity College London (UK);the Ecole Polytechnique (FR) orthe Ecole Centrale de Paris (FR) -courses at these two institutionsare predominantly taught in French.Other partnerships are currentlybeing negotiated—check the Officeof Global Initiatives’ Web site for thelatest updates.2) Students who would like furtherstudy abroad options can choose apeer university for direct enrollmentor a program of study with a thirdparty provider. The Office of GlobalInitiatives (510 Mudd) can help studentsidentify the appropriate choicefor their country of interest and theirmajor. The Office of Global Initiativesand departmental advisers will reviewrequests, and if approved, will helpstudents work out their course equivalenciesso they can graduate ontime. Students can choose to takenon-technical electives overseas, orwith departmental permission, theymay choose technical electives orcourses in their major.It is essential that students beginplanning as early as possible—ideallythis would be during their first year—bymeeting with Dr. Régine Lambrech,director of the Office of Global Initiativesand Education in 510 Mudd. She willhelp students choose their overseasuniversity destination and will explainall SEAS study abroad formalities andrequirements. Early planning is essentialso that students are sure to be ableto find enough courses overseas totransfer back to Columbia. Studentsthen must gain approval from theirdepartmental advisers to ensure thattheir work abroad meets the requirementsof their majors. Students mustalso register with the Office of GlobalPrograms (606 Kent Hall) for studyabroad by November 15 for spring programsand March 15 for summer, falland academic-year programs.Eligibility RequirementsIn order to participate in a semester- oryearlong study-abroad program, studentsmust:finishing the first and second yearrequirementsin the local language, if it is not English.(Please note: For programs in countrieswhere the language of instructionis not English, students must take allcourse work in the local language.)Students’ study-abroad plans mustbe approved by the Office of GlobalInitiatives by October 15 for spring programsand March 15 for summer, falland academic-year programs. A reviewof each student’s academic and disciplinaryrecords is conducted as part ofthis process. Students on academic ordisciplinary probation are not permittedto study abroad during the term of theirprobation.Study-abroad students remainenrolled at Columbia, and tuition is paidto Columbia. Students participatingin Columbia-approved programs payhousing costs directly to their host orsponsoring institution. Students receivingfinancial aid at Columbia will remaineligible for financial aid when they studyabroad with Columbia’s approval.Students who wish to be consideredfor financial aid while studying abroadshould consult the Office of Financial Aidand Educational Financing (407 Lerner).Program InformationChoosing the right university abroad isan important step in planning to studyabroad. Study-abroad options varywidely in size, geographical location,academic philosophy, language requirements,living arrangements, and opportunitiesfor research and internships.Students must establish a set of goalsfor the study-abroad experience, takinginto account their foreign-language skillsand adaptability to new environments,as well as their research objectives andprofessional aspirations.Students should visit the Office ofGlobal Initiatives’ Web site to review thevarious lists of program options andthen consult with the Director of GlobalInitiatives and Education for specific informationor help in choosing an institutionthat offers the best courses in their engineeringmajor. Early planning is crucial sothat study abroad plans can be integratedinto the student’s curriculum plan.Summer study-abroad programsallow students to earn credits for languageinstruction and nontechnical electives.Students can either participate inColumbia-approved summer programsfor transfer credit or on Columbiasponsoredprograms for direct credit.The Columbia-sponsored summer programsinclude the Chinese LanguageProgram in Beijing, the BusinessChinese and Internship Program inShanghai, the Italian Cultural StudiesProgram in Venice, the ColumbiaUniversity Summer Arabic LanguageProgram in Amman, Jordan and theColumbia University Programs in Parisat Reid Hall.Non credit bearing internshipsabroad—the EDGE and CEO programs—arecoordinated by the Centerfor Career Education. Please visit theCenter’s Web site for more information.Other internship options are listedon the Web site of the Office of GlobalInitiatives and may be possible throughSEAS’ international partner institutions.Academic CreditStudents in Columbia-sponsored programsreceive direct Columbia credit,and the courses and grades appear onstudents’ academic transcripts. Theseinclude Reid Hall, Paris; the BerlinConsortium for German Studies; theKyoto Center for Japanese Studies; theColumbia University Summer ArabicLanguage Program in Amman, Jordanand the Tsinghua University program inBeijing.Credit from approved programs thatare not Columbia sponsored is certifiedas transfer credit toward the Columbiadegree upon successful completionof the program verifiable by academictranscript. Students must earn a gradeof C or better in order for credits totransfer. Course titles and grades forapproved programs do not appear onthe Columbia transcript, and the gradesare not factored into students’ GPAs.Faculty from the SEAS academicdepartments have the responsibilityto assess all work completed abroadand make decisions about how thesecourses fit into major requirements. It isimperative that students gain course-bycourseapproval from their department15SEAS 2010–2011

16prior to departure on a study-abroadprogram. The Office of Global Initiativeswill provide students with the forms necessaryto obtain this approval.COMBINED PLAN PROGRAMSThe Fu Foundation School of Engineeringand Applied Science maintains cooperativeprogram relationships with institutionsnationwide, and with other ColumbiaUniversity undergraduate divisions. Theseprograms allow students to complete theequivalent of the First Year–SophomoreProgram and transfer directly to a fieldof specialization in the School, beginningtheir study at the School as junior-levelstudents. Participating Combined Planinstitutions are listed beginning on thispage; see heading Affiliated Colleges andUniversities.The Combined Plan (3-2) Programwithin Columbia UniversityStudents who follow this program applythrough their own school at ColumbiaCollege, Barnard College, or the Schoolof General Studies for admission.Under this plan, the pre-engineeringstudent studies in the appropriate collegefor three years, then attends TheFu Foundation School of Engineeringand Applied Science for two years andis awarded the Bachelor of Arts degreeand the Bachelor of Science degreein engineering upon completion of thefifth year. This five-year program isoptional at Columbia, but the Schoolrecommends it to all students who wishgreater enrichment in the liberal arts andpure sciences.The Combined Plan with OtherAffiliated CollegesThere are more than one hundred liberalarts colleges, including those atColumbia, in which a student can enrollin a Combined Plan program leadingto two degrees. Every affiliated schoolhas a liaison officer who coordinates theprogram at his or her home institution.Inasmuch as each liberal arts collegerequires the completion of a specifiedcurriculum to qualify for the baccalaureatefrom that institution, studentsinterested in this program should informthe liaison officer as early as possible,preferably in the first year.The 3-2 Combined Plan ProgramB.A./B.S. at The Fu Foundation Schoolof Engineering and Applied Science isdesigned to provide students with theopportunity to receive both a B.A. degreefrom an affiliated liberal arts college and aB.S. degree from SEAS within five years.Students complete the requirements forthe liberal arts degree along with a preengineeringcourse of study in three yearsat their college and then complete atColumbia. Combined Plan students arerequired to complete all SEAS requirementswithin four consecutive semesters.Please note that no change of major isallowed after matriculation.Guaranteed admission into TheFu Foundation School of Engineeringand Applied Science’s undergraduateCombined Plan Program is offered toapplicants who have met the followingrequirements:1. Have been enrolled at an affiliatedschool for at least the past twoyears;2. Have received an overall and preengineeringGPA of 3.0 or higheras calculated by Columbia;3. Have received three favorablerecommendations, from theCombined Plan liaison and both ascience and a math instructor atthe home institution;4. Have successfully completed thespecific science and math prerequisitecourses for the intendedmajor listed in the Pre-CombinedPlan Curriculum Guide;5. Have completed the major anddistribution requirements prescribedby your home institutionfor graduation.Admission to SEAS at the end of thejunior year is guaranteed for those studentswho have completed the appropriatesteps outlined above.Another available option is the 4-2B.S. degree program. This is designedto allow students to graduate from theirliberal arts college with a B.A. degreeand then transfer to SEAS to completea B.S. degree in two years. Studentsshould have followed a related courseof study at their liberal arts college.Requirements for guaranteed admissionto the 4-2 B.S. degree program arethe same as above, with the additionalrequirement that if the applicant hasalready graduated from the affiliatedschool, he or she must apply to theCombined Plan Program within one yearof graduating.For further information on the 3-2B.A./B.S. program and the 4-2 B.S.program, you are encouraged to e-mailyour questions to: combinedplan@columbia.edu. You may also call 212-854-2522 or contact Combined PlanCoordinators, Office of UndergraduateAdmissions, 212 Hamilton Hall, MailCode 2807, 1130 Amsterdam Avenue,New York, NY 10027.The 4-2 M.S. program is designedto allow students to complete an M.S.degree at SEAS in two years aftercompletion of a B.A. degree at one ofthe affiliated schools. This program willallow students the opportunity to takeundergraduate engineering courses ifnecessary. Please contact the Officeof Graduate Student Services, The FuFoundation School of Engineering andApplied Science, 524 S. W. Mudd, MailCode 4708, 500 West 120th Street,New York, NY 10027. You may alsoe-mail questions to seasgradmit@columbia.edu.Affiliated Colleges and UniversitiesThe following colleges are affiliated withSEAS in the Combined Plan; admissionrequirements and other information maybe obtained from them or by contactingthe Office of Undergraduate Admissions.For more information, go to www.studentaffairs.columbia.edu/admissions/engineering/combined.Adelphi University, Garden City, NYAlbion College, Albion, MIAlfred University, Alfred, NYAllegheny College, Meadville, PAArcadia University, Glenside, PAAugustana College, Sioux Falls, SDAustin College, Sherman, TXBaldwin-Wallace College, Berea, OHBard College, Annandale-on-Hudson, NYBarnard College, New York, NYBates College, Lewiston, MEBeloit College, Beloit, WIBethany College, Bethany, WVBirmingham-Southern College, Birmingham, ALBowdoin College, Brunswick, MEBrandeis University, Waltham, MACarleton College, Northfield, MNCarroll College, Helena, MTCentenary College of Louisiana, Shreveport, LACentre College, Danville, KYClaremont McKenna College, Claremont, CAClark University, Worcester, MASEAS 2010–2011

Colgate University, Hamilton, NYCollege of Idaho, Caldwell, IDCollege of Notre Dame, Baltimore, MDCollege of the Holy Cross, Worcester, MACollege of William and Mary, Williamsburg, VAColorado College, Colorado Springs, COColumbia College, New York, NYDavidson College, Davidson, NCDenison University, Granville, OHDePauw University, Greencastle, INDillard University, New Orleans, LODoane College, Crete, NEDrew University, Madison, NJEarlham College, Richmond, INEckerd College, St. Petersburg, FLElon College, NCFairfield University, Fairfield, CTFordham University, Bronx, NYFranklin and Marshall College, Lancaster, PAGeorgetown University, Washington, DCGettysburg College, Gettysburg, PAGrinnell College, Grinnell, IAHamilton College, Clinton, NYHartwick College, Oneonta, NYHastings College, Hastings, NEHendrix College, Conway, ARHobart and William Smith Colleges, Geneva, NYHofstra University, Hempstead, NYIllinois Wesleyan University, Bloomington, ILJacksonville University, Jacksonville, FLJuniata College, Huntingdon, PAKansas Wesleyan University, Salina, KSKnox College, Galeburg, ILLawrence University, Appleton, WILewis and Clark College, Portland, ORLoyola University Chicago, Chicago, ILLoyola University Maryland, Baltimore, MDManchester College, North Manchester, INMarietta College, Marietta, OHMiami University, Oxford, OHMiddlebury College, Middlebury, VTMillsaps College, Jackson, MIMorehouse College, Atlanta, GAMuhlenberg College, Allentown, PANebraska Wesleyan University, Lincoln, NEOberlin College, Oberlin, OHOccidental College, Los Angeles, CAPacific Lutheran University, Tacoma, WAPitzer College, Claremont, CAProvidence College, Providence, RIQueens College, Flushing, NYRandolph-Macon College, Ashland, VAReed College, Portland, ORRollins College, Winter Park, FLSt. John Fisher College, Rochester, NYSt. Lawrence University, Canton, NYSarah Lawrence College, Bronxville, NYSchool of General Studies, Columbia University,New York, NYScripps College, Claremont, CASeattle Pacific University, Seattle, WASimon’s Rock College of Bard, GreatBarrington, MASpelman College, Atlanta, GAState University of New York, Fredonia, NYState University of New York, Geneseo, NYSweet Briar College, Sweet Briar, VAUniversity of Puget Sound, Tacoma, WAUniversity of Richmond, Richmond, VAUniversity of the South, Sewanee, TNUniversity of the Virgin Islands, St. Thomas, VIUrsinus College, Collegeville, PAWabash College, Crawfordsville, INWashington and Jefferson College,Washington, PAWells College, Aurora, NYWesleyan University, Middletown, CTWhitman College, Walla Walla, WAWhitworth College, Spokane, WAWillamette University, Salem, ORWilliam Jewell College, Liberty, MOWilliams College, Williamstown, MAWittenberg University, Springfield, OHWofford College, Spartanburg, SCYeshiva University, New York, NYTHE JUNIOR-SENIORPROGRAMSStudents may review degree progressvia DARS (Degree Audit ReportingSystem) as presented on StudentServices Online. Required courses notcompleted by this time are detailed asdeficiencies and must be completedduring summer session or carried asoverload courses during the final twoyears of study.Having chosen their program major,students are assigned to an adviser inthe department in which the programis offered. In addition to the coursesrequired by their program, studentsmust continue to satisfy certain distributiverequirements, choosing electivecourses that provide sufficient contentin engineering sciences and engineeringdesign. The order and distributionof the prescribed course work may bechanged with the adviser’s approval.Specific questions concerning courserequirements should be addressed tothe appropriate department or division.The Vice Dean’s concurrent approval isrequired for all waivers and substitutions.Tau Beta PiThe Tau Beta Pi Association, a nationalengineering honor society, was foundedin 1885 “to mark in a fitting mannerthose who have conferred honor upontheir Alma Mater by distinguishedscholarship and exemplary characteras undergraduates in engineering, or bytheir attainments as alumni in the fieldof engineering, and to foster a spirit ofliberal culture in engineering colleges.”Columbia’s chapter, New York Alpha,is the ninth oldest and was founded in1902. Many Columbia buildings havebeen named for some of the moreprominent chapter alumni: CharlesFredrick Chandler, Michael IdvorskyPupin, Augustus Schermerhorn, and, ofcourse, Harvey Seeley Mudd.Undergraduate students whosescholarship places them in the topeighth of their class in their next-to-lastyear or in the top fifth of their class intheir last college year are eligible formembership consideration. These scholasticallyeligible students are furtherconsidered on the basis of personalintegrity, breadth of interest both insideand outside engineering, adaptability,and unselfish activity.Taking Graduate Courses as anUndergraduateWith the faculty adviser’s approval, astudent may take graduate courseswhile still an undergraduate in theSchool. Such work may be creditedtoward one of the graduate degreesoffered by the Faculty of Engineeringand Applied Science, subject to the followingconditions: (1) the course mustbe accepted as part of an approvedgraduate program of study; (2) thecourse must not have been used to fulfilla requirement for the B.S. degree andmust be so certified by the Dean; and(3) the amount of graduate credit earnedby an undergraduate cannot exceed 15points. Undergraduates may not takeCVN courses.The Bachelor of Science DegreeStudents who complete a four-yearsequence of prescribed study areawarded the Bachelor of Sciencedegree. The general requirement forthe Bachelor of Science degree isthe completion of a minimum of 128academic credits with a minimumcumulative grade-point average (GPA)of 2.0 (C) at the time of graduation.The program requirements, specifiedelsewhere in this bulletin, include theFirst Year–Sophomore course requirements,the Junior-Senior major departmentalrequirements, and technical and17SEAS 2010–2011

18nontechnical elective requirements.Students who wish to transfer pointsof credit may count no more than 68transfer points toward the degree, andmust satisfy the University’s residencerequirements by taking at least 60points of credit at Columbia. Coursesmay not be repeated for credit.The bachelor’s degree in engineeringand applied science earned atColumbia University prepares studentsto enter a wide range of professions.Students are, however, encouragedto consider graduate work, at leastto the master’s degree level, which isincreasingly considered necessary formany professional careers.The Engineering AccreditationCommission (EAC) of the AccreditationBoard for Engineering and Technology(ABET), an organization formed by themajor engineering professional societies,accredits university engineeringprograms on a nationwide basis.Completion of an accredited programof study is usually the first step towarda professional engineering license.Advanced study in engineering at agraduate school sometimes presupposesthe completion of an accreditedprogram of undergraduate study.The following undergraduateprograms are accredited by theEngineering Accreditation Commissionof the Accreditation Board forEngineering and Technology: biomedicalengineering, chemical engineering,civil engineering, Earth and environmentalengineering, electrical engineering,and mechanical engineering.The 4-1 Program at ColumbiaCollegeStudents who are admitted as first-yearstudents to The Fu Foundation Schoolof Engineering and Applied Science, andsubsequently complete the four-yearprogram for the Bachelor of Sciencedegree, have the opportunity to applyfor admission to either Columbia Collegeor Barnard College and, after one additionalyear of study, receive the Bachelorof Arts degree.The program will be selective, andadmission will be based on the followingfactors: granting of the B.S. at SEASat the end of the fourth year; fulfillmentof the College Core requirements bythe end of the fourth year at SEAS; aminimum GPA of 3.0 in the College Coreand other courses; and the successfulcompletion of any prerequisites for theCollege major or concentration. To beadmitted to the program, a plan needsto be in place for the student to completethe major or concentration in thefifth year.Interested students should contact theirAdvising Center for further information.MinorsUndergraduates in The Fu FoundationSchool of Engineering and AppliedScience may choose to add minorsto their programs. This choice shouldbe made in the fall of their sophomoreyear, when they also decide on amajor.In considering a minor, studentsmust understand that all minors arenot, and cannot, be available to allstudents. In addition, the School cannotguarantee that a selected minorcan be completed within the usualresidence period needed for a major.Indeed, students choosing minorsshould expect to encounter schedulingdifficulties. The potential for the successfulcompletion of a minor dependson the student’s major and theminor chosen, as well as the courseschedules and availability, which maychange from year to year. The list ofminors, as well as their requirements,appear on pages 194–200.PROGRAMS IN PREPARATIONFOR OTHER PROFESSIONSThe Fu Foundation School ofEngineering and Applied Science preparesits students to enter any numberof graduate programs and professionsoutside of what is generally thought ofas the engineering field. In an increasinglytechnological society, where theline between humanities and technologyis becoming increasingly blurred,individuals with a thorough groundingin applied mathematics and thephysical and engineering sciencesfind themselves highly sought after asprofessionals in practically all fields ofendeavor.Engineering students interestedin pursuing graduate work in suchareas as architecture, business,education, journalism, or law will findthemselves well prepared to meet thegenerally flexible admissions requirementsof most professional schools.Undergraduate students should,however, make careful inquiry into thekinds of specific preparatory work thatmay be required for admission intohighly specialized programs such asmedicine.Pre-MedEngineering students seeking admissionto dental, medical, optometric,osteopathic, or veterinary schoolsdirectly after college must complete allentrance requirements by the end ofthe junior year, and should plan theirprogram accordingly. Students shouldconsult with their adviser and theOffice of Preprofessional Advising toplan an appropriate program. Studentsshould also connect with the Office ofPreprofessional Advising to learn moreabout extracurricular and researchopportunities related to premed studies.It is necessary to apply for admissionto health professions schools alittle over one year in advance of theentry date. If candidates are interestedin going directly on to health professionsschool following graduation,they should complete all requirementsand the Medical College AdmissionsTest (MCAT) by the summer followingthe junior year. It is, however, entirelyacceptable to delay application andentrance to these schools severalyears beyond graduation, if desired.Candidates planning for an applicationto medical or dental schoolwill also need to be evaluated by thePremedical Advisory Committee priorto application. A Premedical AdvisoryCommittee application is madeavailable each year in December.Please consult with the Office ofPreprofessional Advising for moreinformation regarding this process.The Engineering School’s curriculumcovers many of the premedicalcourses required by medical schools.However, in addition to completing themathematics, chemistry, and physicscourses required by the First Year–Sophomore Program, most medicalschools ask for a full year of organicSEAS 2010–2011

chemistry, a full year of biology, and afull year of English.The following courses are requiredby medical schools:schoolslabs will qualify)(required by some schools)For further information, pleaseconsult the Office of PreprofessionalAdvising at 212-854-8722 orpreprofessional@columbia.Pre-LawStudents fulfilling the curriculum of TheFu Foundation School of Engineeringand Applied Science are well preparedto apply to and enter professionalschools of law, which generally do notrequire any specific prelaw course work.Schools of law encourage undergraduatestudents to complete a curriculumcharacterized by rigorous intellectualtraining involving relational, syntactical,and abstract thinking. A sound liberaleducation is best for most prelaw students.While selecting courses, keepin mind the need to hone your writingskills, your communication skills, andyour capacity for logical analysis.Courses in history, political science,economics, statistics, and anthropologyhelp students understand thestructure of society and the problemsof social ordering with which the law isconcerned. The study of philosophy,literature, fine arts, foreign languages,and other cultures imparts familiaritywith traditions of universal thought andtrends that influence legal developmentsnationally and internationally. Theexamination of human behavior throughsociology and psychology will aid aprospective law student in understandingthe types and effects of behavior towhich the law relates.The systematic ordering of abstractionsand ideas in logic and the sciencescontributes much to a prelaw student’sability to analyze, understand, andrationally organize his or her thoughts.Finally, it is useful in some fields of lawfor a student to have a fundamentalknowledge of technology, engineering,computers, and accounting.New York State Initial Certificationin Adolescence Education Grades7–12 for Teachers of Mathematicsand the Sciences or in ChildhoodEducation Grades 1–6The Barnard Education Program providescourses leading to certification toteach in New York State (with reciprocalagreements with forty-one other states)at either the elementary or secondarylevel. Students gain experience anddevelop skills in urban school classrooms.Interested students should applyfor admission to the program and supplyan essay and letters of recommendationno later than the first Monday in Octoberof the junior year. These may be downloadedfrom the Barnard College Officeof Education Web site or picked up inthe 336 Milbank Hall office. Course workrequired includes courses in psychologyand education, including practicum andstudent teaching, totaling 23–26 pointsof credit depending on level of certificationsought (please see the Web site forspecific courses).Certification to teach mathematicsrequires 36 points in mathematics. Purescience courses required are: 36 pointsin the sciences, of which 15 must bein the area of the certification sought:chemistry, biology, physics, or Earthscience.Application deadline is the firstMonday in October of the student’sjunior year. Students who plan to studyabroad during their junior year shouldapply during the fall semester of theirsophomore year. Students shoulddecide on their interest in teacher certificationby the end of the first year inorder to start course work in the sophomoreyear.Barnard College Education Program336 Milbank Hall212-854-7072JOINT PROGRAMSSchool of LawEach year The Fu Foundation School ofEngineering and Applied Science maynominate two highly qualified juniorsfor a joint program with the ColumbiaUniversity School of Law, enablingstudents to complete the requirementsfor the degrees of Bachelor of Scienceand Doctor of Jurisprudence in sixyears instead of seven. Students shouldspeak to the Office of Pre-ProfessionalAdvising in the fall semester to expresstheir interest and prepare to take theLSAT by February of their junior year.The application process is conductedMarch through April.School of International and PublicAffairsThe Fu Foundation School of Engineeringand Applied Science and the Schoolof International and Public Affairs atColumbia offer a joint program enablinga small number of students to completethe requirements for the degreesof Bachelor of Science and Master ofInternational Affairs in five years insteadof six. Not only an excellent academicrecord but also maturity, fluency inan appropriate foreign language, andpertinent experience will determineadmission to this program. Applicationsare processed in the junior year by theCenter for Student Advising.REGISTERED PROGRAMSThe New York State Department ofEducation requires that this bulletininclude a listing of registered programs,both undergraduate and graduate (seechart on page 20). Enrollment in otherthan registered or otherwise approvedprograms may jeopardize a student’seligibility for certain student aid awards.The letter “X” or the name of adegree on the chart indicates that aprogram is registered with the New YorkState Department of Education.19SEAS 2010–2011

20Programs Registered with the New York State Department of EducationProgram Title HEGIS code B.S. M.S. Professional M.Phil. Eng.Sc.D. Ph.D.Applied Mathematics 913 X X X XApplied Physics 919 X X X X XBiomedical Engineering 905 X X X X XChemical Engineering 906 X X Chemical Engineer X X XCivil Engineering 908 X Civil EngineerCivil Engineering and Engineering Mechanics 908 X X X XCombined Plan w/Affiliated College; Dual B.S. (M.S.)/B.A. 999 X XComputer Engineering 999 X XComputer Science 701 X X X X X909 Computer SystemsEngineerComputer Science/Business: Dual M.S./M.B.A. 701 XComputer Science/Journalism: Dual M.S. 701 XEarth and Environmental Engineering 918 X X X X XEarth and Environmental Engineering/Business:Dual M.S./M.B.A. 913 XElectrical Engineering 909 X X Electrical Engineer X X XElectrical Engineering: Dual B.S./M.S. 909 X XEngineering Mechanics 921 X Mechanics EngineerFinancial Engineering 913 X Financial Engineer*Financial Engineering/Business:Dual M.S./M.B.A. 913 XIndustrial Engineering 913 X X Industrial Engineer X X XIndustrial Engineering/Business: Dual M.S./M.B.A. 913 XMaterials Science and Engineering 915 X X X X XMechanical Engineering 910 X X Mechanical Engineer X X XMedical Physics 1299 XMetallurgical Engineering 914 Metallurgical EngineerMining Engineering 918 Engineer of MinesMining Engineering and Applied Geophysics 918 XOperations Research 913 X X X X XOperations Research:Engineering and Management Systems 913 X XOperations Research: Financial Engineering 913 XSolid State Science and Engineering 919 X X X X*State approval pending.SEAS 2010–2011

UNDERGRADUATE ADMISSIONS21Office of Undergraduate AdmissionsColumbia University212 Hamilton Hall, Mail Code 28071130 Amsterdam AvenueNew York, NY 10027Fax: 212-854-3393Phone: 212-854-2522www.studentaffairs.columbia.edu/admissionsADMISSION AS A FIRST-YEARSTUDENTEach autumn The Fu Foundation Schoolof Engineering and Applied Scienceenrolls approximately 300 highly qualifiedmen and women, chosen from awide range of applicants. All becomefull, active participants in a rich anddiverse university setting. Therefore, theAdmissions Committee is interested inachievements not only in mathematicsand science, but also in other fields:English, the social sciences, languages,and the arts. Considerable value isplaced on personal qualities and attributeslike diversity of interests, specialabilities, maturity, motivation, curiosity,and independence. Secondary schoolrecords and recommendations are carefullyevaluated to ascertain the contentand difficulty of the applicant’s preparatorystudies and the degree to whichthis preparation correlates with standardizedtests. Of importance also isthe candidate’s participation in extracurricularor community activities. Here theemphasis is placed on the depth andsignificance of involvement rather thanon the number of activities. For its finalselection, the School seeks studentswith unique achievements and talentsas well as diverse economic, social, andgeographic backgrounds.Accordingly, the School ofEngineering and Applied Science prescribesno standardized course of studyfor secondary school students applyingfor first-year admission. The Schooldoes, however, strongly recommend thefollowing academic preparation:(preferably through calculus)and recommends as well:languagesocial studiesThe Application ProcessStudents are strongly encouraged toapply online. Columbia utilizes TheCommon Application and requires a supplement.Both are available as of August1, 2010 on the Office of UndergraduateAdmissions Web site. If you do not haveaccess to the Internet, please call theOffice of Undergraduate Admissions at212-854-2522 to request an application.The Common Application andsupplement should be filled out andsubmitted as early as possible alongwith the $80 application fee or an officialfee waiver request.All parts of the application must bepostmarked no later than January 1.(See below for Early Decision deadlines.)Decision letters are mailed out inearly April.The Early Decision ProgramCandidates for whom Columbia is thefirst choice may apply under the EarlyDecision Program. In order to qualify forthis program, all application materialsmust be postmarked by November 1.In mid-December, Early Decisionapplicants receive notice of their acceptance,denial, or deferral to regular decisionstatus. Applicants admitted underthe Early Decision program are obligatedto accept Columbia’s offer of admissionand must withdraw their applications atother colleges if they are provided with afinancial aid package that enables themto attend Columbia.Required Standardized TestingPlease go to the Office of UndergraduateAdmissions Web site for our standardizedtesting requirements. You must registerwith the appropriate testing agencywell in advance of the date on whichyou wish to be tested. Please note thatscores reported to Columbia’s School ofGeneral Studies (2095) will not reach ouroffice and will not be considered for evaluation.Columbia reserves the right notto evaluate a candidate whose scoresare not reported directly by the testingagency. Please do not utilize the “rush”service in sending your test scores toColumbia. Doing so does not speed upthe processing of your test scores. Weobtain all testing via a secure Web siteto which we are provided access by theappropriate testing agency. Scores thatare sent via the “rush” service are sent tous in paper form, which we are no longerable to process.SEAS 2010–2011

22Applicants may submit results of theAmerican College Testing (ACT) examinationsin lieu of the SAT, but may notsubstitute any other examinations for therequired SAT Subject Tests.The Test of English as a ForeignLanguage (TOEFL) or InternationalEnglish Language Testing System(IELTS) is required of all applicantswhose principal language of instructionhas not been English and who have notlived in an English-speaking environmentfor at least five years.Applicants must be certain whentaking standardized tests to have theirresults reported directly to ColumbiaUniversity by the testing agency.Students are required to report all standardizedtesting. The following codesshould be used when completing testregistration forms:SAT Reasoning, SAT Subject Tests,TOEFL: use code 2116ACT: use code 2719Educational Testing ServiceRosedale RoadPrinceton, NJ 08541Phone: 609-921-9000www.ets.orgAmerican College Testing ProgramBox 313Iowa City, IW 52243Phone: 319-337-1270www.act.orgTest of English as a Foreign LanguageBox 899Princeton, NJ 08451609-771-7100www.toefl.orgInternational English Language TestingSystemwww.ielts.orgAdvanced PlacementThe School gives recognition tothe Advanced Placement program.Appropriate placement and credit will begiven to students who score accordingto the School’s criteria (see page 14) inthe Advanced Placement examinationsgiven in May by the College EntranceExamination Board. In addition, requiredcourses may be waived on the basis offaculty placement conferences, permittingstudents with special preparation toadvance in prescribed sequences. Nocredit is given for college courses takenprior to high school graduation, butappropriate placements may be made.Egleston ScholarsThe Egleston Scholars Programis named after Professor ThomasEgleston, who founded the ColumbiaSchool of Mines in 1864. Known in histime as one of the foremost experts onmining and metallurgy, Egleston servedas president of the American Instituteof Mining Engineers and twice receivedFrance’s highest decoration, the Légiond’honneur. The Thomas EglestonMedal for Distinguished EngineeringAchievement was established in 1939in his honor and is the School’s mostprestigious alumni award, recognizinggraduates of Columbia Engineering whohave made exceptional contributions tothe world of engineering and applied science.In this spirit, the Egleston ScholarsProgram recognizes undergraduatestudents of Columbia Engineering whoembody the mission of the School atlarge: “to educate socially-responsibleengineering and applied science leaderswhose work results in the betterment ofthe human condition, locally, nationally,and globally.”C. Prescott Davis Scholars ProgramEach year, outstanding high schoolseniors are nominated for selectionas C. Prescott Davis Scholars by theAdmissions Committee. After a rigorousselection process, the Scholars arechosen to participate throughout theirfour undergraduate years in academicand cocurricular opportunities, includingresearch with faculty, professionalinternships, and meetings with worldrenownedscholars, innovators, andleaders.Higher Education OpportunityProgram (HEOP) and NationalOpportunity Program (NOP)The Higher Education OpportunityProgram (HEOP) is sponsored bythe New York State Department ofEducation and Columbia University. Theprogram is designed for New York Stateresidents who have particular educationaland economic needs with regard toadmission requirements. HEOP studentsmust be U.S. citizens or permanent residentswho have lived in New York Statefor one year prior to enrolling in college.HEOP’s individualized counseling andtutoring services help students meet thechallenges of a major university and professionalschool. New students attendan intensive pre-first-year SummerBridge Program on the Columbia campus.Students in the School’s undergraduateHigher Education OpportunityProgram can follow a five-year curriculumwhich spreads the first and secondyearrequirements over three years andallows for the inclusion of several extracourses designed to provide academicsupport.Because of the different pace of thisprogram, students are considered to bemaking minimum satisfactory progresswhen they complete 24 points of creditin one academic year. HEOP students’academic performance is otherwiseevaluated by the same standardsapplied to all undergraduates. HEOPsupport is available to students wishingto pursue only the Bachelor of Sciencedegree or Columbia’s Combined PlanProgram for both the Bachelor of Artsand Bachelor of Science in five years.The National Opportunity Program(NOP) is a replication of the HigherEducation Opportunity Program andprovides access to a Columbia educationfor students outside of New YorkState. Requirements for NOP are thesame as those for HEOP, except for theNew York State residency requirement.For further information concerningthe Engineering School’s OpportunityPrograms, contact:Academic Success ProgramsColumbia UniversityNew York, NY 10027Phone: 212-854-3514www.studentaffairs.columbia.edu/asp/programsAPPLICANTS WITHADVANCED STANDING(TRANSFER APPLICANTS)The Fu Foundation School ofEngineering and Applied Scienceaccepts applications for transfer into thesophomore or junior year from studentsin four-year programs at arts and sciencescolleges and engineering schools.SEAS 2010–2011

The School also accepts applicationsfrom students with strong academicrecords in pre-engineering programs attwo-year community colleges. All studentswho are considering applying tothe School of Engineering and AppliedScience are encouraged to complete acourse of study similar to the School’sFirst Year–Sophomore Program.Transfers, who are guaranteed housing,may enter Columbia only in Septemberand may count no more than 68 pointsof credit toward the Columbia degree.Transfer students must also satisfy theUniversity’s residence requirements bytaking at least 60 points at Columbia.Credit for transfer students to TheFu Foundation School of Engineeringand Applied Science is determined bythe equivalence of the courses takenat a previous institution with courses atColumbia. A minimum final course gradeof B must be achieved in order for transfercredit to be awarded. At the time ofadmission, transfer students are providedwith a Tentative Statement of Credit,which is an evaluation based on thestudent’s transcript. Prior to enrolling,transfer students are required to submitcourse descriptions and/or syllabi for allcourses for which they wish to receivecredit. The classes for the first yearsophomoreprogram are evaluated anda determination is made by the Centerfor Student Advising as to the degreeto which the materials covered overlapwith the similar course at Columbia. Ifthe overlap is deemed to be sufficient,the student will receive both credit andexemption for that class. It is possiblehowever for students to receive creditfor a class taken elsewhere, but notexemption. For classes to fulfill the nontechnical,technical and major courserequirements, students are requiredto submit petitions to the Center forStudent Advising. These petitions arereviewed by the appropriate facultycommittee and a determination is madeas to whether or not the student shouldreceive credit and/or exemption.Transfer applicants should providethe scores of College BoardExaminations as part of their application.Applicants must submit resultsof the SAT or the American CollegeTesting (ACT) examinations. Resultsof the SAT Subject Tests are requiredonly if the tests were taken in highschool. Students in a non-English–speaking environment and whoseprimary language of instruction has notbeen English for at least five years arerequired to take an English proficiencyexamination, TOEFL or IELTS. Thesestudents must submit the results ofat least one of the exams and will berequired to take an English placementtest on arrival, before registration.Transfer Applications can only becompleted online at the Web site of theOffice of Undergraduate Admissions.www.studentaffairs.columbia.edu/admissions/applications/transfer.phpApplications must be received by March15 for September admission.The Combined Plan ProgramsThe Combined Plan programs at The FuFoundation School of Engineering andApplied Science are designed to providestudents the opportunity to receiveboth a Bachelor of Arts or Bachelorof Science degree from an affiliatedliberal arts college and a Bachelor ofScience or Master of Science degreefrom Columbia. Details concerning theseprograms are contained in the TheUndergraduate Programs section of thisbulletin.Secondary school students who wishto follow one of the Combined Plan programsat one of the affiliated CombinedPlan schools should apply directly to theaffiliated school’s admissions office.Third-year undergraduate studentsalready in a Combined Plan programshould apply to the Columbia UniversitySchool of Engineering and AppliedScience Combined Plan Program. Thedeadlines for applying to these programs,each of which is described in theUndergraduate Programs section of thisbulletin, are:the 3-2 Combined Plan ProgramCombined Plan ProgramPlan B.S. ProgramPlan M.S. ProgramFor further information on the 3-2 and4-2 B.S. programs, visit the Office ofUndergraduate Admissions online, www.studentaffairs.columbia.edu/admissions.You may also contact the Office ofUndergraduate Admissions by phone, at212-854-2522, or e-mail to combinedplan@columbia.edu.For further informationon the 4-2 M.S. program, contactthe Office of Graduate Student Services,524 S. W. Mudd, New York, NY 10027or phone 212-854-6438.CAMPUS VISITS ANDINTERVIEWSProspective students are encouraged tovisit the Columbia campus throughoutthe year. The Office of UndergraduateAdmissions hosts information sessionsand campus tours through theVisitors Center, located in 213 LowLibrary. Group information sessions areconducted by members of the admissionsstaff and offer the opportunity tolearn more about Columbia University’sacademic and student life as well asadmissions and financial aid. Campustours immediately follow the informationsession and are led by a currentundergraduate student. Engineeringtours, designed to offer prospectivestudents an in-depth look into The FuFoundation School of Engineering andApplied Science, are led by currentColumbia engineering students andare available every Friday at 1:00 p.m.,except for holidays. Please note thatthe Engineering School tour is designedto supplement, but not replace, theUndergraduate Admissions informationsession and general campus tour. Forfurther information and a detailed scheduleof visit opportunities, please seeVisiting Columbia on the UndergraduateAdmissions Web site (www.studentaffairs.columbia.edu/admissions).Columbia does not conduct interviewson campus. Interviews areinstead conducted around the countryand the world by the members of theAlumni Representative Committee.The University provides the names ofcandidates to the Committee, whichconducts interviews from Octoberthrough February. Candidates will becontacted by a Committee member duringthis time if interviews are available.Candidates should not call or write theAdmissions Office to arrange alumniinterviews.23SEAS 2010–2011

24UNDERGRADUATE TUITION, FEES, AND PAYMENTSThe 2010–2011 tuition and feesare estimated. Tuition and feesare prescribed by statute and aresubject to change at the discretion ofthe Trustees.University charges such as tuition,fees, and residence hall and meal plansare billed in the first Student AccountStatement of the term, which is sentout in July and December of each yearfor the upcoming term. This accountis payable and due in full on or beforethe payment due date announced inthe Statement, typically at the end ofAugust or early January before thebeginning of the billed term. Any studentwho does not receive the firstStudent Account Statement is expectedto pay at registration.If the University does not receivethe full amount due for the term on orbefore the payment due date of thefirst Statement, a late payment chargeof $150 will be assessed. An additionalcharge of 1 percent per billing cycle maybe imposed on any amount past duethereafter.Students with an overdue accountbalance may be prohibited from registering,changing programs, or obtaininga diploma or transcripts. In the case ofpersistently delinquent accounts, theUniversity may utilize the services of anattorney and/or collection agent to collectany amount past due. If a student’saccount is referred for collection, thestudent may be charged an additionalamount equal to the cost of collection,including reasonable attorney’s fees andexpenses incurred by the University.TUITIONUndergraduate students enrolled in TheFu Foundation School of Engineeringand Applied Science pay a flat tuitioncharge of $20,580 per term, regardlessof the number of course credits taken.MANDATORY FEESOrientation fee: $415 (one-time chargein the first term of registration)Student Life fee: $634 per termHealth Service fee: $438 per termInternational Services charge: $50 perterm (international students only)Transcript fee: $95 (one-time charge)OTHER FEESApplication and late feession:$80admission: $80istration:$50; after late registration:$100Books and course materials: Dependsupon courseLaboratory fees: See course listingsRoom and board (estimated): $10,200HEALTH INSURANCEColumbia University offers the StudentMedical Insurance Plan, which providesboth Basic and Comprehensivelevels of coverage. Full-time studentsare automatically enrolled in the Basiclevel of the Plan and billed for the insurancepremium in addition to the HealthService fee. Visit the Health ServicesWeb site (www.health.columbia.edu) fordetailed information about medical insurancecoverage options and directionsfor making confirmation, enrollment, orwaiver requests.PERSONAL EXPENSESStudents should expect to incur miscellaneouspersonal expenses for suchitems as clothing, linen, laundry, drycleaning, and so forth. Students shouldalso add to the above expenses thecost of two round trips between homeand the University to cover travel duringthe summer and the month-long, midyearbreak.The University advises students toopen a local bank account upon arrivalin New York City. Since it often takes aslong as three weeks for the first depositto clear, students should plan to coverimmediate expenses using either a creditcard, traveler’s checks, or cash draftdrawn on a local bank. Students areurged not to arrive in New York withoutsufficient start-up funds.LABORATORY CHARGESStudents may need to add another$100 to $300 for drafting materials orlaboratory fees in certain courses. Eachstudent taking laboratory courses mustfurnish, at his or her own expense, thenecessary notebooks, blank forms,and similar supplies. In some laboratorycourses, a fee is charged to coverexpendable materials and equipmentmaintenance. Students engaged inSEAS 2010–2011

25special tests, investigations, theses, orresearch work are required to meet thecosts of expendable materials as maybe necessary for this work and in accordancewith such arrangements as maybe made between the student and thedepartment immediately concerned.DAMAGESAll students will be charged for damageto instruments or apparatus caused bytheir carelessness. The amount of thecharge will be the actual cost of repair,and, if the damage results in total loss ofthe apparatus, adjustment will be madein the charge for age or condition. Toensure that there may be no questionas to the liability for damage, studentsshould note whether the apparatus is ingood condition before use and, in caseof difficulty, request instruction in itsproper operation. Where there is dangerof costly damage, an instructor shouldbe requested to inspect the apparatus.Liability for breakage will be decided bythe instructor in charge of the course.When the laboratory work is doneby a group, charges for breakage willbe divided among the members of thegroup. The students responsible for anydamage will be notified that a charge isbeing made against them.The amount of the charge will bestated at that time or as soon as it canbe determined.TUITION AND FEE REFUNDSStudents who make a complete withdrawalfrom a term are assessed a withdrawalfee of $75. Late fees, applicationfees, withdrawal fees, tuition deposits,special fees, computer fees, specialexamination fees, and transcript fees arenot refundable.The Health Service Fee, HealthInsurance Premium, University facilitiesfees, and student activity fees are notrefundable after the change of programperiod.Students who withdraw within thefirst 60 percent of the academic periodare subject to a refund calculation,which refunds a portion of tuition basedon the percentage of the term remainingafter the time of withdrawal. Thiscalculation is made from the date thestudent’s written notice of withdrawal isreceived by the Dean’s Office.Percentage Refund for Withdrawalduring First Nine Weeks of Term(prorated for calendars of a differentduration)1st week 100%2nd week 90%3rd week 80%4th week 80%5th week 70%6th week 60%7th week 60%8th week 50%9th week 40%10th week and after 0%For students receiving federal studentaid, refunds will be made to the federalaid programs in accordance withDepartment of Education regulations.Refunds will be credited in the followingorder:Federal Unsubsidized Stafford LoansFederal Stafford LoansFederal Perkins LoansFederal PLUS Loans (when disbursedthrough the University)Federal Pell GrantsFederal Supplemental EducationalOpportunity GrantsOther Title IV fundsWithdrawing students should beaware that they will not be entitled toany portion of a refund until all Title IVprograms are credited and all outstandingcharges have been paid.SEAS 2010–2011

26FINANCIAL AID FOR UNDERGRADUATE STUDYOffice of Financial Aid and EducationalFinancingColumbia University618 Alfred Lerner HallMail Code 28022920 BroadwayNew York, NY 10027Phone: 212-854-3711Fax: 212-854-5353E-mail: ugrad-finaid@columbia.eduwww.studentaffairs.columbia.edu/finaidAdmission to Columbia is need-blind forall students who are U.S. citizens, U.S.permanent residents, Canadian citizens,or Mexican citizens. Financial aid isawarded only to students who demonstrateneed. Columbia is committed tomeeting the full demonstrated financialneed of all applicants admitted as firstyearstudents. Financial aid is availablefor all four undergraduate years, providingstudents continue to demonstratefinancial need.While transfer admission is needblind,financial aid resources for transferstudents are very limited. Therefore, TheFu Foundation School of Engineeringand Applied Science is unable to meetthe full need of transfer applicants, withthe exception of students who enter theCombined Plan Program and those whotransfer from Columbia CollegeDETERMINING ELIGIBILITYColumbia determines the amount eachfamily can contribute to educationalcosts through an evaluation of the family’sfinancial information as reported onthe application forms described in thesection How to Apply for Financial Aid.The difference between the family contributionand the total cost of attendanceat Columbia (including tuition, room,board, fees, books, travel, and personalexpenses) represents the student’sdemonstrated need.The family contribution to the costof attending Columbia consists of twoelements: the parent contribution andthe student contribution. The parentcontribution is determined through anevaluation of parent income and assets,family size, and the number of familymembers attending college. The studentcontribution consists of a percentageof the student’s assets and a minimumcontribution from income. Each studentis expected to work during the summerand save a certain amount to contributeto educational costs.The minimum contribution from earningsis currently:First Year $2,400Sophomore $2,700Junior $2,900Senior $3,000The expected summer earningsamount is separate from the amountthat students are expected to earn byworking a part-time job during the academicyear.Eligibility for Columbia grant aidis normally limited to eight terms ofundergraduate study. Students mustreapply for financial aid each year andbe registered for a minimum of 12points during any term for which aidis requested. Changes in the family’scircumstances—for example, increasedincome or a change in the number offamily members attending college—willresult in changes in the family contribution.In addition, the individual elementsin the financial aid package may varyfrom year to year.The Office of Financial Aid andEducational Financing reserves theright to revise a financial aid award ifthe student withdraws from school orif any information reported on financialaid applications conflicts with informationon tax returns or other verificationdocuments. If a family’s financial circumstanceschange after submission of thefinancial aid application, an appeal maybe made to the Office of Financial Aidand Educational Financing, in writing,for a reconsideration of the financial aidpackage. An appeal may be made atany time during the year if circumstanceswarrant; otherwise appeals in directresponse to award letters must be madein writing within two weeks of receipt ofaid packages.Satisfactory Academic ProgressStudents must continue to make satisfactoryacademic progress toward thedegree to remain eligible for financialaid. Satisfactory academic progress isreviewed at the end of each term bythe Committee on Academic Screening.All students are considered for financialaid purposes to be making satisfactoryacademic progress as long as they areallowed to continue enrollment. Fordetails of The Fu Foundation Schoolof Engineering and Applied Science’sprocess for evaluating student’s academicprogress, see the section onConduct and Discipline in this bulletin.A student who is required to withdrawSEAS 2010–2011

27because of failure to make satisfactoryacademic progress may appeal thedecision to the Committee on AcademicScreening. Upon returning to the Schoolof Engineering and Applied Science followinga required withdrawal period, astudent regains eligibility for financial aid.FINANCIAL AID AWARDSFinancial aid is awarded in the form ofa “package,” consisting of a combinationof the various types of financial aidfor which the student is eligible. Mostfinancial aid packages include a combinationof grant and “self-help.” The selfhelpportion of a financial aid packageconsists of a part-time job during theacademic year. Grants from governmentsources or directly from Columbia coverany remaining need beyond that coveredby the self-help award.Columbia determines the institutional,federal, and New York State financialaid programs for which each student iseligible and awards funds appropriately.In addition to applying to Columbia forassistance, all financial aid applicantsare expected to apply for any othergrant/ scholarship aid for which theymay be eligible. Students must notify theOffice of Financial Aid and EducationalFinancing if any outside awards arereceived.Students who receive financial aidfrom Columbia grant permission to theOffice of Financial Aid and EducationalFinancing to release relevant personal,academic, and financial informationto persons or organizations outsideColumbia in order to institute or to continuefinancial assistance that they mightbe eligible to receive from such sources.Students can expect that Columbia willrespect their right to privacy and releaseinformation only as necessary.The following sources of financial aidmay be included in a financial aid packagefrom Columbia.SEAS 2010–2011

28A. Grants and ScholarshipsThrough the Columbia University Grant(CUG) program, need-based grants aremade to full-time matriculated Columbiastudents without expectation of repayment.Grants are funded through avariety of University resources, includingannual gifts and endowed accounts.Federal Supplemental EducationalOpportunity Grants (SEOG) are grantsmade under Title IV of the HigherEducation Act of 1965, as amended,from funds supplied entirely by thefederal government. These funds areawarded to students who demonstratefinancial need and are made withoutexpectation of repayment. The amountof an individual grant may range from$200 to $4,000 per year.The Federal Pell Grant programis authorized by the EducationAmendments of 1972. Under this programthe federal government providesgrants to students who qualify on thebasis of financial need. Pell grants rangefrom $976 to $5,350.The New York State TuitionAssistance Program (TAP) providesgrants to full-time, matriculated NewYork State residents who meet NewYork State’s eligibility standards. CurrentTAP award amounts range from $275to $5,000.Other grants/scholarships may beavailable to students from a variety ofoutside sources. These include, but arenot limited to, awards sponsored bysecondary schools, civic organizations,parental employers, corporations, andthe National Merit and National AchievementScholarship programs. Outsidescholarships are used to reduce theself-help component of the financial aidpackage. Only after self-help has beencompletely eliminated will the scholarshipsbegin to reduce any Columbiagrant.B. Student EmploymentAll students who receive financial aidfrom Columbia are expected to have apart-time job to help meet the cost ofeducation. Most students work on ornear campus, but there are many interestingand rewarding jobs throughoutNew York City as well.Columbia maintains an extensivelisting of student employment opportunities,both for federal work-study positionsand other student employmentoptions, which do not receive federalfunding. These listings are availableonline. (studentaffairs.columbia.edu/finaid/forms/workstudy.php)Federal Work-Study StudentEmployment. The Work-Study PayrollOffice is dedicated to assisting Columbiastudents with all processes related tohiring and payment. The Federal Work-Study (FWS) program is designed topromote part-time employment forstudents who are in need of earningsto help finance their education andto encourage participation in communityservice. The goal of ColumbiaUniversity’s FWS program is to providestudent assistance that supports a widerange of career objectives and departmentalneeds within the University andthe community.C. Financing OptionsIn addition to Columbia’s commitment tomeeting 100 percent of every student’sdemonstrated financial need, Columbiais committed to assisting families inmeeting their family contributions. Thefollowing financing options are availableto assist families in making educationalcosts more affordable.Monthly Payment Plan: Columbiaoffers an interest-free monthly paymentplan through which parents may makefive equal monthly payments each termrather than paying the term’s bill in fullat the beginning of each term. The onlycost associated with the plan is a nominalenrollment fee.Parent Loans for UndergraduateStudents (PLUS): Through the PLUSprogram, parents may borrow for achild’s educational expenses. Loansare made by banks and other commerciallenders from their own funds,with guarantees by the federal government.Under the PLUS program, parentsmay borrow up to the total cost ofattendance less any other financial aidreceived. Parents need not demonstrateneed to qualify; however, they must becitizens or permanent residents of theUnited States and must pass a standardcredit check. A fee of up to 3 percentwill be deducted from the loan at thetime that it is disbursed. Repaymentbegins sixty days after the second disbursementof the loan.HOW TO APPLY FORFINANCIAL AIDIn order to be considered for needbasedinstitutional financial aid at anytime during their four years of undergraduatestudy, students must applyfor financial aid at the time they applyfor admission. Exceptions may begranted only in the case of extenuatingcircumstances that result in a significantchange in the family’s financialsituation. Continuing students mustreapply for financial aid each year.Continuing Student financial aid applicationforms are made available by theOffice of Financial Aid and EducationalFinancing in mid-March. The student’sname and Columbia ID number shouldbe printed on all documents submittedto the Office of Financial Aid andEducational Financing. Financial aidapplicants whose application materialsare submitted after the published deadlinescannot be guaranteed institutionalfinancial aid.All Columbia application materialscan be accessed through www.studentaffairs.columbia.edu/finaid.1. College Scholarship Service (CSS)PROFILE FormFirst-time applicants (first-year andtransfer applicants, and continuingstudents who are applying for financialaid for the first time) must register withCSS for the PROFILE Form by visitingCSS online at www.collegeboard.com/profile. Applicants who register onlineshould complete the CSS Profile online(requires a secure browser and creditcard). All students must include theColumbia University School of Engineeringand Applied Science’s CSS code ontheir PROFILE Form.CSS code for SEAS: 2111The deadlines to submit online are:November 15: First-year early decisionMarch 1: First-year regular decisionApril 20: Transfer applicantsMay 5: Continuing students2. Free Application for FederalStudent Aid (FAFSA)First-year applicants should obtain aFAFSA online at www.fafsa.ed.gov/,SEAS 2010–2011

29from their high school guidance office,or by calling 1-800-4FED-AID.Transfer applicants should obtain aFAFSA online, from their current college’sfinancial aid office, or by callingthe number above.Continuing students should applyonline each year.All students must include theColumbia University School ofEngineering and Applied Science’sschool code on the FAFSA form.FAFSA code for SEAS: E00486Students and their parents submittingthe FAFSA online should request PINnumbers from the FAFSA Web site, sothat they may complete the FAFSA withan online signature. FAFSA applicantswithout PIN numbers may print a signaturepage and mail it in to the FAFSAProcessor. All online FAFSA applicantsshould wait for and print out the confirmationpage, to ensure that their onlinesubmission has been received.Columbia recommends waiting untilafter federal income tax returns havebeen completed before completing theFAFSA form, but no later than the followingdeadlines:March 1:April 20:May 5:First-year candidates, both early andregular decisionTransfer applicantsContinuing students3. Noncustodial ProfileColumbia believes that the principalresponsibility for meeting educationalcosts belongs to the family and offersfinancial aid only to supplement the family’sresources. If the student’s naturalparents are divorced or separated,Columbia requires each parent to providefinancial information as part of thestudent’s application for financial aid.The parent with whom the applicantlives most of the year should completethe PROFILE Form and the FAFSA.The noncustodial parent should submitan income tax return and the CSSNoncustodial Profile (online form providedas a link once the CSS PROFILEis submitted).First-year and transfer applicants andcontinuing students should complete theCSS Noncustodial PROFILE. The deadlinesfor completing this form are:November 15: First-year early decision candidatesMarch 1: First-year regular decision candidatesApril 20: Transfer applicantsMay 5: Continuing students4. Business/Farm InformationIf the student or parents own all or partof a business, corporations, or partnership,or are farm tenants, a completecopy of the most recent business taxreturn (including all schedules) must besubmitted to Columbia. Sole proprietorsmust submit Schedule C. The deadlinesto return these documents to the financialaid office are:November 15:March 1:April 20:May 5:First-year early decision candidatesFirst-year regular decision candidatesTransfer applicantsContinuing students5. Federal Income Tax ReturnsSigned copies of parent and studentfederal income tax returns, includingW-2 forms and all schedules, arerequired for verification of the informationreported on the PROFILE Form andFAFSA. The financial aid office stronglyencourages families of first-year applicantsto complete their federal incometaxes in February. Signed copies of federaltax returns for parents and, if applicable,for students should be submittedto the financial aid office as soon as theyare completed. The preferred deadlinesfor submission of signed federal taxreturns are:March 1:April 20:May 5:First-year candidates (early andregular decision)Transfer applicantsContinuing studentsSEAS 2010–2011

30TAX WITHHOLDING FORNONRESIDENT ALIENSCHOLARSHIP ANDFELLOWSHIP RECIPIENTSUnited States tax law requires theUniversity to withhold tax at the rate of14 percent on scholarship and fellowshipgrants paid to nonresident alienswhich exceed the cost of tuition, books,fees, and related classroom expenses.Certain countries have entered intotax treaties with the United States, whichmay serve to reduce this rate of withholding.However, even when such a treatyapplies, the student and the Universitymust report the full amount of suchexcess to the Internal Revenue Service.If a student claims tax treaty benefits, heor she must also report this amount tohis or her country of residence.The International Students andScholars Office has prepared a packetof tax information, which is revisedannually and is available to students.International Students and ScholarsOfficeColumbia University524 Riverside Drive, Mail Code 5724New York, NY 10027Phone: 212-854-3587Fax: 212-854-8579www.columbia.edu/cu/gsas/sub/2009/orientation/isso/The tax law is complex and may varywith regard to individual circumstances.Therefore, as the University is not in aposition to offer individual tax advice,students are advised to consult witha qualified tax professional and/or theconsulate of their country of residence.SEAS 2010–2011

Graduate Studies

32THE GRADUATE PROGRAMSGraduate programs of studyin The Fu Foundation Schoolof Engineering and AppliedScience are not formally prescribed, butare planned to meet the particular needsand interests of each individual student.Departmental requirements for eachdegree, which supplement the generalrequirements given below, appear inthe sections on individual graduate programs.Applicants for a graduate programare required to have completed anundergraduate degree and to furnish anofficial transcript as part of the admissionsapplication. Ordinarily the candidatefor a graduate degree will havecompleted an undergraduate course inthe same field of engineering in whichhe or she seeks a graduate degree.However, if the student’s interests havechanged, it may be necessary to makeup such basic undergraduate coursesas are essential to graduate study in hisor her new field of interest.In order to complete the requirementsfor any graduate degree, thestudent must plan a program withthe department of major interest andthen have it approved by the Office ofGraduate Student Services; the programmay be modified later with the permissionof the department and the AssistantDean. No more than one term of coursework or, in the case of part-time students,no more than 15 points of creditof course work, completed before theprogram is approved, may be countedtoward the degree. Students registeredin the School have a minimum requirementfor each Columbia degree of 30points of credit of course work completedat Columbia University. The studentmust enroll for at least 15 of thesepoints while registered as a matriculatingstudent in a degree program in theEngineering School. (See also the sectionSpecial Nondegree Students andthe chapter Columbia Video Network.)Students wishing to change from thePh.D. degree to the Eng.Sc.D. degreemust therefore enroll for at least 15points while registered in the School.For residence requirements for studentsregistered in the Graduate School ofArts and Sciences or those wishing tochange from the Eng.Sc.D. degree tothe Ph.D. degree, see the bulletin of theGraduate School of Arts and Sciences.Students admitted to graduate studyare expected to enter upon and continuetheir studies in each succeedingregular term of the academic year. Anysuch student who fails to register for thefollowing term will be assumed to havewithdrawn unless a leave of absencehas been granted by the Office ofGraduate Student Services.While many candidates study on afull-time basis, it is usually possible toobtain all or a substantial part of thecredit requirement for the master’s, professional,or Eng.Sc.D. degrees throughpart-time study.Under special conditions, and withthe prior approval of the departmentof his or her major interest and of theAssistant Dean, a student may bepermitted to take a required subject atanother school. However, credit for suchcourses will not reduce the 30-pointminimum that must be takenCompetence in written and spokenEnglish is required of every degree candidate.See English proficiency requirements.For graduation, a candidate forany degree except a doctoral degreemust file an Application for Degree orCertificate on the date specified in theAcademic Calendar. Candidates for adoctoral degree must apply for the finalexamination. If the degree is not earnedby the next regular time for the issuanceof diplomas subsequent to the date offiling, the application must be renewed.Degrees are awarded three times ayear—in October, February, and May.THE MASTER OF SCIENCEDEGREEThe Master of Science degree is offeredin many fields of engineering and appliedscience upon the satisfactory completionof a minimum of 30 points of creditof approved graduate study extendingover at least one academic year.While a suitable Master of Scienceprogram will necessarily emphasizesome specialization, the program shouldbe well balanced, including basic subjectsof broad importance as well astheory and applications. The history ofmodern economic, social, and politicalinstitutions is important in engineering,and this is recognized in the prescribedundergraduate program of the School.If the candidate’s undergraduate educationhas been largely confined to purescience and technology, a program ofgeneral studies, totaling from 6 to 8points, may be required. Supplementarystatements covering these specialrequirements are issued by the School’sseparate departments. An applicantSEAS 2010–2011

33who lacks essential training will berequired to strengthen or supplementthe undergraduate work by taking orrepeating certain undergraduate coursesbefore proceeding to graduate study.No graduate credit (that is, credit towardthe minimum 30-point requirement forthe Master of Science degree) will beallowed for such subjects. Accordingly,Master of Science programs mayinclude from 35 to 45 points and mayrequire three terms for completion.Doctoral research credits cannot beused toward M.S. degree requirements.All degree requirements must becompleted within five years of thebeginning of graduate study. Underextraordinary circumstances, a writtenrequest for an extension of this timelimit may be submitted to the student’sdepartment for approval by the departmentchairman and the Assistant Dean.A minimum grade-point average of 2.5is required for the M.S. degree. A studentwho, at the end of any term, hasnot attained the grade-point averagerequired for the degree may be asked towithdraw.The 4-2 Master of Science ProgramThe 4-2 Master of Science Programprovides the opportunity for studentsholding bachelor’s degrees from affiliatedliberal arts colleges (see the listingunder the heading The CombinedPlan—Affiliated Colleges and Universitieswith majors in mathematics, physics,chemistry, or certain other physicalsciences to receive the M.S. degreeafter two years of study at Columbia inthe following fields of engineering andapplied science: biomedical, chemical,civil, computer, Earth and environmental,electrical, industrial, and mechanicalengineering; applied physics; appliedmathematics; engineering mechanics;operations research; materials science;and computer science.Each applicant must produce evidenceof an outstanding undergraduaterecord, including superior performancein physics and mathematics throughdifferential equations. The program ofstudy will be individually worked out inconsultation with a faculty adviser andwill be designed to integrate undergraduatework with the field of engineering orapplied science the student chooses tofollow. During the first year, the programwill consist primarily of basic undergraduatecourses; during the second year, ofgraduate courses in the selected field.The student must complete at least 30credits of graduate study to qualify forthe degree.A student whose background mayrequire supplementary preparation insome specific area, or who has beenout of school for a considerable period,will have to carry a heavier than normalcourse load or extend the programbeyond two years.Please contact the Office ofGraduate Student Services, The FuFoundation School of Engineering andApplied Science, 524 S. W. Mudd, MailCode 4708, 500 West 120th Street,New York, NY 10027; you should alsocontact the Combined Plan liaison atyour school for program information.You may, in addition, e-mail questionsto seasgradmit@columbia.edu.Dual Degree Program with theSchool of Journalism in ComputerScienceThe Graduate School of Journalismand the Engineering School offer a dualdegree program leading to the degreesof Master in Science in Journalism andthe Master of Science in ComputerScience. (See Computer Science.)Joint Program with the School ofBusiness in Industrial EngineeringThe Graduate School of Businessand the Engineering School offer ajoint program leading to the degreesof Master of Business Administrationand the Master of Science in IndustrialEngineering. (See Industrial Engineeringand Operations Research.)Joint Program with the School ofBusiness in Operations ResearchThe Graduate School of Business andthe Engineering School offer a jointprogram leading to the degrees ofMaster of Business Administration andthe Master of Science in OperationsResearch. (See Industrial Engineeringand Operations Research.)Joint Program with the Schoolof Business in Earth ResourcesEngineeringThe Graduate School of Businessand the Engineering School offer ajoint program leading to the degreesof Master of Business Administrationand the Master of Science in EarthResources Engineering. (See Earth andEnvironmental Engineering.)SEAS 2010–2011

34Special Studies with the HarrimanInstituteA candidate for an advanced degree inthe Engineering School may combinethese studies with work in the HarrimanInstitute. Upon completion of the courserequirements in the Institute and satisfactionof the language requirement (inany language indigenous to the formerUSSR), the student may qualify for theprofessional certificate of the HarrimanInstitute. The manner in which theInstitute and departmental requirementsare combined is to be determined bythe student in consultation with departmentaland Institute advisers. Advancedstudies and research may, whereappropriate, be supervised by facultymembers from both the School and theInstitute.THE PROFESSIONAL DEGREEAn undergraduate engineering degree isprerequisite for admission to the professionaldegree program. The programleading to the professional degrees inchemical, civil, computer, electrical,industrial, mechanical, metallurgical andmining engineering, and engineeringmechanics is planned for engineers whowish to do advanced work beyond thelevel of the M.S. degree but who do notdesire to emphasize research.The professional degree is awardedfor satisfactory completion of a graduateprogram at a higher level of coursework than is normally completed for theM.S. degree. Students who find it necessaryto include master’s-level coursesin their professional degree programwill, in general, take such courses asdeficiency courses. A candidate isrequired to maintain a grade-point averageof at least 3.0. A student who, atthe end of any term, has not attainedthe grade-point average required forthe degree may be asked to withdraw.At least 30 points of credit of graduatework beyond the M.S. degree, or 60points of graduate work beyond theB.S. degree, are required for the professionaldegree.The final 30 points required for theprofessional degree must be completedin no more than five years.DOCTORAL DEGREES:ENG.SC.D. AND PH.D.Two doctoral degrees in engineering areoffered by the University: the Doctor ofEngineering Science, administered byThe Fu Foundation School of Engineeringand Applied Science, and the Doctorof Philosophy, administered by theGraduate School of Arts and Sciences.The Eng.Sc.D. and Ph.D. programshave identical academic requirementswith regard to courses, thesis, andexaminations, but differ in residencerequirements and in certain administrativedetails.Doctoral students may submit a petitionto the Office of Graduate StudentServices to change from the Eng.Sc.D.degree to the Ph.D. degree or from thePh.D. degree to the Eng.Sc.D. degree.The petition must be submitted withinthe first year of enrollment or by thecompletion of 30 points. Any petitionssubmitted after this period will not beconsidered. Doctoral degree status canbe changed only once; students, therefore,must determine which doctoraldegree program is most appropriatefor their academic and professionalendeavors.Requirements for the DegreesA student must obtain the master’sdegree (M.S.) before enrolling as a candidatefor either the Ph.D. or Eng.Sc.D.degree. Application for admission as adoctoral candidate may be made while astudent is enrolled as a master’s degreecandidate. The minimum requirement incourse work for either doctoral degreeis 60 points of credit beyond the bachelor’sdegree.Candidates for the Ph.D. degreemust register full time and complete sixResidence Units. A master’s degreefrom an accredited institution maybe accepted in the form of advancedstanding as the equivalent of one yearof residence (30 points of credit or twoResidence Units) for either doctoraldegree. An application for advancedstanding must be completed during thefirst semester of study. Candidates forthe Eng.Sc.D. degree must (in additionto the 60-point requirement) accumulate12 points of credit in the departmentalcourse E9800: Doctoral researchinstruction. A holder of the professionaldegree who wishes to continue worktoward the Eng.Sc.D. degree will berequired to complete not less than 30additional points of credit in residence.All doctoral programs are subject toreview by the Committee on Instructionof the School. In no case will more than15 points of credit be approved for thedissertation and research and studiesdirectly connected therewith withoutspecial approval by this Committee.Normally, a doctoral candidate specializesin a field of interest acceptable to adepartment of the School.Departmental requirements mayinclude comprehensive written and oralqualifying examinations. Thereafter,the student must write a dissertationembodying original research under thesponsorship of a member of his or herdepartment and submit it to the department.If the department recommendsthe dissertation for defense, the studentapplies for final examination, which isheld before an examining committeeappointed by the Dean. This applicationmust be made at least three weeksbefore the date of the final examination.A student must have a satisfactorygrade-point average to be admittedto the doctoral qualifying examination.Consult the department requirementsfor details.The candidate for the degree ofDoctor of Engineering Science mustsubmit evidence that his or her dissertationhas been filed in compliancewith requirements set by the Faculty ofEngineering and Applied Science.The defense of the dissertation constitutesthe final test of the candidate’squalifications. It must be demonstratedthat the candidate has made a contributionto knowledge in a chosen area. Incontent the dissertation should, therefore,be a distinctly original contributionin the selected field of study. In formit must show the mastery of writtenEnglish which is expected of a universitygraduate.Ph.D. candidates should obtain acopy of the bulletin of the GraduateSchool of Arts and Sciences, in whichare printed the faculty requirements forthe Ph.D. degree. These are supplementedby the requirements of thedepartment of major interestSEAS 2010–2011

Doctoral Research InstructionIn order that the University may recoverthe costs that are not defrayed by theUniversity’s income from tuition, chargesfor research required for the Eng.Sc.D.are assessed as given below.Ph.D. candidates should consult thebulletin of the Graduate School of Artsand Sciences for the research instructionrequirements that apply to them.An Eng.Sc.D. candidate is requiredto do the following:1. At the time the student begins doctoralresearch, the student is eligibleto register for E9800 (3, 6, 9, or 12points of credit). Twelve points musthave been accumulated by the timethe student is to receive the degree.2. Registration for E9800 at a time otherthan that prescribed above is not permitted,except by written permissionof the Dean.3. Although 12 points of E9800 arerequired for the doctoral degree, nopart of this credit may count towardthe minimum residence requirementof 30 points (or 60 points beyond thebachelor’s degree).4. If a student is required to take coursework beyond the minimum residencerequirements, the 12 points of doctoralresearch instruction must stillbe taken in addition to the requiredcourse work.5. A student must register continuouslythrough the autumn and spring terms.This requirement does not include thesummer session.Completion of RequirementsThe requirements for the Eng.Sc.D.degree must be completed in no morethan seven years. The seven-year timeperiod begins at the time the studentbecomes a candidate for the Eng.Sc.D.degree or a candidate for the professionaldegree, whichever occurs first,and extends to the date on which thedissertation defense is held.Extension of the time allowed forcompletion of the degree may be grantedon recommendation of the student’ssponsor and the department chairmanto the Dean when special circumstanceswarrant. Such extensions are initiatedby submitting a statement of work inprogress and a schedule for completiontogether with the sponsor’s recommendationto the department chairman.SPECIAL NONDEGREESTUDENTSQualified persons who are not interestedin a degree program but who wish onlyto take certain courses may be permittedto register as special students, providedfacilities are available.Many graduate courses in The FuFoundation School of Engineering andApplied Science are offered in thelate afternoon and evening in orderto make them available to workingindividuals who wish to further theirknowledge in the areas of engineeringand applied science. Individuals whofind it difficult or impossible to attendclasses on the Columbia campus maybe able to receive instruction from theSchool through the Columbia VideoNetwork without leaving their work sites.Individuals interested in this programshould read the section describingthe distance learning Columbia VideoNetwork (CVN), which follows in thisbulletin.Special students receive grades andmust maintain satisfactory attendanceand performance in classes or laboratoriesand will be subject to the same rulesas degree candidates. Should a specialstudent decide to pursue a degree program,work completed as a special studentmay be considered for advancedstanding, but no more than 15 points ofcourse work completed as a special studentmay be counted toward a graduatedegree.For additional information and regulationspertaining to special students, seeGraduate Admissions.35SEAS 2010–2011

36COLUMBIA VIDEO NETWORKColumbia Video NetworkColumbia University540 S. W. Mudd, Mail Code 4719500 West 120th StreetNew York, NY 10027E-mail: info@cvn.columbia.eduPhone: 212-854-6447www.cvn.columbia.eduBACKGROUNDContinuing a tradition of nearly 250years of academic excellence andinnovation, Columbia University’s FuFoundation School of Engineeringand Applied Science established theColumbia Video Network (CVN) in 1986to meet a growing need within the engineeringcommunity for a graduate distanceeducation program. Classes anddegrees offered through CVN are fullyaccredited; the degrees are granted byColumbia University.Classes available through CVNare taught on campus by ColumbiaUniversity faculty in multimedia classrooms.Faculty and students meet inclassrooms equipped with cameras,electronic writing tablets, and SMARTboards. The recorded lectures are fullydownloadable for study at home, office,or on the road.CVN students take the same classes,have the same homework assignments,take the same exams, andearn the same degrees as on-campusstudents in Master of Science (M.S.) orProfessional Degree (P.D.) programs.COURSE OFFERINGS ANDDEGREE PROGRAMSCVN makes select SEAS graduatecourses available to off-campus studentsin autumn (September–December)and spring (January–May) terms. CVNadministrators work closely with facultyrepresentatives from each department toselect the classes that best fit the needsof new and continuing students aroundthe world. During the summer semester(and occasionally the autumn andspring terms), CVN makes prerecordedcourses available. SEAS currently offersM.S. degrees in the following disciplinesthrough CVN:For students who wish to doadvance work beyond the M.S., butdo not wish to emphasize research,Professional Degrees are also availablein the following areas: computer science,electrical engineering, industrialengineering/operations research, andmechanical engineering.STUDENT REGISTRATIONStudents who have earned an undergraduatedegree in engineering, mathematics,or related field can apply totake classes for credit or audit withoutfirst enrolling in a degree program at theUniversity or taking the GRE or TOEFLexams by registering as nondegreestudents. CVN also offers Certificates ofProfessional Achievement programs invarious fields, which may lead to studyin a related M.S. or P.D. program.Although you need not be admittedto a degree program to begin takingclasses through CVN, you should applyas soon as possible if you would like toearn a degree from Columbia University;up to 15 credits taken as a CVN nondegreestudent may be counted towarda degree when applying through CVN,subject to the approval of the student’sdepartmental adviser. Earning credit asa nondegree student does not guaranteeacceptance into a degree program.Only CVN students may transferup to 6 credits from another universitytoward an M.S. or P.D. degree, subjectto the approval of the student’s adviserand the department.Columbia University students admittedto an on-campus program are noteligible to take CVN courses.PROGRAM BENEFITSThe CVN program allows working professionalsto enroll in courses and earngraduate engineering degrees withoutleaving their communities, their families,or their jobs. The key component ofCVN is flexibility without compromiseto the high-caliber teaching, resources,and standards inherent in The FuFoundation School of Engineering andApplied Science. CVN students are apart of the Columbia community andmay take classes on campus. To furtherenhance the sense of community, CVNhas developed a completely automatedonline Student Center. It provides aplace where CVN students and facultycan communicate. Homework andexams are submitted and graded there,and course notes and other referencematerials are available for downloading.Professors and teaching assistantsare available via e-mail or phone toaddress academic questions. CVN’sadministrative staff is available to assistwith registration procedures, technicalqueries, and academic advising soworking professionals can devote theirenergies to their studies, their families,and their careers.SEAS 2010–2011

GRADUATE ADMISSIONS37Office of Graduate Student ServicesThe Fu Foundation School ofEngineering and Applied ScienceColumbia University524 S. W. Mudd, Mail Code 4708500 West 120th StreetNew York, NY 10027Phone: 212-854-6438Fax: 212-854-5900www.engineering.columbia.eduThe basic requirement for admissionas a graduate student is a bachelor’sdegree received from an institution ofacceptable standing. Ordinarily, theapplicant will have majored in the fieldin which graduate study is intended, butin certain programs, preparation in arelated field of engineering or science isacceptable. The applicant will be admittedonly if the undergraduate recordshows promise of productive and effectivegraduate work.Students who hold an appropriatedegree in engineering may applyfor admission to study for the Ph.D.degree. However, students are requiredto obtain the master’s degree first.Applications for admission as a doctoralcandidate may be made after completionof 15 points of work as a candidatefor the master’s degree.Students may be admitted in one ofthe following six classifications: candidatefor the M.S. degree, candidate forthe M.S. degree leading to the Ph.D.degree, candidate for the professionaldegree, candidate for the Doctor ofEngineering Science degree, candidatefor the Doctor of Philosophy degree (seealso the bulletin of the Graduate Schoolof Arts and Sciences), or special student(not a degree candidate). Note: Notmore than 15 points of credit completedas a special nondegree student may becounted toward a degree.APPLICATION REQUIREMENTSApplicants must submit an online applicationand required supplemental materials,as described below. When filing theonline application, the candidate shouldobtain one official transcript from eachpost-secondary institution attended andsubmit them in the original sealed envelope.Consideration for admission will bebased not only on the completion of anearlier course of study, but also uponthe quality of the record presented andupon such evidence as can be obtainedconcerning the candidate’s personal fitnessto pursue professional work.Additionally, candidates must providethree letters of recommendation and theresults of required standardized exams.The Graduate Record Examination (general)is required for all candidates. GREscores are valid for five years from thetest date. The Test of English as a ForeignLanguage (TOEFL) or International EnglishLanguage Testing System (IELTS) isrequired of all candidates who receivedtheir bachelor’s degree in a country inwhich English is not the official and spokenlanguage. TOEFL and IELTS scoresare valid for two years from the test date.Applicants can only apply to one degreeprogram per admission term.ENGLISH PROFICIENCYREQUIREMENTAdmitted graduate students who arerequired to submit official TOEFL orIELTS results must attain levels of proficiencyas described below. Studentswill not be cleared for graduation unlessthey satisfy the following requirements:didatesmust reach level 8 on theEnglish Proficiency Essay Examoffered by Columbia’s AmericanLanguage Program (ALP).candidates must attain level 10 onthe English Proficiency Essay Examoffered by Columbia’s AmericanLanguage Program (ALP).The English Proficiency Essay Exammust be taken at Orientation (the feefor this administration of the exam willbe covered by SEAS). A student whomisses this administration of the EssayExam must take the exam at his or herown expense at the beginning of the firstsemester enrolled and submit the officialscore to the Graduate Student ServicesOffice. (CVN students are exempt fromthe English Proficiency requirement.)A student who does not pass theEssay Exam at the required level of proficiencymay be required to enroll in anappropriate ALP course. For more informationon the administration of the EssayExam, please contact the GraduateStudent Services Office. The GraduateStudent Services Office reserves the rightto modify the English Proficiency requirementat any given time.APPLICATION FEESA nonrefundable application processingfee of $80 is required of all degree andnondegree applicants. Failure to submitthe application fee can delay processingof application materials.GRADUATE ADMISSIONCALENDARApplicants are admitted twice yearly, forthe fall and spring semesters.December 1 for Ph.D., Eng.Sc.D.,and M.S. leading to Ph.D. programs,and applicants to the M.S. program infinancial engineering; February 15 forprofessional, M.S. only, and nondegreeapplicants.SEAS 2010–2011

38lines:October 1 for all departmentsand degree levels.Applicants who wish to be consideredfor scholarships, fellowships, and assistantshipsshould file complete applicationsfor fall admission.ONE-TERM SPECIAL STUDENTSTATUSIndividuals who meet the eligibilityrequirements, who are U.S. citizens orU.S. permanent residents, and who wishto take courses for enrichment, maysecure faculty approval to take up totwo graduate-level courses for one termonly as a one-term special student. Thisoption is also appropriate for individualswho missed applications deadlines.Applications for special student statusare available at the Office of GraduateStudent Services and must be submittedduring the first week of the fall orspring semester.If a one-term special student subsequentlywishes either to continue takingclasses the following term or to becomea degree candidate, a formal applicationmust be made through the Office ofGraduate Student Services.TRANSFER APPLICANTSMaster degree students are not eligiblefor transfer credits.Students possessing a conferredM.S. degree may be awarded 2 residenceunits toward their Ph.D., as wellas 30 points of advanced standingtoward their Ph.D. or Eng.Sc.D. withdepartmental approval.SEAS 2010–2011

GRADUATE TUITION, FEES, AND PAYMENTS39The 2010–2011 tuition and feesare estimated. Tuition and feesare prescribed by statute and aresubject to change at the discretion ofthe Trustees.University charges such as tuition,fees, and residence hall and meal plansare billed in the first Student AccountStatement of the term, which is sent outin July and December of each year for theupcoming term. This account is payableand due in full on or before the paymentdue date announced in the Statement,typically at the end of August or earlyJanuary before the beginning of the billedterm. Any student who does not receivethe first Student Account Statement isexpected to pay at registration.If the University does not receivethe full amount due for the term on orbefore the payment due date of thefirst Statement, a late payment chargeof $150 will be assessed. An additionalcharge of 1 percent per billing cycle maybe imposed on any amount past duethereafter.Students with an overdue accountbalance may be prohibited from registering,changing programs, or obtaininga diploma or transcripts. In the case ofpersistently delinquent accounts, theUniversity may utilize the services of anattorney and/or collection agent to collectany amount past due. If a student’saccount is referred for collection, thestudent may be charged an additionalamount equal to the cost of collection,including reasonable attorney’s fees andexpenses incurred by the University.TUITIONGraduate students enrolled in M.S.,Professional Degree, and Eng.Sc.D.programs pay $1,372 per credit, exceptwhen a special fee is fixed. Graduatetuition for Ph.D. students is $18,230 perResidence Unit. The Residence Unit,full-time registration for one semesterrather than for individual courses (whetheror not the student is taking courses),provides the basis for tuition charges.Ph.D. students should consult the bulletinfor the Graduate School of Arts andSciences.COMPREHENSIVE FEE/MATRICULATION ANDFACILITIESEng.Sc.D. candidates engaged onlyin research, and who have completedtheir twelve (12) credits of DoctoralResearch Instruction (see “The GraduatePrograms” in this bulletin), are assesseda Comprehensive Fee of $1,615 perterm by The Fu Foundation School ofEngineering and Applied Science.Ph.D. candidates engaged only inresearch are assessed $1,615 per termfor Matriculation and Facilities by theGraduate School of Arts and Sciences.MANDATORY FEESUniversity facilities feeper termtermHealth Service fee: $438 per termInternational Services charge: $50 perterm (international students only)Transcript fee: $95 (one-time charge)OTHER FEESApplication and late fees$80istration:$50; after late registration:$100Books and course materials: Dependsupon courseLaboratory fees: See course listingsHEALTH INSURANCEColumbia University offers the StudentMedical Insurance Plan, which providesboth Basic and Comprehensivelevels of coverage. Full-time studentsare automatically enrolled in the Basiclevel of the Plan and billed for the insurancepremium in addition to the HealthService fee. Visit www.health.columbia.edu (www.health.columbia.edu) fordetailed information about medical insurancecoverage options and directionsfor making confirmation, enrollment, orwaiver requests.PERSONAL EXPENSESStudents should expect to incur miscellaneouspersonal expenses for suchitems as food, clothing, linen, laundry,dry cleaning, and so forth.The University advises students toopen a local bank account upon arrivalin New York City. Since it often takes aslong as three weeks for the first depositto clear, students should plan to coverimmediate expenses using either a creditcard, traveler’s checks, or cash draftdrawn on a local bank. Students areurged not to arrive in New York withoutsufficient start-up funds.SEAS 2010–2011

40LABORATORY CHARGESStudents may need to add another$100 to $300 for drafting materials orlaboratory fees in certain courses. Eachstudent taking laboratory courses mustfurnish, at his or her own expense, thenecessary notebooks, blank forms,and similar supplies. In some laboratorycourses, a fee is charged to coverexpendable materials and equipmentmaintenance; the amount of the feeis shown with the descriptions in thecourse listings. Students engaged inspecial tests, investigations, theses, orresearch work are required to meet thecosts of expendable materials as maybe necessary for this work and in accordancewith such arrangements as maybe made between the student and thedepartment immediately concerned.DAMAGESAll students will be charged for damageto instruments or apparatus caused bytheir carelessness. The amount of thecharge will be the actual cost of repair,and, if the damage results in total loss ofthe apparatus, adjustment will be madein the charge for age or condition. Toensure that there may be no questionas to the liability for damage, studentsshould note whether the apparatus is ingood condition before use and, in caseof difficulty, request instruction in itsproper operation. Where there is dangerof costly damage, an instructor shouldbe requested to inspect the apparatus.Liability for breakage will be decided bythe instructor in charge of the course.When the laboratory work is done bya group, charges for breakage will bedivided among the members of thegroup. The students responsible for anydamage will be notified that a charge isbeing made against them. The amountof the charge will be stated at that timeor as soon as it can be determined.TUITION AND FEE REFUNDSStudents who make a complete withdrawalfrom a term are assessed a withdrawalfee of $75. Late fees, applicationfees, withdrawal fees, tuition deposits,special fees, computer fees, specialexamination fees, and transcript fees arenot refundable.The Health Service Fee, HealthInsurance Premium, University facilitiesfees, and student activity fees are notrefundable after the change of programperiod.Students who withdraw within thefirst 60 percent of the academic periodare subject to a pro rata refund calculation,which refunds a portion of tuitionbased on the percentage of the termremaining after the time of withdrawal.This calculation is made from the datethe student’s written notice of withdrawalis received by the Office of GraduateStudent Services.Percentage Refund for Withdrawalduring First Nine Weeks of TermProrated for calendars of a differentduration, if the entire program isdropped:1st week 100%2nd week 90%3rd week 80%4th week 80%5th week 70%6th week 60%7th week 60%8th week 50%9th week 40%10th week and after 0%Refund Policy When DroppingIndividual CoursesTuition for courses dropped by the lastday of the Change-of-Program periodis refunded in full. There is no refund oftuition for individual courses droppedafter the last day of the Change-of-Program period. The Change-of-Program period is usually the first twoweeks of the fall or spring semesters(please note that the first week of thesemester usually begins on a Tuesday).Please note: The prorated scheduleabove does not pertain to individualclasses dropped (unless your entireschedule consists of only one class).The prorated schedule pertains to withdrawals.Withdrawal is defined as droppingone’s entire program.For students receiving federal studentaid, refunds will be made to thefederal aid programs in accordance withDepartment of Education regulations.Refunds will be credited in the followingorder:through the University)Opportunity GrantsWithdrawing students should beaware that they will not be entitled toany portion of a refund until all Title IVprograms are credited and all outstandingcharges have been paid.SEAS 2010–2011

FINANCIAL AID FOR GRADUATE STUDY41FINANCING GRADUATEEDUCATIONThe academic departments of TheFu Foundation School of Engineeringand Applied Science and the Office ofFinancial Aid and Educational Financingseek to ensure that all academicallyqualified students have enough financialsupport to enable them to work towardtheir degree. Possible forms of supportfor tuition, fees, books, and livingexpenses are: institutional grants, fellowships,teaching and research assistantships,readerships, preceptorships, onoroff-campus employment, and studentloans. The Office of Financial Aid andEducational Financing works closely withstudents to develop reasonable financialplans for completing a degree.Columbia University graduate fundsare administered by two separatebranches of the University, and theapplication materials required by thetwo branches differ slightly. Institutionalgrants, fellowships, teaching andresearch assistantships, readerships,and preceptorships are all departmentallyadministered funds. Questionsand problems regarding these awardsshould be directed to your academicdepartment. Federal Student Loans(Subsidized, Unsubsidized, GraduatePLUS and Perkins), private studentloans and New York State TAP grantsare administered by the Office ofFinancial Aid and Educational Financing.Questions and problems with regard toawards should be directed to your financialaid adviser.INSTRUCTIONS FORFINANCIAL AID APPLICANTSFormsProspective and continuing graduatestudents of The Fu Foundation Schoolof Engineering and Applied Sciencemust do the following to be consideredfor all forms of graduate financing (bothdepartmentally administered and financialaid–administered funds):1a. Prospective Students—complete anapplication for admission and submitit to The Fu Foundation School ofEngineering and Applied Science’sOffice of Graduate Student Services;1b. Continuing Students—preregisterfor classes during the preregistrationperiod;2. Complete a Free Application forFederal Student Aid (FAFSA) formand submit it to the U.S. Departmentof Education (only U.S. citizens,permanent residents and federallyeligible noncitizens must complete theFAFSA; International students do notneed to complete a FAFSA.);3. Complete an Express TAP applicationand submit it to the New YorkState Higher Education ServicesCorporation (only U.S. citizens orpermanent residents who reside inNew York State must complete theExpress TAP application; if you arenot a New York State resident, youdo not need to submit this form);4. Students who want to borrowstudent loans must also completethe Graduate Engineering StudentLoan Request Form and submit itto the Office of Financial Aid andEducational Financing.Application ProcessBefore you can complete the FreeApplication for Federal Student Aid(FAFSA) form, you must obtain a personalidentification number (PIN) fromthe U.S. Department of Education. ThePIN serves as your identifier and yourpersonal electronic signature on theFAFSA. It will also allow you to accessyour personal information in variousU.S. Department of Education systems.Apply for your PIN at www.pin.ed.gov.Approximately three business days afteryou request your PIN, you will receivean e-mail with instructions on how toretrieve it electronically. If you ask to benotified of your PIN by mail, it will arrivein seven to ten business days via theU.S. Postal Service.Once you have your PIN, you mustcomplete a FAFSA-on-the-Web applicationat www.fafsa.ed.gov. ColumbiaUniversity prefers that you apply forfinancial aid online. Information collectedon the FAFSA will help Columbiato determine your need for financialaid. You must give permission for theapplication data to be sent to ColumbiaUniversity by entering the Fu FoundationSchool of Engineering and AppliedScience Title IV school code (E00120)on the FAFSA form.Once your FAFSA-on-the-Web applicationis complete, your online confirmationpage will give you a link to the TAPon-the-Webapplication. New York Stateuses the information provided on yourTAP application to determine your eligibilityfor a Tuition Assistance Program(TAP) grant. The TAP-on-the-Web onlineform will be partially completed withsome information from your FAFSA.SEAS 2010–2011

42Review this data, supply any missinginformation, and submit the completedform. If you do not finish the onlineTAP-on-the-Web application, you will bemailed a paper Express TAP Application.As with the TAP-on-the-Web application,your Express TAP Application willalso be partially completed with some ofyour FAFSA data. Verify that the partiallycompleted data is correct, complete theremainder of the form, and return it toHESC in the envelope provided.Preregister for classes during thepreregistration period if you are a continuingstudent. Students who want toborrow student loans must completeand submit the Graduate EngineeringStudent Loan Request Form availableonline at www.studentaffairs.columbia.edu/finaid/downloads. The GraduateEngineering Student Loan Request Formprovides the University with informationabout your planned program, includingthe number of courses in which you planto enroll and the amount and type ofloans for which you are applying.DeadlinesApply for financial aid at the sametime that you apply for admissions.Your admissions application must bereceived by the December 1 deadlineto be eligible for The Fu FoundationSchool of Engineering and AppliedScience departmental funding (institutionalgrants, fellowships, teaching andresearch assistantships, readerships,and preceptorships). Spring admissionsapplicants will not be considered fordepartmental funding.Incoming applicants and continuingstudents must complete their FAFSAform after January 1 and by May 1.Guidelines for continuing studentsare available from departmental advisersin advance of the established deadline.All continuing supported students mustpreregister for classes during the preregistrationperiod.GRADUATE SCHOOLDEPARTMENTAL FUNDINGThe graduate departments of The FuFoundation School of Engineering andApplied Science offer an extensive arrayof funding. Funding decisions, basedsolely on merit, and contingent uponmaking satisfactory academic progress,are made by the departments. As aprospective student you must applyfor admission and complete the financialaid forms as stated on page 41.Continuing students must preregister forclasses during the preregistration periodand complete the applicable forms asstated in the Application Process section.Outside scholarships for whichyou qualify must be reported to yourdepartment and the Office of FinancialAid and Educational Financing. The FuFoundation School of Engineering andApplied Science reserves the right toadjust your institutional award if you holdan outside scholarship, fellowship, orother outside funding.Institutional GrantsInstitutional grants are awarded to graduatestudents on the basis of academicmerit. Recipients must maintain satisfactoryacademic standing. All applicantsfor admission and continuing studentsmaintaining satisfactory academic standingwill be considered for these funds.FellowshipsFellowships are financial and intellectualawards for academic merit that providestipends to be used by fellows to furthertheir research. If you are awarded a fellowship,you are expected to devotetime to your own work, and you are notrequired to render any service to theUniversity or donor. You may publishresearch produced by your fellowshipwork. As a fellow, you may not engagein remunerative employment withoutconsent of the Dean. All applicantsfor admission and continuing studentsmaintaining satisfactory academic standingwill be considered for these funds.Applicants should contact the departmentdirectly for information. See thecomplete listing of fellowships on pages228–229.AssistantshipsTeaching and research assistantships,available in many departments, providetuition exemption and a living stipend.Duties may include teaching, laboratorysupervision, participation in facultyresearch, and other related activities.Teaching and research assistantshipsrequire up to twenty hours of work perweek. The appointments generally lastfrom nine to twelve months. If you areparticipating in faculty research that fulfillsdegree requirements, you may applyfor a research assistantship. Readersand preceptors receive partial tuitionexemption and a stipend. Assistantshipsare awarded on the basis of academicmerit. All applicants for admission andcontinuing students maintaining satisfactoryacademic standing will beconsidered for these funds. Applicantsshould contact the department directlyfor information.ALTERNATIVE FUNDINGSOURCESExternal AwardsBecause it is not possible to offer fullgrant and fellowship support to allgraduate students and because of theprestige inherent in holding an awardthrough open competition, applicantsare encouraged to consider majornational and international fellowshipopportunities. It is important that prospectivegraduate students exploreevery available source of funding forgraduate study.In researching outside funding youmay look to faculty advisers, careerservices offices, deans of students, andoffices of financial aid where frequentlyyou may find resource materials, books,and grant applications for a wide varietyof funding sources. You must notifyboth your academic department at TheFu Foundation School of Engineeringand Applied Science and the Office ofFinancial Aid and Educational Financingof any outside awards that you will bereceiving.Funding for International StudentsTo secure a visa, international studentsmust demonstrate that they have sufficientfunding to complete the degree.Many international students obtain supportfor their educational expenses fromtheir government, a foundation, or aprivate agency.International students who applyto doctoral programs of study by theDecember 1 deadline and are admitted toa doctoral program in The Fu FoundationSchool of Engineering and AppliedScience are automatically considered fordepartmental funding (institutional grants,SEAS 2010–2011

fellowships, teaching and researchassistantships, readerships, and preceptorships)upon completion of therequired financial aid forms referred toabove. Spring admissions applicantswill not be considered for departmentalfunding. Continuing internationalstudents must preregister for classesduring the preregistration period andcomplete an enrollment status form tobe considered for departmental funding.Most private student loan programsare restricted to U.S. citizens and permanentresidents. However, internationalstudents may be eligible to apply forthese domestic loan programs with acredit worthy cosigner who is a citizenor permanent resident in the UnitedStates. Depending on the loan program,you may need a valid U.S. SocialSecurity number.Students who study at The FuFoundation School of Engineering andApplied Science on temporary visasshould fully understand the regulationsconcerning possible employment underthose visas. Before making plans foremployment in the United States, internationalstudents should consult withthe International Students and ScholarsOffice (ISSO), located at 524 RiversideDrive, Suite 200; 212-854-3587. TheirWeb site is www.columbia.edu/cu/isso/isso.html.OTHER FINANCIAL AID—FEDERAL, STATE, AND PRIVATEPROGRAMSEligibilityTo be considered for nondepartmentalfinancial aid (federal Stafford loans,federal unsubsidized Stafford loans,federal Perkins loans, and New YorkState TAP grants), you must be a U.S.citizen or permanent resident admittedas at least a half-time student to adegree program in The Fu FoundationSchool of Engi-neering and AppliedScience. If you are taking courses butare not yet admitted into a degreeprogram, then you do not qualify forfederal or state aid. In addition, topreserve your aid eligibility, you mustmaintain satisfactory academic progress,as defined in “The GraduatePrograms” section.To apply for funds, you must completea Free Application for FederalStudent Aid (FAFSA) form, a GraduateEngineering Student Loan RequestForm, and an Express TAP application(if you are a New York State resident).Federal Student Loan borrowers mustalso complete a Columbia UniversityLoan Entrance Interview and a MasterPromissory Note. The informationsupplied on the FAFSA form is usedto determine your eligibility for federalaid. The Express TAP application actsas your request for New York StateTuition Assistance Program funds.Columbia University prefers thatthe FAFSA be filed after January 1, butpreferably before May 1, for fall enrollment.Students must give permissionfor the application data to be sent toColumbia University by entering TheFu Foundation School of Engineeringand Applied Science Title IV schoolcode (E00120) on the FAFSA form.It is your responsibility to supplyaccurate and complete informationon the FAFSA and to notify the Officeof Financial Aid and EducationalFinancing immediately of any changesin your enrollment plans, housingstatus, or financial situation, includinginformation about any institutionalor outside scholarships you will bereceiving.The Graduate Engineering StudentLoan Request Form is available onlineat www.studentaffairs.columbia.edu/finaid/downloads.Determination of your eligibility forfinancial aid is, in part, based uponthe number of courses for which youregister. If you enroll in fewer coursesthan you initially reported on yourGraduate Engineering Student LoanRequest Form, your financial aid maybe reduced.University-administered federal andstate awards are not automaticallyrenewed each year. Continuing graduatestudents must submit a RenewalFAFSA each year by the ColumbiaUniversity deadline. Renewal dependson the annual reevaluation of yourneed, the availability of funds, and satisfactoryprogress toward the completionof your degreeNew York State Tuition AssistanceProgram (TAP)Legal residents of New York State whoare enrolled in a full-time degree programof at least 12 points a term, or theequivalent, may be eligible for awardsunder this program. To apply for TAP,list the Columbia University school code(E00120) on the FAFSA form. Whenthe FAFSA has been processed, anExpress TAP application will be mailedto you. Review the information, changeany incorrect items, sign the form, andreturn it to the address indicated.Veterans’ BenefitsVarious Department of Veterans Affairsprograms provide educational benefitsfor sons, daughters, and spouses ofdeceased or permanently disabledveterans as well as for veterans and inservicepersonnel who served on activeduty in the U.S. Armed Forces afterJanuary 1, 1955. In these programsthe amount of benefits varies. Undermost programs the student pays tuitionand fees at the time of registration butreceives a monthly allowance fromVeterans Affairs.Since interpretation of regulationsgoverning veterans’ benefits is subjectto change, veterans and their dependentsshould keep in touch with theDepartment of Veterans Affairs. Foradditional information and assistance incompleting the necessary forms, contact1-800-827-1000, or consult their Website (www.va.gov).Detailed information regarding theveteran population at Columbia and policiesincluding the Veteran’s ReadmissionProvision and Yellow Ribbon Programmay be found on the Veterans AffairsWeb site (veteranaffairs.columbia.edu).Direct LoansFederal Subsidized Student LoanProgramFederal Unsubsidized Loan ProgramFederal Perkins LoanFederal Graduate PLUS LoanDetailed information regarding theabove loan programs may be foundon the Student Financial Services Website (www.columbia.edu/cu/sfs/docs/Grad_Fin_Aid).43SEAS 2010–2011

44Columbia ComprehensiveEducational Financing PlanColumbia University has developed theComprehensive Educational FinancingPlan to assist students and parentswith their financing needs. The plan isa combination of federal, institutional,and private sources of funds thatwe hope will meet the needs of ourdiverse student population, providingoptions to part-time, full-time, andinternational students.Private LoansSeveral private loan programs areavailable to both U.S. citizens andinternational students attendingColumbia University. These loans werecreated to supplement federal andinstitutional aid. These loan programsrequire that you (the applicant) havea good credit standing and not bein default on any outstanding loans.International students may be eligiblefor a private loan with the assistanceof a creditworthy U.S. citizen or permanentresident. In some cases, as aninter-national student, you must havea valid U.S. Social Security number.Contact the financial aid office formore details on this loan program.EMPLOYMENTStudents on fellowship support mustobtain the permission of the Dean beforeaccepting remunerative employment.Students who study at The FuFoundation School of Engineering andApplied Science on temporary visasshould fully understand the regulationsconcerning possible employment underthose visas. Before making plans foremployment in the United States,international students should consultwith the International Students andScholars Office (ISSO) located at 524Riverside Drive, Suite 200; 212-854-3587. Their Web site is www.columbia.edu/cu/isso/ isso.html.On-Campus EmploymentThe Center for Career Education maintainsan extensive listing of studentemployment opportunities. The Center forCareer Education (CCE) is located at EastCampus, Lower Level, 212-854-5609,www.careereducation.columbia.edu.Off-Campus Employment in NewYork CityOne of the nation’s largest urban areas,the city offers a wide variety of opportunitiesfor part-time work. Many studentsgain significant experience in fieldsrelated to their research and study whilethey meet a portion of their educationalexpenses.CONTACT INFORMATIONFor questions about institutional grants,fellowships, teaching and researchassistantships, readerships, and preceptorships,contact your academicdepartment.For questions about on- or offcampusnon-need-based employment,contact the Center for Career Education,located at East Campus, Lower Level,212-854-5609, www.careereducation.columbia.edu.For questions about federal workstudyemployment, New York State TAPgrants, and student loans, contact:Office of Financial Aid and EducationalFinancingColumbia University618 Lerner Hall, Mail Code 28021130 Amsterdam AvenueNew York, New York 10027Phone: 212-854-3711Fax: 212-854-8223E-mail: engradfinaid@columbia.www.studentaffairs.columbia.edu/finaidSEAS 2010–2011

Faculty and Administration

46FACULTY AND ADMINISTRATIONOFFICERSLee C. BollingerB.A., J.D.President of Columbia UniversityClaude M. SteeleB.A., M.A., Ph.D.ProvostFeniosky Peña-MoraB.S., M.S., Sc.D.DeanAndrew LaineB.S., M.S., D.Sc.SecretaryFACULTYAlfred V. AhoLawrence Gussman Professor ofComputer ScienceB.A.Sc., Toronto, 1963;M.A., Princeton, 1965; Ph.D., 1967Peter K. AllenProfessor of Computer ScienceB.A., Brown, 1971; M.S., Oregon, 1976;Ph.D., Pennsylvania, 1985Dimitris AnastassiouProfessor of Electrical EngineeringDipl., National Technical University ofAthens (Greece), 1974;M.S., California, 1975; Ph.D., 1979Gerard H. A. AteshianProfessor of Mechanical Engineeringand of Biomedical EngineeringB.S., Columbia, 1986; M.S., 1987;M.Phil., 1990; Ph.D., 1991Daniel AttingerAssistant Professor of MechanicalEngineeringM.S., EPFL Lausanne, 1997;Ph.D., ETH Zurich, 2001William E. BaileyAssociate Professor of Materials Scienceand of Applied Physics and AppliedMathematicsB.S. and B.A., Brown, 1993;M.S., Stanford, 1995; Ph.D., 1999Guillaume BalProfessor of Applied MathematicsDiplôme, École Polytechnique (France),1993; Ph.D., University Paris VI, 1997Scott A. BantaAssociate Professor of ChemicalEngineeringB.S., University of Maryland, Baltimore,1997; M.S., Rutgers, 2000; Ph.D., 2002Peter BelhumeurProfessor of Computer ScienceB.S., Brown, 1985;M.S., Harvard, 1991; Ph.D., 1993Steven M. BellovinProfessor of Computer ScienceB.A., Columbia, 1972; M.S., NorthCarolina (Chapel Hill), 1977; Ph.D., 1987Keren BergmanProfessor of Electrical EngineeringB.S., Bucknell University, 1988;M.S., MIT, 1991; Ph.D., 1994Raimondo BettiProfessor of Civil EngineeringB.S., Rome, 1985; M.S., SouthernCalifornia, 1988; Ph.D., 1991Daniel BienstockProfessor of Industrial Engineering andOperations Research and of AppliedPhysics and Applied MathematicsB.S., Brandeis, 1982; Ph.D., MIT, 1985Simon J. L. BillingeProfessor of Materials Science and ofApplied Physics and Applied MathematicsB.A., Oxford, 1986;Ph.D., Pennsylvania, 1992Jose BlanchetAssistant Professor of IndustrialEngineering and Operations ResearchB.S., Instituto Tecnológico Autónomo deMéxico, 2000; Ph.D., Stanford, 2004Bruno A. BoleyProfessor of Civil EngineeringB.C.E., College of the City of New York,1943; M.Ac.E., Polytechnic Institute ofBrooklyn, 1945; Eng.Sc.D., 1946Allen H. BoozerProfessor of Applied PhysicsB.A., Virginia, 1966; Ph.D., Cornell, 1970Mark A. CaneG. Unger Vetlesen Professor of Earthand Environmental Sciences andProfessor of Applied Physics andApplied MathematicsB.A., Harvard, 1965; M.A., 1966;Ph.D., MIT, 1975Adam CannonLecturer in Machine LearningB.S., California (Los Angeles), 1991;M.S., 1997; Ph.D., Johns Hopkins, 2000Luca CarloniAssociate Professor of Computer ScienceB.S., Bologna (Italy), 1995;M.S., California (Berkeley), 1997;Ph.D., 2004Marco J. CastaldiAssistant Professor of Earth andEnvironmental Engineering (HenryKrumb School of Mines)B.S., Manhattan College, 1992;M.S., UCLA, 1994; Ph.D., 1997Siu-Wai ChanProfessor of Materials Science (HenryKrumb School of Mines) and of AppliedPhysics and Applied MathematicsB.S., Columbia, 1980;Sc.D., MIT, 1985Kartik ChandranAssistant Professor of Earth andEnvironmental EngineeringB.S., Indian Institute of Technology(Roorkee), 1995; Ph.D., University ofConnecticut, 1999Shih-Fu ChangProfessor of Electrical EngineeringB.S., National Taiwan University, 1985;M.S., California (Berkeley), 1991;Ph.D., 1993SEAS 2010–2011

47Xi ChenAssociate Professor of Earth andEvironmental EngineeringB.E., Xi’an Jiaotong University (P.R.China), 1994; M.E., Tsinghua University(P.R. China), 1997; S.M., Harvard, 1998;Ph.D., 2001Nicola ChiaraAssistant Professor of Civil EngineeringB.S., Università degli Studi di Palermo(Italy), 1995; M.S., University of Texas,2001; Ph.D., Columbia, 2006Maria ChudnovskyAssociate Professor of IndustrialEngineering and Operations ResearchB.A., Israel Institute of Technology,1996; M.S.C. Technion, 1999;M.A., Princeton, 2002; Ph.D., 2003Rama ContAssociate Professor of IndustrialEngineering and Operations ResearchDiplôme, École Polytechnique (France),1994; D.E.A., Ecole Normale Supérieure(France), 1995; Doctorat, Université deParis XI, 1998Patricia J. CulliganProfessor of Civil EngineeringB.Sc., University of Leeds, 1982; M.Phil.,Cambridge University, 1985; Ph.D., 1989Gautam DasguptaProfessor of Civil EngineeringB.Engr., Calcutta, 1967; M.Engr., 1969;Ph.D., California (Berkeley), 1974George DeodatisThe Santiago and Robertina CalatravaFamily Professor of Civil EngineeringB.S., National Technical University ofAthens, 1982; M.S., Columbia, 1984;Ph.D., 1987Emanuel DermanProfessor of Professional Practice ofIndustrial Engineering and OperationsResearchB.Sc., University of Cape Town, 1965;M.A., Columbia, 1968; Ph.D., 1973Paul DiamentProfessor of Electrical EngineeringB.S., Columbia, 1960; M.S., 1961;Ph.D., 1963Paul F. DubyProfessor of Mineral EngineeringIng. Civil M.E., Brussels, 1956;Eng.Sc.D., Columbia, 1962Christopher J. DurningProfessor of Chemical EngineeringB.S., Columbia, 1978;M.A., Princeton, 1979; Ph.D., 1982Stephen A. EdwardsAssociate Professor of Computer ScienceB.S., California Institute of Technology,1992; M.S., California (Berkeley), 1994;Ph.D., 1997Dan EllisAssociate Professor of ElectricalEngineeringB.A., Cambridge University, 1987;M.S., MIT, 1992; Ph.D., 1996Dirk EnglundAssistant Professor of ElectricalEngineering and of Applied PhysicsB.S., California Institute of Technology,2002; M.S., Ph.D., Stanford, 2008;Steven K. FeinerProfessor of Computer ScienceB.A., Brown, 1973; Ph.D., 1985George W. FlynnThomas Alva Edison Professor ofChemistry; Professor of ChemicalEngineeringB.S., Yale, 1960; M.A., Harvard, 1962;Ph.D., Harvard, 1965; PostdoctoralFellow, MIT, 1964–1966Morton B. FriedmanProfessor of Civil Engineering and ofApplied Physics and Applied MathematicsB.S., New York University, 1948;M.S., 1950; D.Sc., 1953Guillermo GallegoProfessor of Industrial Engineering andOperations ResearchB.S., California (San Diego), 1980;Ph.D., Cornell, 1988Pierre GentineAssistant Professor of AppliedMathematicsB.Sc. SupAéro (France), 2002;M.S., MIT, 2006; M.S., Sorbonne, 2009;Ph.D., MIT, 2009Donald GoldfarbAlexander and Hermine AvanessiansProfessor of Industrial Engineering andOperations ResearchB.Ch.E., Cornell, 1963;M.A., Princeton, 1965; Ph.D., 1966Vineet GoyalAssistant Professor of IndustrialEngineering and Operations ResearchB.Tech., Indian Institute of Technology(India), 2003; M.S., Carnegie Mellon,2005; Ph.D., 2008Luis GravanoAssociate Professor of Computer ScienceB.S., Lujan (Argentina), 1990;M.S., Stanford, 1994; Ph.D., 1997Eitan GrinspunAssociate Professor of ComputerScienceB.A., Toronto (Ontario), 1997; M.S.,California Institute of Technology, 2000;Ph.D., 2003Jonathan L. GrossProfessor of Computer ScienceB.S., MIT, 1964; M.A., Dartmouth, 1966;Ph.D., 1968X. Edward GuoProfessor of Biomedical EngineeringB.S., Peking University, 1984;M.S., Harvard-MIT, 1990; Ph.D., 1994Martin HaughLecturer in Discipline, IndustrialEngineering and Operations ResearchB.S., University College, 1993; M.S.,1993; M.S., University of Oxford, 1994;Ph.D., MIT, 2001SEAS 2010–2011

48Xuedong HeAssistant Professor of IndustrialEngineering and Operations ResearchB.S., Peking University, 2005;D.Phil., Oxford, 2009Tony F. HeinzDavid M. Rickey Professor of OpticalCommunications (Electrical Engineering) andProfessor of Physics (Arts and Sciences)B.S., Stanford, 1978; Ph.D., California(Berkeley), 1982Irving P. HermanProfessor of Applied PhysicsB.S., MIT, 1972; Ph.D., 1977Henry HessAssociate Professor of BiomedicalEngineeringB.S., Technical University Clausthal(Germany), 1993; M.Sc., TechnicalUniversity Berlin, 1996; Ph.D., FreeUniversity Berlin, 1999Andreas H. HielscherProfessor of Biomedical Engineering andof Radiology (Health Sciences)B.S., University of Hannover (Germany),1987; M.S., 1991; Ph.D., Rice, 1995Elizabeth M. C. HillmanAssistant Professor of BiomedicalEngineering and of Radiology (HealthSciences)M.Sci., University College London, 1998;Ph.D., 2002Julia HirschbergProfessor of Computer ScienceB.A., Eckert College, 1968; Ph.D.,Michigan, 1976; MSEE, Pennsylvania,1982; Ph.D., 1985James C. HoneAssociate Professor of MechanicalEngineeringB.S., Yale, 1990;Ph.D., California (Berkeley), 1998Hayden HuangAssistant Professor of BiomedicalEngineeringB.S., Johns Hopkins, 1995;S.M., MIT, 1997; Ph.D., 2002Clark T. HungProfessor of Biomedical EngineeringSc.B., Brown, 1990; M.S.E.,Pennsylvania, 1992; Ph.D., 1995James S. ImProfessor of Materials Science (HenryKrumb School of Mines) and of AppliedPhysics and Applied MathematicsB.S., Cornell, 1984; Ph.D., MIT, 1989Garud IyengarProfessor of Industrial Engineering andOperations ResearchB. Tech., Indian Institute of Technology,1993; M.S., Stanford, 1995; Ph.D., 1998Christopher R. JacobsAssociate Professor of BiomedicalEngineeringB.S., Washington University, 1988;M.S., Stanford, 1989; Ph.D., 1994Tony JebaraAssociate Professor of Computer ScienceB.S., McGill, 1996; M.S., MIT, 1998;Ph.D., 2002Pedrag R. JelenkovicProfessor of Electrical EngineeringDipl.Ing., Belgrade University, 1991;M.S., Columbia, 1993; M. Phil., 1995;Ph.D., 1996Jingyue JuProfessor of Chemical EngineeringB.S., Inner Mongolia University, 1985;M.S., Chinese Academy of Sciences,1988; Ph.D., Southern California, 1993Soulaymane KachaniAssociate Professor of ProfessionalPractice of Operations ResearchB.S., Ecole Centrale Paris, 1998;M.S., MIT, 1999; Ph.D., 2002Gail E. KaiserProfessor of Computer ScienceB.S., MIT, 1979; M.S., 1980;Ph.D., Carnegie Mellon, 1985Lance C. KamAssistant Professor of BiomedicalEngineeringB.S., Washington University, 1991;M.S., University of Hawaii, 1994;Ph.D., RPI, 1999John KenderProfessor of Computer ScienceB.S., Detroit, 1970; M.S., Michigan,1972; Ph.D., Carnegie Mellon, 1980Angelos D. KeromytisAssociate Professor of Computer ScienceB.S., Crete, Heraclion, 1996;M.S., Pennsylvania, 1997; Ph.D., 2001David E. KeyesFu Foundation Professor of AppliedMathematicsB.S.E., Princeton, 1978;Ph.D., Harvard, 1984Martha A. KimAssistant Professor of Computer ScienceB.A., Harvard, 2002; M.E., Universitàdella Svizzera Italiana (Lugano,Switzerland), 2003;Ph.D., University of Washington, 2008Philip KimProfessor of Applied Physics and ofPhysics (Arts and Sciences)B.S., Seoul National, 1990; S.M., 1992;M.S., Harvard, 1996; Ph.D., 1999Peter KingetAssociate Professor of ElectricalEngineeringPh.D., Katholieke Universiteit Leuven(Belgium), 1996Jeffrey T. KobersteinPercy K. and Vida L. W. HudsonProfessor of Chemical EngineeringB.S., University of Wisconsin, 1974;Ph.D., University of Massachusetts, 1979Elisa E. KonofagouAssociate Professor of BiomedicalEngineering and of Radiology (HealthSciences)B.S., Université de Paris VI (France),1992; M.S., University of London, 1993;Ph.D., University of Houston, 1999S. G. Steven KouProfessor of Industrial Engineering andOperations ResearchM.A., Columbia, 1992; Ph.D., 1995Harish KrishnaswamyAssistant Professor of ElectricalEngineeringB.Tech., Indian Institute of Technology(Madras), 2001; M.S., SouthernCalifornia, 2003; Ph.D., 2009SEAS 2010–2011

Sanat K. KumarProfessor of Chemical EngineeringB.Tech., Indian Institute of Technology,1981; S.M., MIT, 1984; Ph.D., 1987Aaron KyleLecturer in Biomedical EngineeringB.S., Kettering University, 2002;Ph.D., Perdue, 2007Ioannis KymissisAssistant Professor of ElectricalEngineeringM.Eng., MIT, 1999; Ph.D., 2003Jeffrey W. KysarAssociate Professor of MechanicalEngineeringB.S., Kansas State, 1987; M.S., 1992;S.M., Harvard, 1993; Ph.D., 1998Klaus S. LacknerMaurice Ewing and T. Lamar WorzelProfessor of Geophysics (Earth andEnvironmental Engineering, HenryKrumb School of Mines)B.S., Heidelberg, 1974; M.S., 1976;Ph.D., 1978Andrew F. LaineProfessor of Biomedical Engineering andof Radiology (Health Sciences)B.S., Cornell, 1977; M.S., Connecticut,1980; M.S., Washington (St. Louis),1983; D.Sc., 1989Upmanu LallAlan and Carol Silberstein Professor ofEarth and Environmental Engineering(Henry Krumb School of Mines) and ofCivil EngineeringB.Tech., Indian Institute of Technology(Kampur), 1976; M.S., University ofTexas, 1980; Ph.D., 1981Aurel A. LazarProfessor of Electrical EngineeringB.S., Bucharest Polytechnical Institute,1971; M.S., Darmstadt Institute ofTechnology, 1976; Ph.D., Princeton, 1980Edward F. LeonardProfessor of Chemical EngineeringB.S., MIT, 1953; M.S., Pennsylvania,1955; Ph.D., 1960Jung-Chi LiaoAssistant Professor of MechanicalEngineeringB.S., National Taiwan University, 1993;M.S., MIT, 1997; Ph.D., 2001Qiao LinAssociate Professor of MechanicalEngineeringB.S., Tsinghua University (Beijing), 1985;M.S., 1988; Ph.D., California Institute ofTechnology, 1993Hoe I. LingProfessor of Civil EngineeringB.S., Kyoto University, 1988; M.S.,University of Tokyo, 1990; Ph.D., 1993Richard W. LongmanProfessor of Mechanical Engineeringand Civil EngineeringB.S., California (Riverside), 1965;M.S., California (San Diego), 1967;M.A., 1969; Ph.D., 1969Helen H. LuAssociate Professor of BiomedicalEngineeringB.S., Pennsylvania, 1992; M.S., 1997;Ph.D., 1998Tal MalkinAssociate Professor of Computer ScienceB.S., Bar-Ilan University (Israel), 1993;M.S., Weizmann Institute of CivilEngineering and Engineering Mechanics(Israel), 1995; Ph.D., MIT, 2000Chris A. MarianettiAssistant Professor of Materials Scienceand of Applied Physics and AppliedMathematicsB.S., Ohio State, 1997; M.S., 1998;Ph.D., MIT, 2004Michael E. MauelProfessor of Applied PhysicsB.S., MIT, 1978; M.S., 1979; Sc.D., 1983Nicholas MaxemchukProfessor of Electrical EngineeringB.S., The City College of New York,1968; M.S., Pennsylvania, 1970;Ph.D., 1975Kathleen McKeownHenry and Gertrude RothschildProfessor of Computer ScienceB.A., Brown, 1976;M.S., Pennsylvania, 1979; Ph.D., 1982V. Faye McNeillAssistant Professor of ChemicalEngineeringB.S., California Institute of Technology,1999; M.S., MIT; Ph.D., 2005Christian MeyerProfessor of Civil EngineeringVordiplom, Technical University of Berlin,1965; M.S., California (Berkeley), 1966;Ph.D., 1970Vishal MisraAssociate Professor of Computer ScienceB.S., Indian Institute of Technology,1992; M.S., Massachusetts (Amherst),1996; Ph.D., 2000Vijay ModiProfessor of Mechanical EngineeringB.Tech., Indian Institute of Technology(Bombay), 1978; Ph.D., Cornell, 1984Barclay Morrison IIIAssociate Professor of BiomedicalEngineeringB.S.E., Johns Hopkins, 1992; M.S.E.,Pennsylvania, 1994; Ph.D., 1999Van C. MowStanley Dicker Professor of BiomedicalEngineering and Professor of OrthopedicEngineering (Orthopedic Surgery, HealthSciences)B.A.E., RPI, 1962; Ph.D., 1966Kristin MyersAssistant Professor of MechanicalEngineeringB.S., University of Michigan, 2002;M.S., MIT, 2005; Ph.D., 2008Arvind NarayanaswamyAssistant Professor of MechanicalEngineeringB.Tech., Indian Institute of Technology,1997; Ph.D., MIT, 2007Gerald A. NavratilThomas Alva Edison Professor ofApplied PhysicsB.S., California Institute of Technology,1973; M.S., Wisconsin, 1974; Ph.D., 1976Shree K. NayarT. C. Chang Professor of Computer ScienceB.S., Birla Institute of Technology (India),1984; M.S., North Carolina State, 1986;Ph.D., CarnegieMellon, 199049SEAS 2010–2011

50Jason NiehAssociate Professor of Computer ScienceB.S., MIT, 1989; M.S., Stanford, 1990;Ph.D., 1999Steven M. NowickProfessor of Computer ScienceB.A., Yale, 1976; M.A., Columbia, 1979;Ph.D., Stanford, 1993Ismail Cevdet NoyanProfessor of Materials Science (HenryKrumb School of Mines) and of AppliedPhysics and Applied MathematicsB.S., Middle East Technical University(Turkey), 1978; Ph.D., Northwestern, 1984Mariana Olvera-CraviotoAssistant Professor of IndustrialEngineering and Operations ResearchB.S., Instituto Technológico Autónomode México, 2000; M.S., Stanford, 2004;Ph.D., 2006Richard M. Osgood, Jr.Higgins Professor of ElectricalEngineering and Professor of AppliedPhysicsB.S., U.S. Military Academy, 1965; M.S.,Ohio State, 1968; Ph.D., MIT, 1973Ben O’ShaughnessyProfessor of Chemical EngineeringB.Sc., Bristol (England), 1977; Ph.D.,Cambridge (England), 1984Ah-Hyung Alissa ParkLenfest Junior Professor in AppliedClimate ScienceB.S., University of British Columbia, 1998;M.S., 2000; Ph.D., Ohio State, 2005Thomas S. PedersenAssociate Professor of Applied PhysicsM.Sc., Technical University of Denmark,1995; Ph.D., MIT, 2000Itsik Pe’erAssistant Professor of Computer ScienceB.S., Tel Aviv University, 1990; M.S.,1995; Ph.D., 2002Feniosky Peña-MoraMorris A. and Alma Schapiro Professorof Civil EngineeringB.S., Universidad Nacional PedroHenríquez Ureña (Dominican Republic),1987; S.M., MIT, 1991; Sc.D., 1994Aron PinczukProfessor of Applied Physics and ofPhysics (Arts and Sciences)Licenciado, Buenos Aires (Argentina),1962; Ph.D., Pennsylvania, 1969Lorenzo M. PolvaniProfessor of Applied Mathematics andof Earth and Environmental Sciences(Arts and Sciences)B.Sc., McGill, 1981; M.Sc., 1982;Ph.D., MIT, 1988Kenneth A. RossProfessor of Computer ScienceB.Sc., Melbourne, 1986;Ph.D., Stanford, 1991Dan RubensteinAssociate Professor of ComputerScienceB.S., MIT, 1992; M.A., California (LosAngeles), 1994; Ph.D., Massachusetts(Amherst), 2000Paul SajdaAssociate Professor of BiomedicalEngineering and of Radiology (HealthSciences)B.S., MIT, 1989; M.S., Pennsylvania,1992; Ph.D., 1994José I. SánchezLecturer in Civil Engineering andEngineering MechanicsB.A., Pontifica Universidad CatólicaMadre y Maestre (Dominican Republic),1991; M.A., Pratt, 1994; M.S.,Columbia, 1996Peter SchlosserVinton Professor of Earth andEnvironmental Engineering (HenryKrumb School of Mines) and Professorof Earth and Environmental Sciences(Arts and Sciences)B.S./M.S., Heidelberg, 1981; Ph.D., 1985Henning G. SchulzrinneJulian Clarence Levi Professor ofMathematical Methods and ComputerScience and Professor of ComputerScience and of Electrical EngineeringB.S., Technical University of Darmstadt(Germany), 1984; M.S., Cincinnati, 1987;Ph.D., Massachusetts (Amherst), 1992Amiya K. SenProfessor of Electrical Engineering andof Applied PhysicsDipl., Indian Institute of Science 1952;M.S., MIT, 1958; Ph.D., Columbia, 1963Rocco A. ServedioAssociate Professor of Computer ScienceA.B., Harvard, 1993; M.S., 1997;Ph.D., 2001Lakshminarasimhan SethumadhavanAssistant Professor of Computer ScienceB.S.E., University of Madras, 2000;M.S., University of Texas, 2005;Ph.D., 2007Jay SethuramanAssociate Professor of IndustrialEngineering and Operations ResearchB.E., Birla Institute of Technology andScience (India), 1991; M.S., IndianInstitute of Science, 1994;Ph.D., MIT, 1999Michael P. SheetzWilliam R. Kenan Jr. Professor of CellBiology and Professor of BiomedicalEngineeringB.A., Albion, 1968; Ph.D., CaliforniaTechnical, 1972Kenneth L. ShepardProfessor of Electrical EngineeringB.S.E., Princeton, 1987; M.S.E.E.,Stanford, 1988; Ph.D., 1992Samuel K. SiaAssistant Professor of BiomedicalEngineeringB.Sc., University of Alberta (Edmonton,Canada), 1997; Ph.D., Harvard, 2002Karl SigmanProfessor of Industrial Engineering andOperations ResearchB.A., California (Santa Cruz), 1980;M.A., California (Berkeley), 1983;M.S., 1984; Ph.D., 1986Andrew W. SmythProfessor of Civil EngineeringB.A./B.Sc., Brown, 1992; M.S., Rice,1994; Ph.D., Southern California (LosAngeles), 1998SEAS 2010–2011

Adam H. SobelProfessor of Applied Physics and AppliedMathematics and of EnvironmentalSciences (Arts and Sciences)B.A., Wesleyan, 1989; Ph.D., MIT, 1998Ponisseril SomasundaranLaVon Duddleson Krumb Professor ofMineral EngineeringB.Sc., Kerala (India), 1958; B.E.,Indian Institute of Science, 1961; M.S.,California (Berkeley), 1962; Ph.D., 1964Marc W. SpiegelmanProfessor of Earth and EnvironmentalSciences (Arts and Sciences) andof Applied Physics and AppliedMathematicsB.A. Harvard, 1985; Ph.D. University ofCambridge, U.K., 1989Clifford SteinProfessor of Industrial Engineering andOperations ResearchB.S.E., Princeton, 1987;M.S., MIT, 1989; Ph.D., 1992Fred StolfiSenior Lecturer in MechanicalEngineeringB.S., Fordham University, 1972;M.S., RPI, 1976; Ph.D., 2001Rene B. TestaProfessor of Civil EngineeringB.E., McGill, 1959; M.S., Columbia,1960; Eng.Sc.D., 1963Joseph F. TraubEdwin Howard Armstrong Professor ofComputer ScienceB.S., College of the City of New York,1954; M.S., Columbia, 1955; Ph.D., 1959Van-Anh TruongAssistant Professor of IndustrialEngineering and Operations ResearchB.S., University of Waterloo (Canada);Ph.D., Cornell, 2007Yannis P. TsividisBatchelor Memorial Professor ofElectrical EngineeringB.E., Minnesota, 1972; M.S., California(Berkeley), 1973; Ph.D., 1976Nicholas J. TurroWilliam P. Schweitzer Professor ofChemistry; Professor of ChemicalEngineering and of EnvironmentalEngineering and Materials ScienceB.A., Wesleyan University, 1960; Ph.D.,California Institute of Technology, 1963;NSF Postdoctoral Fellow, Harvard,1963–1964Wen I. WangThayer Lindsley Professor of ElectricalEngineering and Professor of AppliedPhysicsB.S., National Taiwan, 1975;M.E.E., Cornell, 1979; Ph.D., 1981Xiadong WangProfessor of Electrical EngineeringB.S., Shanaha Jiaotong University,1992; M.S., Purdue, 1995;Ph.D., Princeton, 1998Anthony WebsterLecturer in the Discipline of Finance inthe Department of Industrial Engineeringand Operations ResearchB.S., Rutgers, 1980; M.S., Columbia,1983; M.B.A., 1999Michael I. WeinsteinProfessor of Applied MathematicsB.S., Union College, 1977;M.S., Courant Institute-NYU, 1979;Ph.D., 1982Alan C. WestSamuel Ruben-Peter G. Viele Professorof Electrochemistry and ChemicalEngineeringB.S., Case Western Reserve, 1985;Ph.D., California (Berkeley), 198951Salvatore J. StolfoProfessor of Computer ScienceB.S., Brooklyn, 1974; M.S., New YorkUniversity, 1976; Ph.D., 1979Horst StormerII Rabi Professor of Physics (Arts andSciences) and Professor of AppliedPhysicsB.S., Goethe-Universität, Frankfurt(Germany). 1970; Diploma, 1974;Ph.D. Stuttgart (Germany), 1977John E. TaylorAssistant Professor of Civil EngineeringB.S.,Tulane, 1991; M.S., 1996;M.S., Swiss Federal Institute ofTechnology, 1997; Ph.D., Stanford,2006Elon TerrellAssistant Professor of MechanicalEngineeringB.S., University of Texas (Austin), 2002;M.S., 2004; Ph.D., Carnegie Mellon, 2007David VallancourtSenior Lecturer in Circuit and Systems inthe Department of Electrical EngineeringB.S., Columbia, 1981; M.S., 1984;Ph.D., 1987Latha VenkataramanAssistant Professor of Applied PhysicsB.S., MIT, 1993; M.S., Harvard, 1997;Ph.D., 1999Gordana Vunjak-NovakovicProfessor of Biomedical EngineeringB.S., University of Belgrade, 1972;S.M., 1975; Ph.D., 1980Haim WaismanAssistant Professor of Civil EngineeringB.S., Technion (Israel Institute ofTechnology, 1999; M.S. 2002;Ph.D., RPI, 2005Ward WhittWai T. Chang Professor of IndustrialEngineering and Operations ResearchA.B., Dartmouth, 1964;Ph.D., Cornell, 1969Chris H. WigginsAssociate Professor of Applied MathematicsB.A., Columbia, 1993;Ph.D., Princeton, 1998Chee Wei WongAssociate Professor of MechanicalEngineeringB.S., California (Berkeley), 1999;M.S., MIT, 2001; Ph.D., 2003Henryk WozniakowskiProfessor of Computer ScienceM.S., Warsaw, 1969; Ph.D., 1972SEAS 2010–2011

52Cheng Shie WuuProfessor of Clinical Radiation Oncology(in Public Health, Environmental HealthSciences, and Applied Physics)B.S., National Tsinghua University(Taiwan), 1979; M.S., 1982; Ph.D.,Kansas, 1985Junfeng YangAssistant Professor of Computer ScienceB.S., Tsinghua University (Beijing), 2000;M.S., Stanford, 2002; Ph.D., 2007Mihalis YannakakisPercy K. and Vida L. W. HudsonProfessor of Computer ScienceDipl., National Technical University ofAthens (Greece), 1975; M.S., Ph.D.,Princeton, 1979David D. W. YaoProfessor of Industrial Engineering andOperations ResearchM.A.Sc., Toronto, 1981; Ph.D., 1983Y. Lawrence YaoProfessor of Mechanical EngineeringB.E., Shanghai Jiao Tong University,1982; M.S., Wisconsin (Madison), 1984;Ph.D., 1988Tuncel M. YegulalpProfessor of MiningM.S., Technical University (Istanbul),1961; Eng.Sc.D., Columbia, 1968Yechiam YeminiProfessor of Computer ScienceB.Sc., Hebrew (Jerusalem), 1972;M.Sc., 1974; Ph.D., California (LosAngeles), 1978Huiming YinAssistant Professor of Civil EngineeringB.S., Hohai University, 1995; M.S., PekingUniversity, 1998; Ph.D., Iowa, 2004FACULTY MEMBERS-AT-LARGEMartin ChalfieChairman, Department of BiologicalSciencesSteven A. GoldsteinChairman, Department of Earth andEnvironmental SciencesR. Glenn HubbardDean of the Graduate School ofBusinessIgor KricheverChairman, Department of MathematicsWilliam ZajcChairman, Department of PhysicsHenry C. PinkhamDean, Graduate School of Arts andSciencesMichele M. Moody-AdamsDean, Columbia CollegeColin NuckollsChairman, Department of ChemistryEMERITI AND RETIREDOFFICERS (NOT IN RESIDENCE)Daniel N. BeshersProfessor Emeritus of MetallurgyHuk Yuk ChehSamuel Ruben-Peter G. Viele ProfessorEmeritus of ElectrochemistryRene ChevrayProfessor Emeritus of MechanicalEngineeringC. K. ChuFu Foundation Professor Emeritus ofApplied MathematicsAtle GjelsvikProfessor Emeritus of Civil EngineeringFletcher H. GriffisProfessor Emeritus of Civil EngineeringRobert A. GrossPercy K. and Vida L.W. HudsonProfessor Emeritus of Applied Physicsand Dean EmeritusCarl C. GryteProfessor Emeritus of ChemicalEngineeringCyril M. HarrisCharles Batchelor Professor Emeritusof Electrical Engineering and ProfessorEmeritus of ArchitectureHerbert H. KelloggStanley-Thompson Professor Emeritusof Chemical MetallurgyJohn T. F. KuoMaurice Ewing and J. Lamar WorzelProfessor Emeritus of GeophysicsW. Michael LaiProfessor Emeritus of MechanicalEngineeringLeon LidofskyProfessor Emeritus of Applied Physicsand Nuclear EngineeringEugene S. MachlinHenry Marion Howe Professor Emeritusof MetallurgyThomas C. MarshallProfessor Emeritus of Applied PhysicsHenry E. Meadows Jr.Professor Emeritus of ElectricalEngineeringCharles ZukowskiProfessor of Electrical EngineeringB.S., MIT, 1982; M.S., 1982;Ph.D., 1985Gil ZussmanAssistant Professor of ElectricalEngineeringB.S., Technion (Israel Institute of Technology),1995; M.Sc., 1999; Ph.D., 2004Edward G. Coffman Jr.Professor Emeritus of ElectricalEngineeringCyrus DermanProfessor Emeritus of OperationsResearchFrank L. DiMaggioRobert A. W. and Christine S. CarletonProfessor Emeritus of Civil EngineeringGertrude F. NeumarkHowe Professor Emerita of MaterialsScience and Engineering and ProfessorEmerita of Applied Physics and AppliedMathematicsGlenn K. RightmireAssociate in Mechanical EngineeringSEAS 2010–2011

53Enders RobinsonMaurice Ewing and J. Lamar WorzelProfessor Emeritus of AppliedGeophysicsMischa SchwartzCharles Batchelor Professor Emeritus ofElectrical EngineeringJordan L. SpencerProfessor Emeritus of ChemicalEngineeringThomas E. SternDicker Professor Emeritus of ElectricalEngineeringRobert D. StollProfessor Emeritus of Civil EngineeringMalvin Carl TeichProfessor Emeritus of EngineeringScienceNickolas J. ThemelisStanley-Thompson Professor Emeritusof Chemical Metallurgy (Earth andEnvironmental Engineering, HenryKrumb School of Mines)Stephen H. UngerProfessor Emeritus of Computer Scienceand of Electrical EngineeringRimas VaicaitisRenwick Professor Emeritus of CivilEngineeringHoward W. VreelandProfessor Emeritus of GraphicsOmar WingProfessor Emeritus of ElectricalEngineeringEdward S. YangProfessor Emeritus of ElectricalEngineeringADMINISTRATIVE OFFICERSFeniosky Peña-MoraDeanJeff BallingerAssociate Director, WebCommunicationsLeslie BarnaExecutive Assistant to the Senior ViceDeanAudrey BauerAssociate Director, Human Resourcesand Facilities ServicesRyan CarmichaelAssociate Director, AdvancementPaul CassidyAssociate Director, Finance andAdministrationJenifer ChinManager, Grants and ContractsDan CoccoAssistant Director, Engineering FundN. Travoya CollinsAssistant Director, Engineering FundGrace ChungExecutive Director, Columbia VideoNetworkTimothy CrossDirector, Strategic InitiativesPatricia CulliganVice Dean of Academic AffairsPromiti DuttaAssociate Director, Community-BasedLearning ProgramsHolly EvartsDirector, Strategic Communications andMedia RelationsMorton B. FriedmanSenior Vice DeanSEAS 2010–2011

54Timothy G. GreeneStewardship OfficerZachary HowellAssociate Director, Engineering FundYewande JegedeFinancial AnalystScott KellyAlumni Programs CoordinatorMargaret KellyDirector, Internal CommunicationsRégine LambrechDirector, Global Initiatives and EducationBruce LincolnEntrepreneur in ResidenceJane LowryParents Program OfficerPeggy MaherAssociate Dean for AdvancementLindsay N. MontanariAssistant Director, Alumni RelationsJocelyn MoralesAdmissions Officer, Graduate StudentServicesMarie-Pierre MurryExecutive Assistant to the DeanAnna Marie O’NeillAssociate Dean of Finance andAdministrationFredrik C. PalmAssociate Dean of Faculty, Academic,and Diversity AffairsLourdes PineiroDevelopment AssistantElaine RaglandCommunications CoordinatorJack ReillyExecutive AssistantKevin ShollenbergerDean of Student Affairs and AssociateVice President for UndergraduateStudent LifeTiffany M. SimonAssistant Dean of Graduate StudentServicesJonathan R. StarkStudent Affairs Officer, GraduateStudent ServicesElizabeth StraussAssistant Director, Engineering FundYannis P. TsividisUndergraduate Curriculm Adviser to theDeanGreg Van KirkEntrepreneur in ResidenceDana VlcekDirector, Corporate and CommunityRelationsJack McGourtySenior Associate Dean for Corporate,Government, and Global EngagementRebecca RodriguezAssociate Director, EngagedEntrepreneurship ProgramAlex YepesAssociate Director, Small BusinessDevelopment CenterKathleen McKeownVice Dean for ResearchSEAS 2010–2011

Departments andAcademic Programs

56KEY TO COURSE LISTINGSThis section contains a descriptionof the curriculum of eachdepartment in the School, alongwith information regarding undergraduateand graduate degree requirements,elective courses, and suggestions aboutcourses and programs in related fields.All courses are listed, whether or notthey are being offered during the currentyear; if a course is not being given, thatis indicated. Included as well are coursescross-listed with other departmentsand undergraduate divisions within theUniversity.BMEBBMEEBMENBMMEBUSICBMFCHAPBiomedical Engineering/Electrical Engineering/BiologyBiomedical Engineering/Electrical EngineeringBiomedical EngineeringBiomedical Engineering/Mechanical EngineeringBusinessComputer Science/BiomedicalEngineering/Medical InformaticsChemical Engineering/Applied Physics and Applied MathECBMECIAECIEECONEDUCEEBMEECSElectrical Engineering/ComputerScience/Biomedical EngineeringEarth and Environmental Engineering/Civil Engineering/ Internationaland Public AffairsEconomics/Industrial EngineeringEconomicsEducationElectrical Engineering/Biomedical EngineeringElectrical Engineering/Computer ScienceDESIGNATORSEach course is preceded by a four-letterdesignator, which indicates the departmentor departments presenting the course.CHCBCHEECHEMCHENChemistry/Biology/Computer ScienceChemical Engineering/Earth and Environmental EngineeringChemistryChemical EngineeringEEHSEEMEEESCELENElectrical Engineering/HistoryElectrical Engineering/Mechanical EngineeringEarth and Environmental SciencesElectrical EngineeringCourse DesignatorAHISDepartment SubjectArt HistoryAMCS Applied Mathematics/Computer ScienceAMSTAPAMAPBMAPMAAPPHARCHASCEASCMBIOCBIOLBISTBMCHAmerican StudiesApplied Physics/Applied MathematicsApplied Physics/Biomedical EngineeringApplied MathematicsApplied PhysicsArchitectureAsian Civilizations–East AsianAsian Civilizations–Middle EastBiology and ChemistryBiologyBiostatisticsBiomedical Engineering/Chemical EngineeringCHMECIEECIENCOCICOMSCSEECSORDNCEDRANEACEEAEEEAIAChemical Engineering/Mechanical EngineeringCivil Engineering/Earth andEnvironmental EngineeringCivil EngineeringContemporary CivilizationComputer ScienceComputer Science/Electrical EngineeringComputer Science/Operations ResearchDanceDecision, Risk and Operations(Business School)Earth and Environmental Engineering/Civil EngineeringEarth and Environmental EngineeringEarth and Environmental/International and Public AffairsENGIENGLENMEFINCFRENGERMGRAPHISTHUMAIEMEIEORINAFINTAEngineeringEnglishEngineering MechanicsFinance/EconomicsFrenchGermanGraphicsHistoryHumanitiesIndustrial Engineering/Mechanical EngineeringIndustrial Engineering andOperations ResearchInternational AffairsEarth and Environmental Engineering/Civil Engineering/Internationaland Public AffairsSEAS 2010–2011

57MATHMEBMMECEMSAEMSIEMUSIPHEDPHILPHYSPOLSPSLGPSYCRELIMathematicsMechanical Engineering/Biomedical EngineeringMechanical EngineeringMaterials Science and Engineering/Solid-State Science and EngineeringManagement Science/IndustrialEngineering and Operations ResearchMusicPhysical EducationPhilosophyPhysicsPolitical SciencePhysiology and Cellular BiophysicsPsychologyReligionHOW COURSES ARE NUMBEREDThe course number that follows eachdesignator consists of a capital letterfollowed by four digits. The capital letterindicates the University division or affiliateoffering the course:BCEGPSUVWZBusinessColumbia CollegeEngineering and Applied ScienceGraduate School of Arts and SciencesMailman School of Public HealthSummer SessionInternational and Public AffairsInterschool course with BarnardInterfaculty courseAmerican Language ProgramDIRECTORY OF CLASSESRoom assignments and coursechanges for all courses are availableonline at http://www.columbia.edu/cu/bulletin/uwb.The School reserves the right towithdraw or modify the courses ofinstruction or to change the instructorsat any time.SCNCSIEOSOCISPANSTATVIARScienceStatistics/Industrial Engineeringand Operations ResearchSociologySpanishStatisticsVisual ArtsThe first digit indicates the level ofthe course, as follows:0 Course that cannot be creditedtoward any degree1 Undergraduate course2 Undergraduate course, intermediate3 Undergraduate course, advanced4 Graduate course that is open to qualifiedundergraduates6 Graduate course8 Graduate course, advanced9 Graduate research course or seminarAn x following the course numbermeans that the course meets in thefall semester; y indicates the springsemester.SEAS 2010–2011

58APPLIED PHYSICS AND APPLIED MATHEMATICS200 S. W. Mudd, MC 4701, 212-854-4457Applied Physics and Applied Mathematics: www.apam.columbia.edu/Materials Science and Engineering: www.seas.columbia.edu/matsciCHAIRIrving P. Herman208 S. W. MuddDEPARTMENTALADMINISTRATORDina AminPROFESSORSGuillaume BalDaniel Bienstock, IndustrialEngineering andOperations ResearchSimon J. L. BillingeAllen H. BoozerMark A. Cane, Earth andEnvironmental SciencesSiu-Wai ChanMorton B. Friedman,Civil Engineering andEngineering MechanicsIrving P. HermanJames S. ImDavid E. KeyesPhilip Kim, PhysicsMichael E. MauelGerald A. NavratilGertrude F. NeumarkIsmail C. NoyanRichard M. Osgood Jr.,Electrical EngineeringAron PinczukLorenzo M. PolvaniMalvin A. Ruderman,PhysicsChristopher H. Scholz,Earth and EnvironmentalSciencesAmiya K. Sen, ElectricalEngineeringAdam SobelMarc W. SpiegelmanHorst StormerWen I. Wang, ElectricalEngineeringMichael I. WeinsteinCheng Shie Wuu, RadiationOncologyASSOCIATE PROFESSORSWilliam E. BaileyThomas S. PedersenChris H. WigginsASSISTANT PROFESSORSDirk Englund, ElectricalEngineeringPierre GentineChris A. MarianettiLatha VenkataramanADJUNCT PROFESSORSVittorio M. CanutoBarbara E. CarlsonC. Julien ChenAnthony Del GenioSupratik GuhaTimothy M. HallWei-Li LeeRon L. MillerStephen L. OstrowArthur RamirezLawrence N. RothenbergStephen A. SabbaghShalom J. WindYimei ZhuADJUNCT ASSOCIATEPROFESSORBrian CairnsADJUNCT ASSISTANTPROFESSORSKemi BabagbemiAlex CastiDavid MaurerJoseph OsborneAnastasia RomanouADJUNCT LECTURERIan LangmoreSENIOR RESEARCHSCIENTISTSJoze BevkJames BialekRainer BleckLeonard DruyanQiancheng MaJohn MarshallHolger ReimerdesSteven A. SabbaghShalom J. WindADJUNCT SENIORRESEARCH SCIENTISTSDavid LangC. Julien ChenRESEARCH SCIENTISTSMark AdamsJacek ChowdharyJerry I. DadapDarren GarnierIgor GeogdzhayevGeorge TselioudisYuanchong ZhangADJUNCT RESEARCHSCIENTISTMark HolzerASSOCIATE RESEARCHSCIENTISTSMikhail AlexandrovMichael BauerJohn BerkeryEmil BozinYonghua ChenUi-Jin ChungChris FarrowScott GianelliPavol JuhasAlexander LimanovLi LiuChenguang LuDavid MaurerCatherine NaudJan PerlwitzDenis PotapenkoAnastasia RomanouIldar SalakhutdinovJingbo WuRuoxian YingADJUNCT ASSOCIATERESEARCH SCIENTISTSManolis AntonoyiannakisConal MurrayMatthew PutmanPOSTDOCTORAL RESEARCHSCIENTISTSManus BiggsMichael DewarJeremy HansonSarah KangIan LangmoreUttam MannaMatteo PalmaYoung Seouk ParkJoan RaitanoHamish RamseyTiffany ShawShuguang WangRisheng WangASSOCIATEJohn C. ArboSPECIAL LECTURERSDaniel N. BeshersC. K. ChuSPECIAL RESEARCHSCIENTISTThomas C. MarshallThe Department of Applied Physicsand Applied Mathematicsincludes undergraduate andgraduate studies in the fields ofapplied physics, applied mathematics,and materials science and engineering.The graduate program in appliedphysics includes plasma physics andcontrolled fusion; solid-state physics;optical and laser physics; medicalphysics; atmospheric, oceanic, andearth physics; and applied mathematics.The graduate programs inmaterials science and engineering aredescribed on page 173.Current Research Activities inApplied Physics and AppliedMathematicsPlasma physics and fusion energy.In experimental plasma physics,research is being conducted on (1)equilibrium, stability, and transport infusion plasmas: high-beta tokamaks,spherical tokamaks, and levitateddipoles; (2) magnetospheric physics:trapped particle instabilities and stochasticparticle motion; (3) confinementof toroidal nonneutral plasmas; (4)plasma source operation and heatingtechniques; and (5) the development ofnew plasma measurement techniques.The results from our fusion scienceexperiments are used as a basis forcollaboration with large national andinternational experiments. For example,our recent demonstration of activefeedback control of high temperatureplasma instability is guiding research onSEAS 2010–2011

59NSTX at the Princeton Plasma PhysicsLaboratory, on the DIII-D tokamak atGeneral Atomics, and for the designof the next generation burning plasmaexperiment, ITER. In theoretical plasmaphysics, research is conducted in thefluid theory of plasma equilibrium andstability, active control of MHD instabilities,the kinetic theory of transport, andthe development of techniques basedon the theory of general coordinates anddynamical systems. The work is appliedto magnetic fusion, non-neutral andspace plasmas.Optical and laser physics. Active areasof research include inelastic light scatteringin nanomaterials, optical diagnosticsof film processing, new laser systems,nonlinear optics, ultrafast optoelectronics,photonic switching, optical physicsof surfaces, laser-induced crystallization,and photon integrated circuits.Solid-state physics. Research in solidstatephysics covers nanoscience andnanoparticles, electronic transport andinelastic light scattering in low-dimensionalcorrelated electron systems, fractionalquantum Hall effect, heterostructurephysics and applications, molecularbeam epitaxy, grain boundaries andinterfaces, nucleation in thin films,molecular electronics, nanostructureanalysis, and electronic structure calculations.Research opportunities also existwithin the interdisciplinary NSF MaterialsResearch Science and EngineeringCenter, which focuses on complex filmscomposed of nanocrystals; the NSFNanoscale Science and EngineeringCenter, which focuses on electrontransport in molecular nanostructures;and the DOE Energy Frontier ResearchCenter, which focuses on conversionof sunlight into electricity in nanometersizedthin films.Applied mathematics. Current researchencompasses analytical and numericalanalysis of deterministic and stochasticpartial differential equations, large-scalescientific computation, fluid dynamics,dynamical systems and chaos, aswell as applications to various fields ofphysics and biology. The applicationsto physics include condensed-matterphysics, plasma physics, nonlinearoptics, medical imaging, and the earthsciences, notably atmospheric, oceanic,and climate science, and solid earthgeophysics (see below). The applicationsto biology include cellular biophysics,machine learning, and functionalgenomics, including collaborations withColumbia’s Center for ComputationalBiology and Bioinformatics (C2B2),the Center for Computational LearningSystems (CCLS), the NIH-funded Centerfor Multiscale Analysis of Genetic andCellular Networks (MAGNet), and theNIH-funded Nanomedicine Center forMechanobiology. Extensive collaborationsexist with national climate researchcenters (the Geophysical Fluid DynamicsLaboratory and the National Center forAtmospheric Research) and with nationallaboratories of the U.S. Department ofEnergy, custodians of the nation’s mostpowerful supercomputers.Atmospheric, oceanic, and earthphysics. Current research focuses onthe dynamics of the atmosphere and theocean, climate modeling, cloud physics,radiation transfer, remote sensing,geophysical/geological fluid dynamics,geochemistry. The department engagesin ongoing research and instruction withthe NASA Goddard Institute for SpaceStudies and the Lamont-Doherty EarthObservatory. Five faculty members shareappointments with the Department ofEarth and Environmental Sciences.In addition to the faculty and graduatestudents, many others participatein these projects, including full-timeresearch faculty, faculty and studentsfrom other departments, and visitingscientists.Laboratory Facilities in AppliedPhysics and Applied MathematicsThe Plasma Physics Laboratory, foundedin 1961, is one of the leading universitylaboratories for the study of plasmaphysics in the United States. There arefour experimental facilities. The ColumbiaHigh-Beta Tokamak (HBT-EP) supportsthe national program to develop controlledfusion energy. It utilizes high voltage,pulsed power systems, and laserand magnetic diagnostics to study theproperties of high-beta plasmas and theuse of feedback stabilization to increasethe achievable beta. A collaborative programwith the Princeton Plasma PhysicsLaboratory and the DIII-D tokamakgroup at General Atomics is studyingthe properties of high-beta plasmas inorder to maximize fusion power productionin these large, neutral beam-heatedtokamaks and spherical tori. The plasmaphysics group and MIT have jointly constructedthe Levitated Dipole Experiment(LDX), a large plasma confinementexperiment incorporating a levitatedsuperconducting ring. The ColumbiaNonneutral Torus (CNT) is an experimentdevoted to the first study of non-neutralSEAS 2010–2011

60APPLIED PHYSICS PROGRAM: FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS 1 MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and ODE (3) 2PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)C1403 (3)C2601 (3.5)Lab W3081 (2)C1494 (3)Lab C2699 (3)CHEMISTRY/BIOLOGY(choose one course)CHEM C1403 (3), or higher orBIOL W2001 (4) or BIOL C2005 (4), or higherENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 orW1123 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)REQUIREDTECH ELECTIVES(3) Student’s choice, see list of first- and second-year technical electives (professional-level courses;see pages 12–13).COMPUTERSCIENCEPHYSICALEDUCATIONA computer language of the student’s choice at the 1000 level or higherC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1With the permission of the faculty adviser, students with advanced standing may start the calculus sequence at a higher level.2Applied physics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH E1210).Students who take APMA E2101 prior to declaring their major in applied physics may use this course to satisfy their ODE requirement.plasmas confined on magnetic surfaces.The Columbia Linear Machine (CLM)is a continuously operating, linear mirrordevice for the study of collisionlessplasma instabilities, plasma, transport,and feedback stabilization. Columbia’sCollisionless Terrella Experiment investigatesplasma transport in magnetosphericgeometry and the generationof strong plasma flow from nonlinearelectrostatic potentials.Experimental research in solid-statephysics and laser physics is conductedwithin the department and also in associationwith the Columbia Center forIntegrated Science and Engineering andthe School of Mines. Facilities includelaser processing and spectroscopicapparatus, ultrahigh vacuum chambersfor surface analysis, picosecond andfemtosecond lasers, a molecular beamepitaxy machine, and a clean room thatincludes photo-lithography and thin filmfabrication systems. Within this field, theLaser Diagnostics and Solid-State PhysicsLaboratory conducts studies in laserspectroscopy of nanomaterials and semiconductorthin films, and laser diagnosticsof thin film processing. The Laser Labfocuses on the study of materials underhigh pressure, laser surface chemical processing,and new semiconductor structures.Research is also conducted in theshared characterization laboratories andclean room operated by the NSF MaterialsResearch Science and Engineering Centerand the NSF Nanoscale Science andEngineering Center.The department maintains anextensive network of workstations anddesktop computers. The departmenthas recently acquired a SiCortex supercomputerwith 1,458 cores, which isused for a wide range of departmentalcomputational activities. The researchof the Plasma Lab is supported by adedicated data acquisition/data analysissystem, and the applied math group hasaccess to a Beowulf cluster. Throughthe Internet, researchers in the departmentare currently using supercomputingfacilities at the National Center forAtmospheric Research; the San DiegoSupercomputing Center; the NationalEnergy Research Supercomputer Centerin Berkeley, California; the NationalLeadership Class Facility at Oak Ridge,SEAS 2010–2011

APPLIED PHYSICS: THIRD AND FOURTH YEARS61SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIREQUIREDCOURSESPHYS W3003 (3)MechanicsMSAE E3111 (3)ThermodynamicsAPMA E3101 (3)Linear algebraAPPH E4901 (1)SeminarAPPH E3100 (3)Intro. to quantummechanicsAPPH E3300 (3)Applied electromagnetismAPMA E3102 (3)Partial differentialequationsAPPH E4300 (3)Applied electrodynamicsAPPH E4100 (3)Quantum physicsCourse in firstAP area (3)APPH E4903 (2)SeminarCourse in secondAP area (3)APPH E4018 (2)LaboratoryELECTIVESTECH 1 3 points 3 points 2 points 9 pointsNONTECHOR TECH3 points 3 points 3 points 3 pointsTOTAL POINTS 16 15 16 171They must include at least 2 points of laboratory courses. If PHYS W3081 is taken as part of the first two years of the program, these technical electives need notinclude laboratory courses. Technical electives must be at the 3000 level or above unless prior approval is obtained.Tennessee; the IBM SUR cluster atBrookhaven National Laboratory inUpton, New York; and others.Facilities, and research opportunities,also exist within the interdepartmentalMaterials Research Science andEngineering Center, which focuses oncomplex films composed of nanoparticles.Current Research Activities andLaboratory Facilities in MaterialsScience and EngineeringSee page 172.UNDERGRADUATE PROGRAMSThe Department of Applied Physicsand Applied Mathematics offers threeundergraduate programs: applied physics,applied mathematics, and materialsscience and engineering. The materialsscience and engineering program isdescribed on pages 172–173.The applied physics and appliedmathematics programs provide anexcellent preparation for graduate studyor for careers in which mathematical andtechnical sophistication are important.Using the large number of electives inthese programs, students can tailor theirprograms to fit their personal and careerinterests. By focusing their technicalelectives, students can obtain a strongbase of knowledge in a specialized area.In addition to formal minors, some areasof specialization that are available aredescribed on pages 63–65. All technicalelectives are normally at the 3000 levelor above.UNDERGRADUATE PROGRAMSIN APPLIED PHYSICSThe applied physics program stressesthe basic physics that underlies mostdevelopments in engineering and themathematical tools that are important toboth physicists and engineers. Since theadvances in most branches of technologylead to rapid changes in state-ofthe-arttechniques, the applied physicsprogram provides the student with abroad base of fundamental science andmathematics while retaining the opportunityfor specialization through technicalelectives.The applied physics curriculum offersstudents the skills, experience, andpreparation necessary for several careeroptions, including opportunities to minorin economics and to take businessrelatedcourses. In recent years, appliedphysics graduates have entered graduateprograms in many areas of appliedphysics or physics, enrolled in medicalschool, or been employed in varioustechnical or financial areas immediatelyafter receiving the B.S. degree.Opportunities for undergraduateresearch exist in the many research programsin applied physics. These includefusion and space plasma physics, opticaland laser physics, and condensedmatter physics. Undergraduate studentscan receive course credit for researchor an independent project with a facultymember. Opportunities also exist forundergraduate students in the appliedphysics program to participate in thisresearch through part-time employmentduring the academic year and full-timeemployment during the summer, eitherat Columbia or as part of the NSF REUprogram nationwide. Practical researchexperience is a valuable supplementto the formal course of instruction.Applied physics students participate inan informal undergraduate seminar tostudy current and practical problems inapplied physics, and obtain hands-onexperience in at least two advancedlaboratory courses.SEAS 2010–2011

62APPLIED MATHEMATICS PROGRAM: FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS 1 MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202(3)and ODE (3) 2PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)C1403 (3)C2601 (3.5)Lab W3081 (2)C1494 (3)Lab C2699 (3)CHEMISTRY/BIOLOGY(choose one course)CHEM C1403 (3), or higher or BIOL W2001 (4)or BIOL C2005 (4), or higherENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 orW1123 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)REQUIREDTECH ELECTIVES(3) Student’s choice, see list of first- and second-year technical electives (professional-level courses;see pages 12–13).COMPUTERSCIENCEMATLAB course COMS W1005, Introduction to Computer Science and Programming in MATLAB, is requiredfor all Applied Mathematics majors and should be taken during freshman year. (It may be substituted with a C++or Python course with the permission of the Applied Math Program adviser.)PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1With the permission of the faculty adviser, students with advanced standing may start the calculus sequence at a higher level.2Applied mathematics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH E1210). Students who take APMA E2101 priorto declaring their major in applied physics may use this course to satisfy their ODE requirement.Majors are introduced to two areasof application of applied physics (AP) bya course in each of two areas. Approvedareas and courses are:DYNAMICAL SYSTEMS: APMA E4101 orPHYS G4003OPTICAL OR LASER PHYSICS:APPH E4110 or E4112NUCLEAR SCIENCE: APPH E4010PLASMA PHYSICS: APPH E4301PHYSICS OF FLUIDS: APPH E4200CONDENSED MATTER PHYSICS: PHYS G4018BIOPHYSICAL PHYSICAL: APMA E4400In addition to these courses, courseslisted in the Specialty Areas in AppliedPhysics can be used to satisfy thisrequirement with preapproval of theapplied physics adviser.All students must take 30 points ofelectives in the third and fourth years,of which 17 points must be technicalcourses approved by the adviser. The 17points include 2 points of an advancedlaboratory in addition to APPH E4018.Technical electives must be at the 3000level or above unless prior approval isobtained from the department. A numberof approved technical electives are listedin the section on specialty areas following.The remaining points of electives areintended primarily as an opportunity tocomplete the four-year, 27-point nontechnicalrequirement, but any type ofcourse work can satisfy them.UNDERGRADUATE PROGRAMSIN APPLIED MATHEMATICSThe applied mathematics program is flexibleand intensive. A student must takethe required courses listed below, orprove equivalent standing, and then mayelect the other courses from mathematics,computer science, physics, Earthand environmental sciences, biophysics,economics, business and finance, or otherapplication fields. Each student tailors hisor her own program in close collaborationwith an adviser. He or she must also reg-SEAS 2010–2011

APPLIED MATHEMATICS: THIRD AND FOURTH YEARS63SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIREQUIREDCOURSESAPMA E3101 (3) 1Linear algebra(Applied math, I)APMA E4901 (0)SeminarCourse from Group Aor Group B 2APMA E4204 (3) 1Complex variablesAPMA E3102 (3) 1Partial differentialequations(Applied math, II)Course from Group Aor Group B 2APMA E4300 (3)Introduction to numericalmethods (Computationalmath, I)MATH W4061 (3)Modern analysisAPMA E4101 (3)Introduction todynamical systems(Applied math, III)APMA E4903 (4)SeminarAPMA E3900 (3) 3ResearchCourses designatedMATH, APMA, or STAT (3)ELECTIVESTECH 4 3 points 3 points 3 points 6 pointsNONTECH 3 points 3 points 3 points 3 pointsTOTAL POINTS 15 15 16 151MATH V2010 may be substituted for APMA E3101; APMA E4200 or MATH V3028 may be substituted for APMA E3102; MATH V3007 may be substituted forAPMA E4204.2One course from Group A and one course from Group B required for graduation. Group A: IEOR E3658: Probability; SIEO W4105: Probability; SIEO W3600:Introduction to probability and statistics; SIEO W4150: Introduction to probability and statistics; MATH W4155: Probability theory. Group B: STAT W3105:Introduction to statistics; STAT W3107: Statistical inference; STAT W4107: Statistical inference; STAT W4109: Probability and statistical inference; SIEO W 4606:Elementary stochastic processes; IEOR E3106: Introduction to stochastic models; IEOR E4106: Introduction to operations research: stochastic models; IEORE4703: Monte Carlo simulation; COMS W4771: Machine learning.3With an adviser’s permission, an approved technical elective may be substituted.4Any course in science or engineering at the 3000 level or above qualifies as a technical elective.ister for the applied mathematics seminarduring both the junior and senior years.During the junior year, the student attendsthe seminar lectures for 0 points; duringthe senior year, he or she attends theseminar lectures as well as tutorial problemsessions for 3 or 4 points.While it is common for studentsin the program to go on to graduateschool, many graduating seniors will findemployment directly in industry, government,education, or other fields.Of the 27 points of elective contentin the third and fourth years, at least 15points of technical courses approved bythe adviser must be taken. The remainingpoints of electives are intended primarily asan opportunity to complete the four-year,27-point nontechnical requirement, but anytype of course work can satisfy them.Transfers into the applied mathematicsprogram from other majors require aGPA of 3.0 or above, and the approval ofthe applied mathematics program chair.UNDERGRADUATE DOUBLEMAJOR IN APPLIED PHYSICSAND APPLIED MATHEMATICSStudents satisfy all requirements for bothmajors, except for the seminar requirements.They are required to take bothsenior seminars, APMA E4903 and APPHE4903 (taking one in the junior year andone in the senior year, due to timing conflicts),but not the junior seminars, APMAE4901 and APPH E4901. A single coursemay be used to fulfill a requirement inboth majors. Students must maintain aGPA at or above 3.75, and must graduatewith at least 143 points, 15 abovethe regular 128-point requirement. Theseextra 15 points should be technical electivesappropriate for one or both majors.To apply, a student first obtains theapproval of both the general undergraduateAP adviser and the generalundergraduate AM adviser, and then theapproval of the Dean.SPECIALTY AREAS IN APAMBoth applied physics and applied mathematicsstudents can focus their technicalelectives and develop a strong baseof knowledge in a specialty area. Thereis no requirement to focus electives, sostudents may take as many or as few ofthe recommended courses in a specialtyarea as is appropriate to their schedulesand interests. Some specialties aregiven below, but this is not an exclusivelist and others can be worked out incoordination with the student’s adviser.The courses that are often taken, or insome cases need to be taken, in thejunior year are denoted with a “J.”Technical Electives Applications of PhysicsCourses that will give a student abroad background in applications ofphysics are:SEAS 2010–2011

64MSAE E3103x: Elements of materials science (J)ELEN E3000x: Introduction to circuits, systems,and electronics (J)APPH E4010x: Introduction to nuclear scienceAPPH E4110x: Modern opticsAPPH E4112y: Laser physicsAPPH E4200x: Physics of fluidsAPPH E4301y: Introduction to plasma physicsPHYS G4018y: Solid-state physicsAPMA E4101y: Introduction to dynamicalsystems Earth and Atmospheric SciencesThe Earth sciences provide a widerange of problems of interest tophysicists and mathematicians rangingfrom the dynamics of the Earth’sclimate to earthquake physics todynamics of Earth’s deep interior. TheLamont-Doherty Earth Observatory,which is part of Columbia University,provides enormous resources for studentsinterested in this area.A. ATMOSPHERE, OCEANS, AND CLIMATEAPPH E4200x: Physics of fluidsAPPH E4210y: Geophysical fluid dynamicsEESC W4008y: Introduction to atmosphericscienceESC W4925x: Introduction to physicaloceanographyEES W4930y: Earth’s oceans and atmosphereB. SOLID EARTH GEOPHYSICSAPPH E4200x: Physics of fluidsEESC W4941y: Principles of geophysicsEESC W4001x: Advanced general geologyEESC W4113x: Introduction to mineralogyEESC W4701y: Introduction to igneouspetrologyEESC W4950x: Mathematical methods in theEarth sciences(See also courses listed underScientific Computation and ComputerScience on this page.) Basic Physics and AstrophysicsFundamental physics and astrophysicscan be emphasized. Not only is astrophysicsproviding a deeper understandingof the universe, but it is also testingthe fundamental principles of physics.PHYS W3002y: From quarks to the cosmos:applications of modern physicsASTR C3601x: General relativity, black holes,and cosmology (J)ASTR C3602y: Physical cosmology and extragalacticastronomy (J)APMA E4101x: Introduction to dynamicalsystemsASTR G4001y: Astrophysics, I Business and FinanceThe knowledge of physics and mathematicsthat is gained in the appliedphysics and applied mathematics programsis a strong base for a career inbusiness or finance.A. ECONOMICSECON W3211x,y: Intermediate microeconomics(J)ECON W3213x,y: Intermediate macroeconomics(J)B. INDUSTRIAL ENGINEERING ANDOPERATIONS RESEARCHIEOR E4003x: Industrial economicsIEOR E4201x: The engineering of management,IIEOR E4202y: The engineering of management,IIC. FINANCESIEO W4150x,y: Probability and statistics (J)IEOR E4106y: Introduction to operationsresearch: stochastic models (J)IEOR E4700x: Introduction to financial engineeringMATH W4071x: Mathematics of financeECIE W4280: Corporate finance Mathematics Applicable to PhysicsApplied physics students can specializein the mathematics that is applicableto physics. This specialization isparticularly useful for students interestedin theoretical physics.APMA E4101x: Introduction to dynamicalsystemsAPMA E4001y: Principles of applied mathematicsAPMA E4301x: Numerical methods for partialdifferential equationsAPMA E4302x: Parallel scientific computingMATH V3386x: Differential geometryMATH W4386x-W4387y: Geometrical conceptsin physics Fundamental Mathematics inApplied MathematicsThis specialization is intended for studentswho desire a more solid foundationin the mathematical methods andunderlying theory. For example, thisspecialization could be followed bystudents with an interest in graduatework in applied mathematics.APMA E4101x: Introduction to dynamical systemsAPMA W4150x: Applied functional analysisSIEO W4150x,y: Introduction to probability andstatistics (J)MATH V3386x: Differential geometryMATH W4386x-W4387y: Geometrical conceptsin physicsMATH W4032x: Fourier analysisMATH W4062y: Mathematical analysis, II Quantitative BiologyTraditionally biology was considered adescriptive science in contrast to thequantitative sciences that are basedon mathematics, such as physics. Thisview no longer coincides with reality.Researchers from biology as well asfrom the physical sciences, appliedmathematics, and computer scienceare rapidly building a quantitative baseof biological knowledge. Students canacquire a strong base of knowledge inquantitative biology, both biophysicsand computational biology, while completingthe applied physics or appliedmathematics programs.PROFESSIONAL-LEVEL COURSE:APPH E1300y: Physics of the human bodyRECOMMENDED:BIOL C2005x-C2006y: Introduction to molecularand cellular biology,I and IIAPMA E4400y: Introduction to biophysicalmodelingOTHER TECHNICAL ELECTIVES (A COURSEIN AT LEAST TWO AREAS RECOMMENDED):A. BIOLOGICAL MATERIALSCHEN E4650x: BiopolymersBIOL W4070x: The biology and physics ofsingle moleculesB. BIOMECHANICSBMEN E3320y: Fluid biomechanics (J)BMEN E4300y: Solid biomechanics (J)C. GENOMICS AND BIOINFORMATICSECBM E3060x: Introduction to genomicinformation science andtechnology (J)BIOL W3037y: Whole genome bioinformatics(J)CBMF W4761y: Computational genomicsD. NEUROBIOLOGYBIOL W3004x: Cellular and molecular neurobiology(J)BIOL W3005y: Systems neurobiology (J)ELEN G4011x: Computational neuroscienceThe second term of biology will be considereda technical elective if a studenthas credits from at least two other of therecommended courses in quantitativebiology at the 3000 level or above.Scientific Computation andComputer ScienceAdvanced computation has become acore tool in science, engineering, andmathematics and provides challengesSEAS 2010–2011

for both physicists and mathematicians.Courses that build on bothpractical and theoretical aspects ofcomputing and computation include:APMA E4300y: Introduction to numerical methodsAPMA E4301: Numerical methods for partialdifferential equationsAMCS E4302: Parallel scientific computingMATH V3020x: Number theory and cryptography (J)COMS W3137x,y: Data structures and algorithms(or COMS W3139y:Honors data structures andalgorithms) (J)COMS W3157x,y: Advanced programming (J)COMS W3203x,y: Discrete mathematics: introductionto combinatorics andgraph theory (J)COMS W4203y: Graph theoryCOMS W4701x,y: Artificial intelligenceCOMS W4771y: Machine learning Solid-State PhysicsMuch of modern technology is basedon solid-state physics, the study of solidsand liquids. Courses that will build astrong base for a career in this area are:MSAE E3103x: Elements of material science (J)ELEN E3106x: Solid-state devices and materials(J)MSAE E4206x: Electronic and magnetic propertiesof solidsPHYS G4018y: Solid-state physicsMSAE E4207y: Lattice vibrations and crystaldefectsPHYS W3083y: Electronics laboratory (J)UNDERGRADUATE PROGRAMIN MATERIALS SCIENCE ANDENGINEERINGSee page 172.GRADUATE PROGRAMSFinancial aid is available for studentspursuing a doctorate. Fellowships, scholarships,teaching assistantships, and graduateresearch assistantships are awardedon a competitive basis. The Aptitude Testof the Graduate Record Examination isrequired of candidates for admission tothe department and for financial aid; theAdvanced Tests are recommended.M.S. Program in Applied PhysicsThe program of study leading to thedegree of Master of Science, whileemphasizing continued work in basicphysics, permits many options in severalapplied physics specialties. The programmay be considered simply as additionaleducation in areas beyond the bachelor’slevel, or as preparatory to doctoralstudies in the applied physics fields ofplasma physics, laser physics, solidstatephysics, and applied mathematics.Specific course requirements for themaster’s degree are determined in consultationwith the program adviser.M.S. Program in Applied Physics/Concentration in AppliedMathematicsThis 30-point program leads to a professionalM.S. degree. Students must completefive core courses and five electives.The core courses provide a studentwith a foundation in the fundamentalsof applied mathematics and contribute15 points of graduate credit toward thedegree. Students must complete five ofthe following seven courses:APMA E4001: Principles of applied mathematicsAPMA E4101: Introduction to dynamical systemsAPMA E4150: Applied functional analysisAPMA E4200: Partial differential equationsAPMA E4204: Functions of a complex variableAPMA E4300: Introduction to numerical methodsAPMA E4301: Numerical methods for partial differentialequationsAPMA E6301: Analytic methods for partial differentialequationsAPMA E6302: Numerical analysis for partial differentialequationsA student must select five electivecourses from those listed below (or anyof those not used to satisfy the corerequirements from the list above) fora total of 15 points of graduate credit.Additional courses not listed below canbe applied toward the elective requirements,subject to the approval of thefaculty adviser. Computer science electivecourses include:CS0R W4231: Analysis of algorithmsC0MS W4236: Introduction to computationalcomplexityC0MS W4241: Numerical algorithms and complexityC0MS W4252: Computational learning theoryIndustrial engineering/operationsresearch elective courses include:IEOR E4003: Industrial economicsIEOR E4004: Introduction to operations research:deterministic modelsIEOR E4007: Optimization: models and methodsIEOR E4106: Introduction to operations research:stochastic modelsSIE0 W4150: Introduction to probability and statisticsIEOR E4403: Advanced engineering and corporateeconomicsIEOR E4407: Game theoretic models of operationsSIE0 W4606: Elementary stochastic processes,IEOR E4700: Introduction to financial engineeringOther elective courses include:MECE E4100: Mechanics of fluidsMSAE E4215: Mechanical behavior of structuralmaterialsEEME E6601: Introduction to control theoryM.S. Program in Materials Scienceand EngineeringSee page 173.M.S. Program in Medical PhysicsThis CAMPEP-approved 36-point programin medical physics leads to theM.S. degree. It is administered by facultyfrom the School of Engineering andApplied Science in collaboration withfaculty from the College of Physiciansand Surgeons and the Mailman Schoolof Public Health. It provides preparationtoward certification by the AmericanBoard of Radiology. The program consistsof a core curriculum of medicaland nuclear physics courses, anatomy,lab, seminar, a tutorial, and two practicums.Specific course requirements areAPPH E4010, E4710/11, E4500, E4501,E4550, E4600, and APBM E4650, and,in the Mailman School of Public Health,EHSC P6330, P9319, P9330, andP9335. Some opportunities for specializationexist. A passing grade on acomprehensive examination is requiredfor graduation. This examination, onsubjects covered in the curriculum, istaken after two terms of study.Certificate of ProfessionalAchievement in Medical PhysicsThis graduate program of instructionleads to the Certificate of ProfessionalAchievement and requires satisfactorycompletion of at least four of the followingcourses:APPH E4500: Health physicsAPPH E4600: DosimetryEHSC P6330: Radiation scienceEHSC P9319: Clinical nuclear medicine physicsEHSC P9330: Diagnostic radiology physicsEHSC P9335: Radiation therapy physicsAPBM E4650: Anatomy for physicists and engineersThis is a two-semester nondegree program.Students are admitted to the departmentas certificate-track students.65SEAS 2010–2011

66PH.D. AND ENG.SC.D. PROGRAMSAfter completing the M.S. program inapplied physics, doctoral students specializein one applied physics field. Someprograms have specific course requirementsfor the doctorate; elective coursesare determined in consultation with theprogram adviser. Successful completionof an approved 30-point programof study is required in addition to successfulcompletion of a written qualifyingexamination taken after two semestersof graduate study. An oral examination,taken within one year after the writtenqualifying examination, and a thesis proposalexamination, taken within two yearsafter the written qualifying examination,are required of all doctoral candidates.Applied MathematicsThis academic program, for studentsregistered in the Department of AppliedPhysics and Applied Mathematics,emphasizes applied mathematicsresearch in nonlinear dynamics, fluidmechanics, and scientific computation,with a current emphasis on geophysical,biophysical, and plasma physicsapplications.Applied mathematics deals withthe use of mathematical concepts andtechniques in various fields of scienceand engineering. Historically, mathematicswas first applied with great successin astronomy and mechanics. Then itdeveloped into a main tool of physics,other physical sciences, and engineering.It is now important in the biological,geological, and social sciences. With thecoming of age of the computer, appliedmathematics has transcended its traditionalstyle and now assumes an evengreater importance and a new vitality.Compared with the pure mathematician,the applied mathematician is moreinterested in problems coming fromother fields. Compared with the engineerand the physical scientist, he or she ismore concerned with the formulation ofproblems and the nature of solutions.Compared with the computer scientist,he or she is more concerned with theaccuracy of approximations and theinterpretation of results. Needless to say,even in this age of specialization, thework of mathematicians, scientists, andengineers frequently overlaps. Appliedmathematics, by its very nature, hasoccupied a central position in this interplayand has remained a field of fascinationand excitement for active minds.Materials Scienceand Engineering ProgramSee page 173.Plasma PhysicsThis academic program is designedto emphasize preparation for professionalcareers in plasma research,controlled fusion, and space research.This includes basic training in relevantareas of applied physics, with emphasison plasma physics and related areasleading to extensive experimental andtheoretical research in the ColumbiaUniversity Plasma Physics Laboratory.Specific course requirements for theplasma physics doctoral program areAPPH E4018, E4200, E4300, E6101,E6102, and E9142 or E9143, or equivalentstaken at another university.Optical and Laser PhysicsThis academic program involves a basictraining in relevant areas of appliedphysics with emphasis in quantummechanics, quantum electronics, andrelated areas of specialization. Someactive areas of research in which thestudent may concentrate are lasermodification of surfaces, optical diagnosticsof film processing, inelastic lightscattering in nanomaterials, nonlinearoptics, ultrafast optoelectronics photonicswitching, optical physics of surfaces,and photon integrated circuits. Specificcourse requirements for the optical andlaser physics doctoral program are setwith the academic adviser.Solid-State PhysicsThis academic program encompassesthe study of the electrical, optical, magnetic,thermal, high-pressure, and ultrafastdynamical properties of solids, withan aim to understanding them in terms ofthe atomic and electronic structure. Theprogram emphasizes the formation, processing,and properties of thin films, lowdimensionalstructures—such as oneandtwo-dimensional electron gases,nanocrystals, surfaces of electronic andoptoelectronic interest, and molecules.Facilities include a microelectronics laboratory,high-pressure diamond anvil cells,a molecular beam epitaxy machine, ultrahighvacuum systems, lasers, equipmentfor the study of optical properties, andthe instruments in the shared facilitiesof the Materials Research Science andEngineering Center and t`he Nano-scaleScience and Engineering Center. Thereare also significant resources for electricaland optical experimentation at lowtemperatures and high magnetic fields.Specific course requirements for thesolid-state physics doctoral program areset with the academic adviser, in consultationwith the Committee on MaterialsScience and Engineering/ Solid-StateScience and Engineering.COURSES IN APPLIED PHYSICSAPPH E1300y Physics of the human body3 pts. Lect: 3. Professor Herman.Prerequisites: PHYS C1201 or C1401, andCalculus I; corequisites: PHYS C1202 or C1402,and Calculus II. This introductory course analyzesthe human body from the basic principles ofphysics. Topics to be covered include the energybalance in the body, the mechanics of motion,fluid dynamics of the heart and circulation, vibrationsin speaking and hearing, muscle mechanics,gas exchange and transport in the lungs,vision, structural properties and limits, electricalproperties and the development and sensing ofmagnetic fields, and the basics of equilibriumand regulatory control. In each case, a simplemodel of the body organ, property, or functionwill be derived and then applied. The course isapproved as a SEAS technical elective.APAM E1601y Introduction to computationalmathematics and physics3 pts. Lect: 3. Professor Mauel.Introduction to computational methods in appliedmathematics and physics. Students developsolutions in a small number of subject areasto acquire experience in the practical use ofcomputers to solve mathematics and physicsproblems. Topics change from year to year.Examples include elementary interpolation offunctions, solution of nonlinear algebraic equations,curve-fitting and hypothesis testing, wavepropagation, fluid motion, gravitational andcelestial mechanics, and chaotic dynamics. Thebasic requirement for this course is one year ofcollege-level calculus and physics; programmingexperience is not required.APPH E3100y Introduction to quantummechanics3 pts. Lect: 3. Professor Pedersen.Prerequisites: PHYS C1403 or equivalent, anddifferential and integral calculus. Corequisites:APMA E3101 or equivalent. Basic concepts andassumptions of quantum mechanics, Schrodinger’sequation, solutions for one-dimensional problems,including square wells, barriers, and the harmonicoscillator, introduction to the hydrogen atom,atomic physics and X-rays, electron spin.APAM E3105x Programming methods forscientists and engineers3 pts. Lect: 2.5. Lab: 1. Not offered in 2010–2011.Introduction to modern techniques of computer programmingfor the numerical solutions to problemsSEAS 2010–2011

in physics, mathematics, and engineering usingFortran 90. Students develop familiarity with basicand advanced concepts of modern numerical programmingand acquire practical experience solvingrepresentative problems in math and physics.APPH E3300y Applied electromagnetism3 pts. Lect: 3. Professor Venkataraman.Corequisites: APMA E3102. Vector analysis,electrostatic fields, Laplace’s equation, multipoleexpansions, electric fields in matter: dielectrics,magnetostatic fields, magnetic materials, andsuperconductors. Applications of electromagnetismto devices and research areas in applied physics.APPH E3900x and y Undergraduate researchin applied physics0–4 pts. Members of the faculty.This course may be repeated for credit, but nomore than 6 points of this course may be countedtoward the satisfaction of the B.S. degree requirements.Candidates for the B.S. degree may conductan investigation in applied physics or carryout a special project under the supervision of thestaff. Credit for the course is contingent upon thesubmission of an acceptable thesis or final report.APPH E4010x Introduction to nuclear science3 pts. Professor Ostrow.Prerequisites: MATH V1202 and E1210 and PHYSC1403 or their equivalents. This introductorycourse is for individuals with an interest in medicalphysics and other branches of radiation science.Topics covered include basic concepts, nuclearmodels, semiempirical mass formula, interactionof radiation with matter, nuclear detectors, nuclearstructure and instability, radioactive decay processand radiation, particle accelerators, and fission andfusion processes and technologies.APPH E4018y Applied physics laboratory2 pts. Lab: 4. Professor Navratil.Prerequisites: ELEN E3401 or equivalent.Typical experiments are in the areas of plasmaphysics, microwaves, laser applications, opticalspectroscopy physics, and superconductivity.APPH E4090x Nanotechnology3 pts. Lect: 3. Offered in alternate years.Professor Herman.Prerequisites: APPH E3100 and MSAE E3103or their equivalents with instructor’s permission.The science and engineering of creatingmaterials, functional structures and deviceson the nanometer scale. Carbon nanotubes,nanocrystals, quantum dots, size dependentproperties, self-assembly, nanostructured materials.Devices and applications, nanofabrication.Molecular engineering, bionanotechnology.Imaging and manipulating at the atomic scale.Nanotechnology in society and industry.APPH E4100x Quantum physics of matter3 pts. Lect: 3. Professor Venkataranam.Prerequisites: APPH E3100. Corequisites: APMAE3102 or equivalent. Basic theory of quantummechanics, well and barrier problems, the harmonicoscillator, angular momentum identicalparticles, quantum statistics, perturbation theoryand applications to the quantum physics ofatoms, molecules, and solids.APPH E4110x Modern optics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: APPH E3300. Ray optics, matrixformulation, wave effects, interference, Gaussianbeams, Fourier optics, diffraction, image formation,electromagnetic theory of light, polarizationand crystal optics, coherence, guided wave andfiber optics, optical elements, photons, selectedtopics in nonlinear optics.APPH E4112y Laser physics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Recommended but not required:APPH E3100 and APPH E3300 or their equivalents.Optical resonators, interaction of radiationand atomic systems, theory of laser oscillation,specific laser systems, rate processes, modulation,detection, harmonic generation, and applications.CHAP E4120x Statistical mechanics3 pts. Lect: 3. Professor O’Shaughnessy.Prerequisites: CHEN E3210 or equivalent thermodynamicscourse, or instructor’s permission.Fundamental principles and underlying assumptionsof statistical mechanics. Boltzmann’sentropy hypothesis and its restatement in termsof Helmholtz and Gibbs free energies and foropen systems. Correlation times and lengths.Exploration of phase space and observationtimescale. Correlation functions. Fermi-Dirac andBose-Einstein statistics. Fluctuation-responsetheory. Applications to ideal gases, interfaces,liquid crystals, microemulsions and other complexfluids, polymers, Coulomb gas, interactionsbetween charged polymers and charged interfaces,ordering transitions.APPH E4130x Physics of solar energy3 pts. Lect: 3. Professor Chen.Prerequisites: General physics (PHYS C1403or C1602) and mathematics, including ordinarydifferential equations and complex numbers(such as MATH V1202 or E1210) or permissionof instructor. The physics of solar energyincluding solar radiation, the analemma,atmospheric efforts, thermodynamics of solarenergy, physics of solar cells, energy storageand transmission, and physics and economicsin the solar era.APPH E4200x Physics of fluids3 pts. Lect: 3. Professor Mauel.Prerequisites: APMA E3102 or equivalent; PHYS1401 or 1601 or equivalent. An introduction tothe physical behavior of fluids for science andengineering students. Derivation of basic equationsof fluid dynamics: conservation of mass,momentum, and energy. Dimensional analysis.Vorticity. Laminar boundary layers. Potentialflow. Effects of compressibility, stratification, androtation. Waves on a free surface; shallow waterequations. Turbulence.APPH E4210y Geophysical fluid dynamics3 pts. Lect: 3. Professor Polvani.Prerequisites: APMA E3101, APMA E3102 (orequivalents) and APPH E4200 (or equivalent),or permission from instructor. Fundamental conceptsin the dynamics of rotating, stratified flows.Geostrophic and hydrostatic balances, potentialvorticity, f and beta plane approximations, gravityand Rossby waves, geostrophic adjustment andquasigeostrophy, baroclinic and barotropic instabilities,Sverdrup balance, boundary currents,Ekman layers.APPH E4300x Applied electrodynamics3 pts. Lect: 3. Professor Navratil.Prerequisites: APPH E3300. Overview of propertiesand interactions of static electric andmagnetic fields. Study of phenomena of timedependent electric and magnetic fields includinginduction, waves, and radiation as well as specialrelativity. Applications are emphasized.APPH E4301y Introduction to plasma physics3 pts. Lect: 3. Professor Maurer.Prerequisites: PHYS W3008 or APPH E3300.Definition of a plasma. Plasmas in laboratoriesand nature, plasma production. Motion ofcharged particles in electric and magnetic fields,adiabatic invariants. Heuristic treatment of collisions,diffusion, transport, and resistivity. Plasmaas a conducting fluid. Electrostatic and magnetostaticequilibria of plasmas. Waves in coldplasmas. Demonstration of laboratory plasmabehavior, measurement of plasma properties.Illustrative problems in fusion, space, and nonneutralor beam plasmas.APPH E4500y Health physics3 pts. Lect: 3. Professor Christman.Prerequisites: APPH E4600 or Corequisites:APPH E4600 This course presents the fundamentalprinciples of health physics: the physicsof dose deposition, radiation dosimetry, elementaryshielding and radiation protection devices,description and proper use (calibration and maintenance)of health physics instrumentation, andthe regulatory and administrative requirements ofhealth physics programs.APPH E4501y Medical health physics tutorial0 pts.Prerequisites: Permission of the course coordinator.Required for, and limited to, M.S. degreecandidates in the Medical Physics Program.Course addresses procedures for personnel andarea monitoring, radiation and contaminationsurveys, instrument calibration, radioactive wastedisposal, radiation safety compliance, licensurerequirements, and other matters contributing toprofessional competence in the field of medicalhealth physics. Course includes lectures,seminars, tours, and hand-on experience. Thistwo-week tutorial is offered immediately followingspring semester final examinations and is takenfor Pass/Fail only.APPH E4550y Medical physics seminar0 pts. Lect: 1.Required for all graduate students in the medicalphysics program. Practicing professionalsand faculty in the field present selected topics inmedical physics.APPH E4600x Fundamentals of radiologicalphysics and radiation dosimetry2 pts. Lect: 2. Professor Meli.Prerequisites: APPH E4010 or Corequisites:APPH E4010. Basic radiation physics: radioactivedecay, radiation producing devices,67SEAS 2010–2011

68characteristics of the different types of radiation(photons, charged and uncharged particles) andmechanisms of their interactions with materials.Essentials of the determination, by measurementand calculation, of absorbed doses fromionizing radiation sources used in medical physics(clinical) situations and for health physicspurposes.APBM E4650x Anatomy for physicists andengineers3 pts. Lect: 3. Members of the faculty.Prerequisites: Engineering or physics backgroundA systemic approach to the study of thehuman body from a medical imaging point ofview: skeletal, respiratory, cardiovascular, digestive,and urinary systems, breast and women’sissues, head and neck, and central nervous system.Lectures are reinforced by examples fromclinical two- and three-dimensional and functionalimaging (CT, MRI, PET, SPECT, U/S, etc.).APPH E4710x-E4711y Radiation instrumentationand measurement laboratory, I and II3 pts. Lect: 1. Lab: 4. Professor Arbo.Prerequisites: APPH E4010 or Corequisites:APPH E4010 Laboratory fee: $50 each term.E4710: theory and use of alpha, beta, gamma,and x-ray detectors and associated electronicsfor counting, energy spectroscopy, and dosimetry;radiation safety; counting statistics anderror propagation; mechanisms of radiation emissionand interaction. E4711, prerequisite APPHE4710: additional detector types; applicationsand systems including coincidence, low-level,and liquid scintillation counting; neutron activation;TLD dosimetry; diagnostic x-ray and fluoroQ/C; planar gamma camera imaging; imageanalysis.APPH E4901x Seminar: problems in appliedphysics1 pt. Lect: 1. Instructor to be announced.This course is required for, and can be takenonly by, all applied physics majors and minorsin the junior year. Discussion of specific andself-contained problems in areas such as appliedelectrodynamics, physics of solids, and plasmaphysics. Topics change yearly.APPH E4903x Seminar: problems in appliedphysics2 pts. Lect: 1. Tutorial:1. Instructor to beannounced.This course is required for, and can be takenonly by, all applied physics majors in the senioryear. Discussion of specific and self-containedproblems in areas such as applied electrodynamics,physics of solids, and plasma physics.Formal presentation of a term paper required.Topics change yearly.APPH E4990x and y Special topics in appliedphysics1–3 pts. Instructor to be announced.Prerequisites: Permission of the instructor.This course may be repeated for credit. Topicsand instructors change from year to year. Foradvanced undergraduate students and graduatestudents in engineering, physical sciences, andother fields.APAM E4999x and y–S4999 Curricularpractical training1 pt. Members of the faculty.Prerequisites: Obtained internship and approvalfrom adviser. Only for master’s students in theDepartment of Applied Physics and AppliedMathematics who may need relevant work experienceas part of their program of study. Finalreport required. This course may not be taken forpass/fail or audited.APPH E6081x Solid state physics, I3 pts. Lect: 3. Professor Pinczuk.Prerequisites: APPH E3100 or the equivalent.Knowledge of statistical physics on the levelof MSAE E3111 or PHYS G4023 stronglyrecommended. Crystal structure, reciprocal lattices,classification of solids, lattice dynamics,anharmonic effects in crystals, classical electronmodels of metals, electron band structure, andlow-dimensional electron structures.APPH E6082y Solid state physics, II3 pts. Lect: 3. Professor Kim.Prerequisite: APPH E6081 or the instructor’s permission.Semiclassical and quantum mechanicalelectron dynamics and conduction, dielectricproperties of insulators, semiconductors, defects,magnetism, superconductivity, low-dimensionalstructures, and soft matter.APPH E6091x Magnetism and magneticmaterials3 pts. Lect. 3. Offered in alternate years.Professor Bailey.Prerequisites: MSAE E4206, APPH E6081, orequivalent. Types of magnetism. Band theory offerromagnetism. Magnetic metals, insulators, andsemiconductors. Magnetic nanostructures: ultrathinfilms, superlattices, and particles. Surfacemagnetism and spectroscopies. High speedmagnetization dynamics. Spin electronics.APPH E6101x Plasma physics, I3 pts. Lect: 3. Professor Pedersen.Prerequisites: APPH E4300. Debye screening.Motion of charged particles in space- andtime-varying electromagnetic fields. Two-fluiddescription of plasmas. Linear electrostatic andelectromagnetic waves in unmagnetized andmagnetized plasmas. The magnetohydrodynamic(MHD) model, including MHD equilibrium, stability,and MHD waves in simple geometries. Fluidtheory of transport.APPH E6102y Plasma physics, II3 pts. Lect: 3. Professor Boozer.Prerequisites: APPH E6101. Magnetic coordinates.Equilibrium, stability, and transport oftorodial plasmas. Ballooning and tearing instabilities.Kinetic theory, including Vlasov equation,Fokker-Planck equation, Landau damping, kinetictransport theory. Drift instabilities.APPH E6110x Laser interactions with matter3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: APPH E4112 or equivalent, andquantum mechanics. Principles and applicationsof laser-matter coupling, nonlinear optics,three- and four-wave mixing, harmonic generation,laser processing of surfaces, laser probingof materials, spontaneous and stimulated lightscattering, saturation spectroscopy, multiphotonexcitation, laser isotope separation, transientoptical effects.APAM E6650x and y–S6650 Research project1–6 pts. Members of the faculty.This course may be repeated for credit. A specialinvestigation of a problem in nuclear engineering,medical physics, applied mathematics, appliedphysics, and/or plasma physics consisting ofindependent work on the part of the student andembodied in a formal report.APPH E9142x–E9143y Applied physics seminar3 pts. Sem: 3. Not offered in 2010–2011.These courses may be repeated for credit.Selected topics in applied physics.APAM E9301x and y–S9301 Doctoral research0–15 pts. Members of the faculty.Prerequisite: Qualifying examination for the doctorate.Required of doctoral candidates.APAM E9800x and y–S9800 Doctoralresearch instruction3, 6, 9, or 12 pts. Members of the faculty.A candidate for the Eng.Sc.D. degree must registerfor 12 points of doctoral research instruction.Registration for APAM E9800 may not be usedto satisfy the minimum residence requirement forthe degree.APAM E9900x and y–S9900 Doctoraldissertation0 pts. Members of the faculty.A candidate for the doctorate may be requiredto register for this course every term after thecoursework has been completed, and until thedissertation has been accepted.COURSES IN APPLIEDMATHEMATICSAPMA E2101y Inroduction to appliedmathematics3 pts. Lect: 3. Professor Spiegelman.Prerequisites: Calculus III. A unified, singlesemesterintroduction to differential equationsand linear algebra with emphases on (1) elementaryanalytical and numerical technique and(2) discovering the analogs on the continuousand discrete sides of the mathematics of linearoperators: superposition, diagonalization, fundamentalsolutions. Concepts are illustrated withapplications using the language of engineering,the natural sciences, and the social sciences.Students execute scripts in Mathematica andMATLAB (or the like) to illustrate and visualizecourse concepts (programming not required).APMA E3101x Linear algebra3 pts. Lect: 3. Professor Gentine.Matrix algebra, elementary matrices, inverses,rank, determinants. Computational aspects ofsolving systems of linear equations: existenceuniquenessof solutions, Gaussian elimina-SEAS 2010–2011

tion, scaling, ill-conditioned systems, iterativetechniques. Vector spaces, bases, dimension.Eigenvalue problems, diagonalization, innerproducts, unitary matrices.APMA E3102y Partial differential equations3 pts. Lect: 3. Professor Langmore.Prerequisite: MATH E1210 or equivalent.Introduction to partial differential equations;integral theorems of vector calculus. Partial differentialequations of engineering in rectangular,cylindrical, and spherical coordinates. Separationof the variables. Characteristic-value problems.Bessel functions, Legendre polynomials, otherorthogonal functions; their use in boundary valueproblems. Illustrative examples from the fields ofelectromagnetic theory, vibrations, heat flow, andfluid mechanics.APAM E3105x Programming methods forscientists and engineers3 pts. Lect: 2.5. Lab: 1. Not offered in 2010–2011.Introduction to modern techniques of computerprogramming for the numerical solutions to familiaritywith basic and advanced concepts of modernnumerical programming and acquire practicalexperience solving representative problems inmath and physics.APMA E3900x and y Undergraduate researchin applied mathematics0–4 pts. Members of the faculty.This course may be repeated for credit, butno more than 6 points of this course may becounted toward the satisfaction of the B.S.degree requirements. Candidates for the B.S.degree may conduct an investigation in appliedmathematics or carry out a special project underthe supervision of the staff. Credit for the courseis contingent upon the submission of an acceptablethesis or final report.APMA E4001y Principles of appliedmathematics3 pts. Lect: 3. Professor Gentine.Prerequisites: Introductory Linear Algebrarequired. Ordinary Differential Equationsrecommended. Review of finite-dimensionalvector spaces and elementary matrix theory.Linear transformations, change of basis,eigenspaces. Matrix representation of linearoperators and diagonalization. Applicationsto difference equations, Markov processes,ordinary differential equations, and stability ofnonlinear dynamical systems. Inner productspaces, projection operators, orthogonal bases,Gram-Schmidt orthogonalization. Least squaresmethod, pseudo-inverses, singular valuedecomposition. Adjoint operators, Hermitianand unitary operators, Fredholm AlternativeTheorem. Fourier series and eigenfunctionexpansions. Introduction to the theory of distributionsand the Fourier Integral Transform.Green’s functions. Application to PartialDifferential Equations.APMA E4101x Introduction to dynamicalsystems3 pts. Lect: 3. Professor Weinstein.Prerequisites: APMA E2101 (or MATH V1210)and APMA E3101 or their equivalents, or permissionof instructor. An introduction to the analyticand geometric theory of dynamical systems;basic existence, uniqueness and parameterdependence of solutions to ordinary differentialequations; constant coefficient and parametricallyforced systems; Fundamental solutions;resonance; limit points, limit cycles and classificationof flows in the plane (Poincare-BendixsonTheorem); conservative and dissipative systems;linear and nonlinear stability analysis of equilibriaand periodic solutions; stable and unstable manifolds;bifurcations, e.g., Andronov-Hopf; sensitivedependence and chaotic dynamics; selectedapplications.APMA E4150x Applied functional analysis3 pts. Lect: 3. Professor Bal.Prerequisites: Advanced calculus and coursein basic analysis, or instructor’s approval.Introduction to modern tools in functionalanalysis that are used in the analysis of deterministicand stochastic partial differential equationsand in the analysis of numerical methods:metric and normed spaces, Banach space ofcontinuous functions, measurable spaces, thecontraction mapping theorem, Banach andHilbert spaces bounded linear operators onHilbert spaces and their spectral decomposition,and time permitting distributions andFourier transforms.APMA E4200x Partial differential equations3 pts. Lect: 3. Professor Sobel.Prerequisites: Course in ordinary differentialequations. Techniques of solution of partial differentialequations. Separation of the variables.Orthogonality and characteristic functions,nonhomogeneous boundary value problems.Solutions in orthogonal curvilinear coordinatesystems. Applications of Fourier integrals, Fourierand Laplace transforms. Problems from the fieldsof vibrations, heat conduction, electricity, fluiddynamics, and wave propagation are considered.APMA E4204x Functions of a complexvariable3 pts. Lect. 3. Professor Polvani.Prerequisite: MATH V1202 or equivalent.Complex numbers, functions of a complex variable,differentiation and integration in the complexplane. Analytic functions, Cauchy integraltheorem and formula, Taylor and Laurent series,poles and residues, branch points, evaluation ofcontour integrals. Conformal mapping. Schwarz-Christoffel transformation. Applications to physicalproblems.APMA E4300y Introduction to numericalmethods3 pts. Lect: 3. Instructor to be announced.Prerequisites: MATH V1201, MATH E1210,and APMA E3101 or their equivalents. Someprogramming experience and MATLAB will beextremely useful. Introduction to fundamentalalgorithms and analysis of numerical methodscommonly used by scientists, mathematiciansand engineers. This course is designed to givea fundamental understanding of the buildingblocks of scientific computing that will be used inmore advanced courses in scientific computingand numerical methods for PDEs. Topics includenumerical solutions of algebraic systems, linearleast-squares, eigenvalue problems, solution ofnon-linear systems, optimization, interpolation,numerical integration and differentiation, initialvalue problems and boundary value problems forsystems of ODEs. All programming exercises willbe in MATLAB.APMA E4301x Numerical methods for partialdifferential equations3 pts. Lect: 3. Professor Spiegelman.Prerequisites: APMA E4300 and APMA E3102or APMA E4200 or equivalents. Numericalsolution of partial differential equations (PDE)arising in various physical fields of application.Finite difference, finite element, andspectral methods. Elementary finite volumemethods for conservation laws. Time stepping,method of lines, and simultaneous space-timediscretization. Direct and iterative methods forboundary-value problems. Applied numericalanalysis of PDE, including sources of numericalerror and notions of convergence andstability, to an extent necessary for successfulnumerical modeling of physical phenomena.Applications will include the Poisson equation,heat equation, wave equation, and nonlinearequations of fluid, solid, and gas dynamics.Homework assignments will involve substantialprogramming.AMCS E4302x Parallel scientific computing3 pts. Lect: 3. Instructor to be announced.Prerequisites: APMA E3101, APMA E3102, andAPMA E4300, or their equivalents. Corequisites:APMA E4301, and programming ability in C/C++ or FORTRAN/F90. An introduction to theconcepts, the hardware and software environments,and selected algorithms and applicationsof parallel scientific computing, with an emphasison tightly coupled computations that are capableof scaling to thousands of processors. Includeshigh-level descriptions of motivating applicationsand low-level details of implementation, in orderto expose the algorithmic kernels and the shiftingbalances of computation and communicationbetween them. Students run demonstrationcodes provided on a Linux cluster. Modest programmingassignments using MPI and PETScculminate in an independent project leading to anin-class report.APMA E4400y Introduction to biophysicalmodeling3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: PHYS W1401 or equivalent, andAPMA E2101 or MATH E1210 or equivalent.Introduction to physical and mathematical modelsof cellular and molecular biology. Physicsat the cellular scale (viscosity, heat, diffusion,statistical mechanics). RNA transcription andregulation of genetic expression. Genetic andbiochemical networks. Bioinformatics as appliedto reverse-engineering of naturally-occurringnetworks and to forward-engineering of syntheticbiological networks. Mathematical and physicalaspects of functional genomics.69SEAS 2010–2011

70APMA E4901x Seminar: problems in appliedmathematics0 pts. Lect: 1. Professor Wiggins.This course is required for, and can be takenonly by, all applied mathematics majors inthe junior year. Prerequisites or corequisites:APMA E4200 and E4204 or their equivalents.Introductory seminars on problems and techniquesin applied mathematics. Typical topicsare nonlinear dynamics, scientific computation,economics, operations research, etc.APMA E4903x Seminar: problems in appliedmathematics3–4 pts. Lect: 1. Tutorial: 2. Professor Wiggins.This course is required for all applied mathematicsmajors in the senior year. Prerequisitesor corequisites: APMA E4200 and E4204 ortheir equivalents. For 4 pts. credit, term paperrequired. Examples of problem areas are nonlineardynamics, asymptotics, approximationtheory, numerical methods, etc. Approximatelythree problem areas are studied per term.APMA E4990x and y Special topics in appliedmathematics1–3 pts. Lect: 3. Professor Romanou.Prerequisites: Advanced calculus and junioryear applied mathematics, or their equivalents.This course may be repeated for credit. Topicsand instructors from the Applied MathematicsCommittee and the staff change from year toyear. For advanced undergraduate students andgraduate students in engineering, physical sciences,biological sciences, and other fields.APMA E6209x Approximation theory3 pts. Lect: 2. Not offered in 2010–2011Prerequisites: MATH W4061 or some knowledgeof modern analysis. Theory and application ofapproximate methods of analysis from the viewpointof functional analysis. Approximate numericaland analytical treatment of linear and nonlinearalgebraic, differential, and integral equations.Topics include function spaces, operators innormed and metric spaces, fixed point theoremsand their applications.APMA E6301y Analytic methods for partialdifferential equations3 pts. Lect: 2. Professor Weinstein.Prerequisites: Advanced calculus, basic conceptsin analysis, APMA E3101, and E4200 ortheir equivalents, or permission of the instructor.Introduction to analytic theory of PDEs of fundamentaland applied science; wave (hyperbolic),Laplace and Poisson equations (elliptic), heat(parabolic) and Schroedinger (dispersive) equations;fundamental solutions, Green’s functions,weak/distribution solutions, maximum principle,energy estimates, variational methods, methodof characteristics; elementary functional analysisand applications to PDEs; introduction to nonlinearPDEs, shocks; selected applications.APMA E6302x Numerical analysis of partialdifferential equations3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: APMA E3102 or E4200. Numericalanalysis of initial and boundary value problemsfor partial differential equations. Convergenceand stability of the finite difference method, thespectral method, the finite element method andapplications to elliptic, parabolic, and hyperbolicequations.APMA E6304y Integral transforms3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: APMA E4204 and MATH E1210,or their equivalents. Laplace, Fourier, Hankel,and Mellin transforms. Selection of suitabletransform for a given partial differential equationboundary value problem. Operational propertiesof transforms. Inversion theorems. Approximateevaluation of inversion integrals for small andlarge values of parameter. Application to thesolution of integral equations.APMA E6901x and y–E6901y Special topics inapplied mathematics3 pts. Lect: 3. Professor Langmore.Prerequisites: Advanced calculus and junioryear applied mathematics, or their equivalents.This course may be repeated for credit. Topicsand instructors from the Applied MathematicsCommittee and the staff change from year toyear. For students in engineering, physical sciences,biological sciences, and other fields.APMA E8308y Asymptotic methods in appliedmathematics3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: APMA E4204 or equivalent.Asymptotic treatment of ordinary and partial differentialequations in problems arising in appliedmathematics. Asymptotic series. Asymptoticevaluation of integrals. Expansion of solutionsof ordinary differential equations: connectionproblem and turning points. Stoke’s phenomenon.Differential equations with a parameter:“boundary layer” phenomenon. Application topartial differential equations: problems from fluiddynamics, wave propagation theory, electromagnetictheory.APMA E9101x-E9102y Research1–4 pts. Members of the faculty.Prerequisites: Permission of the supervisingfaculty member. This course may be repeated.Advanced study in a special area.APMA E9810x or y Mathematical earthscience seminar0 pts. Lect: 1. Professor Polvani.Prerequisites: Instructor’s permission. Currentresearch in problems at the interface betweenapplied mathematics and earth and environmentalsciences.APMA E9815x or y Geophysical fluiddynamics seminar1–3 pts. May be repeated for up to 10 points ofcredit. Not offered in 2010–2011.Prerequisites: Instructor’s permission. Problemsin the dynamics of geophysical fluid flows.COURSES IN MATERIALSSCIENCE AND ENGINEERINGSee page 175.SEAS 2010–2011

BIOMEDICAL ENGINEERING351 Engineering Terrace, MC 8904, 212-854-4460bme@columbia.edu, www.bme.columbia.edu71CHAIRVan C. MowVICE CHAIRAndrew F. LaineDEPARTMENTALADMINISTRATORShila MaghjiBUSINESS MANAGERKidest ShenkoruADMINISTRATIVECOORDINATOR FORSTUDENT AFFAIRSJarmaine LomaxADMINISTRATIVEASSISTANT FOR FISCALAFFAIRSMichelle CintronADMINISTRATIVEASSISTANT FORDEPARTMENTAL AFFAIRSPaulette LouissaintLABORATORY MANAGERKeith YeagerCOMPUTER SYSTEMSADMINISTRATORRobert J. FosterCHAIR OF UNDER-GRADUATE STUDIESX. Edward GuoCHAIR OF GRADUATE STUDIESHelen H. LuOMBUDSLance KamPROFESSORSGerard H. A. AteshianX. Edward GuoAndreas H. HielscherClark T. HungAndrew F. LaineEdward F. LeonardVan C. Mow,Stanley Dicker ProfessorMichael P. SheetzGordana Vunjak-NovakovicASSOCIATE PROFESSORSHenry HessChristopher R. JacobsElisa E. KonofagouHelen H. LuJeremy J. MaoBarclay Morrison IIIPaul SajdaASSISTANT PROFESSORSElizabeth HillmanHayden HuangLance C. KamSamuel K. SiaLECTURER IN DISCIPLINEAaron Matthew KyleJOINT FACULTYDimitris Anastassiou,Professor of ElectricalEngineeringAniruddha Das, AssistantProfessor of PsychiatryShunichi Homma, MargaretMilliken Hatch Professorof MedicineElizabeth S. Olson,Assistant Professor ofOtolaryngology/Head andNeck SurgeryR. Theodore Smith,Associate Professor ofOphthalmologyADJUNCT PROFESSORSErnest FeleppaShiro MatsuokaADJUNCT ASSOCIATEPROFESSORNicolas W. ChbatAFFILIATESPeter K. Allen, Professor ofComputer ScienceErnest W. April, AssociateProfessor of Anatomy andCell BiologyRobert DeLaPaz, Professorof RadiologyKung Ming Jan, AssociateProfessor of ClinicalMedicineJung-Chi Liao, AssistantProfessor of MechanicalEngineeringZheng Feng Lu, AssociateProfessor of ClinicalRadiologyJohn Pile-Spellman,Professor of Radiologyand NeurosurgeryHenry M. Spotnitz, GeorgeG. Humphreys II Professorof SurgeryBiomedical engineering is anevolving discipline in engineeringthat draws on collaborationamong engineers, physicians, andscientists to provide interdisciplinaryinsight into medical and biological problems.The field has developed its ownknowledge base and principles that arethe foundation for the academic programsdesigned by the Department ofBiomedical Engineering at Columbia.The programs in biomedical engineeringat Columbia (B.S., M.S., Ph.D.,Eng.Sc.D., and M.D./Ph.D.) preparestudents to apply engineering andapplied science to problems in biology,medicine, and the understanding ofliving systems and their behavior, andto develop biomedical systems anddevices. Modern engineering encompassessophisticated approaches tomeasurement, data acquisition andanalysis, simulation, and systems identification.These approaches are usefulin the study of individual cells, organs,entire organisms, and populations oforganisms. The increasing value ofmathematical models in the analysis ofliving systems is an important sign of thesuccess of contemporary activity. Theprograms offered in the Department ofBiomedical Engineering seek to emphasizethe confluence of basic engineeringscience and applied engineering withthe physical and biological sciences,particularly in the areas of biomechanics,cell and tissue engineering, andbiomedical imaging.Programs in biomedical engineeringare taught by its own faculty, membersof other SEAS departments, andfaculty from other University divisionswho have strong interests and involvementin biomedical engineering. Severalof the faculty hold joint appointmentsin Biomedical Engineering and otherUniversity departments.Courses offered by the Departmentof Biomedical Engineering are complementedby courses offered by otherdepartments in The Fu FoundationSchool of Engineering and AppliedScience, and by many departmentsin the Faculty of Medicine, the Schoolof Dentistry and Oral Surgery, and theMailman School of Public Health, as wellas the science departments within theSEAS 2010–2011

72Graduate School of Arts and Sciences.The availability of these courses in auniversity that contains a large medicalcenter and enjoys a basic commitment tointerdisciplinary research is important tothe quality and strength of the program.Educational programs at all levelsare based on engineering and biologicalfundamentals. From this basis, theprogram branches into concentrationsalong three tracks: biomechanics, celland tissue engineering, and biomedicalimaging. The intrinsic breadth includedwithin these tracks, plus a substantialelective content, prepare bachelor’s andmaster’s students to commence professionalactivity in any area of biomedicalengineering or to go on to graduateschool for further studies in relatedfields. The program also provides excellentpreparation for the health sciencesand the study of medicine. Graduates ofthe doctoral program are prepared forresearch activities at the highest level.Areas of particular interest to Columbiafaculty include orthopaedic and musculoskeletalbiomechanics (ProfessorsAteshian, Guo, Hess, Huang, Jacobs,and Mow), cardiovascular biomechanics(Professor Homma), cellular andtissue engineering and artificial organs(Professors Hung, Kam, Leonard, H. H.Lu, Morrison, Sia, and Vunjak-Novakovic),auditory biophysics (Professor Olson), andbiomedical imaging (Professors Hielscher,Hillman, DeLaPaz, Konofagou, Laine, Z. F.Lu, Pile-Spellman, Sajda, and Smith).FacilitiesThe Department of Biomedical Engineeringhas been supported by Universityfunding, awards from the WhitakerFoundation, and research funding fromthe NIH, NSF, and numerous researchfoundations. The extensive new facilitiesthat have recently been added both atthe Medical Center and Morningsidecampus include new teaching andresearch laboratories that provide studentswith unusual access to contemporaryresearch equipment speciallyselected for its relevance to biomedicalengineering. An undergraduate wetlaboratory devoted to biomechanicsand cell and tissue engineering hasbeen added, together with a biomedicalimaging and data processing laboratory.Each laboratory incorporates equipmentnormally reserved for advanced researchand provides exceptional access to currentpractices in biomedical engineeringand related sciences. Adjacent to thenew laboratories is a lounge that servesas a meeting point for biomedical engineeringundergraduate and graduatestudents.Research facilities of the BiomedicalEngineering faculty include the LiuPing Laboratory for Functional TissueResearch (Professor Mow), the HeffnerBiomedical Imaging Laboratory(Professor Laine), the Laboratoryfor Intelligent Imaging and NeuralComputing (Professor Sajda), theBiophotonics and Optical RadiologyLaboratory (Professor Hielscher),the Bone Bioengineering Laboratory(Professor Guo), the Cell and TissueEngineering Laboratory (ProfessorHung), the Biomaterial and InterfaceTissue Engineering Laboratory(Professor Lu), the Neurotraumaand Repair Laboratory (ProfessorMorrison), the Laboratory for StemCells and Tissue Engineering (ProfessorVunjak-Novakovic), the Ultra- soundand Elasticity Imaging Laboratory(Professor Konofagou), the MicroscaleBiocomplexity Laboratory (ProfessorKam), the Molecular and MicroscaleBioengineering Laboratory (ProfessorSia), the Laboratory for FunctionalOptical Imaging (Professor Hillman),the Cell and Molecular BiomechanicsLaboratory (Professor Jacobs), and theBiomechanics and MechanotransductionLaboratory (Professor Huang), theNanobiotechnology and SyntheticBiology Laboratory (Professor Hess).These laboratories are supplementedwith core facilities, including a tissueculture facility, a histology facility, aconfocal microscope, an atomic forcemicroscope, a 2-photon microscope, anepifluorescence microscope, a freezerroom, biomechanics facilities, a machineshop, and a specimen prep room.UNDERGRADUATE PROGRAMThe objectives of the undergraduateprogram in biomedical engineering areas follows:1. Professional employment in areassuch as the medical device industry,engineering consulting, biomechanics,biomedical imaging, and biotechnology;2. Graduate studies in biomedical engineeringor related fields;3. Attendance at medical or dental school.The undergraduate curriculum isdesigned to provide broad knowledgeof the physical and engineering sciencesand their application to the solutionof biological and medical problems.Students are strongly encouraged totake courses in the order specified in thecourse tables on pages 76–79; implicationsof deviations should be discussedwith a departmental adviser beforeregistration. The first two years providea strong grounding in the physical andchemical sciences, engineering fundamentals,and mathematics. This backgroundis used to provide a unique physicalapproach to the study of biologicalsystems. The last two years of the undergraduateprogram provide substantialexposure to modern biology and includecourses in engineering and engineeringscience that extend the work of the firsttwo years. The program also offers threetracks to guide students in the choice oftechnical courses, while sharing a commoncore curriculum. The tracks aredifferent from one another, and there isgreat breadth within each. These qualitiesallow the faculty to prepare studentsfor activity in all contemporary areas ofbiomedical engineering. Graduates of theprogram are equipped for employmentin the large industrial sector devotedto health care, which includes pharmaceuticals,medical devices, artificialorgans, prosthetics and sensory aids,diagnostics, medical instrumentation, andmedical imaging. Graduates also acceptemployment in oversight organizations(FDA, NIH, OSHA, and others), medicalcenters, and research institutes. They areprepared for graduate study in biomedicalengineering and several related areasof engineering and the health sciences.Students in all three tracks of the programcan meet entrance requirementsfor graduate training in the various alliedhealth professions. No more than threeadditional courses are required in anyof the tracks to satisfy entrance requirementsfor most U.S. medical schools.All biomedical engineering studentsare expected to register for nontechnicalelectives, both those specificallyrequired by the School of Engineeringand Applied Science and those neededSEAS 2010–2011

to meet the 27-point total of nontechnicalelectives required for graduation.First and Second YearsAs outlined in this bulletin, in the first twoyears all engineering students are expectedto complete a sequence of coursesin mathematics, physics, chemistry,computer science, engineering, Englishcomposition, and physical education,as well as nontechnical electives includingthe humanities. For most of thesesequences, the students may choosefrom two or more tracks. If there is aquestion regarding the acceptability of acourse as a nontechnical elective, pleaseconsult the approved listing of coursesbeginning on page 10 or contact youradvising dean for clarification.Please see the charts in this sectionfor a specific description ofcourse requirements.In addition, a professional-level engineeringcourse is required. Students mayselect from a variety of offerings withinSEAS. For students interested in biomedicalengineering, we recommend takingBMEN E1001: Engineering in medicineor APPH E1300y: Physics of the humanbody in fulfillment of this requirement.Note that E1201: Introduction to electricalengineering is required and cannotbe double counted to satisfy the professional-levelcourse requirement. For thecomputer science requirement, studentsmust take COMS W1005.All students must take APMA E2101:Introduction to applied mathematics inaddition to ELEN E1201: Introduction toelectrical engineering and ENME E3105:Mechanics in their second year. For theclasses of 2010 and later, students mustalso take STAT W1211: Introduction tostatistics.Third and Fourth YearsThe biomedical engineering programsat Columbia at all levels are based onengineering and biological fundamentals.This is emphasized in our core requirementsacross all tracks. In the junioryear, all students begin their biomedicalengineering study with the two-semesterIntroduction to molecular and cellularbiology, I and II (BIOL C2005-C2006),which gives students a comprehensiveoverview of modern biology frommolecular to organ system levels. Parallelto these biology studies, all studentstake the two-semester Quantitativephysiology, I and II sequence (BMENE4001-E4002) which is taught bybiomedical engineering faculty andemphasizes quantitative applications ofengineering principles in understandingbiological systems and phenomena frommolecular to organ system levels. In thefields of biomedical engineering, experimentaltechniques and principles arefundamental skills that good biomedicalengineers must master. Beginningin junior year, all students take thethree-semester sequence Biomedicalengineering laboratory, I-III (BMENE3810, BMEN E3820, BMEN E3830).In this three-semester series, studentslearn through hands-on experience theprinciples and methods of biomedicalengineering experimentation, measurementtechniques, quantitative theoriesof biomedical engineering, data analysis,and independent design of biomedicalengineering experiments, the scope ofwhich cover a broad range of topicsfrom all three tracks—biomechanics, celland tissue engineering, and biomedicalimaging. In the senior year, studentstake the required course Ethics forbiomedical engineers (BMEN E4010), aSEAS nontechnical elective that coversa wide range of ethical issues expectedto confront biomedical engineering graduatesas they enter biotechnology industry,research, or medical careers. Alsoin the senior year, students are requiredto take a two-semester capstone designcourse, Biomedical engineering design(BMEN E3910 and BMEN E3920), inwhich students work within a team totackle an open-ended design project inbiomedical engineering. The underlyingphilosophy of these core requirementsis to provide our biomedical engineeringstudents with a broad knowledge andunderstanding of topics in the field ofbiomedical engineering. Parallel to thesestudies in core courses, students taketrack-specific required courses to obtainan in-depth understanding of their chosenconcentration. The curriculum of allthree academic tracks—biomechanics,cell and tissue engineering, and biomedicalimaging—prepares students whowish to pursue careers in medicine bysatisfying most requirements in the premedicalprograms with no more thanthree additional courses. Some of theseadditional courses may also be countedas nonengineering technical electives.Please see the course tables for schedulesleading to a bachelor’s degree inbiomedical engineering.It is strongly advised that studentstake required courses during the specificterm that they are designated in thecourse tables, as conflicts may arise ifcourses are taken out of sequence.Students are required to take up to 9points (6 points in the imaging track) of“technical electives,” allowing for explorationof related technical topics. A technicalelective is defined as a 3000-levelor above course in SEAS or coursestaught by the Departments of Biology,Chemistry, and Biochemistry.Technical Elective RequirementsStudents are required to take at least 48points of engineering content courseworktoward their degree. The 48-pointrequirement is a criterion established bythe Accreditation Board for Engineeringand Technology (ABET). Taking intoconsideration the number of engineeringcontent points conferred by therequired courses of the BME curriculum,a portion of technical electives must beclearly engineering in nature (EngineeringContent Technical Electives), specificallyas defined below:1. Technical elective courses with sufficientengineering content that cancount toward the 48 units of engineeringcourses required for ABETaccreditation:a. All 3000-level or higher coursesin the Department of BiomedicalEngineering, except BMEN E4010,E4103, E4104, E4105, E4106,E4107 and E4108. (Note that only3 points of BMEN E3998 may becounted toward technical electivedegree requirements.)b. All 3000-level or higher coursesin the Department of MechanicalEngineering, except MECE E4007:Creative engineering and entrepreneurshipc. All 3000-level or higher coursesin the Department of ChemicalEngineering, except CHEN E4020:Safeguarding intellectual and businesspropertyd. All 3000-level or higher coursesin the Department of ElectricalEngineering, except EEHS E3900:History of telecommunications:from the telegraph to the Internete. All 3000-level or higher courses73SEAS 2010–2011

74in the Civil Engineering andEngineering Mechanics program,except CIEN E4128, E4129,E4130, E4131, E4132, E4133,E4134, E4135, and E4136f. All 3000-level or higher coursesin the Earth and EnvironmentalEngineering program2. Courses from the following departmentsare not allowed to counttoward the required 48 units of engineeringcourses:a. Department of Applied Physics andApplied Mathematicsb. Department of Computer Sciencec. Department of IndustrialEngineering and OperationsResearchd. Program of Materials Science andEngineeringThe cell and tissue engineering trackrequires 4.5 of the required 9 points oftechnical electives to be from engineeringcourses; in the biomechanics track,2.5 points of technical electives must befrom engineering courses; in the imagingtrack, the requirements satisfy the48 points of engineering content. Once48 points of engineering-content technicalelectives are satisfied, students maychoose any course above the 3000 levelin SEAS as well as biology, chemistry,and biochemistry as technical electives.The accompanying charts describethe eight-semester degree programschedule of courses leading to thebachelor’s degree in biomedicalengineering.GRADUATE PROGRAMSThe graduate curriculum in biomedicalengineering employs the same threetracks that compose the undergraduatecurriculum: biomechanics, cell and tissueengineering, and biomedical imaging.Initial graduate study in biomedicalengineering is designed to expand thestudent’s undergraduate preparation inthe direction of the track chosen. In addition,sufficient knowledge is acquired inother areas to facilitate broad appreciationof problems and effective collaborationwith specialists from other scientific,medical, and engineering disciplines. TheDepartment of Biomedical Engineeringoffers a graduate program leading tothe Master of Science degree (M.S.),the Doctor of Philosophy degree (Ph.D.),and the Doctor of Engineering Sciencedegree (Eng.Sc.D.). Applicants who havea Master of Science degree or equivalentmay apply directly to the doctoral degreeprogram. All applicants are expectedto have earned the bachelor’s degreein engineering or in a cognate scientificprogram. The Graduate Record Examination(General Test only) is required ofall applicants. Students whose bachelor’sdegree was not earned in a countrywhere English is the dominant spokenlanguage are required to take the TOEFLtest. M.S. degree candidates must reachlevel 8 on the English Placement Test(EPT) offered by Columbia’s AmericanLanguage Program (ALP). Doctoraldegree candidates must attain level 10on the English Placement Test (EPT).The ALP examination must be takenat orientation upon arrival. It is stronglyrecommended the students enroll in anappropriate ALP course if they have notachieved the required proficiency afterthe first examination. In addition, the individualtracks require applicants to havetaken the following foundation courses: Biomechanics: One year of biologyand/or physiology, solid mechanics,statics and dynamics, fluid mechanics,ordinary differential equations. Cell and Tissue Engineering: Oneyear of biology and/or physiology, oneyear of organic chemistry or biochemistrywith laboratory, fluid mechanics,rate processes, ordinary differentialequations. Biomedical Imaging: One year ofbiology and/or physiology and/orbiochemistry. Linear algebra, ordinarydifferential equations, Fourier analysis,digital signal processing.Applicants lacking some of thesecourses may be considered for admissionwith stipulated deficiencies thatmust be satisfied in addition to therequirements of the degree program.The Fu Foundation School ofEngineering and Applied Science doesnot admit students holding the bachelor’sdegree directly to doctoral studies;admission is offered either to the M.S.program or to the M.S. program/doctoraltrack. The Department of BiomedicalEngineering also admits students intothe 4-2 program, which provides theopportunity for students holding a bachelor’sdegree from certain physical sciencesto receive the M.S. degree aftertwo years of study at Columbia.CURRICULUM AND EXAMREQUIREMENTSMaster’s DegreeIn consultation with an appointed facultyadviser, M.S. students should selecta program of 30 points of credit ofgraduate courses (4000 level or above)appropriate to their career goals. Thisprogram must include the course incomputational modeling of physiologicalsystems (BMEN E6003); two semestersof BMEN E9700: Biomedical engineeringseminar; at least four other biomedicalengineering courses; and at least onegraduate-level mathematics course.Students with deficiency in physiologycourse work are required to take theBMEN E4001-E4002 sequence beforetaking BMEN E6003. Candidates mustachieve a minimum grade-point averageof 2.5. For students interested in obtainingresearch experience, up to 6 creditsof research (BMEN E9100) may beapplied toward the M.S. degree.Doctoral DegreeStudents admitted to the doctoraldegree program should select coursesto prepare for the doctoral qualifyingexamination and register for researchrotations during the first two semestersof graduate study. To facilitate futurecollaboration with clinicians and biomedicalscientists, students are encouragedto consider courses at the HealthSciences campus or in the Departmentof Biological Sciences.Doctoral students must completea program of 30 points of creditsbeyond the M.S. degree. The course incomputational modeling of physiologicalsystems (BMEN E6003) is requiredfor the doctoral program. At least twograduate mathematics courses must betaken, which may include the mathematicscourse required for the M.S. degree.Students must register for BMEN E9700:Biomedical engineering seminar and forresearch rotations during the first twosemesters of graduate study. Remainingcourses should be selected in consultationwith the student’s faculty adviserto prepare for the doctoral qualifyingexamination and to develop expertisein a clearly identified area of biomedicalengineering. Up to 12 credits of researchSEAS 2010–2011

(BMEN E9500) may be applied towarddoctoral degree course requirements.All graduate students admitted tothe doctoral degree program must satisfythe equivalent of three semesters’experience in teaching (one semesterfor M.D./Ph.D. students). This mayinclude supervising and assistingundergraduate students in laboratoryexperiments, grading, and preparinglecture materials to support the teachingmission of the department. TheDepartment of Biomedical Engineeringis the only engineering department thatoffers Ph.D. training to M.D./Ph.D. students.These candidates are expectedto complete their Ph.D. program within3.5 years, with otherwise the samerequirements.Doctoral Qualifying ExaminationDoctoral candidates are required to passa qualifying examination. This examinationis given once a year, in January. It shouldbe taken after the student has completed30 points of graduate study. The qualifyingexamination consists of oral and writtenexaminations. The oral examination consistsof the analysis of assigned scientificpapers, and the written examination coversthree areas: applied mathematics,quantitative biology and physiology, andtrack-specific material. Students mustdeclare a track (biomedical imaging, biomechanics,or cell and tissue engineering)at the time of registration for the qualifyingexamination. A minimum cumulativegrade-point average of 3.2 is required toregister for this examination.Doctoral Committee and ThesisStudents who pass the qualifyingexamination choose a faculty memberto serve as their research adviser.Each student is expected to submit aresearch proposal and present it to athesis committee that consists of threeto five faculty members. The committeeconsiders the scope of the proposedresearch, its suitability for doctoralresearch and the appropriateness ofthe research plan. The committee mayapprove the proposal without reservationor may recommend modifications.In general, the student is expectedto submit his/her research proposalafter five semesters of doctoral studies.In accord with regulations of TheFu Foundation School of Engineeringand Applied Science, each student isexpected to submit a thesis and defendit before a committee of five faculty,two of whom hold primary appointmentsin another department. Everydoctoral candidate is required to havehad accepted at least one first-authorfull-length paper for publication in apeer-reviewed journal prior to recommendationfor award of the degree.COURSES IN BIOMEDICALENGINEERINGSee also the sections for AppliedPhysics, Chemical Engineering,Computer Science, and ComputerEngineering in this bulletin, and theColumbia College and GraduateSchool of Arts and Sciences bulletinsfor courses in the biological sciences:biomedical informatics, cell biology,microbiology, and physiology.BMEN E1001x Engineering in medicine3 pts. Lect: 3. Professor Konofagou.The present and historical role of engineering inmedicine and health care delivery. Engineeringapproaches to understanding organismic andcellular function in living systems. Engineering inthe diagnosis and treatment of disease. Medicalimaging, medical devices: diagnostic and surgicalinstruments, drug delivery systems, prostheses,artificial organs. Medical informatics andorganization of the health care system. Currenttrends in biomedical engineering research.BMEN E2300x or y Biomechanics track0 pts. Professor Laine.Rising juniors are required to register for thiscourse in the spring of their sophomore year ifthey choose the biomechanics track.BMEN E2400x or y Biomedical imaging track0 pts. Professor Laine.Rising juniors are required to register for thiscourse in the spring of their sophomore year ifthey choose the biomedical imaging track.BMEN E2500x or y Cellular and tissueengineering track0 pts. Professor Laine.Rising juniors are required to register for thiscourse in the spring of their sophomore year ifthey choose the cell and tissue engineering track.ECBM E3060x Introduction to genomicinformation science and technology3 pts. Lect: 3. Professor Anastassiou.Introduction to the information system paradigmof molecular biology. Representation, organization,structure, function and manipulation of thebiomolecular sequences of nucleic acids andproteins. The role of enzymes and gene regulatoryelements in natural biological functions aswell as in biotechnology and genetic engineering.Recombination and other macromolecular processesviewed as mathematical operations withsimulation and visualization using simple computerprogramming. This course shares lectureswith ECBM E4060, but the work requirementsdiffer somewhat.BMEN E3150y The cell as a machine3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MATH V1101 or equivalent.Corequisites: One semester of BIOL C2005or BIOC C3501, and one semester of PHYSC1401 or equivalent Cells as complex micronsizedmachines, basic physical aspects of cellcomponents (diffusion, mechanics, electrostatics,hydrophobicity), energy transduction (motors,transporters, chaperones, synthesis complexes),basic cell functions. Biophysical principles, feedbackcontrols for robust cell function, adaptationto environmental perturbations.BMEN E3320y Fluid biomechanics3 pts. Lect: 3. Professor Huang.Prerequisites: APMA E2101. The principles ofcontinuum mechanics as applied to biological fluidflows and transport. Course covers continuumformulations of basic conservation laws, Navier-Stokes equations, mechanics of arterial andvenous blood flow, blood rheology and non-Newtonianproperties, flow and transport in the microcirculation,oxygen diffusion, capillary filtration.BMCH E3500y Biological transport andrate processes3 pts. Lect: 3. Professor Vunjak-Novakovic.Prerequisites: CHEM C3443, APMA E2101.Corequisites: BIOL C2005 Convective and diffusivemovement and reaction of molecules inbiological systems. Kinetics of homogeneous andheterogeneous reactions in biological environments.Mechanisms and models of transportacross membranes. Convective diffusion with andwithout chemical reaction. Diffusion in restrictedspaces. Irreversible thermodynamic approachesto transport and reaction in biological systems.BMEN E3810x Biomedical engineeringlaboratory, I3 pts. Lab: 4. Professor Kyle.Statistical analysis of experimental measurements:normal distribution, test of significance,linear regression, correlation, error analysis andpropagation. MATLAB programming, EKG signalacquisition and processing, microscopy, cellcounting and scaffold encapsulation, mechanicaltesting of linear and nonlinear biomaterials.BMEN E3820y Biomedical engineeringlaboratory, II3 pts. Lab: 4. Professor Kyle.Statistical analysis of experimental measurements:analysis of variance, power analysis.Circuit implementation of nerve conduction,alginate bead formation, mechanical testing andoptical strain analysis, galvanotaxis, image segmentationand analysis of cells, computer aideddesign, library resources.75SEAS 2010–2011

76BIOMEDICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARSCLASSES OF 2010–2011SEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3)PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)C1403 (3)C2601 (3.5)CHEMISTRY(three tracks,choose one)C1403 (3.5)C1404 (3.5)and Lab C1500 (3) either semesterC1604 (3.5)C2507 (3)C3045 (3.5) C3046 (3.5), C2507 (3)C3443 (3.5)C3443 (3.5)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)COMPUTERSCIENCECOMS W1005 (3) MATLAB (in semester I or III)PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semesterNONTECHNICALREQUIREMENTSHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 (3)or W1123 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)TECHNICALREQUIREMENTSProfessional-level course(except ELEN E1201)(either semester)ELEN E1201Intro. to EE (3.5)APMA E2101Intro. to applied math (3)ENME E3105Mechanics (4)BMEN E3830x Biomedical engineeringlaboratory, III3 pts. Lab: 4. Professor Kyle.Experimental design. Cell adhesion, membranetransport, osmosis, ultrasound, design of cellencapsulation and drug delivery system, respiratoryimpedance. Selected clinical demonstrations:body compositions, magnetic resonanceimaging, echocardiography, blood pressure.BMEN E3910x-E3920y Biomedical engineeringdesign, I and II4 pts. Lect: 1. Lab: 3. Professors Hillman and Kyle.A two-semester design sequence to be taken inthe senior year. Elements of the design process,with specific applications to biomedical engineering:concept formulation, systems synthesis,design analysis, optimization, biocompatibility,impact on patient health and comfort, health carecosts, regulatory issues, and medical ethics.Selection and execution of a project involving thedesign of an actual engineering device or system.Introduction to entrepreneurship, biomedicalstart-ups, and venture capital. Semester I: statisticalanalysis of detection/classification systems(receiver operation characteristic analysis, logisticregression), development of design prototype,need, approach, benefits and competition analysis.Semester II: spiral develop process and testing,iteration and refinement of the initial design/prototype, and business plan development.BMEN E3998x or y Projects in biomedicalengineering1–3 pts. Hours to be arranged. Members of thefaculty.Independent projects involving experimental, theoretical,computational, or engineering design work.May be repeated, but no more than 3 points ofthis or any other projects or research course maybe counted toward the technical elective degreerequirements as engineering technical electives.BMEN E4000y Special topics: Biomaterialsand scaffold design3 pts. Lec: 3. Professor H. Lu.Prerequisite: BMEN E4501 or equivalent. Thiscourse focuses on biomaterial selection andbiomimetic scaffold design for tissue engineeringand regenerative medicine. The emphasis ison strategies for the formulation of bio-inspireddesign criteria, scaffold characterization andtesting, as well as the formation of complex tissuesor organogenesis. The course includes alaboratory component on basic scaffold fabrication,characterization and in vitro evaluation ofbiocompatibility, in addition to group projectstargeting the design of scaffolds for select tissueengineering applications.BMEN E4001x Quantitative physiology, I:cells and molecules3 pts. Lect: 3. Professor Kam.Prerequisites: CHEM C3443 or equivalent; BIOLSEAS 2010–2011

BIOMEDICAL ENGINEERING: THIRD AND FOURTH YEARSCLASSES OF 2010–201177SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIBIOL C2005 (4)Introductory biol., IBIOL C2006 (4)Introductory biol,. IIBMEN E3910 (4)BME design, IBMEN 3920 (4)BME design, IIREQUIREDCOURSES:ALL TRACKSBMEN E4001 (3)Quantitative physiol., IBMEN E4002 (3)Quantitative physiol., IIBMEN E3820 (3)BME laboratory, IIBMEN E3830 (3)BME laboratory, IIISTAT W1211 (3)Intro. to statisticsBMEN E3810 (3)BME laboratory, IBMEN E4010 (2) 4Ethics for BMEsNONTECHELECTIVES0–3 points 3 points 0–3 points 3 pointsBMEN E2500 (0)BMEN E4210 (4)CELL ANDTISSUE ENG. 1 Thermo. biolog. sys.MSAE E3103 (3)Elements of mat. sci.BMCH E3500 (3)Biol. transport. proc.orBMEN E3320 (3)Fluid biomech.Technical elective (3)BMEN E4501 (3)Tissue eng., ITechnical elective (6)BMEN E4502 (3)Tissue eng., IITRACK-SPECIFIC COURSESBIOMECH. 2 BMEN E2300 (0)MECE E3100 (3)Mech. of fluidsBMEN E2400 (0)BIOMED.IMAGING 3 ELEN E3801 (3.5)Signals and systemsBMEN E3320 (3)Fluid biomech.Technical elective (3)BMEN E4420 (3)Biosig. proc. andmodelingTechnical elective (3)ENME E3113 (3)Mech. of solidsMECE E3301 (3)ThermodynamicsTechnical elective (6)ELEN E4810 (3)Dig. sig. processingBMEN E4898 (3)Biomed. imagingBMEN E4430 (3)Principles of MRIBMEN 4300 (3)Solid biomech.BMEN E4410 (3)Ultrasound imagingorBMEN E4894 (3)BiophotonicsTechnical elective (3)TOTAL POINTS 16–17 19 19 151In the cell and tissue engineering track, of the 9 points of technical electives, at least 4.5 must be from engineering courses.2In the biomechanics track, of the 9 points of technical electives, at least 2.5 points must be from engineering courses.3In the imaging track, core requirements satisfy the 48 points of engineering content.4BMEN E4010: Ethics for biomedical engineers is a SEAS nontechnical course.C2005 Physiological systems at the cellular andmolecular level are examined in a highly quantitativecontext. Topics include chemical kinetics, molecularbinding and enzymatic processes, molecular motors,biological membranes, and muscles.BMEN E4002y Quantitative physiology, II:organ systems3 pts. Lect: 3. Professor Morrison.Prerequisites or corequisites: CHEM C3443 orequivalent; BIOL C2005-C2006. Students areintroduced to a quantitative, engineering approachto cellular biology and mammalian physiology.Beginning with biological issues related to the cell,the course progresses to considerations of themajor physiological systems of the human body(nervous, circulatory, respiratory, renal).BMEN E4010y Ethics for biomedical engineers2 pts. Lect: 2. Professor Loike.Prerequisite: senior status in biomedical engineeringor the instructor’s permission. Covers awide range of ethical issues expected to confrontgraduates as they enter the biotechnology industry,research, or medical careers. Topics varyand incorporate guest speakers from Physiciansand Surgeons, Columbia Law School, ColumbiaCollege, and local industry.BMEB W4020x Computational neuroscience:circuits in the brain3 pts. Lect: 3. Professor Lazar.Prerequisites: ELEN E3801 or BIOL W3004.The biophysics of computation: modeling biologicalneurons, the Hodgkin-Huxley neuron,modeling channel conductances and synapsesas memristive systems, bursting neurons andcentral pattern generators, I/O equivalenceand spiking neuron models. Information representationand neural encoding: stimulusrepresentation with time encoding machines,the geometry of time encoding, encodingSEAS 2010–2011

78BIOMEDICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARSCLASS OF 2012 AND LATERSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3)PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)C1403 (3)C2601 (3.5)CHEMISTRY(three tracks,choose one)C1403 (3.5)C1404 (3.5)and Lab C1500 (3) either semesterC1604 (3.5)C2507 (3)C3045 (3.5) C3046 (3.5), C2507 (3)C3443 (3.5)C3443 (3.5)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)COMPUTERSCIENCECOMS W1005 (3) MATLAB (in semester I or III)PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semesterNONTECHNICALREQUIREMENTSHUMA W1121 (3)or W1123 (3)HUMA C1001,COCI C1101,or Global Core (3–4)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)TECHNICALREQUIREMENTSProfessional-level course(except ELEN E1201)(either semester)ELEN E1201Intro. to EE (3.5)APMA E2101Intro. to applied math (3)ENME E3105Mechanics (4)STAT W1211 (3) Intro. to statistics(either semester)with neural circuits with feedback, populationtime encoding machines. Dendritic computation:elements of spike processing and neuralcomputation, synaptic plasticity and learningalgorithms, unsupervised learning and spiketime-dependent plasticity, basic dendritic integration.Projects in MATLAB.ECBM E4060x Introduction to genomicinformation3 pts. Lect: 3. Professor Anastassiou.Prerequisites: None. Introduction to the informationsystem paradigm of molecular biology.Representation, organization, structure,function and manipulation of the biomolecularsequence of nucleic acids and proteins. The roleof enzymes and gene regulatory elements innatural biological functions as well as in biotechnologyand genetic engineering. Recombinationand other macromolecular processes viewedas mathematical operations with simulation andvisualization using simple computer programming.BMEN E4103x Anatomy of the thorax andabdomen2 pts. Lect: 2. Professor April.Prerequisites: graduate standing in BiomedicalEngineering. This course is designed for theBiomedical Engineering graduate studentinterested in acquiring in-depth knowledge ofanatomy relevant to his/her doctoral research.Lectures and tutorial sessions may be takenwith or without the associated laboratory (BMENE4104).BMEN E4104x Anatomy laboratory: thoraxand abdomen2 pts. Lect: 2. Professor April.Prerequisites: Graduate standing in BiomedicalEngineering. Corequisites: (BMEN E4103.)BMEN E4105x Anatomy of the extremities2 pts. Lect: 2. Professor April.Prerequisites: Graduate standing in BiomedicalEngineering. This course is designed for theBiomedical Engineering graduate studentinterested in acquiring in-depth knowledge ofanatomy relevant to his/her doctoral research.Lectures and tutorial sessions may be takenwith or without the associated laboratory (BMENE4106).SEAS 2010–2011

BIOMEDICAL ENGINEERING: THIRD AND FOURTH YEARSCLASS OF 2012 AND LATER79SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIREQUIREDCOURSES:ALL TRACKSBIOL C2005 (4)Introductory biol. IBMEN E3810 (3)BME laboratory, ISTAT W1211 (3)Intro. to statisticsBIOL C2006 (4)Introductory biol. IIBMEN E3820 (3)BME laboratory, IIBMEN E4002 (3)Quantitative physiol., IIBMEN E3910 (4)BME design, IBMEN E3830 (3)BME laboratory, IIIBMEN 3920 (4)BME design, IIBMEN E4010 (2) 4Ethics for BMEsNONTECHELECTIVES0–3 points 3 points 0–3 points 3 pointsBMEN E2500 (0)BMEN E4210 (4)CELL ANDTISSUE ENG. 1 Thermo. biolog. sys.MSAE E3103 (3)Elements of mat. sci.BMCH E3500 (3)Biol. transport. proc.orBMEN E3320 (3)Fluid biomech.BMEN E4501 (3)Tissue eng., ITechnical elective (6)BMEN E4502 (3)Tissue eng., IITRACK-SPECIFIC COURSESBIOMECH. 2 BMEN E2300 (0)MECE E3100 (3)Mech. of fluidsBMEN E2400 (0)BIOMED.IMAGING 3 ELEN E3801 (3.5)Signals and systemsBMEN E3320 (3)Fluid biomech.BMEN E4420 (3)Biosig. proc. andmodelingENME E3113 (3)Mech. of solidsMECE E3301 (3)ThermodynamicsTechnical elective (6)ELEN E4810 (3)Dig. sig. processingBMEN E4898 (3)Biomed. imagingBMEN E4430 (3)Principles of MRIBMEN 4300 (3)Solid biomech.Technical elective (3)BMEN E4410 (3)Ultrasound imagingorBMEN E4898 (3)BiophotonicsTechnical elective (3)Technical elective (3)TOTAL POINTS 16–17 16 19 151In the cell and tissue engineering track, of the 9 points of technical electives, at least 4.5 must be from engineering courses.2In the biomechanics track, of the 9 points of technical electives, at least 2.5 points must be from engineering courses.3In the imaging track, core requirements satisfy the 48 points of engineering content.4BMEN E4010: Ethics for biomedical engineers is a SEAS nontechnical course.BMEN E4106x Anatomy laboratory:extremities2 pts. Lab: 2. Professor April.Prerequisites: Graduate standing in BiomedicalEngineering. Corequisites: (BMEN E4105).BMEN E4107x Anatomy of the head and neck2 pts. Lect: 2. Professor April.Prerequisites: Graduate standing in BiomedicalEngineering. This course is designed for theBiomedical Engineering graduate studentinterested in acquiring in-depth knowledge ofanatomy relevant to his/her doctoral research.Lectures and tutorial sessions may be takenwith or without the associated laboratory(BMEN E4108).BMEN E4108x Anatomy laboratory: headand neck2 pts. Lab: 2. Professor April.Prerequisites: Graduate standing in BiomedicalEngineering. Corequisites: (BMEN E4107).BMEN E4210x Thermodynamics of biologicalsystems4 pts. Lect: 4. Professor Sia.Prerequisites: CHEM C1404 and MATH V1202Corequisites: BIOL C2005 or equivalentIntroduction to the thermodynamics of biologicalsystems, with a focus on connection microscopicmolecular properties to macroscopic states. Bothclassical and statistical thermodynamics areapplied to biological systems; phase equilibria,chemical reactions, and colligative properties.Topics in modern biology, macromolecularbehavior in solutions and interfaces, proteinligandbinding, and the hydrophobic effect.SEAS 2010–2011

80BMEN E4300y Solid biomechanics3 pts. Lect: 3. Professor Jacobs.Prerequisites: ENME-MECE E3105 and ENMEE3113. This course introduces applications ofcontinuum mechanics to the understanding ofvarious biological tissues properties. The structure,function, and mechanical properties of varioustissues in biological systems, such as bloodvessels, muscle, skin, brain tissue, bone, tendon,cartilage, ligaments, etc., are examined. Thefocus is on the establishment of basic governingmechanical principles and constitutive relationsfor each tissue. Experimental determinationof various tissue properties is introduced anddemonstrated. The important medical and clinicalimplications tissue mechanical behavior areemphasized.BMEN E4301x Structure, mechanics, andadaptation of bone3 pts. Lect: 3. Not offered in 2010–2011.Introduction to structure, physiology, and biomechanicsof bone. Structure, function, and physiologyof skeletal bones; linear elastic propertiesof cortical and trabecular bone; anisotropy andconstitutive models of bone tissue; failure anddamage mechanics of bone; bone adaptationand fracture healing; experimental determinationof bone properties; and morphological analysis ofbone microstructure.BMEN E4305y Cardiac mechanics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: BMEN E3310 and BMEN E3320 orequivalents. Cardiac anatomy, passive myocardialconstitutive properties, electrical activation,ventricular pump function, ventricular-vascularcoupling, invasive and noninvasive measures ofregional and global function, models for predictingventricular wall stress. Alterations in muscleproperties and ventricular function resulting frommyocardial infarction, heart failure, and left ventricularassist.BMEN E4340x Biomechanics of cells3 pts. Lect: 3. Professor Huang.Prerequisites: BMEN E3320 and BMEN E4300or equivalents. Survey of experiments and theoreticalanalyses of the mechanical behavior ofindividual living nonmuscle cells. Emphasis onquantitative analytic description using continuummechanics and molecular level theory from thestandpoint of statistical mechanics and mechanicalmodels. Mechanics of erythrocytes, leukocytes,endothelial cells, and fibroblasts; modelsof aggregation, adhesion, locomotion, amoebamotility, cell division and morphogenesis;molecular level models of actin, myosin, microtubules,and intermediate filaments and relation tomechanical properties of cells and cytoskeleton.Alternative models of cytoskeletal mechanics,foam theory, tensegrity. Analysis of experimentaltechniques including micropipette studies, opticaland magnetic cytometry, and nanoindentation.BMEN E4400y Wavelet applications inbiomedical image and signal processing3 pts. Lect: 3.Prerequisites: AMAP 3101 or equivalent. Anintroduction to methods of wavelet analysis andprocessing techniques for the quantification ofbiomedical images and signals. Topics include:frames and overcomplete representations, multiresolutionalgorithms for denoising and image restoration,multiscale texture segmentation and classificationmethods for computer aided diagnosis.BMEN E4410y Ultrasound in diagnosticimaging3 pts. Lect: 3. Professor Konofagou.Prerequisites: MATH V1105 or equivalent,Fourier analysis. Physics of diagnostic ultrasoundand principles of ultrasound imaginginstrumentation. Propagation of plane waves inlossless medium; ultrasound propagation throughbiological tissues; single-element and arraytransducer design; pulse-echo and Doppler ultrasoundinstrumentation, performance evaluationof ultrasound imaging systems using tissue-mimickingphantoms, ultrasound tissue characterization;ultrasound nonlinearity and bubble activity;harmonic imaging; acoustic output of ultrasoundsystems; biological effects of ultrasound.BMEN E4420y Biomedical signal processingand signal modeling3 pts. Lect: 3. Professor Sajda.Prerequisites: APMA E3101 and ELEN E3202 orinstructor’s permission Fundamental concepts ofsignal processing in linear systems and stochasticprocesses. Estimation, detection, and filteringmethods applied to biomedical signals. Harmonicanalysis, auto-regressive model, Wiener andMatched filters, linear discriminants, and independentcomponents. Methods are developed toanswer concrete questions on specific data setsin modalities such as ECG, EEG, MEG, ultrasound.Lectures accompanied by data analysisassignments using MATLAB.BMEN E4430x Principles of magneticresonance imaging3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: APAM E3101, MATH E1210, PHYSC1403 or instructors’ permission. Fundamentalprinciples of Magnetic Resonance Imaging (MRI),including the underlying spin physics and mathematicsof image formation with an emphasis onthe application of MRI to neuroimaging, both anatomicaland functional. The course examines boththeory and experimental design techniques.BMEN E4440y Physiological control systems3 pts. Lect: 3. Professor Chbat.Prerequisites: APMA E2101 and with instructor’sapproval or senior standing Dynamic systemmodeling and simulation of cardiovascular, respiratory,and thermoregulatory systems. Open andclosed physiological loops. Internal and externalcontrollers: baroreflex, chemoreflex, and ventilator.Fundamentals of time and frequency domainanalyses and stability. Emulation of normal andpathophysiological conditions. Clinical relevanceand decision support. MATLAB and SIMULINKprogramming environments are utilized.BMEN E4450y Dental and craniofacial tissueengineering3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MSAE E3103, BMEN E4210, BMENE4501 or equivalent. Principles of dental and craniofacialbioengineering, periodontal tissue engineering:beyond guided tissue regeneration, craniofacialregeneration by stem cells and engineeredscaffolds, biomaterials: Engineering approachesin tissue regeneration, bone biology and development:instructive cues for tissue engineers.BMEN E4501x Tissue engineering, I:biomaterials and scaffold design3 pts. Lect: 3. Professor Hess.Prerequisites: BIOL C2005–C2006; BMENE4001–E4002. An introduction to the strategiesand fundamental bioengineering design criteriain the development of biomaterials and tissueengineered grafts. Material structural-functionalrelationships, biocompatibility in terms of materialand host responses. Through discussions,readings, and a group design project, studentsacquire an understanding of cell-material interactionsand identify the parameters critical in thedesign and selection of biomaterials for biomedicalapplications.BMEN E4502y Tissue engineering, II:biological tissue substitutes3 pts. Lect: 3. Professor Hung.Prerequisites: BIOL C2005–C2006, BMENE4001-E4002 An introduction to the strategiesand fundamental bioengineering design criteriabehind the development of cell-based tissuesubstitutes. Topics include biocompatibility,biological grafts, gene therapy-transfer, andbioreactors.BMEN E4540y Bioelectrochemistry3 pts. Lect: 3. Professor Pilla.Prerequisites: CHEM C3079 and CHEM C3443or equivalent Application of electrochemicalkinetics to interfacial processes occurring inbiomedical systems. Basics of electrochemistry,electrochemical instrumentation, and relevantcell and electrophysiology reviewed. Applicationsto interpretation of excitable and nonexcitablemembrane phenomena, with emphasis onheterogeneous mechanistic steps. Examples oftherapeutic devices created as a result of bioelectrochemicalstudies.BMEN E4550x Micro- and nanostructures incellular engineering3 pts. Lect: 3. Not offered in 2010-2011.Prerequisites: BIOL W2005 and BIOL W2006 orequivalent. Design, fabrication, and application ofmicro-/nanostructured systems for cell engineering.Recognition and response of cells to spatialaspects of their extracellular environment. Focuson neural, cardiac, coculture, and stem cell systems.Molecular complexes at the nanoscale.BMEN E4560y Dynamics of biologicalmembranes3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: BIOL C2005, BMEN E4001 orequivalent. The structure and dynamics of bio-SEAS 2010–2011

logical (cellular) membranes are discussed, withan emphasis on biophysical properties. Topicsinclude membrane composition, fluidity, lipidasymmetry, lipid-protein interactions, membraneturnover, membrane fusion, transport, lipid phasebehavior. In the second half of the semester,students will lead discussions of recent journalarticles.BMEN E4570x Science and engineering ofbody fluids3 pts. Lect: 3. Professor Matsuoka.Prerequisites: General chemistry, organic chemistry,and basic calculus. Body fluids as a dilutesolution of polyelectrolyte molecules in water.Study of physical behavior as affected by thepresence of ions in surrounding environments.The physics of covalent, ionic, and hydrogenbonds are reviewed, in relation to the structure/properties of the body fluid. Selected physiologicalprocesses are examined in physical-chemicalterms for polymers.BMEN E4590y BioMems: cellular andmolecular applications3 pts. Lect: 3. Professor Sia.Prerequisites: Chemistry CHEM C3443 orCHEN C3545 or equivalent and MATH V1201.Corequisites: BIOL W2005 or equivalent Topicsinclude biomicroelectromechanical, microfluidic,and lab-on-a-chip systems in biomedical engineering,with a focus on cellular and molecularapplications. Microfabrication techniques, biocompatibility,miniaturization of analytical anddiagnostic devices, high-throughput cellular studies,microfabrication for tissue engineering, andin vivo devices.BMEN E4601y Cellular electricity3 pts. Lect: 2. Lab: 1. Not offered in 2010–2011.Bioelectricity of the cell membrane. Basis of cellresting voltage, voltage changes that lead to theaction potential and electrical oscillations usedin sensing systems. Laboratory includes buildingelectronic circuits to measure capacitanceof artificial membranes and ion pumping in frogskin. Lab required.APBM E4650x Anatomy for physicists andengineers3 pts. Lect: 3. Instructor to be announced.Prerequisites: Engineering or physics background.A systemic approach to the study of thehuman body from a medical imaging point ofview: skeletal, respiratory, cardiovascular, digestive,and urinary systems, breast and women’sissues, head and neck, and central nervous system.Lectures are reinforced by examples fromclinical two- and three-dimensional and functionalimaging (CT, MRI, PET, SPECT, U/S, etc.).BMME E4702x Advanced musculoskeletalbiomechanics3 pts. Lect: 2.5. Lab: 0.5. Professor Guo.Advanced analysis and modeling of the musculoskeletalsystem. Topics include advancedconcepts of 3D segmental kinematics, musculoskeletaldynamics, experimental measurementsof joint kinematics and anatomy, modeling ofmuscles and locomotion, multibody joint modeling,introduction to musculoskeletal surgicalsimulations.BMEN E4737x Computer control of medicalinstrumentation3 pts. Lect: 2. Lab: 1. Not offered in 2010–2011.Prerequisite: Basic knowledge of the C programminglanguage. Acquisition and presentationof data for medical interpretation. Operatingprinciples of medical devices: technology ofmedical sensors, algorithms for signal analysis,computer interfacing and programming, interfacedesign. Laboratory assignments cover basicmeasurement technology, interfacing techniques,use of Labview software instrument interrogationand control, automated ECG analysis, ultrasonicmeasurements, image processing applied tox-ray images and CAT scans.BMEN E4738y Transduction and acquisitionof biomedical data3 pts. Lect: 2. Lab: 1. Not offered in 2010–2011.Data transduction and acquisition systems usedin biomedicine. Assembly of bio-transducersand the analog/digital circuitry for acquiringelectrocardiogram, electromyogram, and bloodpressure signals. Each small group will developand construct a working data acquisition board,which will be interfaced with a signal generatorto elucidate the dynamics of timing constraintsduring retrieval of bio-data. Lab Required.BMEN E4750y Sound and hearing3 pts. Lect: 3. Professor Olson.Prerequisites: PHYS C1401 and MATH V1105-MATH V1106. Introductory acoustics, basics ofwaves and discrete mechanical systems. Themechanics of hearing -- how sound is transmittedthrough the external and middle ear to the innerear, and the mechanical processing of soundwithin the inner ear.CBMF W4761y Computational genomics3 pts. Lect: 3. Professor Leslie.Prerequisites: Working knowledge of at least oneprogramming language, and some backgroundin probability and statistics. Computational techniquesfor analyzing and understanding genomicdata, including DNA, RNA, protein and geneexpression data. Basic concepts in molecularbiology relevant to these analyses. Emphasison techniques from artificial intelligence andmachine learning. String-matching algorithms,dynamic programming, hidden Markov models,expectation - maximization, neural networks,clustering algorithms, support vector machines.Students with life sciences backgrounds who satisfythe prerequisites are encouraged to enroll.BMCH E4810y Artificial organs3 pts. Lect: 3. Professor Leonard.Analysis and design of replacements for theheart, kidneys, and lungs. Specification and realizationof structures for artificial organ systems.BMEN E4894x Biomedical imaging3 pts. Lect: 3. Professor Hielscher.This course covers image formation, methods ofanalysis, and representation of digital images.Measures of qualitative performance in thecontext of clinical imaging. Algorithms fundamentalto the construction of medical imagesvia methods of computed tomography, magneticresonance, and ultrasound. Algorithms andmethods for the enhancement and quantificationof specific features of clinical importance in eachof these modalities.BMEN E4898y Biophotonics3 pts. Lect: 3. Professor Hielscher.Prerequisites: BMEN E4894 Biomedical imaging,PHYS C1403 Classical and quantum waves, orinstructor’s permission. This course providesa broad-based introduction into the field ofBiophotonics. Fundamental concepts of optical,thermal, and chemical aspects of the light-tissueinteractions will be presented. The applicationof these concepts for medical therapy and diagnosticswill be discussed. The course includestheoretical modeling of light-tissue interactionsas well as optical medical instrument design andmethods of clinical data interpretation.BMEN E6003x Computational modeling ofphysiological systems3 pts. Lect: 3. Professor Morrison.Prerequisites: BMEN E4001 and E4002 orequivalent, and APMA E4200 or equivalent.Advanced computational modeling and quantitativeanalysis of selected physiological systemsfrom molecules to organs. Selected systems areanalyzed in depth with an emphasis on modelingmethods and quantitative analysis. Topics mayinclude cell signaling, molecular transport, excitablemembranes, respiratory physiology, nervetransmission, circulatory control, auditory signalprocessing, muscle physiology, data collectionand analysis.EEBM E6020y Methods of computationalneuroscience4.5 pts. Lect: 3. Instructor to be announced.Prerequisites: BMEB W4011. Formal methods incomputational neuroscience including methodsof signal processing, communications theory,information theory, systems and control, systemidentification and machine learning. Molecularmodels of transduction pathways. Robust adaptationand integral feedback. Stimulus representationand groups. Stochastic and dynamicalsystems models of spike generation. Neuraldiversity and ensemble encoding. Time encodingmachines and neural codes. Stimulus recoverywith time decoding machines. MIMO models ofneural computation. Synaptic plasticity and learningalgorithms. Major project(s) in MATLAB.BMEE E6030y Neural modeling andneuroengineering3 pts. Lect: 3. Professor Sajda.Prerequisites: APMA E3101, ELEN E3801, andBMEB W4011, or equivalent, or instructor’spermission. Engineering perspective on the studyof multiple levels of brain organization, fromsingle neurons to cortical modules and systems.Mathematical models of spiking neurons, neural81SEAS 2010–2011

82dynamics, neural coding, and biologically-basedcomputational learning. Architectures and learningprinciples underlying both artificial and biologicalneural networks. Computational modelsof cortical processing, with an emphasis on thevisual system. Applications of principles in neuroengineering;neural prostheses, neuromorphicsystems and biomimetics. Course includes acomputer simulation laboratory. Lab required.EEBM E6090x or y-E6099 (Section 1)Topics in computational neuroscience andneuroengineering3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: Instructor’s permission. Selectedadvanced topics in computational neuroscienceand neuroengineering. Content varies from yearto year, and different topics rotate through thecourse numbers 6090-6099.BMEN E6301y Modeling of biological tissueswith finite elements3 pts. Lect: 3. Professor Guo.Prerequisites: MECE E6422, or ENME E6315,or equivalent. Structure-function relations andlinear/nonlinear constitutive models of biologicaltissues: anisotropic elasticity, viscoelasticity,porous media theories, mechano-electrochemicalmodels, infinitesimal and large deformations.Emphasis on the application and implementationof constitutive models for biological tissues intoexisting finite element software packages. Modelgeneration from biomedical images by extractionof tissue geometry, inhomogeneity and anisotropy.Element-by-element finite element solverfor large-scale image based models of trabecularbone. Implementation of tissue remodeling simulationsin finite element models.MEBM E6310x-E6311y Mixture theories forbiological tissues, I and II3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MECE E6422 and APMA E4200,or equivalent Development of governing equationsfor mixtures with solid matrix, interstitialfluid, and ion constituents. Formulation ofconstitutive models for biological tissues. Linearand nonlinear models of fibrillar and viscoelasticporous matrices. Solutions to special problems,such as confined and unconfined compression,permeation, indentation and contact, and swellingexperiments.BMEN E6400x Analysis and quantification ofmedical images3 pts. Lect: 3. Professor Laine.Novel methods of mathematical analysisapplied to problems in medical imaging. Designrequirements for screening protocols, treatmenttherapies, and surgical planning. Sensitivity andspecificity in screening mammography and chestradiographs, computer aided diagnosis systems,surgical planning in orthopaedics, quantitativeanalysis of cardiac performance, functionalmagnetic resonance imaging, positron emissiontomography, and echocardiography data.BMEN E6420y Advanced microscopy:fundamentals and applications3 pts. Lect: 3. Professor Hillman.Prerequisites: Physics C1401, C1402, C1403or C1601, C1602, C2601 or C2801, C2802,or equivalent (general Physics sequence).Fundamentals of techniques including confocal,two-photon, atomic force and electron microscopy.Application of methods to modern biomedicalimaging targets. Analysis and interpretationof microscopy data. Enrollment beyond the capmust be completed using an add/drop form inconsultation with class instructor.BMEN E6500x Tissue and molecularengineering laboratory4 pts. Lect: 4. Professor Jacobs.Prerequisites: Biology BIOL C2005 and BIOLC2006 or permission of instructor. Hands-onexperiments in molecular and cellular techniques,including fabrication of living engineered tissues.Covers sterile technique, culture of mammaliancells, microscopy, basic subcloning and gel electrophoresis,creation of cell-seeded scaffolds, andthe effects of mechanical loading on the metabolismof living cells or tissues. Theory, background,and practical demonstration for each techniquewill be presented. Lab required.EEBM E9070x or y Seminar in computationalneuroscience and neuroengineering3 pts. Lect: 3.Prerequisites: Open to doctoral candidates, andqualified M.S. candidates with the instructor’s permission.Study of recent developments in computationalneuroscience and neuroengineering.BMEN E9100x or y Masters research1–6 pts. Members of the faculty.Candidates for the M.S. degree may conductan investigation of some problem in biomedicalengineering culminating in a thesis describingthe results of their work. No more than 6 pointsin this course may be counted for graduatecredit, and this credit is contingent upon the submissionof an acceptable thesis.BMEN E9500x or y Doctoral research1–6 pts. Members of the faculty.Doctoral candidates are required to makean original investigation of a problem in biomedicalengineering, the results of which arepresented in the dissertation. No more than 12points of credit in this course may be grantedtoward the degree.BMEN E9700x or y Biomedical engineeringseminar0 pts. Sem: 1. Professor Kam.All matriculated graduate students are requiredto attend the seminar as long as they are in residence.No degree credit is granted. The seminaris the principal medium of communication amongthose with biomedical engineering interestswithin the University. Guest speakers from otherinstitutions, Columbia faculty, and studentswithin the Department who are advanced in theirstudies frequently offer sessions. Fri., 11:00a.m.–12:15 p.m., 614 Schermerhorn HallBMEN E9800x or y Doctoral researchinstruction3–12 pts. Members of the faculty.A candidate for the Eng.Sc.D. degree in biomedicalengineering must register for 12 points ofdoctoral research instruction. Registration maynot be used to satisfy the minimum residencerequirement for the degree.BMEN E9900x or y Doctoral dissertation0 pts. Members of the faculty.A candidate for the doctorate in biomedicalengineering or applied biology may be requiredto register for this course in every term after thestudent’s course work has been completed anduntil the dissertation has been accepted.SEAS 2010–2011

CHEMICAL ENGINEERING801 S. W. Mudd, MC 4721, 212-854-4453www.cheme.columbia.edu83CHAIRSanat K. KumarDEPARTMENTALADMINISTRATORTeresa ColaizzoPROFESSORSChristopher J. DurningGeorge W. Flynn(Chemistry)Carl C. GryteJingyue JuJeffrey T. KobersteinSanat K. KumarEdward F. LeonardBen O’ShaughnessyNicholas J. Turro(Chemistry)Alan C. WestASSOCIATE PROFESSORScott A. BantaASSISTANT PROFESSORV. Faye McNeillADJUNCT PROFESSORSStanley LeshawRobert I. PearlmanADJUNCT ASSOCIATEPROFESSORSAghavni Bedrossian-OmerMichael I. HillLynn H. LanderADJUNCT ASSISTANTPROFESSORSLouis MattasJack McGourtyChemical engineering is a highlyinterdisciplinary field concernedwith materials and processes atthe heart of a broad range of technologies.Practicing chemical engineers arethe experts in charge of the developmentand production of diverse productsin traditional chemical industries aswell as many emerging new technologies.The chemical engineer guides thepassage of the product from the laboratoryto the marketplace, from ideasandprototypes to functioning articles andprocesses, from theory to reality.This requires a remarkable depth andbreadth of understanding of physicaland chemical aspects of materials andtheir production.The expertise of chemical engineersis essential to production, marketing,and application in such areas as pharmaceuticals,high-performance materialsin the aerospace and automotive industries,biotechnologies, semiconductorsin the electronics industry, paints andplastics, petroleum refining, syntheticfibers, artificial organs, biocompatibleimplants and prosthetics and numerousothers. Increasingly, chemical engineersare involved in new technologiesemploying highly novel materials whoseunusual response at the molecular levelendows them with unique properties.Examples include environmental technologies,emerging biotechnologies ofmajor medical importance employingDNA- or protein-based chemical sensors,controlled-release drugs, new agriculturalproducts, and many others.Driven by this diversity of applications,chemical engineering is perhapsthe broadest of all engineering disciplines:chemistry, physics, mathematics,biology, and computing are all deeplyinvolved. The research of the facultyof Columbia’s Chemical EngineeringDepartment is correspondingly broad.Some of the areas under active investigationare the fundamental physics,chemistry, and engineering of polymersand other soft materials; theelectrochemistry of fuel cells and otherinterfacial engineering phenomena; thebioengineering of artificial organs andimmune cell activation; the engineeringand biochemistry of sequencingthe human genome; the chemistry andphysics of surface-polymer interactions;the biophysics of cellular processesin living organisms; the physics of thinpolymer films; the chemistry of smartpolymer materials with environmentsensitivesurfaces; biosensors withtissue engineering applications; thephysics and chemistry of DNA-DNAhybridization and melting; the chemistryand physics of DNA microarrays withapplications in gene expression anddrug discovery; the physics and chemistryof nanoparticle- polymer compositeswith novel electronic and photonic properties.Many experimental techniquesare employed, from neutron scatteringto fluorescence microscopy, and thetheoretical work involves both analyticalmathematical physics and numericalcomputational analysis.Students enrolling in the Ph.D.program will have the opportunity toconduct research in these and otherareas. Students with degrees in chemicalengineering and other engineeringdisciplines, in chemistry, in physics,in biochemistry, and in other relateddisciplines are all natural participants inthe Ph.D. program and are encouragedto apply. The Department of ChemicalSEAS 2010–2011

84Engineering at Columbia is committedto a leadership role in research and educationin frontier areas of research andtechnology where progress derives fromthe conjunction of many different traditionalresearch disciplines. Increasingly,new technologies and fundamentalresearch questions demand this type ofinterdisciplinary approach.The undergraduate program providesa chemical engineering degreethat is a passport to many careers indirectly related industries as diverse asbiochemical engineering, environmentalmanagement, and pharmaceuticals. Thedegree is also used by many studentsas a springboard from which to launchcareers in medicine, law, management,banking and finance, politics, and so on.For those interested in the fundamentals,a career of research and teachingis a natural continuation of their undergraduatestudies. Whichever path thestudent may choose after graduation,the program offers a deep understandingof the physical and chemical natureof things and provides an insight into anexploding variety of new technologiesthat are rapidly reshaping the societywe live in.Current Research ActivitiesScience and Engineering of Polymersand Soft Materials. Theoretical andexperimental studies of novel or importantmacromolecules and their applications,especially surface-active species:ultrasonic sensor, scanning probemicroscopy and reflectivity studies ofadsorption and self-assembly of highlybranched “dendrimers” at the solidliquidinterface, with the aim of creatingnovel surface coatings; fluorescencetracer studies of molecular level mobilityin ultrathin polymer films with the aimof improving resolution in lithography;reflectivity studies and computer simulationof flexible polymer adsorption andthe response of adsorbed polymerlayers to imposed flows with the aimof improving polymer processing operations;optical microscopy studies andnumerical simulation of microporouspolymer membrane formation with theaim of improving ultrafiltration membranetechnology; synthesis and structuralcharacterization of bio-active polymersurfaces in order to realize new in-vivodevices; contact angle, x-ray photoelectronspectroscopy, and reflectivityanalysis, and lattice model simulation, ofresponsive polymer surfaces based onunique polymeric “surfactants” in orderto develop “smart” surface-active materials;preparation and IR/fluorescencecharacterization of DNA-decorated surfacesfor “recognition” of DNA in solutionin order to further medical diagnostictechnologies; preparation and characterizationvia TEM, AFM, and reflectivityof nanoparticle-block copolymer compositeswith the aim of very high densitymagnetic storage media; self-consistentfield theory of nanoparticle-block copolymercomposites; computer simulationand theory of unique “living” polymerizationprocesses important to syntheticpolymer production and biological systems;theory and simulation of irreversiblepolymer adsorption.Genomics Engineering. Researchand development of novel bioanalyticalreagents, systems, and processes usingchemical science, engineering principles,and experimental biological approachesto study problems in genomics areactively pursued in the Department ofChemical Engineering in collaborationwith the Columbia Genome Center:high-throughput DNA sequencing; novelgene chip development and fundamentalunderstanding of the processes involved;applying the cutting-edge genomic technologiesto study fundamental biologyand for disease gene discovery.Biophysics and Soft Matter Physics.Theoretical and experimental biophysicsof biological soft matter: actin filamentgrowth kinetics and its role in living cellmotility; DNA hybridization, melting andunzipping; DNA microarrays in biotechnology;model gene circuits; DNAmobility in 2D microfluidics. Physics ofsynthetic soft matter: nanoparticles inmesostructured polymer phases andphase transitions; universal scalinglaws in reacting polymer systems andpolymerization phenomena; polymerinterfaceadsorption phenomena;polymer interfacial reactions; diffusionof particles in thin polymer films; interactionsof charged polymer minigels withinterfaces.Bioinductive and BiomimeticMaterials. The thrust of this researchis to develop new strategies for themolecular design of polymeric and softmaterials for biological and biomedicalapplications. Ongoing research pertainsto the development of bioactive hydrogelcoatings for applications in glucose sensors.The objective of the coatings is tocontrol the tissue-sensor interactionsby incorporating cell-signaling motifsinto the hydrogel in such a manner thatthe hydrogel induces the formation ofnew vascular tissue within the surfacecoating. In this fashion, the biosensorcan continue to operate in vivo, even ifthere is an immune response leading tofibrous encapsulation. Complementaryresearch programs are aimed at developingmethods for patterning biologicalsurfaces in order to prepare new biocompatiblesurfaces as well as to fabricateantigen/antibody and protein arraysfor diagnostic applications.Interfacial Engineering andElectrochemistry. Research effortswithin the department are focused onmass transfer and reaction mechanismsin electrochemical systems, and theeffects that such variables have on processdesign and materials properties.Applications of the research programinclude fuel cells, electrodeposition, andcorrosion. Both electrochemical andmicroscopy methods are used extensivelyfor characterization. A significantnumerical simulation component of theresearch programs also exists.Facilities for Teaching andResearchThe Department of Chemical Engineeringis continually striving to provide accessto state-of-the-art research instrumentationand computational facilities for itsundergraduate and graduate students,postdoctoral associates, and faculty.Departmental equipment is considered tobe in most cases shared, which meansthat equipment access is usually open toall qualified individuals with a need to useparticular instrumentation.The most extensive collection ofinstrumentation in the department isassociated with the polymer and softmatter research faculty. Faculty bandedtogether to create a unique shared-facilitieslaboratory, completed at the end of2001. The shared facilities include a fullySEAS 2010–2011

equipped polymer synthesis lab withfour fumes hoods, a 10’x16’ soft wallclean room, metal evaporator system, aMilligen 9050 peptide synthesizer, andpolymer thin film preparation and substratecleaning stations. Also installedare new, computer-controlled thermalanalysis, rheometric, and light-scatteringsetups. Specialized instrumentation forsurface analysis includes an optical/lasersystem dedicated to characterizationof polymer surface dynamics by FluorescenceRecovery after Photobleachingand a PHI 5500 X-ray photoelectronspectrophotometer with monochromatorthat is capable of angle-dependentdepth profiling and XPS imaging. Thesystem can also perform SIMS and ionscattering experiments. A digital imageanalysis system for the characterizationof sessile and pendant drop shapes isalso available for the purpose of polymersurface and interfacial tension measurementsas well as contact angle analysis.An X-ray reflectometer that can performX-ray standing wave–induced fluorescencemeasurements is also housed inthe new shared equipment laboratory,along with instrumentation for characterizingthe friction and wear propertiesof polymeric surfaces. The laboratoryalso houses an infrared spectrometer(Nicolet Magna 560, MCT detector)with a variable angle grazing incidence,temperature-controlled attenuatedtotal-reflectance,transmission, andliquid cell accessories. These facilitiesare suitable for mid-IR, spectroscopicinvestigations of bulk materials as wellas thin films. The laboratory also hasa UV-Vis spectrometer (a Cary 50), anSLM Aminco 8000 spectrofluorimeter,and a high-purity water system (MilliporeBiocel) used for preparation of biologicalbuffers and solutions. Facilities areavailable for cell tissue culture and forexperiments involving biocompatibilizationof materials or cellular engineering.In addition, gel electrophoresisapparatus is available for the molecularweight characterization of nucleic acids.A total-internal-reflection-fluorescence(TIRF) instrument with an automated,temperature-controlled flow cell hasbeen built for dedicated investigations ofsurface processes involving fluorescentlytagged biological and synthetic molecules.The instrument can operate atdifferent excitation wavelengths (typicallyHeNe laser, 633 nm, using Cy5 labelednucleic acids). Fluorescence is collectedby a highly sensitive photomultiplier tubeand logged to a personal computer.Because fluorescence is only excitedin the evanescent wave region near aninterface, signals from surface-boundfluorescent species can be determinedwith minimal background interferencefrom fluorophores in bulk solution.Chemistry Department. Access toNMR and mass spectrometry facilities ispossible through interactions with facultymembers who also hold appointmentsin the Chemistry Department. The NMRfacility consists of a 500 MHz, a 400MHz, and two 300 MHz instrumentsthat are operated by students andpostdocs after training. The mass spectrometryfacility is run by students forroutine samples and by a professionalmass spectrometrist for more difficultsamples. The Chemistry Departmentalso provides access to the services of aglass blower and machine shop and tophotochemical and spectroscopic facilities.These facilities consist of (1) twonanosecond laser flash photolysis instrumentsequipped with UV-VIS, infrared,EPR, and NMR detection; (2) three EPRspectrometers; (3) two fluorescencespectrometers; (4) a single photon counterfor analysis of the lifetimes and polarizationof fluorescence and phosphorescence;and (5) a high-performanceliquid chromatographic instrument foranalysis of polymer molecular weightand dispersity.Columbia Genome Center. Because ofits affiliation with the Columbia GenomeCenter (CGC), the Department ofChemical Engineering also has accessto more than 3,000 sq. ft. of spaceequipped with a high-throughput DNAsequencer (Amersham PharmaciaBiotech Mega-Bace1000), a nucleicacid synthesizer (PE Biosystems 8909Expedite Nucleic Acid/Peptide SynthesisSystem), an UV/VIS spectrophotometer(Perkin-Elmer Lambda 40), a fluorescencespectrophotometer (Jobin Yvon,Inc. Fluorolog-3), Waters HPLC, and asequencing gel electrophoresis apparatus(Life Technologies Model S2), as wellas the facilities required for state-of-theartsynthetic chemistry. The division ofDNA sequencing and chemical biologyat the Columbia Genome Center consistsof 6,000 sq. ft. of laboratory spaceand equipment necessary for carryingout the state-of-the-art DNA analysis.The laboratory has one AmershamPharmacia Biotech MegaBace1000sequencer, three ABI 377 sequencerswith complete 96 land upgrades,a Qiagen 9600 Biorobot, a Hydra 96microdispenser robot, and standardmolecular biology equipment.NSF-Columbia MRSEC SharedFacilities. Through their participation inan NSF-MRSEC grant, faculty also haveaccess to shared facilities located in theSchapiro Center for Engineering andPhysical Science Research at ColumbiaUniversity. The shared facilities include aScintag X2 X-ray diffractometer alignedfor low-angle reflectivity work, and aBeaglehole Instruments Picometermodulated ellipsometer. As needed,these capabilities are available for characterizationof the surface coverageand composition of modified surfacesand thin organic films. Access to atomicforce microscopy, scanning and transmissionelectron microscopy, and scanningtunneling microscopy is possiblethrough collaborations within the NSF-MRSEC program and with colleaguesin the Chemistry and Materials ScienceDepartments. The NSF-ColumbiaMRSEC facility is located within fiveminutes’ walking distance from theChemical Engineering Department.UNDERGRADUATE PROGRAMChemical EngineeringThe undergraduate program in chemicalengineering at Columbia, recentlyrevised, has five formal educationalobjectives:1. Prepare students for careers inindustries that require technicalexpertise in chemical engineering.2. Prepare students to assume leadershippositions in industries thatrequire technical expertise in chemicalengineering.3. Enable students to pursue graduatelevelstudies in chemical engineeringand related technical or scientificfields (e.g., biomedical or environmen-85SEAS 2010–2011

86tal engineering, materials science).4. Provide a strong foundation for studentsto pursue alternative careerpaths, especially careers in business,management, finance, law, medicine,or education.5. Establish in students a commitmentto life-long learning and servicewithin their chosen profession andsociety.The expertise of chemical engineersis essential to production, marketing,and application in such areas aspharmaceuticals, high performancematerials as in the automotive andaerospace industries, semiconductorsin the electronics industry, paints andplastics, consumer products such asfood and cosmetics, petroleum refining,industrial chemicals, synthetic fibers,and just about every bioengineering andbiotechnology area from artificial organsto biosensors. Increasingly, chemicalengineers are involved in exciting newtechnologies employing highly novelmaterials, whose unusual response atthe molecular level endows them withunique properties. Examples includecontrolled release drugs, materials withdesigned interaction with in vivo environments,“nanomaterials” for electronicand optical applications, agriculturalproducts, and a host of others. Thisrequires a depth and breadth of understandingof physical and chemicalaspects of materials and their productionthat is without parallel.The chemical engineering degreealso serves as a passport to excitingcareers in directly related industriesas diverse as biochemical engineering,environmental management, andpharmaceuticals. Because the deepand broad-ranging nature of the degreehas earned it a high reputation acrosssociety, the chemical engineering degreeis also a natural platform from which tolaunch careers in medicine, law, management,banking and finance, politics,and so on. Many students choose itfor this purpose, to have a firm andrespected basis for a range of possiblefuture careers. For those interested inthe fundamentals, a career of researchand teaching is a natural continuation ofundergraduate studies.The first and sophomore years ofstudy introduce general principles ofscience and engineering and include abroad range of subjects in the humanitiesand social sciences. Although theprogram for all engineering students inthese first two years is to some extentsimilar, there are important differences.The Professional Engineering Elective,usually taken in Semester II, is designedto provide an overview of an engineeringdiscipline. Those wishing to learn aboutchemical engineering are encouragedto take CHEN E1040: Molecular engineeringand product design, taught bythe Chemical Engineering Department.Students who major in chemical engineeringare not currently required totake computer science or programming,and should in their sophomore year takeCHEN E3100: Material and energy balances(see table on page 88).In the junior-senior sequence onespecializes in the chemical engineeringmajor. The table on page 89 spells outthe core course requirements, which aresplit between courses emphasizing engineeringscience and those emphasizingpractical and/or professional aspects ofthe discipline. Throughout, skills requiredof practicing engineers are developed(e.g., writing and presentation skills,competency with computers).The table also shows that a significantfraction of the junior-senior programis reserved for electives, both technicaland nontechnical. Nontechnical electivesare courses that are not quantitative,such as those taught in the humanitiesand social sciences. These provide anopportunity to pursue interests in areasother than engineering. A crucial part ofthe junior-senior program is the 12-pointtechnical elective requirement. Technicalelectives are science and/or technologybased and feature quantitative analysis.Generally, technical electives must be3000 level or above but there are a fewexceptions: PHYS C1403, PHYS C2601,BIOL C2005, BIOL C2006, and BIOLW2501. The technical electives are subjectto the following constraints: One technical elective must be withinSEAS but taken outside of chemicalengineering (that is, a course with adesignator other than BMCH, CHEN,CHEE, or CHAP). One technical elective must be withinchemical engineering (i.e., with thedesignator BMCH, CHEN, CHEE, orCHAP). The technical electives must include 6points of “advanced natural science”course work, including chemistry,physics, biology, and certain engineeringcourses. Qualifying engineeringcourses are determined by ChemicalEngineering Department advisers.The junior-senior technical electivesprovide the opportunity to explorenew interesting areas beyond the corerequirements of the degree. Often,students satisfy the technical electivesby taking courses from another SEASdepartment in order to obtain a minorfrom that department. Alternately, youmay wish to take courses in several newareas, or perhaps to explore familiarsubjects in greater depth, or you maywish to gain experience in actual laboratoryresearch. Three points of CHENE3900: Undergraduate research projectmay be counted toward the technicalelective content.The program details discussedabove apply to undergraduates whoare enrolled at Columbia as freshmenand declare the chemical engineeringmajor in the sophomore year. However,the chemical engineering program isdesigned to be readily accessible to participantsin any of Columbia’s CombinedPlans and to transfer students. In suchcases, the guidance of one of thedepartmental advisers in planning yourprogram is required (contact informationfor the departmental UG advisersis listed on the department’s Web site:www.cheme.columbia.edu).Columbia’s program in chemicalengineering leading to the B.S. degreeis fully accredited by the EngineeringAccreditation Commission of theAccreditation Board for Engineering andTechnology (ABET).Requirements for a Minor inChemical EngineeringSee page 195.Requirements for a Minor inBiomedical EngineeringStudents majoring in chemical engineeringwho wish to include in their recordsa minor in biomedical engineeringSEAS 2010–2011

may do so by taking BMEN E4001 orE4002; BIOL C2005; BMEN E4501 andE4502; and any one of several chemicalengineering courses approved by theBME Department. See also, Minor inBiomedical Engineering, page 195.GRADUATE PROGRAMSThe graduate program in chemicalengineering, with its large proportionof elective courses and independentresearch, offers experience in any of thefields of departmental activity mentionedin previous sections. For both chemicalengineers and those with undergraduateeducations in other related fields suchas physics, chemistry, and biochemistry,the Ph.D. program provides the opportunityto become expert in researchfields central to modern technology andscience.M.S. DegreeThe requirements are (1) the corecourses: Chemical process analysis(CHEN E4010), Transport phenomena,III (CHEN E4110), and Statisticalmechanics (CHAP E4120); and (2) 21points of 4000- or 6000-level courses,approved by the graduate coordinatoror research adviser, of which up to 6may be Master’s research (CHEN 9400).Students with undergraduate preparationin physics, chemistry, biochemistry,pharmacy, and related fields may takeadvantage of a special two-year programleading directly to the master’sdegree in chemical engineering. Thisprogram enables such students to avoidhaving to take all undergraduate coursesin the bachelor’s degree program.Doctoral DegreesThe Ph.D. and D.E.S. degrees haveessentially the same requirements. Allstudents in a doctoral program must(1) earn satisfactory grades in the threecore courses (CHEN E4010, CHENE4110, CHAP E4120); (2) pass aqualifying exam; (3) defend a proposal ofresearch within twelve months of passingthe qualifying exam; (4) defend theirthesis; and (5) satisfy course requirementsbeyond the three core courses.For detailed requirements, please consultthe departmental office or graduatecoordinator. Students with degrees inrelated fields such as physics, chemistry,biochemistry, and others are encouragedto apply to this highly interdisciplinaryprogram.Areas of ConcentrationAfter satisfying the core requirementof Chemical process analysis (CHENE4010), Transport phenomena, III(CHEN E4110), and Statistical mechanics(CHAP E4120), chemical engineeringgraduate students are free to choosetheir remaining required courses asthey desire, subject to their researchadviser’s approval. However, a numberof areas of graduate concentration aresuggested below, with associated recommendedcourses. Each concentrationprovides students with the opportunityto gain in-depth knowledge about aparticular research field of central importanceto the department. Graduate studentsoutside the department are verywelcome to participate in these courseconcentrations, many of which arehighly interdisciplinary. The departmentstrongly encourages interdepartmentaldialogue at all levels.Science and Engineering of Polymersand Soft Materials. Soft materialsinclude diverse organic media withsupramolecular structure having scalesin the range 1–100 nm. Their smallscalestructure imparts unique, usefulmacroscopic properties. Examplesinclude polymers, liquid crystals, colloids,and emulsions. Their “softness”refers to the fact that they typically flowor distort easily in response to moderateshear and other external forces.They exhibit a great many unique anduseful macroscopic properties stemmingfrom the variety of fascinatingmicroscopic structures, from the simpleorientational order of a nematic liquidcrystal to the full periodic “crystalline”order of block copolymer mesophases.Soft materials provide ideal testinggrounds for such fundamental conceptsas the interplay between order anddynamics or topological defects. Theyare of primary importance to the paint,food, petroleum, and other industriesas well as a variety of advanced materialsand devices. In addition, mostbiological materials are soft, so thatunderstanding of soft materials is veryrelevant to improving our understandingof cellular function and therefore humanpathologies. At Columbia ChemicalEngineering, we focus on severalunique aspects of soft matter, suchas their special surface and interfacialproperties. This concentration is similarin thrust to that of the “Biophysics andSoft Matter” concentration, except herethere is greater emphasis on syntheticrather than biological soft matter, withparticular emphasis on interfacial propertiesand materials with importantrelated applications. Synthetic polymersare by far the most important materialin this class.CHEE E4252: Introduction to surface and colloidchemistryCHEN E4620: Introduction to polymersCHEN E4640: Polymer surfaces and interfacesCHEN E6620y: Physical chemistry of macromoleculesCHEN E6910: Theoretical methods in polymerphysicsCHEN E6920: Physics of soft matterBiophysics and Soft Matter Physics.Soft matter denotes polymers, gels, selfassembledsurfactant structures, colloidalsuspensions, and many other complexfluids. These are strongly fluctuating, floppy,fluid-like materials that can nonethelessexhibit diverse phases with remarkablelong-range order. In the last fewdecades, statistical physics has achieveda sound understanding of the scaling anduniversality characterizing large lengthscale properties of much synthetic softcondensed matter. More recently, ideasand techniques from soft condensedmatter physics have been applied tobiological soft matter such as DNA,RNA, proteins, cell membrane surfactantassemblies, actin and tubulin structures,and many others. The aim is to shed lighton (1) fundamental cellular processessuch as gene expression or the functionof cellular motors and (2) physicalmechanisms central to the exploding fieldof biotechnology involving systems suchas DNA microarrays and methods suchas genetic engineering. The practitionersin this highly interdisciplinary field includephysicists, chemical engineers, biologists,biochemists, and chemists.The “Biophysics and Soft Matter”concentration is closely related to the“Science and Engineering of Polymersand Soft Materials” concentration, buthere greater emphasis is placed on biologicalmaterials and cellular biophysics.87SEAS 2010–2011

88CHEMICAL ENGINEERING: FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and one of the following:MATH E1210 (3)Ord. diff. equationsorAPMA E2101 (3)Intro. to appl. math.PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)Lab C1493 (3)Lab W3081 (2)CHEMISTRY(three tracks,choose one)C1403 (3.5) andLab C1500 (3)C1604 (3.5)C3045 (3.5)C1404 (3.5)C2507 (3)C3046 (3.5) andLab C2507 (3)C3443 (3.5)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDELECTIVESNONTECHTECHProfessional engineeringelective (3) 1One core humanitieselective (3–4 points) 2Three core humanitieselectives (11 points) 2CHEM. ENG.REQUIREMENTCHEN E3100 (4) 3Material and energybalancesCOMPUTERSCIENCEPHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semesterTOTAL POINTS 4 16.5 16.5 17.5 171Students are encouraged to take CHEN 1040: Molecular engineering and product design.2Four core humanities electives should be taken as follows: In Semester III, HUMA C1001, C1101 (4), or any initial course in one of the Global Core sequencesoffered by the College (3–4); in Semester IV, HUMA C1002, C1102 (4), or the second course in the Global Core sequence elected in Semester III (3–4); also inSemester IV, ECON W1105 (4) with W1105 recitation (0) and either HUMA C1121 or C1123 (3).3Should be taken in Semester III, but may be moved upon adviser’s approval to Semester V if CHEM C3543: Organic chemistry lab is taken in Semester III.4Taking the first track in each row and E1102 in Semester II.Both theory and experiment are cateredto. Students will be introduced to statisticalmechanics and its application to softmatter research and to cellular biophysics.In parallel, the student will learn aboutgenomics and cellular biology to developan understanding of what the central andfascinating biological issues are.CHAP E4120: Statistical mechanicsCHEN E6920: Physics of soft matterBIOC G6300: Biochemistry/molecular biology—eukaryotes, IBIOC G6301: Biochemistry/molecular biology—eukaryotes, IICHEN E4750: The genome and the cellCMBS G4350: Cellular molecular biophysicsGenomic Engineering. Genomicengineering may be defined as theSEAS 2010–2011

CHEMICAL ENGINEERING: THIRD AND FOURTH YEARS89SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIREQUIREDCOURSESCHEN E3110 (4)Transp. phenomena, ICHEE E3010 (4)Principles of chem.eng. thermodynamicsCHEN E3120 (4)Transp. phenomena, IICHEN E3210 (4)Chem. eng.thermodynamicsCHEN E4230 (3)Reaction kinetics andreactor designCHEN E4500 (4)Process and productdesign ICHEN E4140 (3)Chem. and biochem.separationsCHEN E4300 (2)Chem. eng. controlCHEN E4510 (4)Process and productdesign IICHEN E4320 (4)Molecular phenomenonin chem. eng.REQUIRED LABSCHEN C3543 (3) 1Org. chem. labCHEN 3810 (3)Chem. eng. labREQUIREDELECTIVESNONTECH 3 points 3 points 3 pointsTECH 2 3 points 3 points 3 points 3 pointsTOTAL POINTS(normal track)17 17 15 141May be taken in Semester III with adviser’s permission if CHEN E3100: Material and energy balances is taken in Semester V.2The total of 12 points of required technical electives must include one chemical engineering course, one engineering course outside of chemical engineering, and 6points of “advanced natural science” courses (i.e., chemistry, physics, biology, materials science, and certain chemical engineering courses—contact a departmentaladviser for details).development and application of noveltechnologies for identifying and evaluatingthe significance of both selected andall nucleotide sequences in the genomesof organisms. An interdisciplinary courseconcentration in genomic engineering isavailable to graduate students, and toselected undergraduate students. TheNational Science Foundation is sponsoringthe development of this concentration,which is believed to be the first ofits kind. Courses in the concentrationequip students in engineering and computerscience to help solve technicalproblems encountered in the discovery,assembly, organization, and applicationof genomic information. The coursesimpart an understanding of the fundamentalgoals and problems of genomicscience and gene-related intracellularprocesses; elucidate the physical, chemical,and instrumental principles availableto extract sequence information from thegenome; and teach the concepts usedto organize, manipulate, and interrogatethe genomic database.The concentration consists of fivecourses that address the principal areasof genomic technology: sequencingand other means of acquiring genomicinformation; bioinformatics as a meansof assembling and providing structuredaccess to genomic information; andmethods of elucidating how genomicinformation interacts with the developmentalstate and environment of cellsin order to determine their behavior.Professor E. F. Leonard directs theprogram and teaches CHEN E4750.The other instructors are Profs. D.Anastassiou (ECBM E4060), Jingyue Ju(CHEN E4700, CHEN E4730), and C.Leslie (CBMF W4761). The departmentsof Chemical, Biomedical, and ElectricalEngineering and of Computer Sciencecredit these courses toward requirementsfor their doctorates. Studentsmay take individual courses so long asthey satisfy prerequisite requirementsor have the instructor’s permission.All lecture courses in the program areavailable through the Columbia VideoNetwork, which offers a certificate forthose students completing a prescribedset of the courses.The course Introduction to genomicinformation science and technology(ECBM E4060) provides the essentialconcepts of the information systemparadigm of molecular biology andgenetics. Principles of genomic technology(CHEN E4700) provides studentswith a solid basis for understanding boththe principles that underlie genomictechnologies and how these principlesare applied. The Genomics sequencinglaboratory (CHEN E4760) provideshands-on experience in high-throughputDNA sequencing, as conducted in abioscience research laboratory. Thegenome and the cell (CHEN E4750)conveys a broad but precise, organized,and quantitative overview of the celland its genome: how the genome, inpartnership with extragenomic stimuli,influences the behavior of the cell andhow mechanisms within the cell enablegenomic regulation. Computationalgenomics (CBMF W4761) introducesstudents to basic and advanced computationaltechniques for analyzinggenomic data.Interested parties can obtain furtherinformation, including a list of cognateSEAS 2010–2011

90courses that are available and recommended,from Professor Leonard(leonard@columbia.edu).Interfacial Engineering andElectrochemistry. Electrochemicalprocesses are key to many alternativeenergy systems (batteries and fuelcells), to electrical and magnetic-devicemanufacturing (interconnects and magnetic-storage media), and to advancedmaterials processing. Electrochemicalprocesses are also involved in corrosionand in some waste-treatmentsystems. Key employers of engineersand scientists with knowledge of electrochemical/interfacial engineeringinclude companies from the computer,automotive, and chemical industries.Knowledge of basic electrochemicalprinciples, environmental sciences, and/or materials science can be useful to acareer in this area.CHEN E4201: Engineering applications of electrochemistryCHEN E4252: Introduction to surface and colloidscienceCHEN E6050: Advanced electrochemistryCHEN E3900: Undergraduate research projectBioinductive and BiomimeticMaterials. This is a rapidly emergingarea of research, and the department’scourse concentration is under development.At present, students interested inthis area are recommended to attendPolymer surfaces and interfaces (CHENE4640); and Physical chemistry ofmacromolecules (CHEN E6620). Othercourses in the “Science and Engineeringof Polymers and Soft Materials” concentrationare also relevant. Whencomplete, the concentration will includecourses directly addressing biomaterialsand immunological response.COURSES IN CHEMICALENGINEERINGSee also section for BiomedicalEngineering. Note: Check the departmentWeb site for the most currentcourse offerings and descriptions.CHEN E1040y Molecular engineering andproduct design3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: None. An introductory courseintended to expose students to ChemicalEngineering. Examines the ways in whichchemical and biological sciences are interpretedthrough analytical, design, and engineeringframeworks to generate products that enhancehuman endeavor. Students are introduced tothe culture of chemical engineering and thewide variety of chemical engineering practices,through lectures by department faculty and practicingchemical engineers, trips to industrial facilities,reverse-engineering of chemical products,and a chemical design competition.CHEE E3010x Principles of chemicalengineering thermodynamics4 pts. Lect: 4. Professor Castaldi.Prerequisites: CHEM C1403 Introduction tothermodynamics. Fundamentals are emphasized:the laws of thermodynamics are derivedand their meaning explained and elucidatedby applications to engineering problems. Puresystems are treated, followed by an introductionto mixtures and phase equilibrium. Recitationsection required.CHEN E3100x Material and energy balances4 pts. Lect: 4. Professor McNeill.Prerequisites: First-year Chemistry and Physicsor equivalents. This course serves as an introductionto concepts used in the analysis ofchemical engineering problems. Rigorous analysisof material and energy balances on open andclosed systems is emphasized. An introductionto important processes in the chemical and biochemicalindustries is provided.CHEN E3110x Transport phenomena, I4 pts. Lect: 4. Professor Hill.Prerequisites: Classical mechanics, vector calculus,ordinary differential equations. Focuseson the momentum and energy transport in pure(1-component) Newtonian fluids, i.e., elementaryfluid mechanics, elementary conduction-dominatedheat transfer, and forced convection heat transferin fluids. This is an introductory level course. Itincludes a review of the mathematical methodsneeded (vector calculus and ordinary differentialequations). Applications to problems important inmodern chemical engineering are used to illustrateconcepts. Recitation section required.CHEN E3120y Transport phenomena, II4 pts. Lect: 4. Professor Durning.Prerequisites: CHEN E3110. Focuses onthe mass transport in isothermal mixtures ofNewtonian fluids, i.e., elementary diffusion-dominatedmass transfer, and forced convection masstransfer in fluid mixtures. The course followson the previous transport course (CHEN 3110Transport I). It includes instruction in new mathematicalmethods needed (introductory partialdifferential equations). Applications to problemsimportant in modern chemical engineering areused to illustrate concepts.CHEN E3210y Chemical engineeringthermodynamics4 pts. Lect: 3. Professors Kumar and Ortiz.Prerequisites: CHEN E3010 and CHEN E3100.This course deals with fundamental and appliedthermodynamic principles that form the basis ofchemical engineering practice. Topics includephase equilibria, methods to treat ideal andnon-ideal mixtures, and estimation of propertiesusing computer-based methods. Recitation sectionrequired.BMCH E3500y Transport in biologicalsystems3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CHEM C3443 and MATH E1210.Corequisites: BIOL C2005. Convective and diffusivemovement and reaction of molecules inbiological systems. Kinetics of homogeneous andheterogeneous reactions in biological environments.Mechanisms arid models of transportacross membranes. Convective diffusion withand without chemical reaction. Diffusion inrestricted spaces. Irreversible thermodynamicapproaches to transport and reaction in biologicalsystems.CHEN E3810y Chemical engineeringlaboratory3 pts. Lab: 3. Professor Banta.Prerequisites: Completion of core chemicalengineering curricula through the fall semesterof senior year (includes: CHEN E3110, E3120,E4230, E3100, E3010, E3210, E4140, E4500), orinstructor’s permission. The course emphasizesactive, experiment-based resolution of open-endedproblems involving use, design, and optimizationof equipment, products, or materials. Underfaculty guidance students formulate, carry out,validate, and refine experimental procedures,and present results in oral and written form. Thecourse develops analytical, communications, andcooperative problem-solving skills in the contextof problems that span from traditional, largescale separations and processing operations tomolecular level design of materials or products.Sample projects include: scale up of apparatus,process control, chemical separations, microfluidics,surface engineering, molecular sensing,and alternative energy sources. Safety awarenessis integrated throughout the course.CHEN E3900x and y Undergraduate researchproject1–6 pts. Members of the faculty.Candidates for the B.S. degree may conductan investigation of some problem in chemicalengineering or applied chemistry or carry outa special project under the supervision of thestaff. Credit for the course is contingent uponthe submission of an acceptable thesis or finalreport. No more than 6 points in this course maybe counted toward the satisfaction of the B.S.degree requirements.CHEN E4010x Chemical process analysis3 pts. Lect: 3. Not offered in 2010–2011.Open to undergraduates only with the instructor’spermission. Application of selected mathematicalmethods to solution of chemical engineeringproblems.CHEN E4020x Protection of industrial andintellectual property3 pts. Lect: 3. Professor Pearlman.To expose engineers, scientists and technologySEAS 2010–2011

managers to areas of the law they are mostlikely to be in contact with during their career.Principals are illustrated with various case studiestogether with active student participation.CHEE E4050y Principles of industrialelectrochemistry3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CHEN 3010 or equivalent. A presentationof the basic principle underlying electrochemicalprocesses. Thermodynamics, electrodekinetics, and ionic mass transport. Examples ofindustrial and environmental applications illustratedby means of laboratory experiments: electroplating,refining, and winning in aqueous solutionsand in molten salts; electrolytic treatment ofwastes; primary, secondary, and fuel cells.CHEN E4110x Transport phenomena, III3 pts. Lect: 3. Professor Durning.Prerequisites: CHEN E3120. Tensor analysis;kinematics of continua; balance of laws for onecomponentmedia; constituitive laws for freeenergy and stress in one-component media;exact and asymptotic solutions to dynamicproblems in fluids and solids; balance laws formixtures; constitutive laws for free energy, stressand diffusion fluxes in mixtures; solutions todynamic problems in mixtures.CHAP E4120x Statistical mechanics3 pts. Lect: 3. Professor O’Shaughnessy.Prerequisites: CHEN E3010 or equivalent thermodynamicscourse, or instructor’s permission.Fundamental principles and underlying assumptionsof statistical mechanics. Boltzmann’sentropy hypothesis and its restatement in termsof Helmholtz and Gibbs free energies and foropen systems. Correlation times and lengths.Exploration of phase space and observationtimescale. Correlation functions. Fermi-Dirac andBose-Einstein statistics. Fluctuation-responsetheory. Applications to ideal gases, interfaces,liquid crystals, microemulsions and other complexfluids, polymers, Coulomb gas, interactionsbetween charged polymers and charged interfaces,ordering transitions.CHEN E4140x Chemical and biochemicalseparations3 pts. Lect: 3. Professor Banta.Prerequisites: CHEN E3100, E3120, and E3210,or consent of instructor. Design and analysisof unit operations employed in chemical andbiochemical separations. Emphasis is placed onlearning the fundamental aspects of distillation,gas adsorption, and crystallization through acombination of lectures, open-ended problemsolving, self-learning exercises and computerprocess simulation. Recitation section required.CHEN E4201x Engineering applications ofelectrochemistry3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Physical chemistry and a coursein transport phenomena. Engineering analysisof electrochemical systems, including electrodekinetics, transport phenomena, mathematicalmodeling, and thermodynamics. Common experimentalmethods are discussed. Examples fromcommon applications in energy conversion andmetallization are presented.CHEN E4230y Reaction kinetics and reactordesign3 pts. Lect: 3. Professor Leshaw.Prerequisites: CHEN E3010. Reaction kinetics,applications to the design of batch and continuousreactors. Multiple reactions, nonisothermalreactors. Analysis and modeling of reactorbehavior. Recitation section required.CHEE E4252x Introduction to surface andcolloid chemistry3 pts. Lect: 3. Professor Somasundaran.Prerequisites: elementary physical chemistry.Thermodynamics of surfaces, properties of surfactantsolutions and surface films, electrostaticand electrokinetic phenomena at interfaces,adsorption; interfacial mass transfer and modernexperimental techniques.CHEN E4300x Chemical engineering control2 pts. Lab: 2. Professors Bedrossian and West.Prerequisites: Material and energy balances.Ordinary differential equations including Laplacetransforms. Reactor Design. An introduction toprocess control applied to chemical engineeringthrough lecture and laboratory. Concepts includethe dynamic behavior of chemical engineeringsystems, feedback control, controller tuning, andprocess stability.CHEN E4320x Molecular phenomena inchemical engineering4 pts. Lect: 4. Professor O’Shaughnessy.This course located strategically at the end of thecurriculum is intended to provide students witha molecular basis for the engineering conceptscovered in the curriculum. It is meant to bothvalidate the basic science and math foundationsdeveloped earlier and to stimulate the studenttoward applying modern molecular concepts ofchemical engineering that will define their future.Recitation section required.CHEN E4330y Advanced chemical kinetics3 pts. Lect: 3. Professor McNeill.Prerequisites: CHEN E4230 or instructor’s permission.Complex reactive systems. Catalysis.Heterogeneous systems, with an emphasis oncoupled chemical kinetics and transport phenomena.Reactions at interfaces (surfaces, aerosols,bubbles). Reactions in solution.CHEN E4500x Process and product design, I4 pts. Lect: 4. Professors Hill, Kumar, andLeshaw.Prerequisites: CHEN E4140, CHEN E3100. Anintroduction to the process engineering function.The design of chemical process, processequipment, and plants and the economic andecological evaluation of the chemical engineeringproject. Use of statistics to define product qualityis illustrated with case studies. Recitation sectionrequired.CHEN E4510y Process and product design, II4 pts. Lect: 4. Professors Hill and Leonard.Prerequisites: CHEN E4500. Students carryout a semester long process or product designcourse with significant industrial involvement.The project culminates with a formal writtendesign report and a public presentation.Recitation section required.CHEE E4530y Corrosion of metals3 pts. Lect: 3. Professor Duby.Prerequisites: CHEN E3010 or equivalent. Thetheory of electrochemical corrosion, corrosiontendency, rates, and passivity. Application tovarious environments. Cathodic protection andcoatings. Corrosion testing.CHEN E4600x Atmospheric aerosols3 pts. Lect: 3. Professor McNeill.Prerequisites: CHEN E3120 or instructor’s permission.Atmospheric aerosols and their effectson atmospheric composition and climate. Majortopics are aerosol sources and properties, fieldand laboratory techniques for characterization,gas-aerosol interactions, secondary organicaerosols, aerosol direct and indirect effects onclimate.CHEN E4620x Introduction to polymers andsoft materials3 pts. Lect: 3. Professor Durning.Prerequisites: An elementary course in physicalchemistry or thermodynamics. Organic chemistry,statistics, calculus and mechanics arehelpful, but not essential. An introduction to thechemistry and physics of soft material systems(polymers, colloids, organized surfactant systemsand others), emphasizing the connectionbetween microscopic structure and macroscopicphysical properties. To develop an understandingof each system, illustrative experimental studiesare discussed along with basic theoretical treatments.High molecular weight organic polymersare discussed first (basic notions, synthesis,properties of single polymer molecules, polymersolution and blend thermodynamics, rubber andgels). Colloidal systems are treated next (dominantforces in colloidal systems, flocculation,preparation and manipulation of colloidal systems)followed by a discussion of self-organizingsurfactant systems (architecture of surfactants,micelles and surfactant membranes, phasebehavior).CHEN E4640y Polymer surfaces andinterfaces3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CHEN E4620 or consent ofinstructor. A fundamental treatment of the thermodynamicsand properties relating to polymersurfaces and interfaces. Topics include the characterizationof interfaces, theoretical modelingof interfacial thermodynamics and structure, andpractical means for surface modification.CHEN E4645x Inorganic polymers, hybridmaterials, and gels3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Organic chemistry. The focus ofthe first art of the course, taught by Prof. Mark ison the preparation, characterization, and applica-91SEAS 2010–2011

92tions of inorganic polymers, with a heavy emphasison those based on main-group elements. Maintopics are characterization methods, polysiloxanes,polysilanes, polyphosphazenes, ferrocenebasedpolymers, other phosphorous-containingpolymers, boron-containing polymers, preceramicinorganic polymers, and inorganic-organic hybridcomposites. The focus of the second part of thecourse, taught by Prof. Koberstein is on gels,both physical and chemical. Topics will includegel chemistry, including epoxies, polyurethanes,polyesters, vinyl esters and hydrogels, as well astheoretical methods used to characterize the gelpoint and gel properties.CHEN E4660y Biochemical engineering3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: BMEN E4001 or the equivalent.Engineering of biochemical and microbiologicalreaction systems. Kinetics, reactor analysis, anddesign of batch and continuous fermentation andenzyme processes. Recovery and separations inbiochemical engineering systems.CHEN E4680x Soft materials laboratory3 pts. Lect/lab: 3. Not offered in 2010–2011.Prerequisites: Two years of undergraduate sciencecourses and the instructors’ permission.Corequisites: Limited to 15 students. Coversmodern characterization methods for soft materials(polymers, complex fluids, biomaterials).Techniques include differential scanning calorimetry,dynamic light scattering, gel permeationchromatography, rheology, and spectroscopicmethods. Team-taught by several faculty andopen to graduate and advanced undergraduatestudents. Lab required.CHEN E4700x Principles of genomictechnologies3 pts. Lect: 3. Professor Ju.Prerequisites: Undergraduate-level biology,organic chemistry, and instructor’s permission.Chemical and physical aspects of genomestructure and organization, genetic informationflow from DNA to RNA to protein. Nucleic acidhybridization and sequence complexity of DNAand RNA. Genome mapping and sequencingmethods. The engineering of DNA polymerasefor DNA sequencing and polymerase chainreaction. Fluorescent DNA sequencing andhigh-throughput DNA sequencer development.Construction of gene chip and micro array forgene expression analysis. Technology andbiochemical approach for functional genomicsanalysis. Gene discovery and genetics databasesearch method. The application of genetic databasefor new therapeutics discovery.CHEN E4740x Biological transport and ratephenomena, II3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Any two of the following: CHENE3110; BIOL C2005; CHEN E3210 or BMCHE3500. Analysis of transport and rate phenomenain biological systems and in the design ofbiomimetic transport-reaction systems for technologicaland therapeutic applications. Modelingof homogeneous and heterogeneous biochemicalreactions. The Bases of biological transport:roles of convection, ordinary diffusion, forceddiffusion. Systems where reaction and transportinteract strongly. Applications to natural andartificial tissue beds, tumor modeling, controlledrelease, natural and artificial organ function.CHEN E4750x The genome and the cell3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: BIOL C2005, MATH E1210 Theutility of genomic information lies in its capacity topredict the behavior of living cells in physiological,developmental, and pathological situations.The effect of variations in genome structurebetween individuals within a species, includingthose deemed healthy or diseased, and amongspecies, can be inferred statistically by comparisonsof sequences with behaviors, and mechanistically,by studying the action of molecules whosestructure is encoded within the genome. Thiscourse examines known mechanisms that elucidatethe combined effect of environmental stimulationand genetic makeup on the behavior ofcells in homeostasis, disease states, and duringdevelopment, and includes assessments of theprobable effect of these behaviors on the wholeorganism. Quantitative models of gene translationand intracellular signal transduction will be usedto illustrate switching of intracellular processes,transient and permanent gene activation, and cellcommitment, development, and death.CHEN E4760y Genomics sequencinglaboratory3 pts. Lect: 1. Lab: 2. Professor Ju.Prerequisites: Undergraduate level biology,organic chemistry and instructor’s permission.The chemical, biological and engineeringprinciples involved in the genomics sequencingprocess will be illustrated throughout the coursefor engineering students to develop the hands-onskills in conducting genomics research.CHEN E4800x Protein engineering3 pts. Lect: 3. Professor Banta.Prerequisites: CHEN E4230, may be takenconcurrently, or the instructor’s permission.Fundamental tools and techniques currently usedto engineer protein molecules. Methods used toanalyze the impact of these alterations on differentprotein functions with specific emphasis onenzymatic catalysis. Case studies reinforce conceptscovered, and demonstrate the wide impactof protein engineering research. Application ofbasic concepts in the chemical engineering curriculum(reaction kinetics, mathematical modeling,thermodynamics) to specific approachesutilized in protein engineering.BMCH E4810y Artificial organs3 pts. Lect: 3. Professor Leonard.Analysis and design of replacements for theheart, kidneys, and lungs. Specification and realizationof structures for artificial organ systems.CHEN E6050x Advanced electrochemistry3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: The instructor’s permission. Anadvanced overview of the fundamentals ofelectrochemistry, with examples taken frommodern applications. An emphasis is placedon mass transfer and scaling phenomena.Principles are reinforced through the developmentof mathematical models of electrochemicalsystems. Course projects will require computersimulations. The course is intended for advancedgraduate students, conducting research involvingelectrochemical technologies.CHEE E6220y Equilibria and kinetics inhydrometallurgical systems3 pts. Lect: 3. Professor Duby.Prerequisites: Instructor’s permission. Anadvanced overview of the fundamentals ofelectrochemistry, with examples taken frommodern applications. An emphasis is placedon mass transfer and scaling phenomena.Principles are reinforced through the developmentof mathematical models of electrochemicalsystems. Course projects will require computersimulations. The course is intended for advancedgraduate students, conducting research involvingelectrochemical technologies.CHEE E6252y Applied surface and colloidchemistry3 pts. Lect: 2. Lab: 3. Professor Somasundaran.Prerequisites: CHEN 4252. Applications of surfacechemistry principles to wetting, flocculation,flotation, separation techniques, catalysis, masstransfer, emulsions, foams, aerosols, membranes,biological surfactant systems, microbialsurfaces, enhanced oil recovery, and pollutionproblems. Appropriate individual experimentsand projects. Lab required.CHEN E6620y Physical chemistry ofmacromolecules3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CHEN E4620 or the instructor’spermission. Modern studies of static and dynamicbehavior in macromolecular systems. Topicsinclude single-chain behavior adsorption, solutionthermodynamics, the glass transition, diffusion,and viscoelastic behavior. The molecular understandingof experimentally observed phenomenais stressed.CHEN E6630x Special topics in softcondensed matter3 pts. Lect: 3. Not offered in 2010–2011.Tutorial lectures on selected topics in soft condensedmatter.CHEN E6910y Theoretical methods inpolymer physics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CHAP 4120 or equivalent statisticalmechanics course, or instructor’s permission.Modern methods for understanding polymericliquids and critical phenomena are introducedand applied in detail. Scaling and universality.Relationship of high polymer physics to criticalphenomena. Landau theory, self-consistent fieldmethod. Scaling approach. RenormalizationSEAS 2010–2011

group theory. Epsilon expansion for polymer andother critical exponents. Applications to polymerstatics and dynamics, and to other complex fluids.CHEN E6920y Physics of soft matter3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Instructor’s permission. Physicsof polymers, biopolymers (especially DNA),membranes, gels, and other types of soft matter.Statistical mechanics, scaling theory, selfconsistentfield theory; experimental surveys.Dilute, semidilute, and concentrated polymersolutions. Mesophases and self-assembly insoft matter. Polymers at interfaces, polymermembraneinteractions. Fluctuating double helixmodels of DNA, DNA melting, pattern recognitionin DNA. Polyelectrolytes, charged biopolymers,DNA charge-induced condensation.CHEN E8100y Topics in biology3 pts. Lect: 3. Professor O’Shaughnessy.Prerequisites: Instructor’s permission. Thisresearch seminar introduces topics at the forefrontof biological research in a format and languageaccessible to quantitative scientists andengineers lacking biological training. Conceptualand technical frameworks from both biologicaland physical science disciplines are utilized. Theobjective is to reveal to graduate students wherepotential lies to apply techniques from theirown disciplines to address pertinent biologicalquestions in their research. Classes entail reading,criticism and group discussion of researchpapers and textbook materials providingoverviews to various biological areas including:evolution, immune system, development and cellspecialization, the cytoskeleton and cell motility,DNA transcription in gene circuits, protein networks,recombinant DNA technology, aging, andgene therapy.CHEN E9000x and y Chemical engineeringcolloquium0 pts. Col: 1. Professor Banta.All graduate students are required to attend thedepartment colloquium as long as they are inresidence. No degree credit is granted.CHEN E9400x and y Master’s research1–6 pts. Members of the faculty.Prescribed for M.S. and Ch.E. candidates;elective for others with the approval of theDepartment. Degree candidates are requiredto conduct an investigation of some problem inchemical engineering or applied chemistry andto submit a thesis describing the results of theirwork. No more than 6 points in this course maybe counted for graduate credit, and this credit iscontingent upon the submission of an acceptablethesis. The concentration in pharmaceutical engineeringrequires a 2-point thesis internship.CHEN E9500x and y-S9500 Doctoral research1–15 pts. Members of the faculty.Prerequisites: The qualifying examinations forthe doctorate. Open only to certified candidatesfor the Ph.D. and Eng.Sc.D. degrees. Doctoralcandidates in chemical engineering are requiredto make an original investigation of a problem inchemical engineering or applied chemistry, theresults of which are presented in their dissertations.No more than 15 points of credit towardthe degree may be granted when the dissertationis accepted by the department.CHEN E9600x and y Advanced researchproblems2–10 pts. Members of the faculty.Prerequisites: Recommendation of the professorconcerned and approval of the master’s researchdepartment. For postdoctoral students and otherqualified special students who wish to pursueresearch under the guidance of members of thedepartment. Not open to undergraduates or tocandidates for the degrees of Ch.E.,M.S., Ph.D.,or Eng.Sc.D.CHEN E9800x and y Doctoral researchinstruction3, 6, 9 or 12 pts. Members of the faculty.A candidate for the Eng.Sc.D. degree in chemicalengineering must register for 12 points ofdoctoral research instruction. Registration inCHEN E9800 may not be used to satisfy theminimum residence requirement for the degree.CHEN E9900x and y–S9900 Doctoraldissertation0 pts. Members of the faculty.Open only to certified doctoral candidates. A candidatefor the doctorate in chemical engineering maybe required to register for this course in every termafter the student’s course work has been completed,and until the dissertation has been accepted.93SEAS 2010–2011

94CIVIL ENGINEERING AND ENGINEERING MECHANICS610 S. W. Mudd, MC 4709, 854-3143info@civil.columbia.edu, www.civil.columbia.eduCHAIRRaimondo BettiDEPARTMENTALADMINISTRATORElaine MacDonaldPROFESSORSRaimondo BettiBruno A. BoleyPatricia J. CulliganGautam DasguptaGeorge DeodatisMorton B. FriedmanUpmanu Lall, Earthand EnvironmentalEngineeringHoe I. LingRichard W. Longman,Mechanical EngineeringChristian MeyerFeniosky Peña-MoraAndrew SmythRene B. TestaASSISTANT PROFESSORSNicola ChiaraJohn E. TaylorHaim WaismanHuiming YinLECTURER IN DISCIPLINEJosé I. SánchezADJUNCT STAFFWilliam BeckerLogan BrantAine M. BrazilJulius ChangEli B. GottliebBettina GurpideWilliam M. HartWilfred LaufsSamuel A. LeiferElisabeth MalschAly M. MohammadNasri MunfakhRobert D. MutchMysore NagarajaReza NikainGary F. PanarielloTom PapachristosThomas PanayotidiDaniel PetersonRobert RatayRobert A. RubinVincent TiroloRichard L. TomasettiPawel WoelkeBojidar YanevTheodore P. ZoliSTAFF ASSOCIATEAdrian BrüggerINFORMATIONTECHNOLOGY MANAGERJon A. VanThe Department of Civil Engineeringand Engineering Mechanicsfocuses on two broad areas ofinstruction and research. The first, theclassical field of civil engineering, dealswith the planning, design, construction,and maintenance of the built environment.This includes buildings, foundations,bridges, transportation facilities,nuclear and conventional power plants,hydraulic structures, and other facilitiesessential to society. The secondis the science of mechanics and itsapplications to various engineeringdisciplines. Frequently referred to asapplied mechanics, it includes the studyof the mechanical and other propertiesof materials, stress analysis of stationaryand movable structures, the dynamicsand vibrations of complex structures,aero- and hydrodynamics, and themechanics of biological systems.MISSIONThe department aims to provide studentswith a technical foundationanchored in theory together with thebreadth needed to follow diverse careerpaths, whether in the profession viaadvanced study or apprenticeship, or asa base for other pursuits.Current Research ActivitiesCurrent research activities in theDepartment of Civil Engineering andEngineering Mechanics are centeredin the areas outlined below. A numberof these activities impact directly onproblems of societal importance, suchas rehabilitation of the infrastructure,mitigation of natural or man-made disasters,and environmental concerns.Solid mechanics: mechanical propertiesof new and exotic materials, constitutiveequations for geologic materials,failure of materials and components,properties of fiber-reinforced cementcomposites, damage mechanics. Multihazard risk assessment and mitigation:integrated risk studies of thecivil infrastructure form a multihazardperspective including earthquake,wind, flooding, fire, blast, and terrorism.The engineering, social, financial,and decision-making perspectives ofthe problem are examined in an integratedmanner. Probabilistic mechanics: random processesand fields to model uncertainloads and material/soil properties,nonlinear random vibrations, reliabilityand safety of structural systems,computational stochastic mechanics,stochastic finite element and boundaryelement techniques, Monte Carlosimulation techniques, random micromechanics. Structural control and health monitoring:topics of research in this highlycross-disciplinary field include thedevelopment of “smart” systems forthe mitigation and reduction of structuralvibrations, assessment of theSEAS 2010–2011

95health of structural systems based ontheir vibration response signatures,and the modeling of nonlinear systemsbased on measured dynamicbehavior.Fluid mechanics: solid-laden turbulentflows, porous surface turbulence, flowthrough porous media, numerical simulationof flow and transport processes,flow and transport in fractured rock.Environmental engineering/waterresources: modeling of flow and pollutanttransport in surface and subsurfacewaters, unsaturated zone hydrology,geoenvironmental containment systems,analysis of watershed flows includingreservoir simulation.Structures: dynamics, stability, anddesign of structures, structural failureand damage detection, fluid and soilstructure interaction, ocean structuressubjected to wind-induced waves,inelastic dynamic response of reinforcedconcrete structures, earthquake-resistantdesign of structures.Geotechnical engineering: soil behavior,constitutive modeling, reinforcedsoil structures, geotechnical earthquakeengineering, liquefaction and numericalanalysis of geotechnical systems.Structural materials: cement-basedmaterials, micro- and macromodels offiber-reinforced cement composites,utilization of industrial by-productsand waste materials, beneficiation ofdredged material.Earthquake engineering: response ofstructures to seismic loading, seismicrisk analysis, active and passive controlof structures subject to earthquakeexcitation, seismic analysis of long-spancable-supported bridges.Flight structures: aeroelasticity, aeroacoustics,active vibration and noise control,smart structures, noise transmissioninto aircraft, and vibroacoustics of spacestructures.Construction engineering and management:contracting strategies; alternativeproject delivery systems, such asdesign-build, design-build-operate, anddesign-build-finance-operate; minimizingproject delays and disputes; advancedtechnologies to enhance productivityand efficiency; strategic decisions inglobal engineering and constructionmarkets.Infrastructure delivery and management:decision support systems forinfrastructure asset management;assessing and managing infrastructureassets and systems; capital budgetingprocesses and decisions; innovativefinancing methods; procurement strategiesand processes; data managementpractices and systems; indicators ofinfrastructure performance and service.FACILITIESThe offices and laboratories of thedepartment are in the S. W. MuddBuilding and the Engineering Terrace.ComputingThe department manages a substantialcomputing facility of its own in additionto being networked to all the systemsoperated by the University. The departmentfacility enables its users to performsymbolic and numeric computation,three-dimensional graphics, and expertsystems development. Connections towide-area networks allow the facility’susers to communicate with centersthroughout the world. All faculty andstudent offices and department laboratoriesare hardwired to the computingfacility, which is also accessible remotelyto users. Numerous personal computersand graphics terminals exist throughoutthe department, and a PC lab is availableto students in the department inaddition to the larger school-wide facility.LaboratoriesThe Robert A. W. Carleton Strength ofMaterials Laboratory is a very large facilityequipped for research into all types of engineeringmaterials and structural elements.The Heffner Laboratory for HydrologicResearch is a newly established facilityfor both undergraduate instruction andresearch in all aspects of fluid mechanicsand its applications. The Eugene MindlinLaboratory for Structural DeteriorationResearch is a teaching and research facilitydedicated to all facets of the assessmentof structures and the processes of deteriorationof structural performance. Theconcrete laboratory is equipped to performa wide spectrum of experimental researchin cement-based materials. The DonaldM. Burmister Soil Mechanics Laboratory isused in both undergraduate and graduateinstruction for static and dynamic testingSEAS 2010–2011

96CIVIL ENGINEERING PROGRAM: FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)APMA E2101 (3)Intro. to applied math.PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)Lab C1493 (3)or chem. labLab W3081 (2)CHEMISTRYone-semester lecture (3–4): C1403 or C1404 or C3045 or C1604Chem lab C1500 (3) either semester or physics labMECHANICSENME-MECE E3105 (4) either semesterCIVIL ENGINEERINGCIEN E1201 (3) or equivalentCIEN E3004 (3)Urban infra. systemsENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 orW1123 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)COMPUTERSCIENCEComputer Language: W1005 (3) (any semester)PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1EAEE is recommended for students concentrating in environmental engineering and water resources.of soils and foundations. The geotechnicalcentrifuge located in the CarletonLaboratory is used for geotechnical andgeoenvironmental research.The Institute of Flight StructuresThe Institute of Flight Structures wasestablished within the departmentthrough a grant by the Daniel andFlorence Guggenheim Foundation. Itprovides a base for graduate training inaerospace and aeronautical related applicationsof structural analysis and design.Center for Infrastructure StudiesThe Center was established in thedepartment to provide a professionalenvironment for faculty and students froma variety of disciplines to join with industryand government to develop and applythe technological tools and knowledgebases needed to deal with the massiveproblems of the city, state, and regionalinfrastructure. The Center is active inmajor infrastructure projects through aconsortium of universities and agencies.UNDERGRADUATE PROGRAMSThe Department of Civil Engineering andEngineering Mechanics offers undergraduateprograms in civil engineeringand engineering mechanics. Both areintended to prepare students with firmtechnical bases while nurturing decisionmakingand leadership potential.The civil engineering program isdesigned to enable the student, uponcompletion of the B.S. degree program,to enter the profession—for example, inindustry, on a construction project, in aconsulting engineering office, througha government agency—or to begingraduate study, or both. The programis fully accredited by the EngineeringAccreditation Commission (EAC) of theAccreditation Board for Engineeringand Technology (ABET) and provides abroad traditional civil engineering backgroundthat focuses on basic theoryand design. Technical electives can beselected to obtain a strong technicalSEAS 2010–2011

CIVIL ENGINEERING: THIRD AND FOURTH YEARS97SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIICORE REQUIREDCOURSESENME E3113 (3)Mech. of solidsENME E3161 (4)Fluid mech.CIEN E3125 (3)Structural designCIEN E3126 (1)Computer-aidedstruct. designCIEN E3141 (4)Soil mech.CIEN E4111 (3)Uncertainty and risk ininfrastructure systemsCIEN E3129 (3)Proj. mgmt. forconstructionGEOTECHENG. (GE)ORSTRUCT.ENG. (SE)ENME E3106 (3)Dynamics and vibrationsENME E3114 (4)Exper. mech. of materialsCIEN E3121 (3)Struct. anal.CIEN E4332 (3)Finite element anal.CIEN E3127 (3)Struct. design projects(SE)orCIEN E4241 (3)Geotech. eng. fund. (GE)CIEN E3128 (4)Design projectsTECHELECTIVES3 points 3 points 12 pointsCONCENTRATIONSCIVIL ENG.ANDCONSTR.MNGMT.TECHELECTIVESENME E3114 (4)Exper. mech. of materialsCIEN E3121 (3)Struct. anal.orCIEE E3250 (3)Hydrosystems eng.CIEN E4133 (3)Capital facility planningand financingCIEN E3127 (3) orCIEN E4241 (3)CIEN E4131 (3)Princ. of constr. tech.CIEN E3128 (4)Design projects6 points 3 points 9 pointsWATER RES./ENVIRON.ENG.CIEE E3255 (3)Environ. control / pollutionCIEE E3250 (3)Hydrosystems eng.CIEN E3303 (1)Independent studiesCIEN E4163 (3)Environ. eng.wastewaterCIEE E4260 (4)Urban ecology studioCIEN E4250 (3)Waste containm.design and practiceorCIEN E4257 (3)contam. transportin subsurface sys.EAEE E4006 (3)Field methods forenviron. eng.TECHELECTIVESNONTECHELECTIVES6 points 3 points 9 points3 points 3 pointsTOTAL POINTS 16 1715(water res./environ. eng. 16)16(water res./environ. eng. 15)SEAS 2010–2011

98ENGINEERING MECHANICS PROGRAM: FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and ODE (3)PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)Lab C1493 (3)or chem. labLab C3081 (2)CHEMISTRYone-semester lecture (3–4): C1403 or C1404 or C3045 or C1604Chem lab C1500 (3) either semester or physics labMECHANICSENME-MECE E3105 (4) any semesterENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 orW1123 (3)HUMA C1002,COCI C1102or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)REQUIREDTECH ELECTIVES(3) Student’s choice, see list of first- and second-year technical electives (professional-level courses;see pages 12–13).COMPUTERSCIENCEPHYSICALEDUCATIONC1001 (1) C1002 (1)Computer Language: W1005 (3) (any semester)GATEWAY LABE1102 (4) either semesterbase in a particular field of civil engineeringor other engineering disciplines.The engineering mechanics programprovides a strong analytical background inmechanics for students planning to continueon to graduate school and to pursueresearch. Admission to the engineeringmechanics program requires a grade pointaverage of B or better and maintenance ofperformance while in the program.Program ObjectivesIn developing and continually updatingour program to achieve the statedmission of the department, we seek toachieve the following objectives:1. To provide a firm foundation in thebasic math, science, and engineeringsciences that underlie all technologicaldevelopment so our graduates will bewell equipped to adapt to changingtechnology in the profession.2. To provide the broad and fundamentaltechnical base needed by graduateswho will enter the professionthrough the increasingly commonpath of a specialized M.S., but alsoprovide suitable preparation to thosewho choose to enter the professionalworkforce with a B.S. to developspecialized expertise by way ofapprenticeship.3. To provide the breadth and choicesin our programs that can accommodateand foster not only studentswith differing technical objectives, butalso those who will use their technicalback- ground to follow other careerpaths.4. To provide a basis for effective writingand communication as well as abackground to foster awareness ofsocietal issues.Engineering MechanicsThe prerequisites for this program arethe courses listed in the First Year–Sophomore Program (see above), ortheir equivalents, with the provision thatENME E3105: Mechanics be takenin the sophomore year and that thestudent have obtained a grade of B orbetter.SEAS 2010–2011

ENGINEERING MECHANICS: THIRD AND FOURTH YEARS99SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIREQUIREDCOURSESENME E3113 (3)Mech. of solidsENME E3161 (4)Fluid mechanicsAPMA E3101 (3)Applied math., IENME E3106 (3)Dynamics and vibrationsENME E3114 (4)Experimental mech.CIEN E3121 (3)Structural analysisAPMA E3102 (3)Applied math., IICIEN E4332 (3)Finite elementENME E4113 (3)Advanced solidsENME E4215 (3)Theory of vibrationsENME E4202 (3)Advanced mech.ELECTIVESTECH 3 points 6 points 6 points 9 pointsNONTECH 3 points 3 pointsTOTAL POINTS 16 16 18 15Civil EngineeringThe prerequisites for this program arethe courses listed in the First Year–Sophomore Program or their equivalents.The civil engineering programoffers three areas of concentration: civilengineering and construction management,geotechnical engineering or structuralengineering, and water resources/environmental engineering. An optionalminor can be selected in architecture,education, economics, and any of theengineering departments in the School.In the junior and senior years, 18 creditsof technical electives are allocated.The department offers a first-yeardesign course, CIEN E1201: The art ofstructural design, which all students arerequired to take in the spring semesterof the first year or later. An equivalentcourse could be substituted for E1201.Minor in ArchitectureCivil engineering program students maywant to consider a minor in architecture(see page 194).GRADUATE PROGRAMSThe Department of Civil Engineering andEngineering Mechanics offers graduateprograms leading to the degreeof Master of Science (M.S.), the professionaldegrees Civil Engineer andMechanics Engineer and the degreesof Doctor of Engineering Science (Eng.Sc.D.) and Doctor of Philosophy (Ph.D.).These programs are flexible and mayinvolve concentrations in structures,construction engineering, reliability andrandom processes, soil mechanics, fluidmechanics, hydrogeology, continuummechanics, finite element methods,computational mechanics, experimentalmechanics, vibrations and dynamics,earthquake engineering, or any combinationthereof, such as fluid-structureinteraction. The Graduate RecordExamination (GRE) is required for admissionto the department.Civil EngineeringBy selecting technical electives, studentsmay focus on one of several areas ofconcentration or prepare for futureendeavors such as architecture. Sometypical concentrations are: Structural engineering: applicationsto steel and concrete buildings,bridges, and other structures Geotechnical engineering: soilmechanics, engineering geology, andfoundation engineering Construction engineering andmanagement: capital facility planningand financing, strategic management,managing engineering and constructionprocesses, construction industrylaw, construction techniques, managingcivil infrastructure systems, civilengineering and construction entrepreneurship Environmental engineering andwater resources: transport of waterbornesubstances, hydrology, sedimenttransport, hydrogeology, andgeoenvironmental design of containmentsystemsEngineering MechanicsPrograms in engineering mechanicsoffer comprehensive training in theprinciples of applied mathematics andcontinuum mechanics and in the applicationof these principles to the solutionof engineering problems. The emphasisis on basic principles, enabling studentsto choose from among a wide range oftechnical areas. Students may work onproblems in such disciplines as systemsanalysis, acoustics, and stress analysis,and in fields as diverse as transportation,environmental, structural, nuclear,and aerospace engineering. Programareas include: Continuum mechanics: solid andfluid mechanics, theories of elasticand inelastic behavior, and damagemechanics Vibrations: nonlinear and randomvibrations; dynamics of continuousmedia, of structures and rigid bodies,and of combined systems, suchSEAS 2010–2011

100as fluid-structure interaction; active,passive, and hybrid control systemsfor structures under seismic loading;dynamic soil-structure interactioneffects on the seismic response ofstructures Random processes and reliability:problems in design against failureunder earthquake, wind, and waveloadings; noise, and turbulent flows;analysis of structures with randomproperties Fluid mechanics: turbulent flows,two-phase flows, fluid-structure interaction,fluid-soil interaction, flow inporous media, computational methodsfor flow and transport processes,and flow and transport in fracturedrock under mechanical loading Computational mechanics: finiteelement and boundary element techniques,symbolic computation, andbioengineering applicationsA flight structures program isdesigned to meet the needs of industryin the fields of high-speed and spaceflight. The emphasis is on mechanics,mathematics, fluid dynamics, flightstructures, and control. The programis a part of the Guggenheim Instituteof Flight Structures in the department.Specific information regarding degreerequirements is available in the departmentoffice.COURSES IN CIVILENGINEERING (CIEN)See also Engineering Mechanics(ENME), at the end of this section.CIEN E1201y The art of structural design3 pts. Lect: 3. Professor Deodatis.Prerequisites: First-semester calculus andphysics. An introduction to basic scientific andengineering principles used for the design ofbuildings, bridges, and other parts of the builtinfrastructure. Application of these principles tothe analysis and design of a number of actuallarge-scale structures. Experimental verificationof these principles through laboratory experiments.Coverage of the history of major structuraldesign innovations and of the engineerswho introduced them. Critical examination of theunique aesthetic/artistic perspectives inherent instructural design. Consideration of management,socioeconomic, and ethical issues involved in thedesign and construction of large-scale structures.Introduction to some recent developments insustainable engineering, including green buildingdesign and adaptable structural systems.CIEN E3004y Urban infrastructure systems3 pts. Lect: 3. Professor Taylor.Introduction to: (a) the infrastructure systemsthat support urban socioeconomic activities,and (b) fundamental system design and analysismethods. Coverage of water resources,vertical, transportation, communications andenergy infrastructure. Emphasis upon thepurposes that these systems serve, the factorsthat influence their performance, thebasic mechanisms that govern their designand operation, and the impacts that they haveregionally and globally. Student teams completea semester-long design/analysis projectwith equal emphasis given to water resources/ environmental engineering, geotechnicalengineering and construction engineering andmanagement topics.CIEN E3121y Structural analysis3 pts. Lect: 3. Professor Testa.Methods of structural analysis. Trusses, arches,cables, frames; influence lines; deflections;force method; displacement method; computerapplications.CIEN E3125y Structural design3 pts. Lect: 3. Professor Betti.Prerequisites: ENME 3113. Design criteria forvaried structural applications, including buildingsand bridges; design of elements using steel, concrete,masonry, wood, and other materials.CIEN E3126y Computer-aided structuraldesign1 pt. Lect: 1. Lab: 1. Professor Betti.Corequisites: CIEN E3125. Introduction to softwarefor structural analysis and design with lab.Applications to the design of structural elementsand connections. Lab required.CIEN E3127x Structural design projects3 pts. Lect: 3. Professor Meyer.Prerequisites: CIEN E3125 and CIEN E3126 orthe instructor’s permission. Design projects withvarious structural systems and materials.CIEN E3128y Design projects4 pts. Lect: 4. Professor Meyer.Prerequisites: CIEN E3125 and CIEN E3126.Capstone design project in civil engineering. Thisproject integrates structural, geotechnical andenvironmental/water resources design problemswith construction management tasks and sustainability,legal and other social issues. Projectis completed in teams, and communication skillsare stressed. Outside lecturers will addressimportant current issues in engineering practice.Every student in the course will be exposed withequal emphasis to issues related to geotechnicalengineering, water resources/environmentalengineering, structural engineering, and constructionengineering and management.CIEN E3129x Project management forconstruction3 pts. Lect: 3. Professor Taylor.Prerequisites: Senior standing in CivilEngineering or instructor’s permission.Introduction to Project Management for designand construction processes. Elements of planning,estimating, scheduling, bidding, and contractualrelationships. Computer scheduling andcost control. Critical path method. Design andconstruction activities. Field supervision.CIEN E3141y Soil mechanics4 pts. Lect: 3. Lab 3. Professor Ling.Prerequisites: ENME E3113. Index propertiesand classification; compaction; permeability andseepage; effective stress and stress distribution;shear strength of soil; consolidation; slopestability.CIEE E3250y Hydrosystems engineering3 pts. Lect: 3. Instructor to be announced.Prerequisites: CHEN E3110 or ENME E3161 orequivalent, SIEO W3600 or equivalent, or theinstructor’s permission. A quantitative introductionto hydrologic and hydraulic systems, with afocus on integrated modeling and analysis of thewater cycle and associated mass transport forwater resources and environmental engineering.Coverage of unit hydrologic processes such asprecipitation, evaporation, infiltration, runoff generation,open channel and pipe flow, subsurfaceflow and well hydraulics in the context of examplewatersheds and specific integrative problemssuch as risk-based design for flood control,provision of water, and assessment of environmentalimpact or potential for nonpoint sourcepollution. Spatial hydrologic analysis using GISand watershed models. Note: This course is tobe joint listed with CIEN and replaces the previousCIEN 3250.CIEE E3255y Environmental control andpollution reduction systems3 pts. Lect: 3. Professor Castaldi.Prerequisites: ENME E3161 or MECE3100Review of engineered systems for preventionand control of pollution. Fundamentals of materialand energy balances and reaction kinetics.Analysis of engineered systems to addressenvironmental problems, including solid andhazardous waste, and air, water, soil and noisepollution. Life cycle assessments and emergingtechnologies.CIEE E3260y Engineering for developingcommunitiesLect: 3. 3 pts. Professor Culligan.Introduction to engineering problems facedby developing communities and exploration ofdesign solutions in the context of a real projectwith a community client. Emphasis is on thedesign of sustainable solutions that take accountof social, economical, and governance issues,and that can be implemented now or in the nearfuture. The course is open to all undergraduateengineering students. Multidisciplinary teamworkand approaches are stressed. Outside lecturersare used to address issues specific to developingcommunities and the particular project underconsideration.SEAS 2010–2011

CIEN E3303x and y Independent studies incivil engineering for juniors1–3 pts. By conference. Members of the faculty.A project on civil engineering subjects approvedby the chairman of the department. Lab fee:$200.CIEN E3304x and y Independent studies incivil engineering for seniors1–3 pts. By conference. Members of the faculty.A project on civil engineering subjects approvedby the chairman of the department. Lab fee:$200.CIEN E4010y Transportation engineering3 pts. Lect: 3. Instructor to be announced.An overview of the planning, design, operation,and construction of urban highways and masstransportation systems. Transportation planningand traffic studies; traffic and highway engineering;rapid transit and railroad engineering.CIEN E4021x Elastic and plastic analysis ofstructures3 pts. Lect: 3. Professor Meyer.Prerequisites: CIEN E3121 or the equivalent.Overview of classical indeterminate structuralanalysis methods (force and displacement methods),approximate methods of analysis, plasticanalysis methods, collapse analysis, shakedowntheorem, structural optimization.CIEN E4022y Bridge design and management3 pts. Lect: 3. Professor Yanev.Prerequisites: CIEN E3125 or the equivalent.Bridge design history, methods of analysis,loads: static, live, dynamic. Design: allowablestress, ultimate strength, load resistance factor,supply/demand. Steel and concrete superstructures:suspension, cable stayed, prestressed,arches. Management of the assets, life-cyclecost, expected useful life, inspection, maintenance,repair, reconstruction. Bridge inventories,condition assessments, data acquisition andanalysis, forecasts. Selected case histories andfield visits.CIEN E4100y Earthquake and windengineering3 pts. Lect: 3.Prerequisites: ENME E3106 or the equivalent.Basic concepts of seismology. Earthquakecharacteristics, magnitude, response spectrum,dynamic response of structures to groundmotion. Base isolation and earthquake-resistantdesign. Wind loads and aeroelastic instabilities.Extreme winds. Wind effects on structures andgust factors.CIEN E4111x Uncertainty and risk ininfrastructure systems3 pts. Lect: 3. Professor Smyth.Prerequisites: Working knowledge of calculus.Introduction to basic probability; hazard function;reliability function; stochastic models of naturaland technological hazards; extreme value distributions;Monte Carlo simulation techniques;fundamentals of integrated risk assessment andrisk management; topics in risk-based insurance;case studies involving civil infrastructure systems,environmental systems, mechanical andaerospace systems, construction management.CIEN E4128y Civil engineering management3 pts. Available only on CVN.Principles of engineering management with astrong emphasis on planning of infrastructuresystems. The course stresses leadership,creativity, and management analysis. Programplanning with optimization under financial andenvironmental constraints; project planning andscheduling using deterministic and stochasticnetwork theories; production rate developmentand control using statistical, heuristic, simulation,and queuing theory approaches. Students prepareand formally present term projects.CIEN E4129x or y Managing engineering andconstruction processes3 pts. Lect: 3. Instructor to be announced.Prerequisites: Senior standing in CivilEngineering, or instructor’s permission.Introduction to the principles, methods and toolsnecessary to manage design and constructionprocesses. Elements of planning, estimating,scheduling, bidding and contractual relationships.Valuation of project cash flows. Critical pathmethod. Survey of construction procedures. Costcontrol and effectiveness. Field supervision.CIEN E4130x Design of construction systems3 pts. Lect: 3. Professor Tirolo.Prerequisites: CIEN E3125 or the equivalent,or the instructor’s permission. Introduction tothe design of systems that support constructionactivities and operations. Determination of designloads during construction. Design of excavationsupport systems, earth retaining systems,temporary supports and underpinning, concreteformwork and shoring systems. Cranes and erectionsystems. Tunneling systems. Instrumentationand monitoring. Students prepare and presentterm projects.CIEN E4131x or y Principles of constructiontechniques3 pts. Lect: 3. Professor Hart.Prerequisites: CIEN 4129 or equivalent. Currentmethods of construction, cost-effective designs,maintenance, safe work environment. Designfunctions, constructability, site and environmentalissues.CIEN E4132x or y Prevention and resolutionof construction disputes3 pts. Lect: 3. Professor Nikain.Prerequisites: CIEN E 4129 or equivalent.Contractual relationships in the engineering andconstruction industry and the actions that resultin disputes. Emphasis on procedures required toprevent disputes and resolve them quickly andcost-effectively. Case studies requiring oral andwritten presentations.CIEN E4133x or y Capital facility planning andfinancing3 pts. Lect: 3. Professor Chang.Prerequisites: CIEN E4129 or equivalent.Planning and financing of capital facilities witha strong emphasis upon civil infrastructure systems.Project feasibility and evaluation. Designof project delivery systems to encourage bestvalue, innovation and private sector participation.Fundamentals of engineering economyand project finance. Elements of life cycle costestimation and decision analysis. Environmental,institutional, social and political factors. Casestudies from transportation, water supply andwastewater treatment.CIEN E4134y Construction industry law3 pts. Lect: 3. Professors Quintas and Rubin.Prerequisites: Graduate standing or the instructor’spermission. Practical focus upon legalconcepts applicable to the construction industry.Provides sufficient understanding to managelegal aspects, instead of being managed bythem. Topics include contractual relationships,contract performance, contract flexibility andchange orders, liability and negligence, disputeavoidance/resolution, surety bonds, insuranceand site safety.CIEN E4135y Strategic management globaldesign and construction3 pts. Lect: 3. Professor Taylor.Core concepts of strategic planning, managementand analysis within the construction industry.Industry analysis, strategic planning modelsand industry trends. Strategies for informationtechnology, emerging markets and globalization.Case studies to demonstrate key concepts inreal-world environments.CIEN E4136y Global entrepreneurship in civilengineering3 pts. Lect: 3.Capstone practicum where teams develop strategiesand business plans for a new enterprisein the engineering and construction industry.Identification of attractive market segments andlocations; development of an entry strategy;acquisition of financing, bonding and insurance;organizational design; plans for recruiting andretaining personnel; personnel compensation/incentives. Invited industry speakers.CIEN E4163x Environmental engineering:wastewater3 pts. Lect: 3. Professor Becker.Prerequisites: Introductory chemistry (with laboratory)and fluid mechanics. Fundamentals ofwater pollution and wastewater characteristics.Chemistry, microbiology, and reaction kinetics.Design of primary, secondary, and advancedtreatment systems. Small community and residentialsystems.CIEN E4210x Investigation of structural/construction failures3 pts. Lect: 3. Professor Ratay.Prerequisites: CIEN E3125 or equivalent. Reviewof significant failures, civil/structural engineeringdesign and construction practices, ethicalstandards and the legal positions as necessarybackground to forensic engineering. Discussion101SEAS 2010–2011

102of standard-of-care. Study of the process of engineeringevaluation of structural defects and failuresin construction and in service. Examinationof the roles, activities, conduct and ethics of theforensic consultant and expert witness. Studentsare assigned projects of actual cases of nonperformanceor failure of steel, concrete, masonry,geotechnical, and temporary structures, in orderto perform, discuss, and report their own investigationsunder the guidance of the instructor.CIEN E4212y Structural assessmentand failure3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ENME E3113 and CIEN E3121.Laboratory and field test methods in assessmentof structures for rehabilitation and to determinecauses of failure; ASTM and other applicable standards;case histories of failures and rehabilitationin wood, steel, masonry, and concrete structures.CIEN E4213x Elastic and inelastic buckling ofstructures3 pts. Lect: 3. Professor Laufs.Stability of framed structures in the elastic andinelastic ranges. Lateral buckling of beams.Torsional buckling of compression members.Buckling of plates of plate-stiffener combinations.Linear stability analysis of cylindrical shells anddiscussion of its limitations. Discussion of thesemiempirical nature of the elastoplastic relationsused in the case of plates and shells.CIEN E4226y Advanced design of steelstructures3 pts. Lect: 3. Professor Woelke.Prerequisites: CIEN E3125 or equivalent. Reviewof loads and structural design approaches.Material considerations in structural steel design.Behavior and design of rolled steel, welded,cold-formed light-gauge, and composite concrete/steelmembers. Design of multistory buildingsand space structures.CIEN E4232y Advanced design of concretestructures3 pts. Lect: 3. Professor Panayotidi.Prerequisites: CIEN E3125 or equivalent. Designof concrete slabs, deep beams, walls, and otherplane structures; introduction to design of prestressedconcrete structures.CIEE E4233x Design of large-scale bridges3 pts. Lect: 3. Professor Zoli.Prerequisites: CIEN E3121 or equivalent, andCIEN E3127 or equivalent. Design of large-scaleand complex bridges with emphasis on cablesupportedstructures. Static and dynamic loads,component design of towers, superstructuresand cables; conceptual design of major bridgetypes including arches, cable stayed bridges andsuspension bridges.CIEN E4234y Design of large-scale buildingstructures3 pts. Lect: 3. Members of the faculty.Prerequisites: CIEN E3121 and CIEN E3127.Modern challenges in the design of large-scalebuilding structures will be studied. Tall buildings,large convention centers, and majorsports stadiums present major opportunities forcreative solutions and leadership on the part ofengineers. This course is designed to exposethe students to this environment by having themundertake the complete design of a large structurefrom initial design concepts on through allthe major design decisions. The students workas members of a design team to overcome thechallenges inherent in major projects. Topicsinclude overview of major projects, project criteriaand interface with architecture, design offoundations and structural systems, design challengesin the post 9/11 environment and roles,responsibilities and legal issues.CIEN E4241x Geotechnical engineeringfundamentals3 pts. Lect: 3. Professor Mohammad.Prerequisites: CIEN E3141 or instructor’s permission.Bearing capacity and settlement of shallowand deep foundations; earth pressure theories;retaining walls and reinforced soil retaining walls;sheet pile walls; braced excavation; slope stability.CIEN E4242x Geotechnical earthquakeengineering3 pts. Lect: 3. Professor Ling.Prerequisites: CIEN E3141 or equivalent.Seismicity, earthquake intensity, propagation ofseismic waves, design of earthquake motion,seismic site response analysis, in situ andlaboratory evaluation of dynamic soil properties,seismic performance of underground structures,seismic performance of port and harbor facilities,evaluation and mitigation of soil liquefactionand its consequences. Seismic earth pressures,slopes stability, safety of dams and embankments,seismic code provisions and practice. Toalternate with E4244.CIEN E4243x Foundation engineering3 pts. Lect: 3. Professor Brant.Prerequisites: CIEN E3141 or equivalent.Conventional types of foundations and foundationproblems: subsurface exploration and testing.Performance of shallow and deep foundationsand evaluation by field measurements. Case historiesto illustrate typical design and constructionproblems. To alternate with CIEN E4246.CIEN E4244x Geosynthetics and wastecontainment3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CIEN E4241 or the equivalent.Properties of geosynthetics. Geosynthetic designfor soil reinforcement. Geosynthetic applicationsin solid waste containment system. To alternatewith CIEN E4242.CIEN C4245x Tunnel design and construction3 pts. Lect: 3. Professor Munfah.This course cover the engineering design andconstruction of different types of tunnel, includingcut and cover tunnel, rock tunnel, soft groundtunnel, immersed tub tunnel, and jacked tunnel.The design for the liner, excavation, and instrumentationare also covered. A field trip will bearranged to visit the tunneling site.CIEN E4246x Earth retaining structures3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CIEN E3141. Retaining structures,bulkheads, cellular cofferdams, and bracedexcavations. Construction dewatering andunderpinning. Instrumentation to monitor actualperformances. Ground improvement techniques,including earth reinforcement, geotextiles, andgrouting. To alternate with CIEN E4243.CIEN E4250y Waste containment designand practice3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ENME E3161 and CIEN E3141,or equivalents. Strategies for the containment ofburied wastes. Municipal and hazardous wastelandfill design; bioreactor landfills; vertical barriers,evapotranspiration barriers and capillary barriers;hydraulic containment; in situ stabilizationand solidification techniques; site investigation;monitoring and stewardship of buried wastes;options for land reuse/redevelopment.CIEE E4252x Environmental engineering3 pts. Lect: 3. Professor Chandran.Prerequisites: CHEM C1403 or equivalent;ENME E3161 or the equivalent. Engineeringaspects of problems involving human interactionwith the natural environment. Review of fundamentalsprinciples that underlie the disciplineof environmental engineering, i.e., constituenttransport and transformation processes in environmentalmedia such as water, air and ecosystems.Engineering applications for addressingenvironmental problems such as water qualityand treatment, air pollutant emissions, andhazardous waster remediation. Presented inthe context of current issues facing practicingengineers and government agencies, includinglegal and regulatory framework, environmentalimpact assessments, and natural resourcemanagement.CIEN E4253y Finite elements in geotechnicalengineering3 pts. Lect: 3. Professor Ling.Prerequisites: CIEN E3141 and CIEN E4332.State-of-the-art computer solutions in geotechnicalengineering; 3D consolidation, seepageflows, and soil-structure interaction; elementand mesh instabilities. To be offered in alternateyears with CIEN E4254.CIEN E4254y Geotechnical engineering inhighway design3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CIEN E3141. Reinforced earthslopes; static and seismic analyses; piles; flexibleand rigid pavement design.CIEN E4255y Flow in porous media3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CIEE E3250 or equivalent.Principles of groundwater flow, steady andtransient flow through porous media; pumpingtests, well hydraulics, potential theory; parameteridentification and calibration of groundwaterflow models; stochastic description ofheterogeneous porous media; physically-basedSEAS 2010–2011

numerical models for solution of groundwaterproblems; geostatistical simulation applicationsto groundwater problems; unsaturated flowproblems.CIEE E4257y Contaminant transport insubsurface systems3 pts. Lect: 3. Professor Mutch.Prerequisites: CIEE E3250 or equivalent. Singleand multiple phase transport in porous media;contaminant transport in variably saturatedheterogeneous geologic media; physically basednumerical models of such processes.CIEN E4260x Urban ecology studio4 pts. Lect: 3. Lab: 3. Professor Culligan.Prerequisites: Senior standing or instructor’spermission. Conjoint studio run with theGraduate School of Architecture, Planning andPreservation (GSAPP) that explores solutionsto problems of urban density. Engineering andGSAPP students will engage in a joint projectthat address habitability and sustainability issuesin an urban environment, and also provides communityservice. Emphasis will be on the integrationof science, engineering and design withina social context. Interdisciplinary approachesand communication will be stressed. The studiocan be used as a replacement for the capstonedesign project in CEEM Water Resources/Environmental Engineering concentration, orthe undergraduate design project in Earth andEnvironmental Engineering.CIEN E6131x Quantitative infrastructure riskmanagement3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: IEOR E4003, CIEN E4133 or theequivalent. Core concepts of risk analysis, riskmitigation, and quantitative risk managementapplied to civil infrastructure systems. State ofart of simulation applied to infrastructure riskmanagement during construction and operation.Public Private Partnership (PPP) risk management:identification, quantification, mitigation ofrisks in transportation and energy PPP systems.Risk management during construction using theenvelop method.CIEN E6132y Advanced systems andtechnologies for global project collaboration3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CIEN E4129 or the equivalent.Systems and technologies that support collaborativework in global projects. Informationtechnologies for design, visualization, projectmanagement, and collaboration in globallydistributed networks of design, fabrication, andconstruction organizations, including Web-based,parametric computer-aided modeling, projectorganizational simulation, and other emergingapplications. Global team project with students atcollaborating universities abroad.CIEN E6133y Advanced construction andinfrastructure risk management using realoptionsNot offered in 2010–2011.Prerequisites: CIEN E6131 Advanced conceptsof risk analysis and management applied to civilengineering systems. Identifying and valuingflexibility in construction and operation. Toolsto perform risk analysis in flexible civil infrastructuresystems. Valuation methods for realoptions. Risk flexibility analysis; integrating realoptions analysis with quantitative risk analysis.Applications to case studies on constructionmanagement, life-cycle cost analysis for infrastructureassets, public-private partnerships projects,real estate developments, and renewableenergy infrastructure projects.CIEN E6232x Advanced topics in concreteengineering3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CIEN E3125 or the equivalent.Behavior of concrete under general states ofstress, numerical modeling of steel and concrete,finite element analysis of reinforced concrete,design of slabs and their shell concrete structures.CIEN E6246y Advanced soil mechanics3 pts. Lect: 2.5. Professor Ling.Prerequisites: CIEN E3141. Stress-dilatancy ofsand; failure criteria; critical state soil mechanics;limit analysis; finite element method and casehistories of consolidation analysis.CIEN E6248x Experimental soil mechanics3 pts. Lect: 2.5. Not offered in 2010–2011.Prerequisites: CIEN E3141. Advanced soil testing,including triaxial and plane strain compressiontests; small-strain measurement. Modeltesting; application (of test results) to design.ENME E6333y Finite element analysis, II3 pts. Lect: 2.5. Professor Waisman.Prerequisites: CIEN E4332 or the instructor’spermission. Galerkin finite element formulation.Convergence requirements. Element and meshinstabilities. Stress calculation. Finite elementsin heat flow and dynamics. Nonlinear problems.Introduction to boundary element method.CIEN E9101x and y–S9101 Civil engineeringresearch1–4 pts. Members of the faculty.Advanced study in a specialized field under thesupervision of a member of the department staff.Before registering, the student must submit anoutline of the proposed work for approval of thesupervisor and the department chair.CIEN E9120x and y–S9120 Independentstudies in flight sciences3 pts. By conference.Prerequisites: the instructor’s permission. Thiscourse is geared toward students interested inflight sciences and flight structures. Topics relatedto aerodynamics, propulsion, noise, structuraldynamics, aeroelasticity, and structures may beselected for supervised study. A term paper isrequired.CIEN E9130x and y–S9130 Independentstudies in construction3 pts. By conference.Prerequisites: Permission by department chair andinstructor. Independent study of engineering andconstruction industry problems. Topics related tocapital planning and financing, project management,contracting strategies and risk allocation,dispute mitigation and resolution, and infrastructureassessment and management may be selected forsupervised study. A term paper is required.CIEN E9165x and y–S9165 Independentstudies in environmental engineering4 pts. By conference.Prerequisites: CIEN E4252 or the equivalent.Emphasizes a one-on-one study approach tospecific environmental engineering problems.Students develop papers or work on designproblems pertaining to the treatment of solidand liquid waste, contaminant migration, andmonitoring and sampling programs for remediationdesign.CIEN E9201x and y–S9201 Civil engineeringreports1–4 pts. By conference.A project on some civil engineering subjectapproved by department chair.CIEN E9800x and y–S9800 Doctoral researchinstruction3–12 pts. May be taken for 3, 6, 9, or 12 points,dependent on instructor’s permission.A candidate for the Eng.Sc.D. degree in civilengineering must register for 12 points of doctoralresearch instruction. Registration in CIENE9800 may not be used to satisfy the minimumresidence requirement for the degree.CIEN E9900x and y–S9900 DoctoraldissertationMembers of the faculty.A candidate for the doctorate may be required toregister for this course every term after the student’scoursework has been completed and untilthe dissertation has been accepted.COURSES IN ENGINEERINGMECHANICSSee also Civil Engineering.ENME E3105x or y Mechanics4 pts. Lect: 4. Professors Hone and Testa.Prerequisites: PHYS C1406 and MATHV1101-V1102 and V1201. Elements of statics;dynamics of a particle and systems of particles;dynamics of rigid bodies.ENME E3106x Dynamics and vibrations3 pts. Lect: 2. Professor Smyth.Prerequisites: Math E1201. Corequisites: ENMEE3105. Kinematics of rigid bodies; momentumand energy methods; vibrations of discrete andcontinuous systems; eigenvalue problems, naturalfrequencies and modes. Basics of computersimulation of dynamics problems using MATLABor Mathematica.ENME E3113x Mechanics of solids3 pts. Lect: 3. Professor Deodatis.Stress, stress resultants, equilibrium.Deformation. Material behavior in two dimen-103SEAS 2010–2011

104sions. Thermal stresses. Problems in flexure andtorsion, pressure vessels. Buckling.ENME E3114y Experimental mechanics ofmaterials4 pts. Lect: 2. Lab: 3. Professor Yin.Prerequisites: ENME E3113. Material behaviorand constitutive relations. Mechanical propertiesof metals and cement composites. Cementhydration. Modern construction materials.Experimental investigation of material propertiesand behavior of structural elements includingfracture, fatigue, bending, torsion, buckling.ENME E3161x Fluid mechanics4 pts. Lect: 3. Lab: 3. Professor Dasgupta.Prerequisites: ENME E3105 and ordinary differentialequations. Fluid statics. Fundamentalprinciples and concepts of flow analysis.Differential and finite control volume approach toflow analysis. Dimensional analysis. Applicationof flow analysis: flow in pipes, external flow, flowin open channels.ENME E4113x Advanced mechanics of solids3 pts. Lect: 3. Professor Yin.Stress and deformation formulation in two-andthree-dimensional solids; viscoelastic and plasticmaterial in one and two dimensions.ENME E4114y Mechanics of fractureand fatigue3 pts. Lect: 3. Professor Testa.Prerequisites: Undergraduate mechanics ofsolids course. Elastic stresses at a crack; energyand stress intensity criteria for crack growth;effect of plastic zone at the crack; fracture testingapplications. Fatigue characterization bystress-life and strain-life; damage index; crackpropagation; fail safe and safe life analysis.ENME E4202y Advanced mechanics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ENME E3105 or equivalent.Differentiation of vector functions. Review ofkinematics. Generalized coordinates and constraintequations. Generalized forces. Lagrange’sequations. Impulsive forces. Collisions.Hamiltonian. Hamilton’s principle.ENME E4214y Theory of plates and shells3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ENME E3113. Static flexuralresponse of thin, elastic, rectangular, and circularplates. Exact (series) and approximate(Ritz) solutions. Circular cylindrical shells.Axisymmetric and nonaxisymmetric membranetheory. Shells of arbitrary shape.ENME E4215x Theory of vibrations3 pts. Lect: 3. Professor Betti.Frequencies and modes of discrete and continuouselastic systems. Forced vibrations-steadystateand transient motion. Effect of damping.Exact and approximate methods. Applications.ENME E4332x Finite element analysis, I3 pts. Lect: 3. Professor Waisman.Prerequisites: Mechanics of solids, structuralanalysis, elementary computer programming, linearalgebra. Matrix methods of structural analysis:displacement method and flexibility methods.Principle of stationary potential energy. Rayleigh-Ritz approximation. Finite element approximation.Displacement-based elements for structuralmechanics. Isoparametric formulation.ENME E6220x Random processes inmechanics3 pts. Lect: 2.5. Professor Deodatis.Prerequisites: ENME E4215 or equivalent.Random variables, stationary and ergodic randomprocesses, correlation functions, and powerspectra. Input-output relations of linear systems:analysis of response of discrete and continuousstructures to random loadings. Crossing rates,peak distributions, and response analysis of nonlinearstructures to random loading. Simulation ofstationary random processes.ENME E6315x Theory of elasticity3 pts. Lect: 2.5. Professor Dasgupta.Foundations of continuum mechanics. Generaltheorems of elasticity. Application to stressanalysis and wave propagation.ENME E8320y Viscoelasticity and plasticity4 pts. Lect: 3. Professor Dasgupta.Prerequisites: ENME E6315 or equivalent, orinstructor’s permission. Constitutive equationsof viscoelastic and plastic bodies. Formulationand methods of solution of the boundary value,problems of viscoelasticity and plasticity.ENME E8323y Nonlinear vibrations3 pts. Lect: 2.5. Professor Smyth.Prerequisites: ENME E4215 or equivalent. Freeand forced motion of simple oscillators withnonlinear damping and stiffness. Exact, perturbation,iteration, and graphical methods of solution.Stability of motion. Chaotic vibrations.COURSES IN GRAPHICSGRAP E1115x and y Engineering graphics3 pts. Lect: 1. Lab: 3. Professor Sánchez.Open to all students. Visualization and simulationin virtual environments; computer graphicsmethods for presentation of data. 3-D modeling;animation; rendering; image editing; technicaldrawing. Lab fee: $300. 1220 S. W. MuddBuilding.GRAP E2005y Computer-aided engineeringgraphics3 pts. Lect: 1.5. Lab: 2.5. Professor Dasgupta.Prerequisites: MATH V1105. Basic conceptsneeded to prepare and understand engineeringdrawings and computer-aided representations:preparation of sketches and drawings, preparationand transmission of graphic information.Lectures and demonstrations, hands-on computeraidedgraphics laboratory work. Term project.GRAP E3115y Advanced computer modelingand animation3 pts. Lect: 1. Lab: 3. Professor Sánchez.Prerequisites: GRAP E1115 or instructor’s permission.Explores applications of 3D modeling,animation, and rendering techniques in the arts,architecture, engineering, entertainment and science.Visualization through conceptual modelingand animation techniques for product design andrealistic presentations. Lab fee: $300.GRAP E4005y Computer graphics inengineering3 pts. Lect: 3. Professor Dasgupta.Prerequisites: Any programming languageand linear algebra. Numerical and symbolic(algebraic) problem solving with Mathematica.Formulation for graphics application in civil,mechanical, and bioengineering. Example of twoandthree-dimensional curve and surface objectsin C++ and Mathematica; special projects ofinterest to electrical and computer science.SEAS 2010–2011

COMPUTER ENGINEERING PROGRAMAdministered by both the Electrical Engineering and Computer ScienceDepartments through a joint Computer Engineering Committee. Studentrecords are kept in the Electrical Engineering Department.1300 S. W. Mudd, MC 4712, 212-854-3105 / 450 Computer Sciencewww.compeng.columbia.edu105IN CHARGESteven M. Nowick508 Computer ScienceCOMPUTER ENGINEERINGCOMMITTEELuca Carloni, AssociateProfessor ofComputer ScienceStephen A. EdwardsAssociate Professor ofComputer ScienceThe computer engineeringprogram is run jointly by theComputer Science and ElectricalEngineering departments. It offers bothB.S. and M.S. degrees.The program covers some of engineering’smost active, exciting, andcritical areas, which lie at the interfacebetween CS and EE. The focus of themajor is on computer systems involvingboth digital hardware and software.Some of the key topics covered arecomputer design (i.e., computer architecture);embedded systems (i.e., thedesign of dedicated hardware/softwarefor cell phones, automobiles, robots,games, and aerospace); digital andVLSI circuit design; computer networks;design automation (i.e., CAD); andparallel and distributed systems (includingarchitectures, programming, andcompilers).The undergraduate major includesone substantial senior design course,either designing an entire microprocessor(EECS E4340), or an embeddedsystem (CSEE W4840) (including bothsoftware and hardware components),Martha A. KimAssistant Professor ofComputer ScienceVishal MisraAssociate Professor ofComputer ScienceSteven M. NowickProfessor of ComputerScienceDaniel RubensteinAssociate Professor ofComputer ScienceSimha SethumadhavanAssistant Professor ofComputer ScienceKenneth L. ShepardProfessor of ElectricalEngineeringStephen H. UngerProfessor Emeritus ofComputer Science (andElectrical Engineering)Charles A. ZukowskiProfessor of ElectricalEngineeringor providing hands-on experience indesigning and using a computer network(CSEE W4140).Students in the programs have two“home” departments. The ElectricalEngineering Department maintains studentrecords and coordinates advisingappointments.UNDERGRADUATE PROGRAMThis undergraduate program incorporatesmost of the core curricula in bothelectrical engineering and computerscience so that students will be wellprepared to work in the area of computerengineering, which substantiallyoverlaps both fields. Both hardwareand software aspects of computer scienceare included, and, in electricalengineering, students receive a solidgrounding in circuit theory and in electroniccircuits. The program includesseveral electrical engineering laboratorycourses as well as the ComputerScience Department’s advancedprogramming course. Detailed lists ofrequirements can be found atwww.compeng.columbia.edu/pages/ugrad.Students will be prepared to workon all aspects of the design of digitalhardware, as well as on the associatedsoftware that is now often an integralpart of computer architecture. They willalso be well equipped to work in thegrowing field of telecommunications.Students will have the prerequisites todelve more deeply into either hardwareor software areas, and enter graduateprograms in computer science, electricalengineering, or computer engineering.For example, they could take moreadvanced courses in VLSI, communicationstheory, computer architecture,electronic circuit theory, software engineering,or digital design.Minors in electrical engineering andcomputer science are not open to computerengineering majors, due to excessiveoverlapTechnical ElectivesThe Computer Engineering Programincludes 15 points of technical electives.Any 3000-level or higher courses listedin the Computer Science or ElectricalEngineering sections of this bulletincan be used for this requirement withthe following exceptions: ELEN E3000,EEHS E3900/4900, EEJR E4901, COMSW3101, COMS W4400, COMS W4405,courses used for other computer engineeringrequirements (including COMSW3203 and either CSEE W4840, EECSE4340, or CSEE W4140), and coursesthat have significant overlap with otherrequired or elective courses (e.g., COMSW3137 and COMS W3139). Up to oneSEAS 2010–2011

106COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARSEARLY-STARTING STUDENTSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and APMA E2101 (3) 3C1401 (3)C1402 (3)Lab C1493 (3) orchem. lab C1500 (3)PHYSICS(three tracks,choose one)C1601 (3.5)C1602 (3.5)Lab C1493 (3) orchem. lab C1500 (3)C2801 (4.5)C2802 (4.5)Lab W3081 (2) orchem. lab C1500 (3)CHEMISTRYone-semester lecture (3–4)C1403 or C1404 orC3045 or C1604Lab C1500 (3) either semester orphysics lab C1493 (3)CORE REQUIREDCOURSESELEN E1201 (3.5)Intro. to elec. eng. (either semester)ELEN E3801 (3.5)Signals and systemsCOMS W3137 (3) orW3139 (4)Data structuresCSEE W3827 (3)Fund. of computer sys.REQUIRED LABSELEN E3084 (1)Signals and systems labELEN E3082 (1)Digital systems labENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)HUMA C1001,HUMA C1002,COCI C1101,COCI C1102,REQUIREDor Global Core (3–4) or Global Core (3–4)NONTECHNICALELECTIVES 1 HUMA W1121 or ECON W1105 (4) andW1123 (3) 1 W1155 recitation (0)COMPUTERSCIENCECOMS W1004 (3) 2COMS W1007 (3) orW1009W3203 (3)Discrete math.PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1Some of these courses can be postponed to the junior or senior year to make room for taking the required core computer engineering courses.2Only required if needed to prepare for COMS W1007/W1009.3APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.SEAS 2010–2011

COMPUTER ENGINEERING: THIRD AND FOURTH YEARSEARLY-STARTING STUDENTS107SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIICORE REQUIREDCOURSESIEOR E3658 (3)ProbabilityCOMS W3157 (3)Advanced programmingELEN E3331 (3)Electronic circuitsCOMS W3261 (3)Computer sci. theoryCOMS W4118 (3)Operating systemsCOMS W4115 (3)Programming lang.ELEN E3201 (3.5)Circuit analysisCSEE W4823 (3)Advanced logic designorCSEE W4119 (3)Computer networksREQUIRED LABSELEN E3081 (1)Circuit analysis labELEN E3083 (1)Electronic circuits labEECS E4340 (3)Computer hardware designor CSEE W4840 (3)Embedded sys. designor CSEE W4140 (4)Networking labELECTIVESTECH 15 points required; see details on pages 105–107NONTECHComplete 27-point requirement; see page 10 or www.seas.columbia.edu for details(administered by the advising dean)TOTAL POINTS 1 16.5 17 15 15For a discussion about programming languages used in the program, please see www.compeng.columbia.edu. Check the late-starting student chart for footnotesabout various courses.1“Total points” assumes that 20 points of nontechnical electives and other courses are included.course may be chosen from outsidethe departments with adviser approval.Courses at the 3000 level or higher inother areas of engineering, math, andscience can be considered for approval,as long as they do not significantlyoverlap with other required or electivecourses. Economics courses cannot beused as technical electives.Starting EarlyStudents are strongly encouraged tobegin taking core computer engineeringcourses as sophomores. Theystart with ELEN E1201: Introductionto electrical engineering in the secondsemester of their first year and maycontinue with other core courses onesemester after that. For sample “earlystarting”and “late-starting” programs,see these degree track charts. It mustbe emphasized that these charts presentexamples only; actual schedulesmay be customized in consultation withacademic advisers.GRADUATE PROGRAMThe Computer Engineering Programoffers a course of study leading to thedegree of Master of Science (M.S.).The basic courses in the M.S. programcome from the Electrical Engineeringand Computer Science Departments.Students completing the program areprepared to work (or study further) insuch fields as digital computer design,digital communications, and the designof embedded computer systems.Applicants are generally expectedto have a bachelor’s degree in computerengineering, computer science, orelectrical engineering with at least a 3.2GPA in technical courses. The GraduateRecord Examination (GRE), General Testonly, is required of all applicants.Students must take at least 30 pointsof courses at Columbia University ator above the 4000 level. These mustinclude at least 15 points from thecourses listed below that are deemedcore to computer engineering. At least6 points must be included from eachdepartment. CSEE and EECS coursescan count toward either departmentminimum. Other courses may be chosenwith the prior approval of a facultyadviser in the Computer EngineeringProgram.Core Computer Engineering CoursesCOMS W4115: Programming languages andtranslatorsCOMS W4118: Operating systems, ICOMS W4995: Principles and practice of parallelprogrammingCOMS W6998: Topics in computer science: formalverification of hardware/softwaresystemsCSEE W4119: Computer networksCSEE W4140: Networking laboratoryCOMS W4180: Network securityCSEE W4823: Advanced logic designCSEE W4824: Computer architectureCSEE W4825: Digital systems design*CSEE W4840: Embedded systemsCOMS E6118: Operating systems, II*CSEE E6180: Modeling and performance evaluationCOMS E6181: Advanced Internet servicesCSEE E6824: Parallel computer architectureSEAS 2010–2011

108COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARSLATE-STARTING STUDENTSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and APMA E2101 (3) 3C1401 (3)C1402 (3)Lab C1493 (3) orchem. lab C1500 (3)PHYSICS(three tracks,choose one)C1601 (3.5)C1602 (3.5)Lab C1493 (3) orchem. lab C1500 (3)C2801 (4.5)C2802 (4.5)Lab W3081 (2) orchem. lab C1500 (3)CHEMISTRYone-semester lecture (3–4)C1403 or C1404 orC3045 or C1604Lab C1500 (3) either semester orphysics lab C1493 (3)CORE REQUIREDCOURSESELEN E1201 (3.5) 2Intro. to elec. eng. (either semester)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 orW1123 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)COMPUTERSCIENCECOMS W1004 (3) 1COMS W1007 (3) orW1009W3203 (3) 2Discrete math.PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1Only required if needed to prepare for COMS W1007/W1009.2Transfer and combined-plan students are expected to have completed the equivalent of the first- and second-year program listed above before starting theirjunior year. Note that this includes some background in discrete math (see COMS W3203) and electronic circuits (see ELEN E1201). Transfer and combined-planstudents are also expected to be familiar with Java before they start their junior year. If students must take the one-point Java course (COMS W3101-03) junior year,prerequisite constraints make it difficult to complete the remaining computer engineering program by the end of the senior year.3APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.SEAS 2010–2011

COMPUTER ENGINEERING: THIRD AND FOURTH YEARSLATE-STARTING STUDENTS109SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIIEOR E3658 (3) 1ProbabilityCOMS W3157 (3)Advanced programmingCOMS W4118 (3)Operating systemsCOMS W4115 (3)Programming lang.CORE REQUIREDCOURSESCOMS W3137 (3) orW3139 (4)Data structuresELEN E3201 (3.5)Circuit analysisELEN E3801 (3.5)Signals and systemsELEN E3331 (3)Electronic circuitsCOMS W3261 (3) 3Models of comp.CSEE W3827 (3)Fund. of computersystemsCSEE W4119 (3)Computer networksorCSEE W4823 (3)Advanced logic designREQUIRED LABSELEN E3081 (1) 2Circuit analysis labELEN E3084 (1) 2Signals and systems labELEN E3083 (1) 2Electronic circuits labELEN E3082 (1) 2Digital systems labEECS E4340 (3)Computer hardware designor CSEE W4840 (3)Embedded sys. designor CSEE W4140Networking labELECTIVESTECH 15 points required; see details on pages 105–107. 4NONTECHComplete 27-point requirement; see page 10 or www.seas.columbia.edu for details(administered by the advising dean).TOTAL POINTS 5 15 17 15 18For a discussion about programming languages used in the program, please see www.compeng.columbia.edu.1SIEO W3600, SIEO W4105, STAT W4105, and SIEO W4150 can be used instead of IEOR E3658, but W3600 and W4150 may not provide enough probabilitybackground for elective courses such as ELEN E3701. Students completing an economics minor who want such a background can take IEOR E3658 and augmentit with STAT W1211.2If possible, ELEN E3081 and ELEN E3084 should be taken along with ELEN E3201 and ELEN 3801 respectively, and ELEN E3083 and ELEN E3082 taken withELEN E3331 and CSEE W3827 respectively.3COMS W3261 can be taken one semester later than pictured.4The total points of technical electives is reduced to 12 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010.5Assuming technical electives taken Semesters VII and VIII, and 9 points of nontechnical electives taken Semesters VI, VII, and VIII.CSEE E6831: Sequential logic circuits*CSEE E6832: Topics in logic design theory*CSEE E6847: Distributed embedded systemsCSEE E6861: Computer-aided design of digitalsystemsELEN E4321: Digital VLSI circuitsELEN E4332: VLSI design laboratory*EECS E4340: Computer hardware designELEN E4702: Digital communicationsELEN E4810: Digital signal processingELEN E4830: Digital image processingELEN E4896: Music signal processingELEN E6321: Advanced digital electronic circuitsELEN E6488: Optical interconnects andinterconnection networksELEN E6761: Computer communicationnetworks, IELEN E6762: Computer communication networks, II*ELEN E6850: Visual information systemsELEN E6860: Advanced digital signal processing* Occasionally offeredThe overall program must include atleast 15 points of 6000-level ELEN,EECS, CSEE, or COMS courses (exclusiveof seminars). No more than 9 pointsof research may be taken for credit. Nomore than 3 points of a nontechnicalelective (at or above the 4000 level) maybe included. A minimum GPA of at least2.7 must be maintained, and all degreerequirements must be completed withinfive years of the beginning of the firstcourse credited toward the degree.SEAS 2010–2011

110COMPUTER SCIENCE450 Computer Science, MC 0401, 212-939-7000www.cs.columbia.eduCHAIRShree Kumar Nayar450 Computer Science212-939-7004VICE CHAIRVishal Misra512 Computer Science212-939-7061ASSOCIATE CHAIRFOR UNDERGRADUATEEDUCATIONAdam Cannon459 Computer Science212-939-7016DEPARTMENTALADMINISTRATORPatricia HerveyPROFESSORSAlfred V. AhoPeter K. AllenPeter BelhumeurSteven M. BellovinSteven K. FeinerJonathan L. GrossJulia HirschbergGail E. KaiserJohn R. KenderKathleen R. McKeownShree Kumar NayarSteven M. NowickKenneth A. RossHenning G. SchulzrinneSalvatore J. StolfoJoseph F. TraubHenryk WozniakowskiMihalis YannakakisYechiam YeminiASSOCIATE PROFESSORSLuca CarloniStephen A. EdwardsLuis GravanoTony JebaraAngelos D. KeromytisTal MalkinVishal MisraJason NiehDaniel S. RubensteinRocco ServedioASSISTANT PROFESSORSAugustin ChaintreauEitan GrinspunMartha Allen KimItsik Pe’erSimha SethumadhavanJunfeng YangLECTURER IN DISCIPLINEAdam CannonASSOCIATED FACULTYEdward G. Coffman JrDana Pe’erClifford SteinSteven H. Unger(professor emeritus)Vladimir Vapnik*SENIOR RESEARCHSCIENTISTSDavid L. Waltz*Arthur G. WerschulzMoti YungRESEARCH SCIENTISTSRebecca PassonneauOwen Rambow*ASSOCIATE RESEARCHSCIENTISTSMarta Arias*Jiang Chen*Wei Chu*Mona Diab*Nizar Habash*Claire Monteleoni*Anargyros PapageorgiouCynthia Rudin*Ansaf Salleb-Audissi**Columbia Center for Computational Learning SystemsThe function and influence of thecomputer is pervasive in contemporarysociety. Today’s computersprocess the daily transactionsof international banks, the data fromcommunications satellites, the imagesin video games, and even the fuel andignition systems of automobiles.Computer software is as commonplacein education and recreation as it isin science and business. There is virtuallyno field or profession that does not relyupon computer science for the problemsolvingskills and the production expertiserequired in the efficient processing ofinformation. Computer scientists, therefore,function in a wide variety of roles,ranging from pure theory and design toprogramming and marketing.The computer science curriculumat Columbia places equal emphasis ontheoretical computer science and mathematicsand on experimental computertechnology. A broad range of upper-levelcourses is available in such areas asartificial intelligence, computational complexityand the analysis of algorithms,combinatorial methods, computer architecture,computer-aided digital design,computer communications, databases,mathematical models for computation,optimization, and software systemsLaboratory FacilitiesThe department has well-equipped labareas for research in computer graphics,computer-aided digital design, computervision, databases and digital libraries,data mining and knowledge discovery,distributed systems, mobile and wearablecomputing, natural-language processing,networking, operating systems,programming systems, robotics, userinterfaces, and real-time multimedia.The computer facilities include ashared infrastructure of Sun and Linuxmultiprocessor file servers, NetApp fileservers, a student interactive teaching andresearch lab of high-end multimedia workstations,a load balanced Web cluster with6 servers and business process servers,a large student laboratory, featuring 18Windows machines and 33 Linux towerseach with 8 cores and 24GB memory; aremote Linux cluster with 17 servers, alarge Linux compute cluster and a numberof computing facilities for individualresearch labs. In addition, the data centerhouses a compute cluster consisting of aLinux cloud with 43 servers each with 2Nehalem processors, 8 cores and 24GBmemory. This cloud can support approximately5000 of VMware instances.SEAS 2010–2011

111Research labs contain Puma 500and IBM robotic arms; a UTAH-MITdexterous hand; an Adept-1 robot; threemobile research robots; a real-timedefocus range sensor; PC interactive3-D graphics workstations with 3-Dposition and orientation trackers; prototypewearable computers, wall-sizedstereo projection systems; see-throughheadmounted displays; a networkingtestbed with three Cisco 7500 backbonerouters, traffic generators, Ethernetswitches, Sun Ray thin clients, and a17-node (34CPU) IBM Netfinity cluster.The department uses a 3COM SIP IPphone system. The protocol was developedin the department.The servers are connected on a gigabitnetwork; all have remote consolesand remote power for easy maintenanceafter hours. The rest of the department’scomputers are connected via a switched100 Mb/s Ethernet network, which hasdirect connectivity to the campus OC-3Internet and Internet2 gateways. Thecampus has 802.11a/b wireless LANcoverage.The research facility is supported bya full-time staff of professional systemadministrators and programmers, aidedby a number of part-time student systemadministrators.UNDERGRADUATE PROGRAMComputer science majors at Columbiastudy an integrated curriculum, partiallyin areas with an immediate relationshipto the computer, such as programminglanguages, operating systems,and computer architecture, and partiallyin theoretical computer science andmathematics. Thus, students obtain thebackground to pursue their interestsboth in applications and in theoreticaldevelopments.Practical experience is an essentialcomponent of the computer scienceprogram. Undergraduate studentsare often involved in advanced facultyresearch projects using state-of-the-artcomputing facilities. Qualified majorssometimes serve as consultants at theComputer Center, which operates severallabs with microcomputers and terminalsavailable at convenient locationson the campus.Upper-level students in computerscience may assist faculty memberswith research projects, particularly in thedevelopment of software. Ongoing facultyprojects include algorithmic analysis,computational complexity, softwaretool design, distributed computation,modeling and performance evaluation,computer networks, computer architecture,CAD for digital systems, computergraphics, programming environments,expert systems, natural language processing,computer vision, robotics,multicomputer design, user interfaces,VLSI applications, artificial intelligence,combinatorial modeling, virtual environments,and microprocessor applications.Students are strongly encouraged toarrange for participation by consultingindividual faculty members.Most graduates of the computer scienceprogram at Columbia step directlyinto career positions in computer sciencewith industry or government, orcontinue their education in graduatedegree programs. Many choose to combinecomputer science with a secondcareer interest by taking additional programsin business administration, medicine,or other professional studies.For further information on the undergraduatecomputer science program,please see the home page (www.cs.columbia.edu/education/undergrad)and the Quick Guide (www.cs.columbia.edu/education/undergrad/seasguide).Technical ElectivesAll technical electives except thosenoted in each track must be approvedby the adviser. In every case, the technicalelective course must be at the 3000level or higher. All technical electivesshould be taken in computer science.With the adviser’s approval, however,courses in other departments may betaken as technical electives; in everysuch case, the subject of the coursemust have a strong and obvious connectionwith computer science. COMSW4400: Computers and society andELEN E4901: Telecommunication networksand applications are not acceptableas technical electives and are theonly advanced computer science coursesthat cannot be taken as electives.Students are encouraged to selectone of the following five preapprovedgroupings of electives called “tracks.”An advanced version of each track isavailable by invitation for qualified studentswho wish an extra opportunity foradvanced learning.The following courses are requiredas a preparation for all tracks: COMSW1004, W1007 (or W1009), W3137(or W3139), W3157, W3203, W3210,W3251, W3261, CSEE W3827,SEAS 2010–2011

112COMPUTER SCIENCE PROGRAM: FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) COMS W3210 (3)PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)Chemistry or physics lab:PHYS C1493 (3) orCHEM W3081 (2) orCHEM C1500 (3) orCHEM C3085 (4)CHEMISTRY(choose one course)one-semester lecture (3–4)C1403 or C1404 orC3045 or C1604either semesterENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESECON W1105 (4)andW1105 recitation (0)either semesterHUMA C1001,COCI C1101,or Global Core (3–4)HUMA C1121 or C1123 (3)either semesterHUMA C1002,COCI C1102,or Global Core (3–4)REQUIREDTECH ELECTIVESProfessional-level course (3) (see page 12) eithersemesterCOMPUTERSCIENCECOMS W1004 (3)Intro. to computer scienceeither semesterCOMS W1009 (3) orCOMS W1007 (3)Object-orientedprogrammingandCOMS W3203 (3)COMS W3137 (4) orCOMS W3139 (4)Data structuresandCOMS W3157 (4)Discrete mathAdv. programmingPHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semesterand SIEO W4150 (SIEO W3600 isan accepted substitute for W4150).Collectively these courses are called theCS Core Curriculum.Students who pass the ComputerScience Advanced Placement (AP)Exam, either A or AB, with a 4 or 5 willreceive 3 points of credit and exemptionfrom COMS W1004.Note: A maximum of one coursepassed with a grade of D may be countedtoward the major or minor.Track 1: Foundations of CS TrackThe foundations track is suitable forstudents who plan to concentrate ontheoretical computer science in graduateschool or in mathematical topics suchas communications security or scientificcomputation in their career plans.Register for track course COMS E0001.REQUIRED: 3 coursesCSOR W4231: Analysis of algorithmsCOMS W4236: Introduction to computationalcomplexityCOMS W4241: Numerical algorithms and complexityBREADTH: 2 coursesAny COMS 3000- or 4000-level courses exceptthose countable toward the CS core or foundationsof CS trackELECTIVES: any 5 courses from the followinglistCOMS W4203: Graph theoryCOMS W4205: Combinatorial theoryCOMS W4252: Computational learning theoryCOMS W4261: Introduction to cryptographyCOMS W4281: Quantum computingCOMS W4444: Programming and problem solvingCOMS W4771: Machine learningCOMS W4772: Advanced machine learningCOMS W4995: Math foundations of machine learningCOMS E6232: Analysis of algorithms, IISEAS 2010–2011

COMPUTER SCIENCE: THIRD AND FOURTH YEARS113SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIREQUIREDCOURSESCOMS W3251 (3)Computational lin. algebraCOMS W3261 (3)Computer sci. theoryCSEE W3827 (3)Fund. of computer sys.SIEO W4150 (3)orSIEO W3600 (4)Prob. and stat.ELECTIVESNONTECH 3 points 6 points 3 pointsTECH 3 points 6 points 12 points 9 pointsTOTAL POINTS 15 15–16 15 9The primary programming languages for the undergraduate major are C and Java, and students are expected to learn both at an early stage. The language for COMSW1004/W1007/W1009/W3137/W3139 is Java. COMS W1004 is waived for students who have had AP computer science in high school.COMS E6261: Advanced crytographyCOMS E6717: Information theoryCOMS E6998: Approximation algorithmsCOMSW3902: Undergraduate thesis (with adviserapproval; may be repeated for credit)COMSW3998: Projects in Computer Science (withadviser approval; may be repeatedfor credit)COMSW4901: Projects in Computer Science (withadviser approval; may be repeatedfor credit)COMSE6901: Projects in Computer Science (withadviser approval; may be repeatedfor credit)Note: No more than 6 units of project/thesiscourses (COMSW3902, COMSW3998,COMSW4901, and COMSE6901) can counttoward the major.Track 2: Systems TrackThe systems track is for students interestedin the implementation of softwareand/or hardware systems. Register fortrack course COMS E0002.REQUIRED: 3 coursesCOMS W4115: Programming languages andtranslatorsCOMS W4118: Operating systemsCSEE W4119: NetworkingBREADTH: 2 coursesAny COMS 3000- or 4000-level course exceptthose countable for the CS core or systems trackELECTIVES: any 5 courses from the followinglistAny COMS W41xx courseAny COMS W48xx courseCOMS W4444: Programming and problem solvingCOMS W3902: Undergraduate thesis (with adviserapproval; may be repeated for credit)COMS W3998: Undergraduate projects incomputer science (with adviserapproval; may be repeated forcredit)COMS W4901: Projects in computer science (withadviser approval; may be repeatedfor credit)COMS W4995-W4996: Special topics in computerscienceCOMS E6901: Projects in computer science (withadviser approval; may be repeatedfor credit)Any COMS E61xx E68xx course (with adviserapproval)Note: No more than 6 units of project/thesis courses(COMS W3902, COMS W3998, COMS W4901,COMS E6901) can count toward the major.Track 3: Artificial Intelligence TrackThe artificial intelligence track is forstudents interested in machine learning,robots, and systems capable ofexhibiting “human-like” intelligence. Atotal of ten required, breadth, and electivecourses are to be chosen from thefollowing schedule. Register for trackcourse COMS E0003.REQUIRED: 1 courseCOMS W4701: Artificial intelligencePlus any 2 courses from:W4705: Natural language processingCOMS W4731: Computer visionCOMS W4733: Computational aspects of roboticsCOMS W4771: Machine learningBREADTH: 2 coursesAny 3-point COMS 3000- or 4000-level courseexcept those countable toward the CS core orelective courses for the artificial intelligence trackELECTIVES: Up to 5 courses from the followinglistAny COMS W40xx course with adviser approvalCOMS W4165: Pixel processingCOMS W4252: Computational learning theoryAny COMS W47xx course if not used as arequired courseCOMS W4995: Special topics, I (with adviserapproval; may be repeated)COMS W4996: Special topics, II (with adviserapproval; may be repeated)Any COMS W67xx courseCOMS E6998: Topics in computer science, I (withadviser approval)COMS E6999: Topics in computer science, II (withadviser approval)Up to 2 courses from the following listCOMS W3902: Undergraduate thesis (with adviserapproval; may be repeated forcredit)COMS W3998: Undergraduate projects incomputer science (with adviserapproval; may be repeated forcredit)COMS W4901: Projects in computer science (withadviser approval; may be repeatedfor credit)COMS E6901: Projects in computer science (withadviser approval; may be repeatedfor credit)SEAS 2010–2011

114Up to 1 course from the following listCOMS W4111: Database systemsCOMS W4160: Computer graphicsCOMS W4170: User interface designCOMS W4999: Computing and the humanitiesNote: No more than 6 units of project/thesiscourses (COMS W3902, COMS W3998, COMSW4901, COMS E6901) can count toward themajor.Track 4: Applications TrackThe applications track is for studentsinterested in the implementation of interactivemultimedia applications for theInternet and wireless networks. Registerfor track course COMS E0004.REQUIRED: 3 coursesW4115: Programming languages and translatorsCOMS W4170: User interface designCOMS W4701: Artificial intelligenceBREADTH: 2 coursesAny COMS 3000- or 4000-level courses exceptthose countable toward the CS core or applicationstracksELECTIVES: 5 courses from the following listAny COMS W41xx courseAny COMS W47xx courseCOMS W3902: Undergraduate thesis (with adviserapproval; may be repeated forcredit)COMS W3998: Undergraduate projects incomputer science (with adviserapproval; may be repeated forcredit)COMS W4901: Projects in computer science (withadviser approval; may be repeatedfor credit)COMS W4995-W4996: Special topics in computerscience, I and II (withadviser approval)COMS E6901: Projects in computer science(with adviser approval; may berepeated for credit) or otherCOMS E69xx course (with adviserapproval)Any COMS E69xx course (with adviser approval)Note: No more than 6 units of project/thesiscourses (COMS W3902, COMS W3998, COMSW4901, COMS E6901) can count toward themajor.Track 5: Vision and Graphics TrackObjective: The vision and graphics trackexposes students to interesting newfields and focuses on visual informationwith topics in vision, graphics, humancomputerinteraction, robotics, modeling,and learning. Students learn aboutfundamental ways in which visual informationis captured, manipulated, andexperienced. Register for track courseCOMS E0005.REQUIRED: 2 coursesCOMS W4731: Computer visionCOMS W4160: Computer graphicsBREADTH: 2 coursesAny COMS 3000- or 4000-level courses exceptthose countable toward the CS core or vision andgraphics trackELECTIVES: 6 courses from the following listCOMS W4162: Advanced computer graphicsCOMS W4165: Pixel processingCOMS W4167: Computer animationCOMS W4170: User interface designCOMS W4172: 3D user interface designCOMS W4701: Artificial intelligenceCOMS W4733: Computational aspects of roboticsCOMS W4735: Visual interfaces to computersCOMS W4771: Machine learningCOMS W4995: Video game technology anddesignCOMS W3902: Undergraduate thesis (withadviser approval; may be repeatedfor credit)COMS W3998: Undergraduate projects incomputer science (with adviserapproval; may be repeated forcredit)COMS W4901: Projects in computer science (withadviser approval; may be repeatedfor credit)COMS W4995-W4496: Special topics in computerscience, I and II (withadviser approval)COMS E6901: Projects in computer science (withadviser approval; may be repeatedfor credit)Any COMS E691x course (with adviser approval)Note: No more than 6 units of project/thesiscourses (COMS W3902, COMS W3998, COMSW4901 COMS E6901) can count toward the major.Track 6: AdvancedThe advanced track of the B.S. inComputer Science provides extraopportunity for advanced learning. Itcomprises accelerated versions of theother five tracks. Entry is only by collectivefaculty invitation, extended to studentswho have already completed thecore courses and the required coursesfor one of those tracks.REQUIRED TRACK COURSESA student designates one of the five other trackareas and completes the set of required trackcourses for that track, prior to entry into theAdvanced Track. There are two or three courses,depending on the designated area.BREADTH REQUIREMENTTwo breadth courses of the designated track.ELECTIVESAt least two 4000-level lecture courses from themenu for the designated track, plus two 6000-levelcourses in the designated track area.THESISThere is a required 6-point senior thesis.INVITATIONOnly the top 20 percent of computer sciencemajors in course performance in computer sciencecourses will be considered for invitation during thejunior year. (A student in the advanced track whodoes not maintain this status may be required toreturn to his or her previously selected track area.)GRADUATE PROGRAMSThe Department of Computer Scienceoffers graduate programs leading to thedegree of Master of Science, the professionaldegree of Computer SystemsEngineer and the degree of Doctor ofPhilosophy. Both the Aptitude Testand Advanced Tests of the GraduateRecord Examination (GRE) are requiredfor admission to the department’sgraduate programs. Applicants forSeptember admission should take theGREs by October of the preceding year.Applicants for January admission shouldtake these exams by April of the precedingyear.The course requirements in all programsare flexible, and each student isurged to design his or her own programunder the guidance of a faculty adviser.The student’s program should focus ona particular field of computer science.Among the fields of graduate studyin computer science are analysis ofalgorithms, artificial intelligence, expertsystems, natural language understanding,computer vision, multicomputerdesign, VLSI applications, combinatorialmodeling, combinatorial optimization,computational complexity, computerarchitecture and design, computer communicationsnetworks, computer graphics,database machines and systems,microprocessors, parallel computation,programming environments, programminglanguages, robotics, user interfaces,software design, computationalbiology, computer security, and machinelearning.Graduate students are encouragedactively to pursue research.Faculty members of the Departmentof Computer Science are engaged inexperimental and theoretical research inmost of the fields in which courses areoffered. The degree of doctor of philosophyrequires a dissertation based on thecandidate’s original research, which isSEAS 2010–2011

supervised by a faculty member.The professional degree programalso provides the student with theopportunity to specialize beyond thelevel of the Master of Science program.The program leading to thedegree of Computer Systems Engineeris particularly suited to those who wishto advance their professional developmentafter a period of industrialemployment.DUAL DEGREE PROGRAM INJOURNALISM AND COMPUTERSCIENCEThe Graduate School of Journalismand the School of Engineeringand Applied Science offer a dualdegree program leading to the M.S.degree from the Graduate School ofJournalism and the M.S. degree inComputer Science from the School ofEngineering and Applied Science.Admitted students will enroll for atotal of five semesters—approximatelythree in The Fu Foundation School ofEngineering and Applied Science andtwo in the Journalism School. In additionto taking classes already offeredat the journalism and engineeringschools, students will attend a seminarand workshop designed specificallyfor the joint program. The seminar willteach students about the impact ofdigital techniques on journalism; theemerging role of citizens in the newsprocess; the influence of social media;and the changing business modelsthat will support newsgathering. In theworkshop, students will use a handsonapproach to delve deeply intoinformation design, focusing on howto build a site, section, or applicationfrom concept to development, ensuringthe editorial goals are kept uppermostin mind.COURSES IN COMPUTERSCIENCEIn the listing below, the designatorCOMS (Computer Science) is understoodto precede all course numbers forwhich no designator is indicated. NOTE:Students may receive credit for only oneof the following two courses: COMSW1003 and W1004. Likewise studentsmay receive credit for only one of thefollowing four courses: COMS W3133,W3134, W3137, and W3139.COMS W1001x and y Introduction toinformation science3 pts. Lect: 3. Professor Cannon.Basic Introduction to concepts and skills inInformation Sciences: human-computer interfaces,representing information digitally, organizingand searching information on the World WideWeb, principles of algorithmic problem solving,introduction to database concepts, introduction toprogramming in Python.COMS W1003x or y Introduction to computerscience and programming in C3 pts. Lect: 3.A general introduction to computer science concepts,algorithmic problem-solving capabilities,and programming skills in C. Columbia Universitystudents may receive credit for only one of thefollowing three courses: 1003, 1004, and 1005.COMS W1004x and y Introduction tocomputer science and programming in Java3 pts. Lect: 3. Professor Cannon.A general introduction to computer science forscience and engineering students interestedin majoring in computer science or engineering.Covers fundamental concepts of computerscience, algorithmic problem-solving capabilities,and introductory Java programming skills.Assumes no prior programming background.Columbia University students may receive creditfor only one of the following three courses: 1003,1004, and 1005.COMS W1005x and y Introduction tocomputer science and programming inMATLAB3 pts. Lect: 3. Professor Pe’er.Prerequisites: None Corequisites: None A generalintroduction to computer science concepts,algorithmic problem-solving capabilities, and programmingskills in MATLAB. Assumes no priorprogramming background. Columbia Universitystudents may receive credit for only one of thefollowing three courses: 1003, 1004, and 1005.COMS W1007x and y Object-orientedprogramming and design in Java3 pts. Lect: 3. Professor Kender.Prerequisites: COMS W1004 or AP ComputerScience with a grade of 4 or 5. The secondcourse for majors in computer science. A rigoroustreatment of object-oriented concepts usingJava as an example language. Development ofsound programming and design skills, problemsolving and modeling of real world problems fromscience, engineering, and economics using theobject-oriented paradigm.ECBM E3060x Introduction to genomicinformation science and technology3 pts. Lect: 3. Professor Anastassiou.Introduction to the information system paradigmof molecular biology. Representation, organization,structure, function and manipulation of thebiomolecular sequences of nucleic acids andproteins. The role of enzymes and gene regulatoryelements in natural biological functions aswell as in biotechnology and genetic engineering.Recombination and other macromolecular processesviewed as mathematical operations withsimulation and visualization using simple computerprogramming. This course shares lectureswith ECBM E4060, but the work requirementsdiffer somewhat.COMS W3101x and y Programming languages1 pt. Lect: 1. Professors Isukapalli and Boyaci.Prerequisites: Fluency in at least one programminglanguage. Introduction to a programminglanguage. Each section is devoted to a specificlanguage. Intended only for those who arealready fluent in at least one programming language.Sections may meet for one hour per weekfor the whole term, for three hours per week forthe first third of the term, or for two hours perweek for the first six weeks. May be repeated forcredit if different languages are involved.COMS W3133x or y Data structures in C3 pts. Lect: 3.Prerequisites: COMS W1003 or knowledge ofC. Not intended for computer science majors.Data types and structures: arrays, stacks, singlyand doubly linked lists, queues, trees, sets, andgraphs. Programming techniques for processingsuch structures: sorting and searching, hashing,garbage collection. Storage management.Rudiments of the analysis of algorithms. Taughtin C. Note: Due to significant overlap, studentsmay receive credit for only one of the followingfour courses: COMS W3133, W3134, W3137,and W3139.COMS W3134x and y Data structures in Java3 pts. Lect: 3. Professor Hershkop.Prerequisites: COMS W1004 or knowledge ofJava. Not intended for computer science majors.Data types and structures: arrays, stacks, singlyand doubly linked lists, queues, trees, sets, andgraphs. Programming techniques for processingsuch structures: sorting and searching,hashing, garbage collection. Storage management.Rudiments of the analysis of algorithms.Taught in Java. Note: Due to significant overlap,students may receive credit for only one of thefollowing four courses: COMS W3133, W3134,W3137, and W3139.COMS W3137x and y Data structures andalgorithms4 pts. Lect: 3. Professor Blaer.Prerequisites: COMS W1007. Corequisites:COMS W3203. Data types and structures:arrays, stacks singly and doubly linked lists,queues, trees, sets, and graphs. Programmingtechniques for processing such structures: sortingand searching, hashing, garbage collection.115SEAS 2010–2011

116Storage management. Design and analysis ofalgorithms. Taught in Java. Note: Due to significantoverlap, students may receive credit for onlyone of the following four courses: COMS W3133,W3134, W3137, and W3139.COMS W3157x and y Advanced programming4 pts. Lect: 4. Professor Keromytis.Prerequisites: COMS W1007. Practical, hands-onintroduction to programming techniques and toolsfor professional software construction, includinglearning how to write code to given specificationsas well as document the results. Providesintroductory overview of C and C++ in a UNIXenvironment, for students with Java background.Also introduces scripting languages (Perl) andbasic web programming. UNIX programming utilitiesare also covered. Lab required.COMS W3203x and y Discrete mathematics:introduction to combinatorics and graphtheory3 pts. Lect: 3. Professor Gross.Prerequisites: Any introductory course in computerprogramming. Logic and formal proofs,sequences and summation, mathematical induction,binomial coefficients, elements of finiteprobability, recurrence relations, equivalencerelations and partial orderings, and topics ingraph theory (including isomorphism, traversability,planarity, and colorings).COMS W3210y Scientific computation3 pts. Lect: 3.Prerequisites: Two terms of calculus. Introductionto computation on digital computers. Designand analysis of numerical algorithms. Numericalsolution of equations, integration, recurrences,chaos, differential equations. Introduction toMonte Carlo methods. Properties of floating pointarithmetic. Applications to weather prediction,computational finance, computational science,and computational engineering.COMS W3251x Computational linear algebra3 pts. Lect: 3. Professor Papageorgiou.Prerequisites: two terms of calculus.Computational linear algebra, solution of linearsystems, sparse linear systems, least squares,eigenvalue problems, and numerical solution ofother multivariate problems as time permits.COMS W3261x and y Computer science theory3 pts. Lect: 3. Professor Aho.Prerequisites: COMS W3203. Corequisites:COMS W3137. Regular languages: deterministicand nondeterministic finite automata, regularexpressions. Context-free languages: contextfreegrammars, push-down automata. Turingmachines, the Chomsky hierarchy, and theChurch-Turing thesis. Introduction to complexitytheory and NP-completeness.CSEE W3827x and y Fundamentals ofcomputer systems3 pts. Lect: 3. Professor Rubenstein.Prerequisites: An introductory programmingcourse. Fundamentals of computer organizationand digital logic. Boolean algebra, Karnaughmaps, basic gates and components, flip-flopsand latches, counters and state machines, basicsof combinational and sequential digital design.Assembly language, instruction sets, ALUs,single-cycle and multi-cycle processor design,introduction to pipelined processors, caches, andvirtual memory.COMS W3902x and y Undergraduate thesis1–6 pts.Prerequisites: Agreement by faculty member toserve as thesis adviser. An independent theoreticalor experimental investigation by an undergraduatemajor of an appropriate problem incomputer science carried out under the supervisionof a faculty member. A formal written reportis mandatory and an oral presentation may alsobe required. May be taken over more than oneterm, in which case the grade is deferred untilall 6 points have been completed. Consult thedepartment for section assignment.COMS W3995x or y Special topics incomputer science3 pts. Lect: 3.Prerequisites: Instructor’s permission. Consult thedepartment for section assignment. Special topicsarranged as the need and availability arise. Topicsare usually offered on a one-time basis. Sincethe content of this course changes each time it isoffered, it may be repeated for credit.COMS W3998x and y Undergraduate projectsin computer science1–3 pts.Prerequisites: Approval by a faculty memberwho agrees to supervise the work. Independentproject involving laboratory work, computer programming,analytical investigation, or engineeringdesign. May be repeated for credit, but notfor a total of more than 3 points of degree credit.Consult the department for section assignment.ECBM E4060x Introduction to genomicinformation3 pts. Lect: 3. Professor Anastassiou.Introduction to the information system paradigmof molecular biology. Representation, organization,structure, function, and manipulation of thebiomolecular sequences of nucleic acids andproteins. The role of enzymes and gene regulatoryelements in natural biological functions aswell as in biotechnology and genetic engineering.Recombination and other macromolecular processesviewed as mathematical operations withsimulation and visualization using simple computerprogramming. This course shares lectureswith ECBM E3060, but the work requirementsdiffer somewhat.COMS W4111x and y Introduction to databases3 pts. Lect: 3. Professor Gravano.Prerequisites: COMS W3137 or W3134, fluencyin Java; or permission of the instructor. Thefundamentals of database design and applicationdevelopment using databases: entity-relationshipmodeling, logical design of relational databases,relational data definition and manipulation languages,SQL, XML, query processing, physicaldatabase tuning, transaction processing, security.Programming projects are required.COMS W4112y Database systemimplementation3 pts. Lect: 2.5.Prerequisites: COMS W4111; fluency in Java orC++. CSEE W3827 is recommended. The principlesand practice of building large-scale databasemanagement systems. Storage methodsand indexing, query processing and optimization,materialized views, transaction processing andrecovery, object-relational databases, paralleland distributed databases, performance considerations.Programming projects are required.COMS W4115x and y Programming languagesand translators3 pts. Lect: 3. Professor Edwards.Prerequisites: COMS W3137 or equivalent,W3261, and CSEE W3827, or instructor’s permission.Modern programming languages andcompiler design. Imperative, object-oriented,declarative, functional, and scripting languages.Language syntax, control structures, data types,procedures and parameters, binding, scope,run-time organization, and exception handling.Implementation of language translation toolsincluding compilers and interpreters. Lexical,syntactic and semantic analysis; code generation;introduction to code optimization. Teamsimplement a language and its compiler.COMS W4117x or y Compilers andinterpreters3 pts. Lect: 3.Prerequisites: COMS W4115 or instructor’spermission. Continuation of COMS W4115, withbroader and deeper investigation into the designand implementation of contemporary languagetranslators, be they compilers or interpreters.Topics include: parsing, semantic analysis, codegeneration and optimization, run-time environments,and compiler-compilers. A programmingproject is required.COMS W4118x and y Operating systems, I3 pts. Lect: 3. Professor Nieh.Prerequisites: CSEE W3827 and knowledge ofC and programming tools as covered in W3157or W3101, or instructor’s permission. Designand implementation of operating systems.Topics include process management, processsynchronization and interprocess communication,memory management, virtual memory, interrupthandling, processor scheduling, device management,I/O, and file systems. Case study of theUNIX operating system. A programming projectis required.SEAS 2010–2011

CSEE W4119x and y Computer networks3 pts. Lect: 3. Professor Misra.Corequisites: SIEO W3600 or IEOR E3658 orequivalent Introduction to computer networks andthe technical foundations of the Internet, includingapplications, protocols, local area networks,algorithms for routing and congestion control,security, elementary performance evaluation.Several written and programming assignmentsrequired.CSEE W4140x or y Networking laboratory4 pts. Lect: 3. Professor Zussman.Prerequisites: CSEE 4119 or equivalent In thiscourse, students will learn how to put “principlesinto practice,” in a hands-on networking labcourse. The course will cover the technologiesand proctocols of the Internet using equipmentcurrently available to large Internet serviceproviders such as CISCO routers and end systems.A set of laboratory experiments provideshands-on experience with engineering wideareanetworks and will familiarize students withthe Internet Protocol (IP), Address ResolutionProtocol (ARP), Internet Control MessageProtocol (ICMP), User Datagram Protocol (UDP)and Transmission Control Protocol (TCP), theDomain Name System (DNS), routing protocols(RIP, OSPF, BGP), network management protocols(SNMP, and application-level protocols(FTP, TELNET, SMTP).COMS W4156x Advanced software engineering3 pts. Lect: 3. Professor Kaiser.Prerequisites: Substantial software developmentexperience in Java, C++ or C# beyond the levelof COMS W3157. Recommended corequisites:COMS W4111. Software lifecycle from theviewpoint of designing and implementing N-tierapplications (typically utilizing Web browser,web server, application server, database). Majoremphasis on quality assurance (code inspection,unit and integration testing, security and stresstesting). Centers on a student-designed teamproject that leverages component services (e.g.,transactions, resource pooling, publish/subscribe)for an interactive multi-user applicationsuch as a simple game.COMS W4160y Computer graphics3 pts. Lect: 3.Prerequisites: COMS W3137 or W3139,W4156 is recommended. Strong programmingbackground and some mathematical familiarityincluding linear algebra is required. Introductionto computer graphics. Topics include 3D viewingand projections, geometric modeling using splinecurves, graphics systems such as OpenGL,lighting and shading, and global illumination.Significant implementation is required: the finalproject involves writing an interactive 3D videogame in OpenGL.COMS W4162x or y Advanced computergraphics3 pts. Lect: 3.Prerequisites: COMS W4160 or equivalent, orinstructor’s permission. A second course in computergraphics covering more advanced topicsincluding image and signal processing, geometricmodeling with meshes, advanced image synthesisincluding ray tracing and global illumination,and other topics as time permits. Emphasis willbe placed both on implementation of systemsand important mathematical and geometric conceptssuch as Fourier analysis, mesh algorithmsand subdivision, and Monte Carlo sampling forrendering. Note: Course will be taught everytwo years.COMS W4167x or y Computer animation3 pts. Lect: 3.Prerequisites: COMS W3137 and W4156 isrecommended. Previous familiarity with C is recommended.Intensive introduction to computeranimation, including: fundamental theory andalgorithms for computer animation, keyframing,kinematic rigging, simulation, dynamics, freeformanimation, behavioral/procedural animation,particle systems, post-production; small groupsimplement a significant animation project;advanced topics as time permits.COMS W4170x User interface design3 pts. Lect: 3. Professor Feiner.Prerequisites: COMS W3137. Introduction to thetheory and practice of computer user interfacedesign, emphasizing the software design ofgraphical user interfaces. Topics include basicinteraction devices and techniques, human factors,interaction styles, dialogue design, andsoftware infrastructure. Design and programmingprojects are required.COMS W4172y 3D user interfaces andaugmented reality3 pts. Lect: 3.Prerequisites: COMS W4160 or COMS W4170or instructor’s permission. Design, development,and evaluation of 3D user interfaces. Interactiontechniques and metaphors, from desktop toimmersive. Selection and manipulation. Traveland navigation. Symbolic, menu, gestural, andmultimodal interaction. Dialogue design. 3Dsoftware support. 3D interaction devices anddisplays. Virtual and augmented reality. Tangibleuser interfaces. Review of relevant 3D math.COMS W4180x or y Network security3 pts. Lect: 3.Prerequisites: COMS W3137 and W4119, orinstructor’s permission. Introduction to networksecurity concepts and mechanisms. Foundationsof network security and an in-depth reviewof commonly-used security mechanisms andtechniques, security threats and network-basedattacks, applications of cryptography, authentication,access control, intrusion detectionand response, security protocols (IPsec, SSL,Kerberos), denial of service, viruses and worms,software vulnerabilities, Web security, wirelesssecurity, and privacy.COMS W4187x or y Security architecture andengineering3 pts. Lect: 3. Professor Bellovin.Prerequisites: COMS W4118; W4180 and/orW4119 recommended. Secure programming.Cryptograhic engineering and key handling.Access controls. Trade-offs in security design.Design for security.COMS W4203y Graph theory3 pts. Lect: 3. Professor Gross.Prerequisites: COMS W3203. General introductionto graph theory. Isomorphism testing, algebraicspecification, symmetries, spanning trees,traversability, planarity, drawings on higher-ordersurfaces, colorings, extremal graphs, randomgraphs, graphical measurement, directed graphs,Burnside-Polya counting, voltage graph theory.COMS W4205x Combinatorial theory3 pts. Lect: 3.Prerequisites: COMS W3203 and course incalculus. Sequences and recursions, calculus offinite differences and sums, elementary numbertheory, permutation group structures, binomialcoefficients, Stilling numbers, harmonic numbers,generating functions.CSOR W4231x Analysis of algorithms, I3 pts. Lect: 3. Professor Yannakakis.Prerequisites: COMS W3137 or W3139, andW3203. Introduction to the design and analysisof efficient algorithms. Topics include modelsof computation, efficient sorting and searching,algorithms for algebraic problems, graphalgorithms, dynamic programming, probabilisticmethods, approximation algorithms, andNP-completeness.COMS W4236y Introduction to computationalcomplexity3 pts. Lect: 3.Prerequisites: COMS W3261. Develops a quantitativetheory of the computational difficulty ofproblems in terms of the resources (eg., time,space) needed to solve them. Classification ofproblems into complexity classes, reductions andcompleteness. Power and limitations of differentmodes of computation such as nondeterminism,randomization, interaction and parallelism.COMS W4241y Numerical algorithms andcomplexity3 pts. Lect: 3.Prerequisites: Knowledge of a programminglanguage. Some knowledge of scientific computationis desirable. Modern theory and practiceof computation on digital computers. Introductionto concepts of computational complexity.Design and analysis of numerical algorithms.117SEAS 2010–2011

118Applications to computational finance, computationalscience, and computational engineering.COMS W4252x or y Introduction tocomputational learning theory3 pts. Lect: 3.Prerequisites: CSOR W4231 or COMS W4236or COMS W3203 and permission of instructoror COMS W3261 and permission of instructor.Possibilities and limitations of performing learningby computational agents. Topics includecomputational models of learning, polynomialtime learnability, learning from examples andlearning from queries to oracles. Computationaland statistical limitations of learning. Applicationsto Boolean functions, geometric functions,automata.COMS W4261x or y Introduction tocryptography3 pts. Lect: 2.5. Professor Gennaro.Prerequisites: Comfort with basic discrete mathand probability. Recommended: COMS W3261or CSOR W4231. An introduction to moderncryptography, focusing on the complexitytheoreticfoundations of secure computation andcommunication in adversarial environments; arigorous approach, based on precise definitionsand provably secure protocols. Topics includeprivate and public key encryption schemes,digital signatures, authentication, pseudorandomgenerators and functions, one-way functions,trapdoor functions, number theory and computationalhardness, identification and zero knowledgeprotocols.COMS W4281x or y Introduction to quantumcomputing3 pts. Lect: 3.Prerequisites: Knowledge of linear algebra. Priorknowledge of quantum mechanics is not requiredalthough helpful. Introduction to quantum computing.Shor’s factoring algorithm, Grover’s databasesearch algorithm, the quantum summationalgorithm. Relationship between classical andquantum computing. Potential power of quantumcomputers.EECS E4340x Computer hardware design3 pts. Lect: 2. Professor Sethumadhavan.Prerequisites: ELEN E3331 plus ELEN E3910or CSEE W3827. Practical aspects of computerhardware design through the implementation,simulation, and prototyping of a PDP-8 processor.High-level and assembly languages, I/O,interrupts, datapath and control design, piplelining,busses, memory architecture. Programmablelogic and hardware prototyping with FPGAs.Fundamentals of VHDL for register-transferlevel design. Testing and validation of hardware.Hands-on use of industry CAD tools for simulationand synthesis. Lab required.COMS W4444x Programming and problemsolving3 pts. Lect: 3. Professor Ross.Prerequisites: COMS W3137 and CSEE W3827.Hands-on introduction to solving open-endedcomputational problems. Emphasis on creativity,cooperation, and collaboration. Projects spanninga variety of areas within computer science,typically requiring the development of computerprograms. Generalization of solutions to broaderproblems, and specialization of complex problemsto make them manageable. Team-orientedprojects, student presentations, and in-classparticipation required.COMS W4560x Introduction to computerapplications in health care and biomedicine3 pts. Lect: 3.Prerequisites: Experience with computers anda passing familiarity with medicine and biology.Undergraduates in their senior or junior yearsmay take this course only if they have adequatebackground in mathematics and receive permissionfrom the instructor An overview of the fieldof biomedical informatics, combining perspectivesfrom medicine, computer science, andsocial science. Use of computers and informationin health care and the biomedical sciences, coveringspecific applications and general methods,current issues, capabilities and limitations ofbiomedical informatics. Biomedical Informaticsstudies the organization of medical information,the effective management of information usingcomputer technology, and the impact of suchtechnology on medical research, education,and patient care. The field explores techniquesfor assessing current information practices,determining the information needs of health careproviders and patients, developing interventionsusing computer technology, and evaluating theimpact of those interventions.COMS W4701x or y Artificial intelligence3 pts. Lect: 3. Professor Pasik.Prerequisites: COMS W3137. Provides a broadunderstanding of the basic techniques for buildingintelligent computer systems. Topics includestate-space problem representations, problemreduction and and-or graphs, game playing andheuristic search, predicate calculus, and resolutiontheorem proving, AI systems and languagesfor knowledge representation, machine learningand concept formation and other topics such asnatural language processing may be included astime permits.COMS W4705x Natural language processing3 pts. Lect: 3. Professor Hirschberg.Prerequisites: COMS W3133, or W3134, orW3137, or W3139, or instructor’s permission.Computational approaches to natural languagegeneration and understanding. Recommendedpreparation: Some previous or concurrent exposureto AI or machine learning. Topics includeinformation extraction, summarization, machinetranslation, dialogue systems, and emotionalspeech. Particular attention is given to robusttechniques that can handle understanding andgeneration for the large amounts of text on theWeb or in other large corpora. Programmingexercises in several of these areas.COMS W4706y Spoken language processing3 pts. Lect: 3. Not offered in 2010– 2011.Prerequisites: COMS W3133, or W3134, orW3137, or instructor’s permission. Computationalapproaches to speech generation and understanding.Topics include speech recognition andunderstanding, speech analysis for computationallinguistics research, and speech synthesis.Speech applications including dialogue systems,data mining, summarization, and translation.Exercises involve data analysis and building asmall text-to-speech system.COMS W4725x or y Knowledge representationand reasoning3 pts. Lect: 3.Prerequisites: COMS W4701. General aspectsof knowledge representation (KR). The twofundamental paradigms (semantic networksand frames) and illustrative systems. Topicsinclude hybrid systems, time, action/plans,defaults, abduction, and case-based reasoning.Throughout the course particular attentionis paid to design trade-offs between languageexpressiveness and reasoning complexity, andissues relating to the use of KR systems in largerapplications.COMS W4731x or y Computer vision3 pts. Lect: 3.Prerequisites: The fundamentals of calculus,linear algebra, and C programming. Studentswithout any of these prerequisites are advised tocontact the instructor prior to taking the course.Introductory course in computer vision. Topicsinclude image formation and optics, imagesensing, binary images, image processing andfiltering, edge extraction and boundary detection,region growing and segmentation, pattern classificationmethods, brightness and reflectance,shape from shading and photometric stereo,texture, binocular stereo, optical flow and motion,2D and 3D object representation, object recognition,vision systems and applications.COMS W4733x or y Computational aspectsof robotics3 pts. Lect: 3. Professor Allen.Prerequisites: COMS W3137. Introduction torobotics from a computer science perspective.Topics include coordinate frames and kinematics,computer architectures for robotics, integrationand use of sensors, world modeling systems,design and use of robotic programming languages,and applications of artificial intelligencefor planning, assembly, and manipulation.SEAS 2010–2011

COMS W4735x or y Visual interfaces tocomputers3 pts. Lect: 3.Prerequisites: COMS W3137. Visual inputas data and for control of computer systems.Survey and analysis of architecture, algorithms,and underlying assumptions of commercial andresearch systems that recognize and interprethuman gestures, analyze imagery such as fingerprintor iris patterns, generate natural languagedescriptions of medical or map imagery. Exploresfoundations in human psychophysics, cognitivescience, and artificial intelligence.COMS W4737x or y Biometrics3 pts. Lect: 3. Professor Belhumeur.Prerequisites: A background at the sophomorelevel in computer science, engineering, or likediscipline. Corequisites: None In this course wewill explore the latest advances in biometrics aswell as the machine learning techniques behindthem. Students will learn how these technologieswork and how they are sometimes defeated.Grading will be based on homework assignmentsand a final project. There will be no midtermor final exam. This course shares lectures withCOMS E6737. Students taking COMS E6737 arerequired to complete additional homework problemsand undertake a more rigorous final project.Students will only be allowed to earn credit forCOMS W4737 or COMS E6737 but not both.CBMF W4761x or y Computational genomics3 pts. Lect: 3.Prerequisites: Introductory probability and statisticsand basic programming skills. Providescomprehensive introduction to computationaltechniques for analyzing genomic data includingDNA, RNA and protein structures; microarrays;transcription and regulation; regulatory,metabolic and protein interaction networks. Thecourse covers sequence analysis algorithms,dynamic programming, hidden Markov models,phylogenetic analysis, Bayesian network techniques,neural networks, clustering algorithms,support vector machines, Boolean models ofregulatory networks, flux based analysis ofmetabolic networks and scale-free networkmodels. The course provides self-containedintroduction to relevant biological mechanismsand methods.COMS W4771y Machine learning3 pts. Lect: 3.Prerequisites: Any introductory course in linearalgebra and any introductory course in statisticsare both required. Highly recommended: COMSW4701 or knowledge of Artificial Intelligence.Topics from generative and discriminativemachine learning including least squares methods,support vector machines, kernel methods,neural networks, Gaussian distributions, linearclassification, linear regression, maximum likelihood,exponential family distributions, Bayesiannetworks, Bayesian inference, mixture models,the EM algorithm, graphical models and hiddenMarkov models. Algorithms implemented inMATLAB.COMS W4772x Advanced machine learning3 pts. Lect: 3. Professor Jebara.Prerequisites: COMS W4771 or permissionof instructor; knowledge of linear algebra andintroductory probability or statistics is required.An exploration of advanced machine learningtools for perception and behavior learning.How can machines perceive, learn from, andclassify human activity computationally? Topicsinclude Appearance-Based Models, Principaland Independent Components Analysis,Dimensionality Reduction, Kernel Methods,Manifold Learning, Latent Models, Regression,Classification, Bayesian Methods, MaximumEntropy Methods, Real-Time Tracking, ExtendedKalman Filters, Time Series Prediction, HiddenMarkov Models, Factorial HMMs, Input-OutputHMMs, Markov Random Fields, VariationalMethods, Dynamic Bayesian Networks, andGaussian/Dirichlet Processes. Links to cognitivescience.CSEE W4823x or y Advanced logic design3 pts. Lect: 3. Professor Nowick.Prerequisites: CSEE 3827, or a half semesterintroduction to digital logic, or equivalent. Anintroduction to modern digital system design.Advanced topics in digital logic: controller synthesis(Mealy and Moore machines); adders andmultipliers; structured logic blocks (PLDs, PALs,ROMs); iterative circuits. Modern design methodology:register transfer level modelling (RTL);algorithmic state machines (ASMs); introductionto hardware description languages (VHDL orVerilog); system-level modelling and simulation;design examples.CSEE W4824x or y Computer architecture3 pts. Lect: 3. Professor Carloni.Prerequisites: CSEE W3827 or equivalent.Focuses on advanced topics in modern computerarchitecture, illustrated by recent casestudies. Fundamentals of quantitative analysis.Pipelined, out-of-order, and speculative execution.Superscalar, VLIW, and vector processors.Embedded processors. Memory hierarchydesign. Multiprocessors and thread-level parallelism.Synchronization and cache coherenceprotocols. Interconnection networks.CSEE W4840y Embedded systems3 pts. Lect: 3.Prerequisites: CSEE W4823. Embedded systemdesign and implementation combining hardwareand software. I/O, interfacing, and peripherals.Weekly laboratory sessions and term project ondesign of a microprocessor-based embeddedsystem including at least one custom peripheral.Knowledge of C programming and digital logicrequired. Lab required.COMS W4901x and y Projects in computerscience1–3 pts.Prerequisites: Approval by a faculty member whoagrees to supervise the work. A second-levelindependent project involving laboratory work,computer programming, analytical investigation,or engineering design. May be repeated forcredit, but not for a total of more than 3 points ofdegree credit. Consult the department for sectionassignment.COMS W4910x and y Curricular practicaltraining1 pt.Prerequisites: Obtained internship and approvalfrom faculty adviser. Only for M.S. students inthe Computer Science department who needrelevant work experience as part of their programof study. Final report required. This course maynot be taken for pass/fail credit or audited.COMS W4995x or y Special topics incomputer science, I3 pts. Lect: 3. Professors Kim, Saraswat, Yeeand Swamy.Prerequisites: Instructor’s permission. Special topicsarranged as the need and availability arises.Topics are usually offered on a one-time basis.Since the content of this course changes each timeit is offered, it may be repeated for credit. Consultthe department for section assignment.COMS W4996x or y Special topics incomputer science, II3 pts. Lect: 3.Prerequisites: Instructor’s permission. A continuationof COMS W4995 when the special topicextends over two terms.COMS E6111y Advanced database Systems3 pts. Lect: 2.Prerequisites: COMS W4111 and knowledge ofJava or instructors permission. Continuation ofCOMS W4111, covers latest trends in both databaseresearch and industry: information retrieval,web search, data mining, data warehousing,OLAP, decision support, multimedia databases,and XML and databases. Programming projectsrequired.COMS E6113y Topics In database systems3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: COMS W4111. Concentration onsome database paradigm, such as deductive,heterogeneous, or object-oriented, and/or somedatabase issue, such as data modeling, distribution,query processing, semantics, or transactionmanagement. A substantial project is typicallyrequired. May be repeated for credit with instructor’spermission.COMS E6117x or y Topics in programminglanguages and translators3 pts. Lect: 2.Prerequisites: COMS W4115 or instructor’s permission.Concentration on the design and imple-119SEAS 2010–2011

120mentation of programming languages, and toolsfocused on advanced applications in new areasin software verification, distributed systems,programming in the large, and web computing. Asubstantial project is typically required. May berepeated for credit.COMS E6118y Operating systems, II3 pts. Lect: 2. Not offered in 2010 –2011.Prerequisites: COMS W4118. Corequisites:COMS W4119. Continuation of COMS W4118 ,with emphasis on distributed operating systems.Topics include interfaces to network protocols,distributed run-time binding, advanced virtualmemory issues, advanced means of interprocesscommunication, file system design, design forextensibility, security in a distributed environment.Investigation is deeper and more hands-onthan in COMS W4118. A programming projectis required.COMS E6123x or y Programmingenvironments and software tools (PEST)3 pts. Lect: 2.Prerequisites: At least one COMS W41xx orCOMS E61xx course and/or COMS W4444, orinstructor’s permission. Strongly recommended:COMS W4156. Software methodologies andtechnologies concerned with developmentand operation of today’s software systems.Reliability, security, systems management andsocietal issues. Emerging software architecturessuch as enterprise and grid computing. Termpaper and programming project. Seminar focuschanges frequently to remain timely.COMS E6125y Web-enhanced informationmanagement (WHIM)3 pts. Lect: 2.Prerequisites: At least one COMS W41xx orCOMS E61xx course and/or COMS W4444, orinstructor’s permission. Strongly recommended:COMS W4111. History of hypertext, markup languages,groupware and the Web. Evolving Webprotocols, formats and computation paradigmssuch as HTTP, XML and Web Services. Novelapplication domains enabled by the Web andsocietal issues. Term paper and programmingproject. Seminar focus changes frequently toremain timely.COMS E6160x or y Topics in computergraphics3 pts. Lect: 2.Prerequisites: COMS W4160 or instructor’s permission.An advanced graduate course, involvingstudy of an advanced research topic in ComputerGraphics. Content varies between offerings, andthe course may be repeated for credit. Recentofferings have included appearance models ingraphics, and high quality real-time rendering.COMS E6174y Interaction design: aperceptual approach3 pts. Lect: 3.Prerequisites: CS W4170 or instructor’s permissionDesign methology for special-purpose userinterfaces. Emphasis on how psychology andperception inform good design. Interviewingand task modeling, participatory design, andlow-fidelilty prototyping. Applications of brainresearch, graphic design and art to develop customuser interfaces components, screen layouts,and interaction techniques for application-specificsystems.COMS E6176x or y User interfaces for mobileand wearable computing3 pts. Lect: 2.Prerequisites: COMS W4170 or instructor’spermission. Introduction to research on userinterfaces for mobile and wearable computingthrough lectures, invited talks, student-led discussionsof important papers, and programmingprojects. Designing and authoring for mobilityand wearability. Ubiquitous/pervasive computing.Collaboration with other users. Display,interaction, and communication technologies.Sensors for tracking position, orientation, motion,environmental context, and personal context.Applications and social consequences.CSEE E6180x or y Modeling and performance3 pts. Lect: 2.Prerequisites: COMS W4118 and SIEO W4150.Introduction to queuing analysis and simulationtechniques. Evaluation of time-sharing and multiprocessorsystems. Topics include priority queuing,buffer storage, and disk access, interferenceand bus contention problems, and modeling ofprogram behaviors.COMS E6181x or y Advanced Internetservices3 pts. Lect: 2.In-depth survey of protocols and algorithmsneeded to transport multimedia informationacross the Internet, including audio and videoencoding, multicast, quality-of-service, voice-overIP, streaming media and peer-to-peer multimediasystems. Includes a semester-long programmingproject.COMS E6183x or y Advanced topics innetwork security3 pts. Lect: 3.Prerequisites: COMS W4180, CSEE 4119and COMS W4261 recommended. Reviewthe fundamental aspects of security, includingauthentication, authorization, access control,confidentiality, privacy, integrity, and availability.Review security techniques and tools, and theirapplications in various problem areas. Studythe state of the art in research. A programmingproject is required.COMS E6184y Seminar on anonymity andprivacy3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: COMS W4261 or W4180 or CSEEW4119 or instructor’s permission. This coursecovers the following topics: Legal and socialframework for privacy. Data mining and databases.Anonymous commerce and Internet usage.Traffic analysis. Policy and national security considerations.Classes are seminars with studentspresenting papers and discussing them. Seminarfocus changes frequently to remain timely.COMS E6185x or y Intrusion and anomalydetection systems2 pts. Lect: 2. Professor Stolfo.Prerequisites: COMS W4180 Network Security.Corequisites: COMS W4180 Network Security.The state of threats against computers, andnetworked systems. An overview of computersecurity solutions and why they fail. Provides adetailedtreatment for network and host-basedintrusion detection and intrusion prevention systems.Considerable depth is provided on anomalydetection systems to detect new attacks.Covers issues and problems in e-mail (spam,and viruses) and insider attacks (masqueradingand impersonation).COMS E6204x or y Topics in graph theory3 pts. Lect: 2.Prerequisites: COMS W4203 or instructor’s permission.Content varies from year to year. Thiscourse may be repeated for credit. Concentrationon some aspect of graph theory, such as topologicalgraph theory, algebraic graph theory,enumerative graph theory, graphical optimizationproblems, or matroids.COMS E6206x or y Topics in combinatorialtheory3 pts. Lect: 2.Prerequisites: COMS W4203 or W4205, orinstructor’s permission. Concentration on someaspect of combinatorial theory. Content variesform year to year. This course may be repeatedfor credit.COMS E6232x or y Analysis of algorithms, II3 pts. Lect: 2.Prerequisites: CSOR W4231. Continuation ofCSOR W4231.COMS E6253y Advanced topics incomputational learning theory3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CSOR W4231 or equivalent,COMS W4252 or COMS W4236 helpful butnot required. In-depth study of inherent abilitiesand limitations of computationally efficientlearning algorithms. Algorithms for learning richBoolean function classes in online, ProbablyApproximately Correct, and exact learning models.Connections with computational complexitytheory emphasized. Substantial course project orterm paper required.COMS E6261x or y Advanced cryptography3 pts. Lect: 3.Prerequisites: W4261 A study of advancedcryptographic research topics such as: securecomputation, zero knowledge, privacy, anonymity,cryptographic protocols. Concentration onSEAS 2010–2011

theoretical foundations, rigorous approach, andprovable security. Contents varies between offerings.May be repeated for credit.COMS E6291x or y Theoretical topics incomputer science3 pts. Lect: 3.Prerequisites: Instructor’s permission.Concentration on some theoretical aspect ofcomputer science. Content varies from year toyear. May be repeated for credit.COMS E6732x or y Computational imaging3 pts. Lect: 3.Prerequisites: COMS W4731 or instructor’spermission. Computational imaging uses acombination of novel imaging optics and acomputational module to produce new formsof visual information. Survey of the state ofart in computational imaging. Review of recentpapers on: omnidirectional and panoramicimaging, catadioptric imaging, high dynamicrange imaging, mosaicing and superresolution.Classes are seminars with the instructor, guestspeakers, and students presenting papers anddiscussing them.COMS E6733x or y 3D photography3 pts. Lect: 2.Prerequisites: Experience with at least one ofthe following topics: Computer graphics, computervision, pixel processing, robotics or computer-aideddesign, or permission of instructor.Programming proficiency in C, C++, or JAVA.3D Photography—the process of automaticallycreating 3D, texture-mapped models of objectsin detail. Applications include robotics, medicine,graphics, virtual reality, entertainment and digitalmovies etc. Topics include 3D data acquisitiondevices, 3D modeling systems and algorithmsto acquire, create, augment, manipulate, render,animate and physically build such models.COMS E6734y Computational photography3 pts. Lect: 3.Prerequisites: COMS W4160, COMS W4731, ora working knowledge of photography are recommended.Students should have knowledge inany of three core areas: computer vision, computergraphics, or photography. Computationaltechniques are used to produce a new levelof images and visual representations. Topicsinclude HDR imaging, feature matching usingRANSAC, image mosaics, image-based rendering,motion magnification, camera lens arrays,programmable lighting, face detection, single andmultiview geometry, and more.COMS E6735y Visual databases3 pts. Lect: 3. Not offered in 2010 –2011.Prerequisites: COMS W3133, W3134, or W3137required. COMS W4731 COMS W4735 helpfulbut not required. Contact instructor if uncertain.The analysis and retrieval of large collectionsof image and video data, with emphasis onvisual semantics, human psychology, and userinterfaces. Low-level processing: features andsimilarity measures; shot detection; key frameselection; machine learning methods for classification.Middle-level processing: organizationalrules for videos, including unedited (home,educational), semiedited (sports, talk shows),edited (news, drama); human memory limits;progressive refinement; visualization techniques;incorporation of audio and text. High-levelprocessing: extraction of thematic structures;ontologies, semantic filters, and learning;personalization of summaries and interfaces;detection of pacing and emotions. Examples anddemonstrations from commercial and researchsystems throughout. Substantial course projector term paper required.COMS E6737x or y Biometrics3 pts. Lect: 3.Prerequisites: Background at the sophomorelevel in computer science, engineering, or likediscipline. Corequisites: None In this course wewill explore the latest advances in biometrics aswell as the machine learning techniques behindthem. Students will learn how these technologieswork and how they are sometimes defeated.Grading will be based on homework assignmentsand a final project. There will be no midtermor final exam. This course shares lectures withCOMS W4737. Students taking COMS E6737are required to complete additional homeworkproblems and undertake a more rigorous finalproject. Students will only be allowed to earncredit for COMS W4737 or COMS E6737 butnot both.CSEE E6824y Parallel computer architecture3 pts. Lect: 2. Not offered in 2010 –2011.Prerequisites: CSEE W4824 Parallel computerprinciples, machine organization and design ofparallel systems including parallelism detectionmethods, synchronization, data coherence andinterconnection networks. Performance analysisand special purpose parallel machines.CSEE E6831y Sequential logic circuits3 pts. Lect: 3. Not offered in 2010 –2011.Prerequisites: CSEE W3827 or any introductionto logic circuits Generation and manipulation offlow table descriptions to asynchronous sequentialfunctions. Coding of flow tables to satisfyvarious design criteria. Delays, races, hazards,metastability. Analysis of latches to determinekey parameters. Bounds of input rates. Clockingschemes for synchronous systems. Synthesisof self-timed systems using 4-phase or 2-phasehandshakes.CSEE E6832x or y Topics in logic designtheory3 pts. Lect: 3.Prerequisites: CSEE W3827 or any introductionto logic circuits. A list of topics for each offeringof the course is available in the department officeone month before registration. May be takenmore than once if topics are different Iterativelogic circuits applied to pattern recognition. Finitestate machines; alternative representations,information loss, linear circuits, structure theory.Reliability and testability of digital systems.CSEE E6847y Distributed embedded systems3 pts. Lect: 2. Not offered in 2010 –2011.Prerequisites: Any COMS W411X, CSEEW48XX, or ELEN E43XX course, or permissionof instructor. An interdisciplinary graduate-levelseminar on the design of distributed embeddedsystems. System robustness in the presenceof highly variable communication delaysand heterogeneous component behaviors.The study of the enabling technologies (VLSIcircuits, communication protocols, embeddedprocessors, RTOSs), models of computation,and design methods. The analysis of moderndomain-specific applications including on-chipmicro-networks, multiprocessor systems, faulttolerantarchitectures, and robust deploymentof embedded software. Research challengessuch as design complexity, reliability, scalability,safety, and security. The course requiressubstantial reading, class participation and aresearch project.CSEE E6861y Computer-aided design ofdigital systems3 pts. Lect: 2.Prerequisites: (i) one semester of advanceddigital logic (CSEE W4823 or equivalent,or instructor’s permission); and (ii) a basiccourse in data structures and algorithmsCOMS W3133, 3134, 3137, 3139, or 3157, orequivalent, and familiarity with programming.Introduction to modern digital CAD synthesisand optimization techniques. Topics include:modern digital system design (high-levelsynthesis, register-transfer level modeling,algorithmic state machines, optimal schedulingalgorithms, resource allocation and binding,retiming), controller synthesis and optimization,exact and heuristic two-level logic minimization,advanced multilevel logic optimization,optimal technology mapping to library cells (fordelay, power and area minimization), advanceddata structures (binary decision diagrams),SAT solvers and their applications, static timinganalysis, and introduction to testability.Includes hands-on small design projects usingand creating CAD tools.EECS E6870x or y Speech recognition3 pts. Lect: 3.Prerequisites: Basic probability and statisticsTheory and practice of contemporary automaticspeech recognition. Gaussian mixture distributions,hidden Markov models, pronunciationmodeling, decision trees, finite-state transducers,and language modeling. Selected advanced topicswill be covered in more depth.121SEAS 2010–2011

122COMS E6900x and y Tutorial in computerscience1–3 pts.Prerequisites: Instructor’s permission. A readingcourse in an advanced topic for a small numberof students, under faculty supervision.COMS E6901x Projects in computer science1–12 pts.Prerequisites: Instructor’s permission. Softwareor hardware projects in computer science. Beforeregistering, the student must submit a writtenproposal to the instructor for review. The proposalshould give a brief outline of the project,estimated schedule of completion, and computerresources needed. Oral and written reportsare required. May be taken over more thanone semester, in which case the grade will bedeferred until all 12 points have been completed.No more than 12 points of COMS E6901 maybe taken. Consult the department for sectionassignment.COMS E6902x and y Thesis1–9 pts.Available to M.S. and CSE candidates. Anindependent investigation of an appropriate problemin computer science carried out under thesupervision of a faculty member. A formal writtenreport is essential and an oral presentation mayalso be required. May be taken over more thanone semester, in which case the grade will bedeferred until all 9 points have beem completed.No more than 9 points of COMS E6902 maybe taken. Consult the department for sectionassignment.COMS E6998x and y Topics in computerscience3 pts. Members of the faculty.Prerequisites: Instructor’s permission. Selectedtopics in computer science. Content varies fromyear to year. May be repeated for credit.COMS E6999x and y Topics in computerscience, II3 pts.Prerequisites: COMS E6998. Continuation ofCOMS E6998.COMS E9800x and y Directed research incomputer science1–15 pts.Prerequisites: Submission of outline of proposedresearch for approval by faculty member whowill supervise. The department must approve thenumber of points. May be repeated for credit.This course is only for Eng.Sc.D. candidates.COMS E9910x and y Graduate research, I1–6 pts.Prerequisites: Prerequisites: Submission of anoutline of the proposed research for approvalby the faculty member who will supervise.The department must approve the number ofcredits. May be repeated for credit. This courseis only for M.S. candidates holding GRA or TAappointments. Note: It is NOT required that astudent take Graduate research, I prior to takingGraduate research, II. Consult the departmentfor section assignment.COMS E9911x and y Graduate research, II1-15 pts.Prerequisites: Submission of an outline of theproposed research for approval by the facultymember who will supervise. The departmentmust approve the number of points. May berepeated for credit. This course is only for M.S./Ph.D. track students. Note: It is NOT requiredthat a student take Graduate research, I prior totaking Graduate research, II. Consult the departmentfor section assignment.SEAS 2010–2011

EARTH AND ENVIRONMENTAL ENGINEERINGHenry Krumb School of Mines918 S. W. Mudd, MC 4711, 212-854-2905www.eee.columbia.edu123OUR MISSIONEarth and Environmental Engineering at the Henry Krumb Schoolof Mines fosters excellence in education and research for thedevelopment and application of science and technology tomaximize the quality of life for all, through the sustainable use andresponsible management of Earth’s resources.CHAIRKlaus LacknerVICE CHAIRTuncel M. YegulalpDEPARTMENTALADMINISTRATORPeter RennéeADMINISTRATIVEASSISTANTGary S. HillPROFESSORSPaul F. DubyKlaus LacknerUpmanu LallIsmail C.NoyanPeter SchlosserPonisseril SomasundaranNickolas J. ThemelisNicholas J. TurroTuncel M. YegulalpASSOCIATE PROFESSORXi ChenASSISTANT PROFESSORSMarco CastaldiKartik ChandranAh-Hyung (Alissa) ParkADJUNCT PROFESSORSWilliam BeckerRobert FarrautoYuri GorokhovichIan MorrisonADJUNCT ASSOCIATEPROFESSORLei ZhangADJUNCT ASSISTANTPROFESSORSMichael BellPietro CeccatoScott KaufmanSri RangarajanGreg YetmanINSTRUCTORChris GazzeDOHERTY RESEARCHSCIENTISTWade McGillisSENIOR RESEARCHSCIENTISTVasilis FthenakisASSOCIATE RESEARCHSCIENTISTSIrina ChernyshovaS. Murthy KhondrikaHyung Chul KimADJUNCT SENIORRESEARCH SCIENTISTRay FarinatoEARTH RESOURCES AND THEENVIRONMENTThe Earth and EnvironmentalEngineering program fosters educationand research in the development andapplication of technology for the sustainabledevelopment, use, and integratedmanagement of Earth’s resources.Resources are identified as minerals,energy, water, air, and land, as well asthe physical, chemical, and biologicalcomponents of the environment. Thereis close collaboration with other engineeringdisciplines, the Lamont-DohertyEarth Observatory, the InternationalResearch Institute for ClimatePrediction, the Center for EnvironmentalResearch and Conservation, and otherColumbia Earth Institute units.THE HENRY KRUMB SCHOOLOF MINES AT COLUMBIAUNIVERSITYThe School of Mines of ColumbiaUniversity was established in 1864 andwas the first mining and metallurgydepartment in the U.S. It became thefoundation for Columbia’s School ofEngineering and Applied Sciences andhas been a pioneer in many areas ofmining and metallurgy, including the firstmining (Peele) and mineral processing(Taggart) handbooks, flotation, chemicalthermodynamics and kinetics, surfaceand colloid chemistry, and materialsscience.Nearly 100 years after its formation,the School of Mines was renamedHenry Krumb School of Mines (HKSM)in honor of the generous Columbiabenefactor of the same name. TheHenry Krumb School of Mines (SEAS)supports three components: Department of Earth andEnvironmental Engineering(www.eee.columbia.edu) (EEE), oneof the nine departments of SEAS. gramin Materials Science andEngineering (www.seas.columbia.edu/matsci) (MSE). This program,administered by the Departmentof Applied Physics and AppliedMathematics, is described in anothersection of this bulletin. The Earth Engineering Center(www.seas.columbia.edu/earth). Thecurrent research areas include energy,materials, and water resources.EARTH AND ENVIRONMENTALENGINEERING (EEE)Starting in 1996, the educationalprograms of Columbia University inmining and mineral engineering weretransformed into the present programin Earth and Environmental Engineering(EEE). This program is concerned withthe environmentally sound extractionand processing of primary materials(minerals, fuels, water), the managementand development of land and waterresources, and the recycling or disposalof used materials. EEE offers theBachelor of Science (B.S.) in Earth andEnvironmental Engineering, the Masterof Science (M.S.) in Earth ResourcesEngineering, the professional degreesof Engineer of Mines and MetallurgicalEngineer, and the doctorate degrees(Ph.D., Eng.Sc.D.) in EEE.SEAS 2010–2011

124The EEE program welcomesCombined Plan students. An EEE minoris offered to all Columbia engineeringstudents who want to enrich their academicrecord by concentrating someof their technical electives on Earth/Environment subjects. There is closecollaboration between EEE and theDepartments of Civil Engineering andEarth and Environmental Sciences,including several joint appointments.EEE and the Earth EngineeringCenter are the contributions of The FuFoundation School of Engineering andApplied Science to The Earth Instituteof Columbia University, a major educationand research initiative of theUniversity. The Department of Earth andEnvironmental Engineering combinesthe long-standing and proud traditionof Columbia’s School of Mines withforward-thinking courses and programs,innovative research, and a deep concernfor the environment.RESEARCH CENTERSASSOCIATED WITH EARTHAND ENVIRONMENTALENGINEERINGColumbia Water Center. The ColumbiaWater Center, in collaboration with otherEarth Institute units and external partners,is leading intellectual inquiry into anassessment, prediction, and solution ofthe potentially global crisis of freshwaterscarcity. Goals are to: ties(e.g., new data sets and modelingtools) for local, regional, and globalwater resource assessment, recognizingchanging climate, demographic,and usage dynamics private investment in future waterresource development, local andregional ecosystem services providedby water and the essential life-supportwater needs of societies giesfor the storage, treatment, andconveyance of water to improve reliable,cost-efficient access atepolicy instruments that facilitatethe implementation of selected incentivesfor higher-value, higher-efficiencywater use, while promoting equity ofuse and life support functions of the policy and technology developmentsin real-world settings, workingwith local institutions and privatesectordevelopers or users in an openand public process edgebase that results from our activitiesto support global water resourcedevelopment and decision making,including the development of a forum,the Global Roundtable on Water(GROW), to facilitate internationalpolicy and technical action to improveour collective water future.For more information: www.water.columbia.eduCenter for Life Cycle Analysis (LCA).The Center for Life Cycle Analysis ofColumbia University was formed in thespring of 2006 with the objective of conductingcomprehensive life cycle analysesof energy systems. LCA provides aframework for quantifying the potentialenvironmental impacts of material andenergy inputs and outputs of a processor product from “cradle to grave.” Themission of the Center is to guide technologyand energy policy decisions withdata- based, well-balanced, and transparentdescriptions of the environmentalprofiles of energy systems. For moreinformation: www.clca.columbia.eduCenter for Sustainable Use ofResources (SUR). The Center forSustainable Use of Resources buildson the strengths of past research atColumbia and North Carolina State onrecycling, composting, waste-to-energy,and landfill engineering. Also, the Centerwill clearly define the impacts of allsolid waste technologies and practiceswith regard to greenhouse gas emissionsand will, on a case-by-case basis,establish and validate protocols thataccount for greenhouse gas emissionsand savings that may be easily replicatedand readily accepted. SUR will alsoidentify technologies that can replacesome virgin feedstock with appropriatelocal waste streams. Through its publications,meetings, and Web page, SURwill disseminate information on the bestwaste management technologies andmethods that, on a life-cycle basis, willresult in reducing the impacts of wastemanagement on global climate change.An equally important objective of theCenter is to provide graduate-leveltraining, at the participating universities,in the ways and means of sustainableresource utilization to engineers andscientists from the U.S. and around theworld, in particular from the developingworld, where the need for modern managementof wastes is most acute. TheEarth Engineering Center, in collaborationwith the Department of Earth andEnvironmental Engineering, has alreadybeen engaged in this role, and some ofour alumni are working in various partsof the waste management industry.There have been more than twenty theseswritten on various aspects of wastemanagement, including in-depth studiesof implementing advanced processesand methodologies in Chile, China,Greece, and India. For more information:www.surcenter.orgEarth Engineering Center. The missionof the Earth Engineering Center isto develop and promote engineeringmethodologies that provide essentialmaterial to humanity in ways that maintainthe overall balance between theconstantly increasing demand for materials,the finite resources of the Earth,and the need for clean water, soil, andair. The Center is dedicated to theadvancement of industrial ecology, i.e.,the reconfiguring of industrial activitiesand products with full knowledge of theenvironmental consequences. Researchis being conducted on a variety ofgeoenvironmental issues with the intentto quantify, assess, and ultimatelymanage adverse human effects on theenvironment. Research areas includemanagement of water and energyresources, hydrology and hydrogeology,numerical modeling of estuarineflow and transport processes, and integratedwaste management. For moreinformation, visit www.seas.columbia.edu/earth/index.html.Environmental Tracer Group (ETG).The Environmental Tracer Group usesnatural and anthropogenic (frequentlytransient) tracers, as well as deliberatelyreleased tracers, to investigate the physicsand chemistry of transport in environmentalsystems. The tracers includenatural or anthropogenically producedisotopes (e.g., tritium or radioactivehydrogen, helium and oxygen isotopes,SEAS 2010–2011

or radiocarbon), as well as noble gasesand chemical compounds (e.g., CFCsand SF6). The ETG analytical facilitiesinclude four mass spectrometric systemsthat can be used in the analysisof tritium and noble gases in water,sediments, and rocks. In addition to themass spectrometric systems, there areseveral gas chromatographic systemsequipped with electron capture detectorsthat are used for measurements ofSF6 in continental waters and CFCs andSF6 in the atmosphere. GC/MS capabilityis being added to the spectrum ofanalytical capabilities.Industry/University CooperativeResearch Center for AdvancedStudies in Novel Surfactants (IUCS).IUCS was established in 1998 bythe Henry Krumb School of Mines,Department of Chemical Engineering,and Department of Chemistry atColumbia University. The Centerencompasses detailed structurepropertyassessment of several classesof surface-active molecules, includingoligomeric, polymeric, and bio-molecules.The aim of IUCS is to developand characterize novel surfactants forindustrial applications such as coatings,dispersions, deposition, gas hydratecontrol, personal care products, soildecontamination, waste treatment,corrosion prevention, flotation, and controlledchemical reactions. The proposedresearch thus focuses on the designand development of specialty surfactants,characterization of their solutionand interfacial behavior, and identificationof suitable industrial applications forthese materials.The goals of IUCS are to performindustrially relevant research to addressthe technological needs in commercialsurfactant and polymer systems; developnew and more efficient surfaceactivereagents for specific applicationsin the industry and methodologies foroptimizing their performance; promotethe use of environmentally benign surfactantsin a wide array of technologicalprocesses; and build a resource centerto perform and provide state-of-the-artfacilities for characterization of surfaceactivereagents: www.columbia.edu/cu/iucrc.International Research Institute forClimate Prediction (IRI). The IRI is theworld’s leading institute for the developmentand application of seasonal to interannualclimate forecasts. The mission ofthe IRI is to enhance society’s capability tounderstand, anticipate, and manage theimpacts of seasonal climate fluctuations,in order to improve human welfare andthe environment, especially in developingcountries. This mission is to be conductedthrough strategic and applied research,education and capacity building, andprovision of forecast and information products,with an emphasis on practical andverifiable utility and partnerships.Langmuir Center for Colloids andInterfaces (LCCI). This Center bringstogether experts from mineral engineering,applied chemistry, chemical engineering,biological sciences, and chemistryto probe complex interactions ofcolloids and interfaces with surfactantsand macromolecules. LCCI activitiesinvolve significant interaction with industrialsponsors and adopt an interdisciplinaryapproach toward state-of-the-artresearch on interfacial phenomena.Major areas of research at LCCI are thinfilms, surfactant and polymer adsorption,environmental problems, enhancedoil recovery, computer tomography, corrosionand catalysis mechanisms, membranetechnology, novel separations ofminerals, biocolloids, microbial surfaces,and interfacial spectroscopy.Lenfest Center for Sustainable Energy.The mission of the Lenfest Center forSustainable Energy is to develop technologiesand institutions to ensure asufficient supply of environmentally sustainableenergy for all humanity. To meetthis goal, the Center supports researchprograms in energy science, engineering,and policy across Columbia Universityto develop technical and policy solutionsthat will satisfy the world’s future energyneeds without threatening to destabilizeEarth’s natural systems.The mission of the Lenfest Center isshaped by two global challenges. First,the Center seeks to reduce the emissionof carbon dioxide into the atmosphereand to forestall a disruption of globalclimate systems that would imposenegative consequences for human welfare.Second, the Center seeks to createenergy options that will meet the legitimateenergy demands of a larger andincreasingly wealthy world population. Inorder to meet these two challenges, theCenter seeks to develop new sources,technologies, and infrastructures.The Lenfest Center focuses primarilyon the technological and institutionaldevelopment of the three energy resourcessufficient to support the world’sprojected population in 2100 withoutincreased carbon emissions: solar,nuclear, and fossil fuels combined withcarbon capture and storage. Althougheach of these options can, in theory, bedeveloped on a scale to satisfy globaldemand, they each face a combination oftechnological and institutional obstaclesthat demand research and developmentbefore they can be deployed.The Center’s main activities arebased within the range of natural scienceand engineering disciplines. At thesame time, it integrates technologicalresearch with analysis of the institutional,economic, and political context withinwhich energy technologies are commercializedand deployed. For more information:www.energy.columbia.eduWaste to Energy Research andTechnology Council (WTERT). TheWaste to Energy Research andTechnology Council brings togetherengineers, scientists, and managersfrom industry, universities, and governmentwith the objective of advancing thegoals of sustainable waste managementglobally. The mission of WTERT is toidentify the best available technologiesfor the treatment of various wastematerials, conduct additional academicresearch as required, and disseminatethis information by means of its publications,the WTERT Web, and annualmeetings. In particular, WTERT strivesto increase the global recovery of energyand materials from used solids and toadvance the economic and environmentalperformance of waste-to-energy(WTE) technologies in the U.S. andworldwide. The guiding principle is thatresponsible management of wastesmust be based on science and thebest available technology and not whatseems to be inexpensive now but canbe very costly in the near future. Formore information: www.seas.columbia.edu/earth/wtert125SEAS 2010–2011

126SCHOLARSHIPS, FELLOWSHIPS,AND INTERNSHIPSThe department arranges for undergraduatesummer internships after the sophomoreand junior years. Undergraduatescan also participate in graduate researchprojects under the work-study program.Graduate research and teaching assistantships,as well as fellowships fundedby the Department, are available toqualified graduate students. GRE scoresare required of all applicants for graduatestudies.UNDERGRADUATE PROGRAMThe Bachelor of Science (B.S.) degreein Earth and Environmental Engineeringprepares students for careers in thepublic and private sector concerned withprimary materials (minerals, fuels, water)and the environment. Graduates arealso prepared to continue with furtherstudies in Earth/Environmental sciencesand engineering, business, public policy,international studies, law, and medicine.The EEE program is accredited as anenvironmental engineering program bythe Accreditation Board for Engineeringand Technology (ABET).What Is Earth and EnvironmentalEngineering?It is now recognized by the U.S. andother nations that continuing economicdevelopment must be accompanied byintelligent use of Earth’s resources andthat engineers can contribute much tothe global efforts for sustainable development.The technologies that havebeen developed for identifying, extracting,and processing primary materialsare also being applied to the twentyfirst-centuryproblems of resourcerecovery from used materials, pollutionprevention, and environmental remediation.The EEE undergraduate programencompasses these technologies.Undergraduate Program Objectives1. Graduates equipped with the necessarytools (mathematics, chemistry,physics, Earth sciences, and engineeringscience) will understand andimplement the underlying principlesused in the engineering of processesand systems.2. Graduates will be able to pursuecareers in industry, governmentagencies, and other organizationsconcerned with the environment andthe provision of primary and secondarymaterials and energy, as well ascontinue their education as graduatestudents in related disciplines.3. Graduates will possess the basicskills needed for the practice of Earthand Environmental Engineering,including measurement and controlof material flows through the environment;assessment of environmentalimpact of past, present, and futureindustrial activities; and analysis anddesign of processes for remediation,recycling, and disposal of usedmaterials.4. Graduates will practice their professionwith excellent written and communicationskills and with professionalethics and responsibilities.The CurriculumThe first two years of the EEE programare similar to those of other engineeringprograms. Students are provided with astrong foundation in basic sciences andmathematics, as well as the liberal artscore. Specific to the EEE program is anearly and sustained introduction to Earthscience and environmental engineering,and options for a number of sciencecourses to meet the specific interestsof each student. The junior and senioryears of the program consist of a groupof required courses in engineering scienceand a broad selection of technicalelectives organized into three distinctconcentrations, representing major areasof focus within the department.Several Columbia departments,such as Civil Engineering, MechanicalEngineering, and Earth and EnvironmentalSciences (Lamont-Doherty EarthObservatory), as well as the MailmanSchool of Public Health, contributecourses to the EEE program. EEE studentsare strongly encouraged to workas summer interns in industry or agencieson projects related to Earth and environmentalengineering. The departmenthelps students get summer internships.Technical Elective ConcentrationsStudents majoring in Earth and EnvironmentalEngineering select one of thefollowing three preapproved technicalelective concentrations. Note that theeight-course sequence for each preapprovedconcentration includes two sciencecourses during sophomore year(fall semester) and six technical electivecourses during junior and senior years.Any deviations from a preapprovedconcentration must be approved by anundergraduate faculty adviser. Alternativesfor junior/senior electives withineach concentration are listed, and othersmay be considered among 3000- to4000-level courses of any SEAS department,as well as courses listed in thesection “Courses in Other Divisions” inthis bulletin. However, at least four ofthe six junior/senior electives must consistof engineering topics. Alternativesfor sophomore-year science courses areshown in the EEE program table.A student may also choose todevelop an individual concentrationconforming to his/her specific interests,provided that it satisfies ABET engineeringaccreditation criteria. Therefore, thismust be developed in close consultationwith and approved by a faculty adviser.Water Resources and Climate RisksConcentrationPreapproved course sequence:PHYS C1403: Introduction to classical and quantumwaves (SEM III)EESC V2100: Climate system (SEM III)EAEE E4006: Field methods for environmentalengineering (SEM VI)EAEE E4009: GIS for resource, environmental,and infrastructure management(SEM VII)EAEE E4350: Planning and management of urbanhydrologic systems (SEM VII)EAEE E4257: Environmental data analysis andmodeling (SEM VIII)ECIA W4100: Management and development ofwater systems (SEM VIII)CIEE E4257: Contaminant transport in subsurfacesystems (SEM VIII)Alternatives for junior/senior electives:EAEE E4001: Industrial ecology of Earth resourcesCIEE E4260: Urban ecology studioCIEE E4163: Environmental engineering: wastewaterCIEN E4250: Waste containment design and practiceCIEN E4255: Flow in porous mediaAPPH E4200: Physics of fluidsEESC W4008: Introduction to atmospheric scienceEESC W4401: Quantitative models of climate-sensitivenatural and human systemsSEAS 2010–2011

EESC W4404: Regional dynamics, climate andclimate impactsSustainable Energy and MaterialsConcentrationPreapproved course sequence:CHEM C3443: Organic chemistry (SEM III)EESC V2200: Solid earth system (SEM III)MECE E3311: Heat transfer (SEM VI)EAEE E4001: Industrial ecology of Earthresources (SEM VII)EAEE E4900: Applied transport and chemical ratephenomena (SEM VII)MECE E4302: Advanced thermodynamics (SEM VIII)EESC W3015: The Earth’s carbon cycle (SEM VIII)MECE E4211: Energy: sources and conversion(SEM VIII)Alternatives for junior/senior electives:CHEN E3110: Transport phenomena, ICHEN E3120: Transport phenomena, IIEAEE E3101: Earth resource production systemsMSAE E3103: Elements of materials scienceCHEM C3071: Introduction to organic chemistryCHEM G4230: Statistical thermodynamicsEAEE E4550: Catalysis for emissions controlEESC W4008: Introduction to atmospheric scienceEAEE E4560: Particle technologyEnvironmental Health EngineeringConcentrationPreapproved course sequence:CHEM C3443: Organic chemistry (SEM III)EESC V2100: Climate system (SEM III)EAEE E4006: Field methods for environmentalengineering (SEM VI)EAEE E4009: GIS for resource, environmentaland infrastructure management(SEM VII)EHSC P6300: Environmental health sciences(SEM VII)EAEE E4257: Environmental data analysis andmodeling (SEM VIII)EAEE E4150: Air pollution prevention and control(SEM VIII)EHSC P6309: Biochemistry basic to environmentalhealth (SEM VIII)Alternatives for junior/senior electives:EAEE E4001: Industrial ecology of Earth resourcesEAEE E4900: Applied transport and chemical ratephenomenaEAEE E4950: Environmental biochemical processesCIEE E4257: Contaminant transport in subsurfacesystemsGRADUATE PROGRAMSM.S. in Earth ResourcesEngineering (M.S.-ERE)The M.S.-ERE program is designedfor engineers and scientists who planto pursue, or are already engaged in,environmental management/developmentcareers. The focus of the programis the environmentally sound mining andprocessing of primary materials (minerals,energy, and water) and the recyclingor proper disposal of used materials.The program also includes technologiesfor assessment and remediation of pastdamage to the environment. Studentscan choose a pace that allows them tocomplete the M.S.-ERE requirementswhile being employed.M.S.-ERE graduates are speciallyqualified to work for engineering, financial,and operating companies engagedin mineral processing ventures, theenvironmental industry, environmentalgroups in all industries, and for city, state,and federal agencies responsible for theenvironment and energy/resource conservation.At the present time, the U.S.environmental industry comprises nearly30,000 big and small businesses withtotal revenues of more than $150 billion.Sustainable development and environmentalquality has become a top priorityof government and industry in the UnitedStates and many other nations.This M.S. program is offered incollaboration with the Departmentsof Civil Engineering and Earth andEnvironmental Sciences. Many ofthe teaching faculty are affiliated withColumbia’s Earth Engineering Center.For students with a B.S. in engineering,at least 30 points (ten courses) arerequired. For students with a nonengineeringB.S. or a B.A., preferably witha science major, up to 48 points (totalof sixteen courses) may be requiredfor makeup courses. All students arerequired to carry out a research projectand write a thesis worth 3–6 points. Anumber of areas of study are availablefor the M.S.-ERE, and students maychoose courses that match their interestand career plans. The areas of studyinclude: agement ment mentand management loidalchemistry and nanotechnology Additionally, there are four optionalconcentrations in the program, in eachof which there are a number of requiredspecific core courses and electives. Ineach case, students are required tocarry out a research project and write athesis (3–6 points). The concentrationsare described briefly below; details andthe lists of specific courses for eachtrack are available from the department.Water Resources and Climate RisksClimate-induced risk is a significantcomponent of decision making for theplanning, design, and operation of waterresource systems, and related sectorssuch as energy, health, agriculture, ecologicalresources, and natural hazardscontrol. Climatic uncertainties can bebroadly classified into two areas: (1)those related to anthropogenic climatechange; (2) those related to seasonaltocentury-scale natural variations.The climate change issues impact thedesign of physical, social, and financialinfrastructure systems to support thesectors listed above. The climate variabilityand predictability issues impactsystems operation, and hence design.The goal of the M.S. concentration inwater resources and climate risks is toprovide (1) a capacity for understandingand quantifying the projections forclimate change and variability in thecontext of decisions for water resourcesand related sectors of impact; and (2)skills for integrated risk assessment andmanagement for operations and design,as well as for regional policy analysisand management. Specific areas ofinterest include: global and regional climate systemsand attendant uncertainties interannual climate variations and theirsectoral impacts water resource systems, consideringclimate and other uncertainties agementacross water resources andrelated sectorsSustainable EnergyBuilding and shaping the energy infrastructureof the twenty-first century isone of the central tasks for modern127SEAS 2010–2011

128engineering. The purpose of the sustainableenergy concentration is to exposestudents to modern energy technologiesand infrastructures and to the associatedenvironmental, health, and resourcelimitations. Emphasis will be on energygeneration and use technologies thataim to overcome the limits to growththat are experienced today. Energy andeconomic well-being are tightly coupled.Fossil fuel resources are still plentiful,but access to energy is limited by environmentaland economic constraints.A future world population of 10 billionpeople trying to approach the standardof living of the developed nations cannotrely on today’s energy technologies andinfrastructures without severe environmentalimpacts. Concerns over climatechange and changes in ocean chemistryrequire reductions in carbon dioxideemissions, but most alternatives to conventionalfossil fuels, including nuclearenergy, are too expensive to fill the gap.Yet access to clean, cheap energy iscritical for providing minimal resources:water, food, housing, and transportation.Concentration-specific classes willsketch out the availability of resources,their geographic distribution, theeconomic and environmental cost ofresource extraction, and avenues forincreasing energy utilization efficiency,such as cogeneration, district heating,and distributed generation of energy.Classes will discuss technologies forefficiency improvement in the generationand consumption sector; energyrecovery from solid wastes; alternativesto fossil fuels, including solar andwind energy, and nuclear fission andfusion; and technologies for addressingthe environmental concerns over theuse of fossil fuels and nuclear energy.Classes on climate change, air quality,and health impacts focus on the consequencesof energy use. Policy and itsinteractions with environmental sciencesand energy engineering will be anotheraspect of the concentration. Additionalspecialization may consider region specificenergy development.Integrated Waste Management (IWM)Humanity generates nearly 2 billion tonsof municipal solid wastes (MSW) annually.Traditionally, these wastes have beendiscarded in landfills that have a finitelifetime and then must be replaced byconverting more greenfields to landfills.This method is not sustainable becauseit wastes land and valuable resources.Also, it is a major source of greenhousegases and of various contaminants ofair and water. In addition to MSW, theU.S. alone generates billions of tons ofindustrial and extraction wastes. Also,the by-product of water purification is asludge or cake that must be disposedin some way. The IWM concentrationprepares engineers to deal with themajor problem of waste generationby exposing them to environmentallybetter means for dealing with wastes:waste reduction, recycling, composting,and waste-to-energy via combustion,anaerobic digestion, or gasification.Students are exposed not only to thetechnical aspects of integrated wastemanagement but also to the associatedeconomic, policy, and urban planningissues.Since the initiation of the Earth andenvironmental engineering program in1996, there have been several graduateresearch projects and theses that exemplifythe engineering problems that willbe encompassed in this concentration: facility digestion of organic materials high-temperature processes anaerobic digestion facilities phenomena in a combustion chamber of solid wastes facilitiesEnvironmental Health EngineeringThe purpose of this concentration is totrain professionals who can addressboth the public health and engineeringaspects of environmental problems.The identification and evaluation of environmentalproblems frequently revolvearound the risks to human health,whereas the development of remediationor prevention strategies frequentlyinvolves engineering approaches.Currently, these two critical steps inaddressing environmental problemsare handled by two separate groups ofprofessionals, public health practitionersand engineers, who usually have verylittle understanding of the role of theother profession in this process. Thegoal is to train those specialists collaboratively,through the Departmentsof Earth and Environmental Engineeringand Environmental Health Sciences.Joint Degree ProgramsThe Graduate School of Business andthe School of Engineering and AppliedScience offer a joint program leading tothe M.B.A. degree from the GraduateSchool of Business and the M.S. degreein Earth resources engineering fromthe School of Engineering and AppliedScience. The purpose of this programis to train students who wish to pursueEarth resource management careers.Students are expected to registerfull time for three terms in the GraduateSchool of Business and for two terms inthe School of Engineering and AppliedScience. It is possible, however, tostudy in the School of Engineering andApplied Science part time. Interestedpersons should contact ProfessorTuncel Yegulalp at 212-854-2984 or bye-mail to: yegulalp@columbia.edu.Doctoral ProgramsEEE offers two doctoral degrees:(1) the Eng.Sc.D. degree, administeredby The Fu Foundation Schoolof Engineering and Applied Science;and (2) the Ph.D. degree, administeredby the Graduate School of Arts andSciences. Qualifying examinations andall other intellectual and performancerequirements for these degrees are thesame. All applicants should use theSchool of Engineering forms. The scopeincludes the design and use of sensorsfor measurement at molecular scale; theunderstanding of surface, colloid, aqueous,and high-temperature phenomena;the integrated management of multipleresources and the mitigation of naturalSEAS 2010–2011

and environmental hazards, at regionalto global scales. The management ofthe interaction between human activities,Earth resources, and ecosystems is ofprimary interest.The engineering objectives of EEEresearch and education include: Provision and disposal of materials:environmentally sustainable extractionand processing of primary materials;manufacturing of derivative products;recycling of used materials; managementof industrial residues and usedproducts; materials-related applicationof industrial ecology. Management of water resources:understanding, prediction, and managementof the processes that governthe quantity and quality of waterresources, including the role of climate;development/operation of waterresource facilities; management ofwater-related hazards. Energy resources and carbonmanagement: mitigation of environmentalimpacts of energy production;energy recovery from waste materials;advancement of energy efficient systems;new energy sources; developmentof carbon sequestration strategies. Sensing and remediation: understandingof transport processes atdifferent scales and in different media;containment systems; modeling flowand transport in surface and subsurfacesystems; soil/water decontaminationand bioremediation.The Professional DegreesThe department offers the professionaldegrees of Engineer of Mines (E.M.)and Metallurgical Engineer (Met.E.).In order to gain admission to bothdegree programs, students must havean undergraduate degree in engineeringand complete at least 30 credits ofgraduate work beyond the M.S. degree,or 60 credits of graduate work beyondthe B.S. degree. These programs areplanned for engineers who wish to doadvanced work beyond the level of theM.S. degree but who do not desire toemphasize research.The professional degrees areawarded for satisfactory completion ofa graduate program at a higher level ofcourse work than is normally completedfor the M.S. degree. Students who findit necessary to include master’s-levelcourses in their professional degree programwill, in general, take such coursesas deficiency courses. A candidate isrequired to maintain a grade-point averageof at least 3.0. A student who, atthe end of any term, has not attainedthe grade-point average required for thedegree may be asked to withdraw. Thefinal 30 credits required for the professionaldegree must be completed in nomore than five years.Specific requirements for both professionaldegrees include a set of corecourses and a number of electivesappropriate for the specific area of concentration.All course work must lead tothe successful completion of a projectin mining engineering. A list of corecourses and electives is available at thedepartment office.COURSES IN EARTHAND ENVIRONMENTALENGINEERINGSee also Chemical Engineering sectionfor courses in applied chemistry.EAEE E1100y A better planet by design3 pts. Lect: 3. Professors Lau and Park.Development of the infrastructure for providingsafe and reliable resources (energy, water andother materials, transportation services) to supporthuman societies while attaining environmentalobjectives. Introduction of a typology of problemsby context, and common frameworks for addressingthem through the application of appropriatetechnology and policy. An interdisciplinary perspectivethat focuses on the interaction between humanand natural systems is provided. Alternatives forresource provision and forecasts of their potentialenvironmental impacts through a context providedby real-world applications and problems.EAEE E2002x Alternative energy resources3 pts. Lect: 3. Professors Walker and Lackner.Unconventional, alternative energy resources.Technological options and their role in the worldenergy markets. Comparison of conventional andunconventional, renewable and non-renewableenergy resources and analysis of the consequencesof various technological choices andconstraints. Economic considerations, energyavailability, and the environmental consequencesof large-scale, widespread use of each particulartechnology. Introduction to carbon dioxide captureand carbon dioxide disposal as a means ofsustaining the fossil fuel option.EAEE E3101y Earth resource productionsystems3 pts. Lect: 3.Technologies and equipment common to a widerange of surface and subsurface engineeringactivities: mine reclamation, hazardous wasteremediation, discovering and operating surfaceand underground mines, detection and removalof hidden underground objects, waste disposal,dredging and harbor rehabilitation, and tunnelingfor transportation or water distribution systems.These methods and equipment are examinedas they apply across the spectrum from miningto environmental engineering projects. The aimis to provide a broad background for earth andenvironmental engineers in careers involvingminerals and industrial, large-scale environmentalprojects.EAEE E3103x Energy, minerals and materialssystems3 pts. Lect: 3. Professors Lackner and Yegulalp.Prerequisites: MSAE E3111 or MECE E3301and ENME E3161 or MECE E3100 or equivalentCorequisites: MSAE E3111 or MECE E3301and ENME E3161 or MECE E3100 or equivalent.Overview of energy resources, resourcemanagement from extraction and processing torecycling and final disposal of wastes. Resourcesavailability and resource processing in thecontext of the global natural and anthropogenicmaterial cycles; thermodynamic and chemicalconditions including nonequilibrium effects thatshape the resource base; extractive technologiesand their impact on the environment and thebiogeochemical cycles; chemical extraction frommineral ores, and metallurgical processes forextraction of metals. In analogy to metallurgicalprocessing, power generation and the refiningof fuels are treated as extraction and refiningprocesses. Large scale of power generation anda discussion of its impact on the global biogeochemicalcycles.MSAE E3111x Thermodynamics, kinetictheory, and statistical mechanics3 pts. Lect: 3. Professor Billinge.An introduction to the basic thermodynamicsof systems, including concepts of equilibrium,entropy, thermodynamic functions, and phasechanges. Basic kinetic theory and statisticalmechanics, including diffusion processes,concept of phase space, classical and quantumstatistics, and applications thereof.EAEE E3112y Introduction to rock mechanics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: EAEE E3101 and ENME 3111,or their equivalents. Rock as an engineeringmaterial, geometry and strength of rock joints,geotechnical classification of rock masses,strength and failure of rock, field investigationsprior to excavation in rock, rock reinforcement,analysis and support of rock slopes and tunnels,and case histories.129SEAS 2010–2011

130EARTH AND ENVIRONMENTAL ENGINEERING PROGRAM:FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATH V1101 (3)MATH V1102 (3)MATH V1201 (3) APMA E2101 (3)MATHEMATICSor Honors Math, I (4)Honors Math, II (4)MATH E1210 (3)ODEC1401 (3)C1402 (3)PHYSICSCHEMISTRYor C1601 (3.5)C1602 (3.5)or C2801 (4.5)C2802 (4.5)C1403 (3.5)C1404 (3.5)and Lab C1500 (3) either semesteror C1604 (3.5)C2507 (3)CHEM C3443 (3.5)orPHYS C1403 (3)orPHYS C2601 (3.5)orBIOL C2005 (4)or C3045 (3.5)C3046 (3.5) andLab C2507 (3)REQUIREDNONTECHNICALELECTIVESC1010 (3)orZ1003 (4)orALP0006 (0)C1010 (3)Z1003 (4)HUMA C1001,COCI C1101,or Global Core (3–4)or C1010 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)HUMA C1121or C1123 (3)REQUIREDPROFESSIONALAND TECHNICALELECTIVESEAEE E1100 (3) Abetter planet by designor other departmentalprofessional-level courseEESC W4001 (4)orEESC V2100 (4.5)orEESC V2200 (4.5)EEAE E2002 (3)Alternative energysourcesCOMPUTERSCIENCEPHYSICALEDUCATIONComputer language: COMS W1003 (3) or W1004 (3) any semesterC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semesterMSAE E3141y Processing of metals andsemiconductors3 pts. Lect: 3. Professor Duby.Prerequisites: MSAE E3103 or equivalent.Synthesis and production of metals and semiconductorswith engineered microstructures fordesired properties. Includes high-temperature,aqueous, and electrochemical processing;thermal and mechanical processing of metalsand alloys; casting and solidification; diffusion,microstructural evolution, and phase transformations;modification and processing of surfacesand interfaces; deposition and removal of thinfilms. Processing of Si and other materials forelemental and compound semiconductor-basedelectronic, magnetic, and optical devices.EAEE E3185y Summer fieldwork for earth andenvironmental engineers0.5 pt.Undergraduates in Earth and EnvironmentalEngineering may spend up to 3 weeks in thefield under staff direction. The course consistsof mine, landfill, plant, and major excavation sitevisits and brief instruction of surveying methods.A final report is required.SEAS 2010–2011

EARTH AND ENVIRONMENTAL ENGINEERING PROGRAM:THIRD AND FOURTH YEARS131SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIEAEE E3103 (3)Energy, minerals, andmaterial systemsCIEE E3255 (3)Environmental control andpollution reductionsystemsEAEE E3998 (2)Undergraduatedesign projectEAEE E3999 (2)Undergraduatedesign projectCIEE E4252 (3)Environmental engineeringCIEE E3250 (3)Hydrosystems engineeringEAEE E4003 (3)Aquatic chemistryEAEE E4160 (3)Solid and hazardouswaste managementREQUIREDCOURSESENME E3161 (4)Fluid mechanicsorMECE E3100 (3)Introduction to mechanicsof fluidsSIEO W3600 (4)Introduction toprobability and statisticsEAEE E3801 (2)Earth and environmentalengineering lab, IICHEE E3010 (4)Principles of chemicalengineeringthermodynamicsorMSAE E3111 (3)Thermodynamics,kinetic theory, andstatistical mechanicsorMECE E3301 (3)ThermodynamicsEAEE E3800 (2)Earth and environmentalengineering lab, IEAEE E3901 (3)EnvironmentalmicrobiologyTECHNICALELECTIVESNONTECHNICALELECTIVES3 points 6 points 9 points3 points 3 points 3 pointsTOTAL POINTS 15–17 18 16 17EAEE E3221x Environmental geophysics3 pts. Lect: 3.Introduction to applied and environmentalgeophysics methods. Overview of principlesof geophysics, geophysical methods andtechniques (seismic, ground penetrating radar,resistivity, frequency em, and magnetics), andtheory and practical aspects of data processingand inversion. Examination of geophysicalcase studies for engineering and environmentalpurposes.CIEE E3250y Hydrosystems engineering3 pts. Lect: 3. Professor Lall.Prerequisites: CHEN E3110 or ENME E3161or equivalent, SIEO W3600 or equivalent,or instructor’s permission. A quantitativeintroduction to hydrologic and hydraulic systems,with a focus on integrated modelingand analysis of the water cycle and associatedmass transport for water resources andenvironmental engineering. Coverage of unithydrologic processes such as precipitation,evaporation, infiltration, runoff generation,open channel and pipe flow, subsurface flowand well hydraulics in the context of examplewatersheds and specific integrative problemssuch as risk-based design for flood control,provision of water, and assessment of environmentalimpact or potential for non-pointsource pollution. Spatial hydrologic analysisusing GIS and watershed models.CIEE E3255y Environmental control andpollution reduction systems3 pts. Lect: 3. Professor Castaldi.Prerequisites: ENME E3161 or MECE E3100.Review of engineered systems for preventionand control of pollution. Fundamentals of materialand energy balances and reaction kinetics.Analysis of engineered systems to addressenvironmental problems including solid andhazardous waste, air, water, soil and noise pollution.Life cycle assessments and emergingtechnologies.EAEE E3800y Earth and environmentalengineering laboratory, I2 pts. Lect: 1. Lab: 3. Professors Castaldi and Duby.Prerequisites: CHEE E3010. Corequisites: EAEEE3255 Experiments on fundamental aspects ofEarth and environmental engineering with emphasison the applications of chemistry, biology andthermodynamics to environmental processes:energy generation, analysis and purification ofwater, environmental biology, and biochemicaltreatment of wastes. Students will learn the laboratoryprocedures and use analytical equipmentfirsthand, hence demonstrating experimentally thetheoretical concepts learned in class.SEAS 2010–2011

132EAEE E3801x Earth and environmentalengineering laboratory, II2 pts. Lect: 1. Lab: 3. Professors Castaldi and Duby.Prerequisites: EAEE E3800 Corequisites: EAEEE4003 A continuation of EAEE E3800, withemphasis on the principles underlying wateranalysis for inorganic, organic, and bacterialcontaminants. Lab Required.EAEE E3900x and y–S3900 Undergraduateresearch in Earth and environmentalengineering0–3 pts. Directed study. Members of the faculty.This course may be repeated for credit, butno more than 3 points of this course may becounted towards the satisfaction of the B. S.degree requirements. Candidates for the B.S.degree may conduct an investigation in Earth andEnvironmental Engineering, or carry out a specialproject under the supervision of EAEE faculty.Credit for the course is contingent on the submissionof an acceptable thesis or final report. Thiscourse cannot substitute for the Undergraduatedesign project (EAEE E3999 or EAEE E3999)EAEE E3901y Environmental microbiology3 pts. Lect: 3. Professor Chandran.Prerequisites: CHEM C1404 or equivalentFundamentals of microbiology, genetics andmolecular biology, principles of microbial nutrition,energetics and kinetics, application of noveland state-of-the-art techniques in monitoring thestructure and function of microbial communitiesin the environment, engineered processes forbiochemical waste treatment and bioremediation,microorganisms and public health, global microbialelemental cycles.EAEE E3998x-E3999y Undergraduate designproject2 pts. (each semester). Lect: 1. Lab: 2.Professors Lall and Park.Prerequisites: senior standing. Students mustenroll for both 3998x and 3999y during theirsenior year. Selection of an actual problem inEarth and environmental engineering, and designof an engineering solution including technical,economic, environmental, ethical, healthand safety, social issues. Use of software fordesign, visualization, economic analysis, andreport preparation. Students may work in teams.Presentation of results in a formal report andpublic presentation.EAEE E4001x Industrial ecology of earthresources3 pts. Lect: 3. Professor Kaufman.Industrial ecology examines how to reconfigureindustrial activities so as to minimize the adverseenvironmental and material resource effects on theplanet. Engineering applications of methodologyof industrial ecology in the analysis of current processesand products and the selection or designof environmentally superior alternatives. Homeassignments of illustrative quantitative problems.EAEE E4003x Introduction to aquaticchemistry3 pts. Lect: 3. Professor Duby.Prerequisites: CHEN E3010 Principles of physicalchemistry applied to equilibria and kineticsof aqueous solutions in contact with mineralsand anthropogenic residues. The scientificbackground for addressing problems of aqueouspollution, water treatment, and sustainable productionof materials with minimum environmentalimpact. Hydrolysis, oxidation-reduction, complexformation, dissolution and precipitation, predominancediagrams; examples of natural water systems,processes for water treatment and for theproduction of inorganic materials from minerals.EAEE E4004x Physical processing andrecovery of solids3 pts. Lect: 3. Not offered in 2010–2011.Generalized treatment of processes for solidsseparation. Applications to materials processingand handling; mining; solid waste, recycling, andresource recovery; construction materials anddebris; scrap materials, yard and park wastes.Economic considerations and context. Relevantmaterials properties and bulk materials analyses.Process system flow-sheets and analysis. Solid/solid, solid/liquid, and solid/gas separationprocess. Liberation, concentration, and auxiliaryprocesses. Design of separation machines: typesand intensities of force involved; scalling-up factors.Laboratory demonstrations and a field tripwill be included.EAEE E4005x Near-surface engineeringgeophysics3 pts. Lect: 3. Not offered in 2010–2011.Geophysical methods as applicable to engineeringproblems. Principles of geophysics and noninvasiveimaging techniques (inversion technology)and benefits and pitfalls of geophysics vs. directimaging methods. Discussion of theory of eachmethod. Discussion of data acquisition, processingand interpretation for each method. Treatmentof several case studies. Class-wide planning andexecution of small-scale geophysical survey.EAEE E4006y Field methods forenvironmental engineering3 pts. Lect: 1.5. Lab: 2. Professor McGillis.Prerequisites: ENME E3161 or equivalent orinstructor’s permission Principles and methodsfor designing, building and testing systems tosense the environment. Monitoring the atmosphere,water bodies and boundary interfacesbetween the two. Sensor systems for monitoringheat and mass flows, chemicals, and biota.Measurements of velocity, temperature, flux andconcentration in the field. The class will involveplanning and execution of a study to sense alocal environmental system.EAEE E4007y Environmental geophysics fieldstudies3 pts. Lect: 3.Application of geophysical methods to noninvasiveassessment of the near surface. First partconsists of series of two-hour lectures of physicsand math involved in instrumental methods anddata acquisition and processing. In the field (ninefield days) students plan surveys; collect andanalyze geophysical data in teams; learn howto integrate geophysical data with invasive data,hydrological, geological, engineering, and contaminanttransport models; and develop a comprehensiveand justifiable model of the subsurface.Geophysical methods include GPR (GroundPenetrating Radar), conductivity, and magneticand seismic methods. Field applications includeinfrastructure/environmental assessment, archeologicalstudies, and high resolution geology.EAEE E4009x Geographic informationsystems (GIS) for resource, environmentaland infrastructure management3 pts. Lect: 3. Professor Yetman.Prerequisites: Permission of the instructor. Basicconcepts of geomatics, spatial data representationand organization, and analytical tools that compriseGIS are introduced and applied to a varietyof problems including watershed protection,environmental risk assessment, material massbalance, flooding, asset management, and emergencyresponse to natural or man-made hazards.Technical content includes geography and mapprojections, spatial statistics, database design anduse, interpolation and visualization of spatial surfacesand volumes from irregularly spaced data,and decision analysis in an applied setting. Taughtin a laboratory setting using ArcGIS. Access toNew York City and other standard databases.Term projects emphasize information synthesistowards the solution of a specific problem.EAEE E4010y Remote sensing andenvironmental change3 pts. Lect: 3.Prerequisites: EAEE E4009 or EESC W4050 orinstructor permission. Practical and theoreticalfoundations for the application of remote sensingtechniques to identification and monitoring ofenvironmental change. Designing and applyingspectral indices for assessment and monitoring,time series analysis of remote sensing data foranalyzing environmental problems. Discussionsof published literature relevant to the centraltopic covered in class. Analysis of remote sensingdata using IRI data library.EAEE E4011y Industrial ecology formanufacturing3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: EAEE E4001 Application of industrialecology to Design for Environment (DFE)of processes and products using environmentalindices of resources consumption and pollutionloads. Introduction of methodology for Life CycleAssessment (LCA) of manufactured products.Analysis of several DFE and LCA case studies.Term project required on use of DFE/LCA ona specific product/process: (a) product designSEAS 2010–2011

complete with materials and process selection,energy consumption, and waste loadings; (b)LCA of an existing industrial or consumer productusing a commercially established method.CHEE E4050x Industrial and environmentalelectrochemistry3 pts. Lect: 3.Prerequisites: CHEN E3010 or equivalent. Apresentation of the basic principle underlyingelectrochemical processes. Thermodynamics,electrode kinetics, and ionic mass transport.Examples of industrial and environmentalapplications illustrated by means of laboratoryexperiments: electroplating, refining, and winningin aqueous solutions and in molten salts; electrolytictreatment of wastes; primary, secondary,and fuel cells.ECIA W4100y Management and developmentof water systems3 pts. Lect: 3. Professor Lall.Decision analytic framework for operating, managing,and planning water systems, consideringchanging climate, values and needs. Publicand private sector models explored throughUS-international case studies on topics rangingfrom integrated watershed management to theanalysis of specific projects for flood mitigation,water and wastewater treatment, or distributionsystem evaluation and improvement.EAEE E4101y Introduction to particletechnology3 pts. Lect: 3. Not offered in 2010–2011.Prerequisite: instructor’s permission. Sizereduction, theory of comminution. Small particlestatistics, particle size measurement, propertiesof particle aggregates, behavior of particles influids, flow and retention of fluids in packings.EAEE E4150y Air pollution prevention andcontrol3 pts. Lect: 3. Professor Fthenakis.Adverse effects of air pollution, sources andtransport media, monitoring and modeling ofair quality, collection and treatment techniques,pollution prevention through waste minimalizationand clean technologies, laws, regulations,standards, and guidelines.EAEE E4160y Solid and hazardous wastemanagement3 pts. Lect: 3. Professor Somasundaran.Generation, composition, collection, transport,storage and disposal of solid and hazardouswaste. Impact on the environment and publichealth. Government regulations. Recycling andresource recovery.CIEE E4163x Environmental engineering:wastewater3 pts. Lect: 3. Professor Becker.Prerequisites: Introductory chemistry (with lab)and fluid mechanics. Fundamentals of water pollutionand wastewater characteristics. Chemistry,microbiology, and reaction kinetics. Design of primary,secondary, and advanced treatment systems.Small community and residential systems.EAEE E4190x Photovoltaic systemsengineering and sustainability3 pts. Lect: 3. Professor Fthenakis.Prerequisites: Senior standing or instructor’s permission.Corequisites: N/A. A systems approachfor intermittent renewable energy involving thestudy of resources, generation, demand, storage,transmission, economics and politic. Study ofcurrent and emerging photovoltaic technologies,with focus on basic sustainability metrics (e.g.,cost, resource availability, and life-cycle environmentalimpacts). The status and potential of firstandsecond-generation photovoltaic technologies(e.g., crystalline and amorphous Si, CdTe, CIGS)and emerging third-generation ones. Storageoptions to overcome the intermittency constraint.Large scales of renewable energy technologiesand plug-in hybrid electric cars.EAEE E4200y Production of inorganicmaterials3 pts. Lect: 3.Prerequisites: CHEN E3010 or equivalent.Production and recycling of inorganic materialsin aqueous and high temperature systems.Industrial and environmental applications ofhydrometallurgy, pyrometallurgy, and electrometallurgy.Reactor systems for, e.g., leaching,precipitation, and solvent extraction, bath andflash smelting reactors, rotary kilns, and fluid bedreactors. Thermodynamic and kinetic factors andmaterials/energy balances involved in the designand performance of such reactors in typicalapplications.EAIA E4200y Alternative energy resources3 pts. Lect: 3.Unconventional, alternative energy resources.Technological options and their role in the worldenergy markets. Comparison of conventional andunconventional, renewable and nonrenewable,energy resources and analysis of the consequencesof various technological choices andconstraints. Economic considerations, energyavailability, and the environmental consequencesof large-scale, widespread use of each particulartechnology. Introduction to carbon dioxidedisposal as a means of sustaining the fossil fueloption. Recitation section required.EAEE E4241x Solids handling and transportsystems3 pts. Lect: 3. Not offered in 2010–2011.Analysis and design of transportation systems forbulk solids in tunnels, mines, and large excavations.Design of hoisting, cable transport, railand trackless haulage systems, conveyor belts,selection of loaders, excavators, off-highwaytrucks, and draglines for large excavations.CHEE E4252x Introduction to surface andcolloid chemistry3 pts. Lect: 3. Professor Somasundaran.Prerequisites: Elementary physical chemistry.Thermodynamics of surfaces, properties of surfactantsolutions and surface films, electrostaticand electrokinetic phenomena at interfaces,adsorption; interfacial mass transfer and modernexperimental techniques.CIEE E4252y Environmental engineering3 pts. Lect: 3. Professor Chandran.Prerequisites: CHEM C1403, or equivalent;ENME E3161 or equivalent. Engineering aspectsof problems involving human interaction with thenatural environment. Review of fundamental principlesthat underlie the discipline of environmentalengineering, i.e., constituent transport andtransformation processes in environmental mediasuch as water, air, and ecosystems. Engineeringapplications for addressing environmentalproblems such as water quality and treatment,air pollution emissions, and hazardous wasteremediation. Presented in the context of currentissues facing the practicing engineers and governmentagencies, including legal and regulatoryframework, environmental impact assessments,and natural resource management.CIEE E4257y Groundwater contaminanttransport and remediation3 pts. Lect: 3.Prerequisites: CIEE E3250 or equivalent.Sources and types of groundwater contamination.Groundwater hydrology. Groundwatercontaminant rate and transport. Flow andtransport in the unsaturated zone. Nonaqueousphase liquids and multiphase flow. Physical andnumerical models for contaminant transport.Characterization and assessment of contaminatedsites. Groundwater remediation alternatives.Regulations.EAEE E4257y Environmental data analysisand modeling3 pts. Lect: 3. Professor Yegulalp.Prerequisites: SIEO W3600 or SIEO W4250 orequivalent. Statistical methods for the analysisof the space and time structure in environmentaldata. Application to problems of climate variationand change; hydrology; air, water and soil pollutiondynamics; disease propagation; ecologicalchange; and resource assessment. Applicationsare developed using the ArcView GeographicalInformation System (GIS), integrated with currentlyavailable statistical packages. Teamprojects that lead to publication-quality analysesof data in various environmental fields of interest.An interdisciplinary perspective is emphasized inthis applications-oriented class.EAEE E4350x Planning and management ofurban hydrologic systems3 pts. Lect: 3. Professor Rangarajan.Prerequisites: ENME E3161 or equivalent.Introduction to runoff and drainage systems in anurban setting, including hydrologic and hydraulicanalyses, flow and water quality monitoring,133SEAS 2010–2011

134common regulatory issues, and mathematicalmodeling. Applications to problems of climatevariation, land use changes, infrastructure operationand receiving water quality, developed usingstatistical packages, public-domain models, andGeographical Information Systems (GIS). Teamprojects that can lead to publication qualityanalyses in relevant fields of interest. Emphasison the unique technical, regulatory, fiscal, policy,and other interdisciplinary issues that pose achallenge to effective planning and managementof urban hydrologic systems.EAEE E4361y Economics of earth resourceindustries3 pts. Lect: 3. Professor Yegulalp.Prerequisites: EAEE E3101 or instructor’spermission. Definition of terms. Survey of Earthresource industries: resources, reserves, production,global trade, consumption of mineralcommodities and fuels. Economics of recyclingand substitution. Methods of project evaluation:estimation of operating costs and capital requirements,project feasibility, risk assessment, andenvironmental compliance. Cost estimation forreclamation/remediation projects. Financing ofreclamation costs at abandoned mine sites andwaste-disposal post-closure liability.CHEE E4530y Corrosion of metals3 pts. Lect: 3. Professor Duby.Prerequisites: CHEN E3010 or equivalent. Thetheory of electrochemical corrosion, corrosiontendency, rates, and passivity. Application tovarious environments. Cathodic protection andcoatings. Corrosion testing.EAEE E4550x Catalysis for emissions control3 pts. Lect: 3. Professor Farrauto.Prerequisites: ENME E3161 and MSAE E3111or equivalent. Fundamentals of heterogeneouscatalysis including modern catalytic preparationtechniques. Analysis and design of catalyticemissions control systems. Introduction to currentindustrial catalytic solutions for controllinggaseous emissions. Introduction to future catalyticallyenabled control technologies.EACE E4560x Particle technology3 pts. Lect: 3. Professor Park.Prerequisites: ENME E3161 and MSAE E3111 orequivalent. Introduction to engineering processesinvolving particulates and powders. The fundamentalsof particle characterization, multiphaseflow behavior, particle formation, processingand utilization of particles in various engineeringapplications with examples in energy andenvironment related technologies. Engineering offunctionalized particles and design of multiphasereactors and processing units with emphasison fluidization technology. Particulate systemsare involved in numerous industrial processesand are present in various natural phenomena.Particle technology is a term that refers to thefield of the science and technology associatedwith the characterization, formation, processingand utilization of particles. It is concernedwith the systems in which one or more of thecomponents are in the form of particles. Theterms particles, powder and particulate solids areoften used interchangeably, and the thus particletechnology is often also referred to as powdertechnology. Recently, the scope of particle technologyhas been extended to cover systems containingnanoparticles, aerosols, liquid droplets,emulsions and bubbles. The range of particulatesystems of industrial importance is vast, as is therange of processes involving particulate systems.Most of the industrial practices that engage inenergy, environment, minerals, chemicals, petroleum,agricultural, food, pharmaceuticals, andadvanced materials, utilize particles or powdersin the course of operation. Hence, understandingthe particle science and technology is essentialto ensure successful particle synthesis and handling,particulate process design and optimizationin operation. Particle technology is an interdisciplinaryfield. Due to the complexity of particulatesystems, particle technology is often treated asart rather than science. In this course, the fundamentalprinciples governing the key aspects ofparticle science and technology are introducedalong with various industrial examples.EAEE E4900x Applied transport and chemicalrate phenomena3 pts. Lect: 3. Professor Chen.Introduction to fluid dynamics, heat and masstransfer, and some applications in heterogeneousreaction systems. Effect of velocity,temperature, and concentration gradients andmaterial properties on fluid flow, heat and masstransfer and rate of chemical reactions; differentialand overall balance; engineering conceptsand semi-empirical correlations; application tochemical and materials processing and environmentalproblems.EAEE E4901y Environmental microbiology3 pts. Lect: 3. Professor Chandran.Basic microbiological principles; microbial metabolism;identification and interactions of microbialpopulations responsible for the biotransformationof pollutants; mathematical modeling of microbiallymediated processes; biotechnology andengineering applications using microbial systemsfor pollution control.EAEE E4950x Environmental biochemicalprocesses3 pts. Lect: 3. Professor Chandran.Prerequisites: EAEE 4901 or CIEE E4252 or EAEEE4003 or instructor’s approval. Qualitative andquantitative considerations in engineered environmentalbiochemical processes. Characterizationof multiple microbial reactions in a community andtechniques for determining associated kinetic andstoichiometric parameters. Engineering design ofseveral bioreactor configurations employed for biochemicalwaste treatment. Mathematical modelingof engineered biological reactors using state-of-theartsimulation packages.EAEE E4980 Urban environmental technologyand policy3 pts. Lect: 3. Not offered in 2010–2011.Progress of urban pollution engineering via contaminantabatement technology, government policy,and public action in urban pollution. Pollutantimpact on modern urban environmental quality,natural resources, and government, municipal,and social planning and management programs.Strong emphasis on current and twentieth-centurywaste management in New York City.EAEE E6132y Numerical methods ingeomechanics3 pts. Lect: 3. Professor Chen.Prerequisites: EAEE E3112 and CIEN E4241or instructor’s permission. A detailed surveyof numerical methods used in geomechanics,emphasizing the Finite Element Method (FEM).Review of the behavior of geological materials.Water and heat flow problems. FEM techniquesfor solving nonlinear problems, and simulatingincremental excavation and loading on the surfaceand underground.EAEE E6150y Industrial catalysis3 pts. Lect: 3. Professor Farrauto.Prerequisites: EAEE E4550 or equivalent, orinstructor’s permission. Fundamental principlesof kinetics, characterization and preparation ofcatalysts for production of petroleum productsfor conventional transportation fuels, specialtychemicals, polymers, food products, hydrogenand fuel cells and the application of catalysisin biomass conversion to fuel. Update of theever changing demands and challenges in environmentalapplications, focusing on advancedcatalytic applications as described in modernliterature and patents.EAEE E6151y Applied geophysics3 pts. Lect: 3. Not offered in 2010–2011.Potential field data, prospecting, wave equations.Huygens’ principle, Green’s functions, Kirchoffequation, WKB approximation, ray tracing. Wavepropagation, parameters. Computer applications.Wavelet processing, filters and seismic data.Stratified Earth model, seismic processing andprofiling. Radon transform and Fourier migration.Multidimensional geological interpretation.EAEE E6200y Theory and applications ofextreme value statistics in engineering andearth sciences3 pts. Lect: 3. Professor Yegulalp.Prerequisites: STAT W4107 or equivalentbackground in probability and statistical inference,or instructor’s permission. Introduction offundamental concepts in extreme value statistics.The exact and asymptotic theory of extremes.Development of statistical methodology for estimatingthe parameters of asymptotic extremaldistributions from experimental data. ExamplesSEAS 2010–2011

of applications of extreme value statistics toregional and global earthquake forecasting,laboratory testing of rocks and metals, fatiguefailure, floods, droughts, extreme wind velocities,and rainfalls.EAEE E6208y Combustion chemistry andprocesses3 pts. Lect: 3. Professor Castaldi.Prerequisites: EAEE E4900 or equivalent orinstructor’s permission. The fundamentals ofcombustion phenomena and the intrinsic chemistryof combustion processes. The theory of theessential combustion processes such as ignition,sustained reaction, stability and flame quenching.Processes that govern reactant consumption andproduct formation, in particular by-products thatare formed that result in pollutant emissions, andthe impacts and implications that combustion haslocally and globally on the environment. Detailedexamination of the entire range of combustionsystems from diffusion flame processes to currentdeveloping technologies including millisecondcatalytic combustion processes, noncarbon fueledcombustion, fuel cells, and plasma combustion.EAEE E6210x Quantitative environmental riskanalysis3 pts. Lect: 3. Professor Yegulalp.Prerequisites: EAEE E3101, SIEO W4150, orequivalent. Comprises the tools necessary fortechnical professionals to produce meaningfulrisk analyses. Review of relevant probability andstatistics; incorporation of probability in facilityfailure analysis. Availability, assessment, andincorporation of risk-related data. Contaminanttransport to exposed individuals; uptake, morbidity,and mortality. Computational tools necessaryto risk modeling. Use and applicability of resultingmeasurements of risk, and their use in publicpolicy and regulation.EAEE E6212y Carbon sequestration3 pts. Lect: 3. Professor Lackner.Prerequisites: EAEE E4900 or equivalent orinstructor’s permission. New technologies forcapturing carbon dioxide and disposing of itaway from the atmosphere. Detailed discussionof the extent of the human modifications to thenatural carbon cycle, the motivation and scopeof future carbon management strategies andthe role of carbon sequestration. Introduction ofseveral carbon sequestration technologies thatallow for the capture and permanent disposal ofcarbon dioxide. Engineering issues in their implementation,economic impacts, and the environmentalissues raised by the various methods.CHEE E6220y Equilibria and kinetics inhydrometallurgical systems3 pts. Lect: 3. Professor Duby.Prerequisites: CHEE E4050 or EAEE E4003.Detailed examination of chemical equilibria inhydrometallurgical systems. Kinetics and mechanismsof homogeneous and heterogeneous reactionsin aqueous solutions.EAEE E6220x Remedial and corrective action3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: EAEE E4160 or equivalent.Integrates the engineering aspects of cleanupof hazardous materials in the environment. Siteassessment/investigation. Site closure, containment,and control techniques and technologies.Techniques used to treat hazardous materialsin the environment, in situ and removal for treatment,focusing on those aspects that are uniqueto the application of those technologies in anuncontrolled natural environment. Management,safety, and training issues.EAEE E6228y Theory of flotation3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: CHEE E4252 or instructor’s permission.A detailed study of the physicochemicalprinciples of the flotation process.EAEE E6240x or y Physical hydrology3 pts. Lect: 3. Professor Lall.Prerequisites: Engineering hydrology or equivalentSpatial/temporal dynamics of the hydrologiccycle and its interactions with landforms and vegetation.Hydroclimatology at regional to planetaryscales, focusing on mechanisms of organizationand variation of water fluxes as a function ofseason, location, reservoir (ocean, atmosphere,land), and time scale. Land-atmosphere interactionand the role of vegetation and soil moisture.Topography as an organizing principle for landwater fluxes. Geomorphology and the evolutionof river networks. Sedimentation, erosion and hillslope hydrology. Dynamics of water movementover land, in rivers and in the subsurface, withan emphasis on modeling interfaces. Integratedmodels and the scale problem. Emphasis ondata-based spatial/temporal modeling and explorationof outstanding theoretical challenges.CHEE E6252y Advanced surface and colloidchemistry3 pts. Lect: 2. Lab: 3. Professor Somasundaran.Prerequisites: CHEE E4252. Applications ofsurface chemistry principles to wetting, flocculation,flotation, separation techniques, catalysis,mass transfer, emulsions, foams, aerosols, membranes,biological surfactant systems, microbialsurfaces, enhanced oil recovery, and pollutionproblems. Appropriate individual experimentsand projects. Lab required.EAEE E6255x-E6256y Methods andapplications of analytical decision making inmineral industries3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Instructor’s permission. Advancedstudy of decision-making problems with criticalsurvey and applications of quantitative decisionmakingtechniques in mineral industries.Systematic development of methods of theformulation, analysis, and resolution of theseproblems.EAEE E8229x Selected topics in processingminerals and wastes3 pts. Lect: 2. Lab: 3.Prerequisites: CHEE E4252 or instructor’s permission.Critical discussion of current researchtopics and publications in the area of flotation,flocculation, and other mineral processing techniques,particularly mechanisms of adsorption,interactions of particles in solution, thinning ofliquid films, and optimization techniques.EAEE E8231y Selected topics in hydro- andelectrometallurgy3 pts. Lect: 3.Prerequisites: EAEE E4003 and CHEE E4050,or instructor’s permission. Review of currentresearch and literature in the field of hydrometallurgy,electrometallurgy, and corrosion. Topicswill be selected by the instructor to illustrate theapplication of thermodynamics and rate phenomenato the design and control of electrochemicalengineering processes.EAEE E8233x and y Research topics inparticle processing0–1 pt. Professor Somasundaran.Emergent findings in the interactions of particleswith reagents and solutions, especially inorganics,surfactants, and polymers in solution, andtheir role in grinding, flotation, agglomeration, filtration,enhanced oil recovery, and other mineralprocessing operations.EAEE E8273x-E8274y Mining engineeringreports0–4 pts. Professor Yegulalp.May substitiute for formal thesis, EAEE E9271,upon recommendation of the student’s adviser.EAEE E9271x and y–S9271 Earth andenvironmental engineering thesis0–6 pts. Members of the faculty.Research work culminating in a creditable dissertationon a problem of a fundamental natureselected in conference between student andadviser. Wide latitude is permitted in choice of asubject, but independent work of distinctly graduatecharacter is required in its handling.EAEE E9273x-E9274y Earth andenvironmental engineering reports0–4 pts.May substitute for the formal master’s thesis,EAEE E9271, upon recommendation of thedepartment.EAEE E9280x and y Earth and environmentalengineering colloquium0–1 pt. Lect: 1.5. Professor Park.All graduate students are required to attend thedepartmental colloquium as long as they arein residence. Advanced doctoral students maybe excused after three years of residence. Nodegree credit is granted.135SEAS 2010–2011

136EAEE E9281x Prospects for nuclear energy–earth and environmental engineering seminar0–1 pt. Lect: 1.5. Professors Gazze and Lackner.This seminar course examines the prospectsfor nuclear energy as a source of safe, secure,and environmentally sustainable energy bothin the U.S. and internationally. In particular, itanalyzes the four key issues that limit the expansionof nuclear energy: cost, safety, proliferationconcerns, and long-term disposal of radioactivewastes. Through readings, research, and classdiscussions, it engages students to criticallyevaluate arguments both for and against nuclearpower. The course builds basic literacy innuclear technology and is open to students withtechnical, policy, or economic backgrounds.EAEE E9302x and y Mining engineeringresearch0–4 pts. Professor Yegulalp.Graduate research directed toward solution oftechnicoscientific problems in mining.EAEE E9305x and y–S9305 Earth andenvironmental engineering research0–12 pts. Members of the faculty.Graduate research directed toward solution ofa problem in mineral processing or chemicalmetallurgy.EAEE E9800x and y–S9800 Doctoral researchinstruction3, 6, 9, or 12 pts. Members of the faculty.A candidate for the Eng.Sc.D. degree in mineralengineering must register for 12 points of doctoralresearch instruction. Registration in EAEEE9800 may not be used to satisfy the minimumresidence requirement for the degree.EAEE E9900x and y–S9900 Doctoraldissertation0 pts. Members of the faculty.A candidate for the doctorate may be requiredto register for this course every term after thestudent’s course work has been completed, anduntil the dissertation has been accepted.SEAS 2010–2011

ELECTRICAL ENGINEERING1300 S. W. Mudd, MC 4712, 212-854-3105www.ee.columbia.edu137CHAIRShih-Fu Chang,1305 S. W. MuddVICE CHAIRCharles Zukowski,1026 SchapiroDEPARTMENTALADMINISTRATORKevin Corridan,1303 S. W. MuddPROFESSORSDimitris AnastassiouKeren BergmanShih-Fu ChangPaul DiamentTony F. HeinzAurel A. LazarPredrag JelenkovicNicholas MaxemchukSteven Nowick,Computer ScienceRichard M. Osgood Jr.Henning G. Schulzrinne,Computer ScienceAmiya K. SenKenneth L. ShepardYannis P. TsividisWen I. WangXiaodang WangCharles A. ZukowskiASSOCIATE PROFESSORSDan EllisPeter KingetASSISTANT PROFESSORSDirk EnglundHarish KrishnaswamyIoannis (John) KymissisGil ZussmanSENIOR LECTURERDavid VallancourtADJUNCT PROFESSORSMiron AbramoviciYuliy BaryshnikovDoru CalinDavid GibbonIrving KaletLurng-Kuo LiuGeorge MoustakidesTom RichardsonKrishnan SabnaniVinay VaishampayanAnwar WalidPhil WhitingShalom WindOmar WingThomas WooADJUNCT ASSOCIATEPROFESSORSYves BaeyensZhu LiuDeepak TuragaMartin RoettelerADJUNCT ASSISTANTPROFESSORSHenrique AndradeNeda CvijeticTimothy DicksonAngel PeterchevSENIOR RESEARCHSCIENTISTRobert LaibowitzASSOCIATE RESEARCHSCIENTISTVladimir SokolovPOSTDOCTORAL RESEARCHSCIENTISTS/FELLOWSYee Him CheungPankaj ChopraCory Raymond DeanDavid HayJonathan S. HodesYugang JiangKean Sub LeeZhenguo LiNadia K. PervezSiddharth RamakrishnanContemporary electrical engineeringis a broad discipline thatencompasses a wide range ofactivities. A common theme is the use ofelectrical and electromagnetic signals forthe generation, transmission, processing,storage, conversion, and controlof information and energy. An equallyimportant aspect is the human interfaceand the role of individuals as the sourcesand recipients of information. The ratesat which information is transmitted todayrange from megabits per second to gigabitsper second and in some cases, ashigh as terabits per second. The range offrequencies over which these processesare studied extends from direct current(i.e., zero frequency), to microwave andoptical frequencies.The need for increasingly faster andmore sophisticated methods of handlinginformation poses a major challenge tothe electrical engineer. New materials,devices, systems, and network conceptsare needed to build the advancedcommunications and information handlingsystems of the future. Previousinnovations in electrical engineering havehad a dramatic impact on the way inwhich we work and live: the transistor,integrated circuits, computers, radio andtelevision, satellite transmission systems,lasers, fiber optic transmission systems,and medical electronics.The faculty of the ElectricalEngineering Department at ColumbiaUniversity is dedicated to the continueddevelopment of further innovationsthrough its program of academicinstruction and research. Our undergraduateacademic program in electricalengineering is designed to preparethe student for a career in industry orbusiness by providing her or him witha thorough foundation of the fundamentalconcepts and analytical tools ofcontemporary electrical engineering. Awide range of elective courses permitsthe student to emphasize specific disciplinessuch as telecommunications,microelectronics, digital systems, orphotonics. Undergraduates have anopportunity to learn firsthand about currentresearch activities by participatingin a program of undergraduate researchprojects with the faculty.A master’s level program in electricalengineering permits the graduate studentto further specialize her/his knowledgeand skills within a wide range ofdisciplines. For those who are interestedin pursuing a career in teaching orresearch, our Ph.D. program offers theSEAS 2010–2011

138opportunity to conduct research underfaculty super-vision at the leading edgeof technology and applied science.Research seminars are offered in a widerange of areas, including telecommunications,very large scale integrated circuits,photonics, and microelectronics.The Electrical EngineeringDepartment, along with the ComputerScience Department, also offers B.S.and M.S. programs in computer engineering.Details on those programs canbe found in the Computer Engineeringsection in this bulletin.Research ActivitiesThe research interests of the facultyencompass a number of rapidly growingareas, vital to the development offuture technology, that will affect almostevery aspect of society: communicationsand information processing; solid-statedevices; ultrafast optics and photonics;microelectronic circuits, integrated systemsand computer-aided design; systemsbiology; and electromagnetics andplasmas. Details on all of these areascan be found at www.ee.columbia.edu/research.Communications research focuseson wireless communication, multimedianetworking, real-time Internet, lightwave(fiber optic) communication networks,optical signal processing and switching,service architectures, network managementand control, the processing ofimage and video information, and mediaengineering. Current studies includewireless and mobile computing environments,broadband kernels, objectorientednetwork management, real-timemonitoring and control, lightwave networkarchitectures, lightweight protocoldesign, resource allocation and networkinggames, real-time Internet services,future all-digital HDTV systems, codingand modulation.Solid-state device research is conductedin the Columbia MicroelectronicsSciences Laboratories. This is an interdisciplinaryfacility, involving aspectsof electrical engineering and appliedphysics. It includes the study of semiconductorphysics and devices, opticalelectronics, and quantum optics. Theemphasis is on laser processing anddiagnostics for submicron electronics,fabrication of compound semiconductoroptoelectronic devices by molecularbeam epitaxy, physics of superlatticesand quantum wells, and interfacedevices such as Schottky barriers, MOStransistors, heterojunctions, and bipolartransistors. Another area of activity is thephysics and chemistry of microelectronicspackaging.Research in photonics includesdevelopment of semi conductor lightsources such as LEDs and injectionlasers, fabrication and analysis of quantumconfined structures, photo conductors,pin diodes, avalanche photodiodes,optical interconnects, and quantumoptics. A major effort is the picosecondoptoelectronics program, focusingon the development of new devicesand their applications to high-speedoptoelectronic measurement systems,photonic switching, and optical logic. Inaddition, research is being performed indetection techniques for optical communicationsand radar. Members ofthe photonics group play a leading rolein a multi-university consortium: TheNational Center for Integrated PhotonicsTechnology.Integrated systems research involvesthe analysis and design of analog, digital,and mixed-signal microelectronic circuitsand systems. These include novelsignal processors and related systems,data converters, radio frequency circuits,low noise and low power circuits, andfully integrated analog filters that sharethe same chip with digital logic. VLSIarchitectures for parallel computation,packet switching, and signal processingare also under investigation. Computeraideddesign research involves thedevelopment of techniques for the analysisand design of large-scale integratedcircuits and systems.Electromagnetics research rangesfrom the classical domains of microwavegeneration and transmission and wavepropagation in various media to modernapplications involving lasers, opticalfibers, plasmas, and solid-state devices.Problems relevant to controlled thermonuclearfusion are under investigation.Laboratory FacilitiesCurrent research activities are fullysupported by more than a dozen wellequippedresearch laboratories run bythe department. Specifically, laboratoryresearch is conducted in the followinglaboratories: Multimedia NetworkingLaboratory, Lightwave CommunicationsLaboratory, Systems Laboratory, Imageand Advanced Television Laboratory,Laser Processing Laboratory, MolecularBeam Epitaxy Laboratory, SurfaceAnalysis Laboratory, MicroelectronicsFabrication Laboratory, DeviceMeasurement Laboratory, UltrafastOptoelectronics Laboratory, ColumbiaIntegrated Systems Laboratory (CISL),Lightwave Communications Laboratory,Photonics Laboratory, Plasma PhysicsLaboratory (in conjunction with theDepartment of Applied Physics).Laboratory instruction is provided inthe Introduction to Electrical EngineeringLaboratory, Marcellus-Hartley ElectronicsLaboratory, Microprocessor Laboratory,Microwave Laboratory, OpticalElectronics Laboratory, Solid-StateLaboratory, VLSI Design Laboratory, andStudent Projects Laboratory, all on thetwelfth floor of the S. W. Mudd Building.UNDERGRADUATE PROGRAMThe undergraduate program in electricalengineering at Columbia University hasfive formal educational objectives:1. Produce graduates with a strongfoundation in the basic sciences andmathematics that will enable them toidentify and solve electrical engineeringproblems.2. Provide our students with a solidfoundation in electrical engineeringthat prepares them for life-longcareers and professional growth infields of their choice.3. Provide our students with the basicskills to communicate effectively andto develop the ability to function asmembers of multi-disciplinary teams.4. Provide our students with a broadbasededucation so that they canappreciate diversity of opinion, betterunderstand ethical issues, and developa perspective of our profession.5. Provide our students with a relevantengineering design experience that isintegrated across the four-year curriculum.Through these experiences,our students will develop an understandingof the relationship betweentheory and practice.The B.S. program in electrical engineeringat Columbia University seeks toSEAS 2010–2011

provide a broad and solid foundationin the current theory and practice ofelectrical engineering, including familiaritywith basic tools of math and science,an ability to communicate ideas, anda humanities background sufficient tounderstand the social implications ofengineering practice. Graduates shouldbe qualified to enter the professionof engineering, to continue toward acareer in engineering research, or toenter other fields in which engineeringknowledge is essential. Required nontechnicalcourses cover civilization andculture, philosophy, economics, and anumber of additional electives. Englishcommunication skills are an importantaspect of these courses. Required sciencecourses cover basic chemistry andphysics, whereas math requirementscover calculus, differential equations,probability, and linear algebra. Basiccomputer knowledge is also included,with an introductory course on usingengineering workstations and two rigorousintroductory computer sciencecourses. Core electrical engineeringcourses cover the main components ofmodern electrical engineering and illustratebasic engineering principles. Topicsinclude a sequence of two courses oncircuit theory and electronic circuits, onecourse on semiconductor devices, oneon electromagnetics, one on signals andsystems, one on digital systems, andone on communications or networking.Engineering practice is developedfurther through a sequence of laboratorycourses, starting with a first-year courseto introduce hands-on experience earlyand to motivate theoretical work. Simplecreative design experiences start immediatelyin this first-year course. Followingthis is a sequence of lab coursesthat parallel the core lecture courses.Opportunities for exploring design canbe found both within these lab coursesand in the parallel lecture courses,often coupled with experimentation andcomputer simulation, respectively. Theculmination of the laboratory sequenceand the design experiences introducedthroughout earlier courses is a seniordesign course (capstone design course),which includes a significant design projectthat ties together the core program,encourages creativity, explores practicalaspects of engineering practice,and provides additional experience withcommunication skills in an engineeringcontext. Finally, several technical electivesare required, chosen to provide bothbreadth and depth in a specific area ofinterest. More detailed program objectivesand outcomes are posted at www.ee.columbia.edu/academics/undergrad.The program in electrical engineeringleading to the B.S. degree is accreditedby the Engineering AccreditationCommission of the Accreditation Boardfor Engineering and Technology (ABET).There is a strong interaction betweenthe Department of Electrical Engineeringand the Departments of ComputerScience, Applied Physics and AppliedMathematics, Industrial Engineeringand Operations Research, Physics, andChemistry.EE Core CurriculumAll electrical engineering (EE) studentsmust take a set of core courses, whichcollectively provide the student withfundamental skills, expose him/herto the breadth of EE, and serve as aspringboard for more advanced work,or for work in areas not covered in thecore. These courses are shown on thecharts in Undergraduate Degree Tracks.A full curriculum checklist is also postedat www.ee.columbia.edu/academics/undergrad.Technical ElectivesThe 18-point technical elective requirementfor the electrical engineeringprogram consists of three components:depth, breadth, and other. A generaloutline is provided here, and more specificcourse restrictions can be found atwww.ee.columbia.edu/academics/undergrad.For any course not clearly listedthere, adviser approval is necessary.The depth component must consistof at least 6 points of electrical engineeringcourses in one of four defined areas:(a) photonics, solid-state devices, andelectromagnetics; (b) circuits and electronics;(c) signals and systems; and (d)communications and networking. Thedepth requirement provides an opportunityto pursue particular interests andexposure to the process of exploring adiscipline in depth—an essential processthat can be applied later to other disciplines,if desired.The breadth component must consistof at least 6 additional points ofengineering courses that are outside ofthe chosen depth area. These coursescan be from other departments withinthe School. The breadth requirementprecludes overspecialization. Breadth isparticularly important today, as innovationrequires more and more of an interdisciplinaryapproach, and exposure toother fields is known to help one’s creativityin one’s own main field. Breadthalso reduces the chance of obsolescenceas technology changes.Any remaining technical electivecourses, beyond the minimum 12 pointsof depth and breadth, do not have tobe engineering courses (except for studentswithout ELEN E1201 or approvedtransfer credit for ELEN E1201) but mustbe technical. Generally, math and sciencecourses that do not overlap withcourses used to fill other requirementsare allowed.Starting EarlyThe EE curriculum is designed to allowstudents to start their study of EE in theirfirst year. This motivates students earlyand allows them to spread nontechnicalrequirements more evenly. It also makesevident the need for advanced math andphysics concepts, and motivates thestudy of such concepts. Finally, it allowsmore time for students to take classesin a chosen depth area, or gives themmore time to explore before choosinga depth area. Students can start withELEN E1201: Introduction to electricalengineering in the second semester oftheir first year, and can continue withother core courses one semester afterthat, as shown in the “early-starting students”chart. It is emphasized that boththe early- and late-starting sample programsshown in the charts are examplesonly; schedules may vary depending onstudent preparation and interests.Transfer StudentsTransfer students coming to Columbiaas juniors with sufficient general backgroundcan complete all requirementsfor the B.S. degree in electrical engineering.Such students fall into one oftwo categories:139SEAS 2010–2011

140ELECTRICAL ENGINEERING: FIRST AND SECOND YEARSEARLY-STARTING STUDENTSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and APMA E2101 (3) 3PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)CHEMISTRYone-semester lecture(3–4)C1403 or C1404 orC3045 or C1604CORE REQUIREDCOURSESELEN E1201 (3.5) Introduction to electricalengineering (either semester)ELEN E3201 (3.5)Circuit analysisELEN E3801 (3.5)Signals and systemsELEN E3331 (3)Electronic circutsCSEE E3827 (3)Fund. of computer sys.REQUIRED LABSELEN E3081 (1) 2Circuit analysis labELEN E3084 (1) 2Signals and systems labELEN E3083 (1) 2Electronic circuits labELEN E3082 (1) 2Digital systems labENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESHUMA C1001, COCI C1101, or Major Cultures (3–4); HUMA W1121 or W1123 (3); HUMA C1002, COCIC1102, or Global Core (3–4); ECON W1105 (4) and W1155 recitation (0); some of these courses can bepostponed to the junior or senior year, to make room for taking the above electrical engineering courses.COMPUTERSCIENCEPHYSICALEDUCATIONC1001 (1) C1002 (1)COMS W1007 (3) any semester 1GATEWAY LABE1102 (4) either semester1COMS W1007 may be replaced by COMS W1003, W1004, or W1009, but impact on later options should be considered(see www.ee.columbia.edu/academics/undergrad).2If possible, these labs should be taken along with their corresponding lecture courses.3APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.Plan 1: Students coming to Columbiawithout having taken the equivalent ofELEN E1201 must take this course intheir junior year. This requires postponingthe core courses in circuitsand electronics until the senior year,and thus does not allow taking electivesin that area; thus, such studentscannot choose circuits and electronicsas a depth area.Plan 2: This plan is for students whoSEAS 2010–2011have taken a course equivalent toELEN E1201 at their school of origin,including a laboratory component.See the bulletin for a description ofthis course. Many pre-engineeringprograms and physics departmentsat four-year colleges offer suchcourses. Such students can start takingcircuits at Columbia immediately,and thus can choose circuits andelectronics as a depth area.It is stressed that ELEN E1201 or itsequivalent is a key part of the EE curriculum.The preparation provided bythis course is essential for a number ofother core courses.Sample programs for both Plan 1and Plan 2 transfer students can befound at www.ee.columbia.edu/academics/undergrad.

ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARSEARLY-STARTING STUDENTS141SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIPHYSICS(tracks continued)C1403 (3)C2601 (3.5)Lab W3081 (2)Lab C1494 (3) 1Lab C2699 (3)EE COREREQUIREDCOURSESELEN E3106 (3.5)Solid-state devices andmaterialsELEN E3401 (4)ElectromagneticsELEN E3701 (3) 2Intro. tocommunication systemsorCSEE W4119 (3) 2Computer networksEE REQUIRED LABSELEN E3043 (3)Solid state, microwave,and fiber optics labELEN E3399 (1)EE practiceOne capstone designcourse 3 (ELEN E3390,ELEN E4332,EECS E4340,or CSEE W4840)OTHER REQUIREDCOURSESIEOR E3658 or STAT 4105 4 ; and COMS W3137 (or W3133, W3134, or W3139)(Some of these courses are not offered both semesters. Students with an adequatebackground can take some of these courses in the sophomore year)EE DEPTHTECHAt least two technical electives in one depth area. The four depth areas are(a) photonics, solid-state devices, and electromagnetics; (b) circuits and electronics;(c) signals and systems; and (d) communications and networking(For details, see www.ee.columbia.edu/academics/undergrad)ELECTIVESBREADTHTECHOTHERTECHAt least two technical electives outside the chosen depth area; must be engineering courses(see www.ee.columbia.edu/academics/undergrad)Additional technical electives (consisting of more depth or breadth courses, or further options listed at www.ee.columbia.edu/academics/undergrad) as required to bring the total points of technical electives to 18 5NONTECHComplete 27-point requirement; see page 10 or www.seas.columbia.edu for details(administered by the advising dean)TOTAL POINTS 6 16.5 17 16 181Chemistry lab (CHEM 1500) may be substituted for physics lab, although this is not generally recommended.2These courses can be taken in the sophomore year if the prerequisites/corequisites are satisfied.3The capstone design course provides ELEN majors with a “culminating design experience.” As such, it should be taken near the end of the program and involve aproject that draws on material from a range of courses.4SIEO W3600 and W4150 cannot generally be used to replace IEOR E3658 or STAT W4105.5The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010.6“Total points” assumes that 20 points of nontechnical electives and other courses are included.B.S./M.S. ProgramThe B.S./M.S. degree program is opento a select group of undergraduatestudents. This double degree programmakes possible the earning of boththe Bachelor of Science and Master ofScience degrees simultaneously. Upto 6 points may be credited to bothdegrees, and some graduate classestaken in the senior year may counttoward the M.S. degree. Both degreesmay be conferred at the same time.Interested students can find furtherinformation at www.ee.columbia.edu/academics/undergrad and can discussoptions directly with their faculty adviser.Students must be admitted prior to thestart of their seventh semester at SEAS.SEAS 2010–2011

142ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARSLATE-STARTING STUDENTSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101(3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and APMA E2101 (3) 3PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)C1403 (3)C2601 (3.5)Lab W3081 (2)Lab C1494 (3) 4Lab C2699 (3)CHEMISTRYone-semester lecture(3–4)C1403 or C1404 orC3045 or C1604ELECTRICALENGINEERINGELEN E1201 (3.5) either semester 1ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 orW1123 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)COMPUTERSCIENCEPHYSICALEDUCATIONCOMS W1007 (3) either semester 2C1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1Transfer students and 3-2 Combined Plan students who have not taken ELEN E1201 prior to the junior year are expected to have taken a roughly equivalent coursewhen they start ELEN E3201.2COMS W1007 may be replaced by COMS W1003, W1004, or W1009, but impact on later options should be considered(see www.ee.columbia.edu/academics/undergrad).3APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.4Chemistry lab (CHEM C1500) may be substituted for physics lab, although this is not generally recommended.Students in the 3-2 Combined Planundergraduate program are not eligiblefor admission to this program.GRADUATE PROGRAMSThe Department of Electrical Engineeringoffers graduate programs leading tothe degree of Master of Science (M.S.),the graduate professional degree ofElectrical Engineer (E.E.), and thedegrees of Doctor of EngineeringScience (Eng.Sc.D.) and Doctor ofPhilosophy (Ph.D.). The GraduateRecord Examination (General TestSEAS 2010–2011only) is required of all applicants exceptspecial students. An undergraduategrade point average equivalent to B orbetter from an institution comparable toColumbia is expected.Applicants who, for good reasons,are unable to submit GRE test resultsby the deadline date but whose undergraduaterecord is clearly superior mayfile an application without the GREscores. An explanatory note should beadded to ensure that the application willbe processed even while incomplete. Ifthe candidate’s admissibility is clear, thedecision may be made without the GREscores; otherwise, it may be deferreduntil the scores are received.There are no prescribed courserequirements in any of the regulargraduate degree programs. Students, inconsultation with their faculty advisers,design their own programs, focusing onparticular fields of electrical engineering.Among the fields of graduate study aremicroelectronics, communications andsignal processing, integrated circuit andsystem analysis and synthesis, photonics,electromagnetic theory and applications,plasma physics, and quantumelectronics.

ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS 1LATE-STARTING STUDENTS143SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIICSEE W3827(3)Fund. of computer sys.EE COREREQUIREDCOURSESELEN E3106 (3.5)Solid-state devices andmaterialsELEN E3201 (3.5)Circuit analysisELEN E3801 (3.5)Signals and systemsELEN E3331 (3)Electronic circuitsELEN E3401 (4)ElectromagneticsELEN E3701 (3)Intro. tocommunication systemsorCSEE W4119 (3)Computer networksEE REQUIRED LABSELEN E3081 (1) 2Circuit analysis labELEN E3084 (1) 2Signals and systems labELEN E3083 (1) 2Electronic circuits labELEN E3082 (1) 2Digital systems labELEN E3043 (3)Solid state, microwave,and fiber optics labELEN E3399 (1)EE practiceOne capstone designcourse 3 ( ELEN E3390,ELEN E4332,EECS E4340,or CSEE W4840)OTHER REQUIREDCOURSESIEOR E3658 or STAT W4105 4 ; and COMS W3137 (or W3133, W3134, or W3139)(Some of these courses are not offered both semesters)EE DEPTHTECHAt least two technical electives in one depth area. The four depth areas are(a) photonics, solid-state devices, and electromagnetics; (b) circuits andelectronics; (c) signals and systems; and (d) communications and networking(For details, see www.ee.columbia.edu/academics/undergrad)ELECTIVESBREADTHTECHOTHERTECHAt least two technical electives outside the chosen depth area; must beengineering courses (see www.ee.columbia.edu/academics/undergrad)Additional technical electives (consisting of more depth or breadth courses, or further options listed atwww.ee.columbia.edu/academics/undergrad) as required to bring the total points of technical electives to 18 5NONTECHComplete 27-point requirement; see page 10 or www.seas.columbia.edu for details(administered by the advising dean)TOTAL POINTS 6 15.5 18 16 181This chart shows one possible schedule for a student who takes most of his or her major program in the final two years. Please refer to the previous chart fora recommended earlier start.2If possible, these labs should be taken along with their corresponding lecture courses.3The capstone design course provides ELEN majors with a “culminating design experience.” As such, it should be taken near the end of the program and involvea project that draws on material from a range of courses.4SIEO W3600 and W4150 cannot generally be used to replace IEOR E3658 or STAT W4105.5The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010.6“Total points” assumes that 9 points of nontechnical electives are included.Graduate course charts for severalfocus areas can be found at www.ee.columbia.edu/academics/masters.Master of Science DegreeCandidates for the M.S. degree in electricalengineering must complete 30points of credit beyond the bachelor’sdegree. A minimum of 15 points of creditmust be at the 6000 level or higher.No credit will be allowed for undergraduatecourses (3000 or lower).At least 15 points must be taken inEE courses (i.e., courses listed by theSEAS 2010–2011

144Electrical Engineering Department) orcourses designated COMS, of whichat least 10 points must be EE courses.Courses to be credited toward theM.S. degree can be taken only uponprior approval of a faculty adviser in theDepartment of Electrical Engineering.This applies to the summer session aswell as the autumn and spring terms.Certain 4000-level courses will notbe credited toward the M.S. degree,and no more than 6 points of researchmay be taken for credit. Up to 3 pointsof credit for approved graduate coursesoutside of engineering and science maybe allowed. The general school requirementslisted earlier in this bulletin, suchas minimum GPA, must also be satisfied.All degree requirements must becompleted within five years of the beginningof the first course credited towardthe degree.More details and a checklist foradviser approvals can be found at www.ee.columbia.edu/academics/masters.Professional DegreeThe professional degree in electricalengineering is intended to provide specializationbeyond the level of the M.S.degree, in a focused area of electricalengineering selected to meet the professionalobjectives of the candidate.A minimum of 30 points of credit isrequired.The prospective E.E. candidate followsa program of study formulated inconsultation with, and approved by, afaculty adviser. At least three courseswill be in a specific, focused area ofelectrical engineering, and at leasttwo-thirds of the entire program will bein electrical engineering or computerscience. No thesis is required, but theprogram may optionally include a seminaror project or research for which areport is produced; up to 6 points ofsuch projects may be credited towardthe degree.The level of the courses will generallybe higher than is typical of a master’sdegree program, although courses atthe 4000 level may be included to preparefor more advanced work. A candidateis required to maintain a gradepointaverage of at least 3.0.All degree requirements must becompleted within five years of the beginningof the first course credited towardthe degree.Doctoral DegreeThe requirements for the Ph.D. and Eng.Sc.D. degrees are identical. Both require adissertation based on the candidate’s originalresearch, conducted under the supervisionof a faculty member. The work may betheoretical or experimental or both.Students who wish to becomecandidates for the doctoral degree inelectrical engineering have the option ofapplying for admission to the Eng.Sc.D.program or the Ph.D. program. Studentswho elect the Eng.Sc.D. degree registerin the School of Engineering and AppliedScience; those who elect the Ph.D.degree register in the Graduate Schoolof Arts and Sciences.Doctoral candidates must obtain aminimum of 60 points of formal coursecredit beyond the bachelor’s degree.A master’s degree from an accreditedinstitution may be accepted as equivalentto 30 points. A minimum of 30points beyond the master’s degree mustbe earned while in residence in the doctoralprogram.More detailed information regardingthe requirements for the doctoral degreemay be obtained in the departmentoffice and at www.ee.columbia.edu/academics/phd.Optional M.S. ConcentrationsStudents in the electrical engineeringM.S. program often choose to use someof their electives to focus on a particularfield. Students may pick one of anumber of optional, formal concentrationtemplates or design their own M.S.program in consultation with an adviser.These concentrations are not degreerequirements. They represent suggestionsfrom the faculty as to how onemight fill one’s programs so as to focuson a particular area of interest. Studentsmay wish to follow these suggestions,but they need not. The degree requirementsare quite flexible and are listed inthe Master of Science Degree section,above. All students, whether followinga formal concentration template or not,are expected to include breadth in theirprogram. Not all of the elective courseslisted here are offered every year. Forthe latest information on available courses,visit the Electrical Engineering homepage at www.ee.columbia.edu.Concentration in MultimediaNetworkingAdvisers: Prof. Henning Schulzrinne,Prof. Predrag Jelenkovic1. Satisfy M.S. degree requirements.2. Both ELEN E6711: Stochastic signalsand noise and ELEN E6761:Computer communication networks, I.3. Either COMS W4118: Operatingsystems or COMS W4111: Databasesystems.4. COMS E6181: Advanced Internetservices.With an adviser’s approval, any of thecourses above can be replaced by thefollowing closely related subjects: CSEEE4140: Networking laboratory; CSEEW4119: Computer networks; COMSW4180: Network security; ELEN E6762:Computer communication networks, II;ELEN E6850: Visual information systems;ELEN E6950: Wireless and mobilenetworking, I; ELEN E6951: Wirelessand mobile networking, II.Concentration in TelecommunicationsEngineeringAdvisers: Prof. Henning Schulzrinne,Prof. Pedrag Jelenkovic, Prof. EdCoffman, Prof. Nicholas Maxemchuk,Prof. Gil Zussman1. Satisfy the M.S. degree requirements.2. One basic hardware or softwarecourse such as: ELEN E4321:Digital VLSI circuits; ELEN E4411:Fundamentals of photonics; COMSW4118: Operating systems, I; COMSW4111: Database systems.3. One basic systems course such as:ELEN E4702: Communication theory;ELEN E4703: Wireless communications;CSEE W4119: Computernetworks; ELEN E6761: Computercommunication networks, I.4. At least two approved courses froma focus area such as Signal/ImageProcessing and Telecommunications/Multimedia Networks.Concentration in Media EngineeringAdvisers: Prof. Shi-Fu Chang, Prof. DanEllis, Prof. Xiaodong WangSEAS 2010–2011

1. Satisfy the basic M.S. degree requirements.2. Both ELEN E4810: Digital signalprocessing and ELEN E4830: Digitalimage processing.3. Either ELEN E6761: Computer communicationnetworks, I or CSEEW4119: Computer networks.4. At least two approved advancedcourses such as: ELEN E4896: Musicsignal processing; ELEN E6820:Speech and audio processing andrecognition; ELEN E6850: Visualinformation systems; ELEN E6860:Advanced digital signal processing;ELEN E688x: Topics in signalprocessing; ELEN E6762: Computercommunication networks, II; ELENE6717: Information theory; COMSE6181: Advanced internet services;ELEN E6950: Wireless and mobilenetworking, I; or ELEN E6001-E6002:Advanced projects in electrical engineeringwith an appropriate project.A cross-disciplinary project in areasrelated to new media technology isespecially encouraged.Concentration in Lightwave(Photonics) EngineeringAdvisers: Prof. Keren Bergman, Prof.Paul Diament, Prof. Richard Osgood,Prof. Amiya Sen, Prof. Tony Heinz1. Satisfy the M.S. degree requirements.2. Take both ELEN E4411:Fundamentals of photonics and ELENE6403: Classical electromagnetictheory (or an equivalent, such asAPPH E4300: Applied electrodynamicsor PHYS G6092: Electromagnetictheory).3. One more device/circuits/photonicscourse such as: ELEN E4401:Wave transmission and fiber optics;ELEN E6412: Lightwave devices;ELEN E6413: Lightwave systems;ELEN E4405: Classical nonlinearoptics; ELEN E6414: Photonicintegrated circuits; ELEN E4314:Communication circuits; ELEN E4501:Electromagnetic devices and energyconversion.4. At least two approved courses inphotonics or a related area.Concentration in Wireless and MobileCommunicationsAdviser: Prof. Gil Zussman1. Satisfy M.S. degree requirements.2. One basic circuits course such as:ELEN E4312: Analog electric circuits;ELEN E4314: Communication circuits;ELEN E6314: Advanced communicationcircuits; ELEN E6312: Advancedanalog ICs.3. Two communications or networkingcourses such as: CSEE W4119:Computer networks; ELEN E4702:Digital communications; ELEN E4703:Wireless communications; ELENE6711: Stochastic signals and noise;ELEN E4810: Digital signal processing;ELEN E6950: Wireless andmobile networking, I; ELEN E6951:Wireless and mobile networking, II;ELEN E6761: Computer communicationnetworks, I; ELEN E6712:Communication theory; ELEN E6713:Topics in communications; ELENE6717: Information theory.4. At least two approved courses in wirelesscommunications or a related area.Concentration in MicroelectronicCircuitsAdvisers: Prof. Yannis Tsividis, Prof.Charles Zukowski, Prof. KennethShepard, Prof. Peter Kinget1. Satisfy M.S. degree requirements.2. One digital course: ELEN E4321:Digital VLSI circuits or ELEN E6321:Advanced digital electronic circuits.3. One analog course such as: ELENE4312: Analog electronic circuits;ELEN E4215: Analog filter synthesisand design; ELEN E6312: Advancedanalog integrated circuits; ELENE6316: Analog circuits and systemsin VLSI; ELEN E4314: Communicationcircuits; ELEN E6314: Advancedcommunication circuits.4. One additional course such as:ELEN E4332: VLSI design laboratory;ELEN E6211: Circuit theory; ELENE6261: Computational methods ofcircuit analysis; ELEN E6304: Topicsin electronic circuits; ELEN E6318:Microwave circuit design.5. At least two additional approvedcourses in circuits or a related area.Concentration in MicroelectronicDevicesAdvisers: Prof. Wen Wang, Prof. RichardOsgood, Prof. Ioannis (John) Kymissis1. Satisfy M.S. degree requirements.2. One basic course such as: ELENE4301: Introduction to semiconductordevices or ELEN E4411:Fundamentals of photonics.3. One advanced course such as: ELENE4193: Modern display science andtechnology; ELEN E4944: Principlesof device microfabrication; ELENE4503: Sensors, actuators, andelectromechanical systems; ELENE6151: Surface physics and analysisof electronic materials; ELEN E6331:Principles of semiconductor physics,I; ELEN E6332: Principles of semiconductorphysics, II; ELEN E6333:Semiconductor device physics; ELENE6945: Nanoscale fabrication anddevices.4. At least two approved courses indevices or a related area.Concentration in Systems BiologyAdvisers: Prof. Dimitris Anastassiou,Prof. Pedrag Jelenkovic, Prof. AurelLazar, Prof. Kenneth Shepard, Prof.Xiaodong Wang, Prof. Charles Zukowski1. Satisfy M.S. degree requirements.2. Take both ECBM E4060: Introductionto genomic information scienceand technology and BMEB W4011:Computational neuroscience, I: circuitsin the brain3. Take at least one course from CBMFW4761: Computational genomics;CHBC W4510: Molecularsystems biology, I; CHBC W4511:Molecular systems biology, II; BISTP8139: Theoretical genetic modeling(Biostatistics); ELEN E6010: Systemsbiology; EEBM E6020: Methodsin computational neuroscience;BMEE E6030: Neural modeling andneuroengineering; APMA E4400:Introduction to biophysical modeling;CHEN E4700: Principles of genomictechnologies; ELEN E4312: Analogelectronic circuits.4. Take at least one course from ELENE608x: Topics in systems biology;ELEN E6717: Information theory;ELEN E6201: Linear systems theory;EEME E6601: Introduction to controltheory; ELEN E6711: Stochasticmodels in information systems;ELEN E6860: Advanced digital signalprocessing; EEBM E6090: Topicsin computational neuroscience andneuroengineering; ELEN E6261:Computational methods of circuitanalysis.145SEAS 2010–2011

146COURSES IN ELECTRICALENGINEERINGELEN E1101x or y The digital information age3 pts. Lect: 3. Professor Vallancourt.An introduction to information transmission andstorage, including technological issues. Binarynumbers; elementary computer logic; digitalspeech and image coding; basics of compactdisks, telephones, modems, faxes, UPC barcodes, and the World Wide Web. Projectsinclude implementing simple digital logic systemsand Web pages. Intended primarily for studentsoutside the School of Engineering and AppliedScience. The only prerequisite is a workingknowledge of elementary algebra.ELEN E1201x and y Introduction to electricalengineering3.5 pts. Lect: 3. Lab:1. Professor Vallancourt.Prerequisites: MATH V1101. Basic concepts ofelectrical engineering. Exploration of selectedtopics and their application. Electrical variables,circuit laws, nonlinear and linear elements,ideal and real sources, transducers, operationalamplifiers in simple circuits, external behaviorof diodes and transistors, first order RC and RLcircuits. Digital representation of a signal, digitallogic gates, flip-flops. A lab is an integral part ofthe course. Required of electrical engineeringand computer engineering majors.ELEN E3043x Solid state, microwave andfiber optics laboratory3 pts. Lect: 1. Lab: 6. Professor W. Wang.Prerequisites: ELEN E3106 and ELEN E3401.Optical electronics and communications.Microwave circuits. Physical electronics.ECBM E3060x Introduction to genomicinformation science and technology3 pts. Lect: 3. Professor Anastassiou.Introduction to the information system paradigm ofmolecular biology. Representation, organization,structure, function and manipulation of the biomolecularsequences of nucleic acids and proteins.The role of enzymes and gene regulatory elementsin natural biological functions as well as in biotechnologyand genetic engineering. Recombinationand other macromolecular processes viewed asmathematical operations with simulation and visualizationusing simple computer programming. Thiscourse shares lectures with ECBM E4060, but thework requirements differ somewhat.ELEN E3081x Circuit analysis laboratory1 pt. Lab: 3. Professor Zukowski.Prerequisites: ELEN E1201 or equivalent.Corequisites: ELEN E3201. Companion labcourse for ELEN E3201. Experiments cover suchtopics as: use of measurement instruments;HSPICE simulation; basic network theorems;linearization of nonlinear circuits using negativefeedback; op-amp circuits; integrators; secondorder RLC circuits. The lab generally meets onalternate weeks.ELEN E3082y Digital systems laboratory1 pt. Lab: 3. Professor Shepard.Corequisites: CSEE W3827. Recommendedpreparation: ELEN E1201 or equivalent.Companion lab course for CSEE W3827.Experiments cover such topics as logic gates;flip-flops; shift registers; counters; combinationallogic circuits; sequential logic circuits; programmablelogic devices. The lab generally meets onalternate weeks.ELEN E3083y Electronic circuits laboratory1 pt. Lab: 3. Professor Vallancourt.Prerequisites: ELEN E3081. Corequisites: ELENE3331. Companion lab course for ELEN E3331.Experiments cover such topics as macromodelingof nonidealities of opamps using SPICE;Schmitt triggers and astable multivibrations usingopamps and diodes; logic inverters and amplifiersusing bipolar junction transistors; logic invertersand ring oscillators using MOSFETs; filterdesign using op-amps. The lab generally meetson alternate weeks.ELEN E3084x Signals and systems laboratory1 pt. Lab: 3. Professor X. Wang.Corequisites: ELEN E3801. Companion labcourse for ELEN E3801. Experiments covertopics such as: introduction and use of MATLABfor numerical and symbolic calculations; linearityand time invariance; continuous-time convolution;Fourier-series expansion and signal reconstruction;impulse response and transfer function;forced response. The lab generally meets onalternate weeks.ELEN E3106x Solid-state devices andmaterials3.5 pts. Lect: 3. Recit: 1. Professor Kymissis.Prerequisites: MATH V1201 or equivalent.Corequisites: PHYS C1403 or PHYS C2601 orequivalent. Crystal structure and energy bandtheory of solids. Carrier concentration and transportin semiconductors. P-n junction and junctiontransistors. Semiconductor surface and MOS transistors.Optical effects and optoelectronic devices.ELEN E3201x Circuit analysis3.5 pts. Lect: 3. Recit: 1. Professor Zukowski.Prerequisites: ELEN E1201 or equivalent.Corequisites: MATH V1201. A course on analysisof linear and nonlinear circuits and their applications.Formulation of circuit equations. Networktheorems. Transient response of first and secondorder circuits. Sinusoidal steady state-analysis.Frequency response of linear circuits. Poles andzeros. Bode plots. Two-port networks.ELEN E3331y Electronic circuits3 pts. Lect: 3. Professor Vallancourt.Prerequisites: ELEN E3201. Operational amplifiercircuits. Diodes and diode circuits. MOS andbipolar junction transistors. Biasing techniques.Small-signal models. Single-stage transistoramplifiers. Analysis and design of CMOS logicgates. A/D and D/A converters.ELEN E3390y Electronic circuit designlaboratory3 pts. Lab: 6. Professor Vallancourt.Prerequisites: ELEN E3082, E3083, E3331,E3401, E3801. Advanced circuit design laboratory.Students work in teams to specify, design,implement and test an engineering prototype.The work involves technical as well as non-technicalconsiderations, such as manufacturability,impact on the environment, and economics. Theprojects may change from year to year.ELEN E3399x Electrical engineering practice1 pt. Professor Vallancourt.Design project planning, written and oral technicalcommunication, practical aspects of engineeringas a profession, such as career developmentand societal and environmental impact.Generally taken senior year.ELEN E3401y Electromagnetics4 pts. Lect: 3. Professor Diament.Prerequisites: MATH V1201, PHYS C1402 orPHYS C1602, or equivalents. Basic field concepts.Interaction of time-varying electromagneticfields. Field calculation of lumped circuit parameters.Transition from electrostatic to quasistaticand electromagnetic regimes. Transmissionlines. Energy transfer, dissipation, and storage.Waveguides. Radiation.EEME E3601x Classical control systems3 pts. Lect: 3. Professor Longman.Prerequisites: MATH E1210. Analysis and designof feedback control systems. Transfer functions;block diagrams; proportional, rate, and integralcontrollers; hardware; implementation. Routhstability criterion, root locus, Bode and Nyquistplots, compensation techniques.ELEN E3701y Introduction to communicationsystems3 pts. Lect: 3.Prerequisites: ELEN E3801. Corequisites: IEORE3658. A basic course in communication theory,stressing modern digital communication systems.Nyquist sampling, PAM and PCM/DPCM systems,time division multipliexing, high frequencydigital (ASK, OOK, FSK, PSK) systems, andAM and FM systems. An introduction to noiseprocesses, detecting signals in the presence ofnoise, Shannon’s theorem on channel capacity,and elements of coding theory.ELEN E3801x Signals and systems3.5 pts. Lect: 3. Professor X. Wang.Corequisites: MATH V1201. Modeling, description,and classification of signals and systems.Continuous-time systems. Time domain analysis,convolution. Frequency domain analysis, transferfunctions. Fourier series. Fourier and Laplacetransforms. Discrete-time systems and the Ztransform.SEAS 2010–2011

CSEE W3827x and y Fundamentals ofcomputer systems3 pts. Lect: 3. Professor Rubenstein.Prerequisites: An introductory programmingcourse. Fundamentals of computer organizationand digital logic. Boolean algebra, Karnaughmaps, basic gates and components, flipflops andlatches, counters and state machines, basicsof combinational and sequential digital design.Assembly language, instruction sets, ALUs,single-cycle and multi-cycle processor design,introduction to pipelined processors, caches, andvirtual memory.ELEN E3998x and y Projects in electricalengineering0 to 3 pts.May be repeated for credit, but no more than3 total points may be used for degree credit.Prerequisite: approval by a faculty member whoagrees to supervise the work. Independent projectinvolving laboratory work, computer programming,analytical investigation, or engineeringdesign.BMEB W4020x Computational neuroscience:circuits in the brain3 pts. Lect: 3. Professor Lazar.Prerequisites: ELEN E3801 or Biology W3004.The biophysics of computation: modeling biologicalneurons, the Hodgkin-Huxley neuron,modeling channel conductances and synapsesas memristive systems, bursting neurons andcentral pattern generators, I/O equivalence andspiking neuron models. Information representationand neural encoding: stimulus representationwith time encoding machines, the geometry oftime encoding, encoding with neural circuits withfeedback, population time encoding machines.Dendritic computation: elements of spike processingand neural computation, synaptic plasticityand learning algorithms, unsupervised learningand spike time-dependent plasticity, basicdendritic integration. Projects in MATLAB.ECBM E4060x Introduction to genomicinformation science and technology3 pts. Lect: 3. Professor Anastassiou.Introduction to the information system paradigmof molecular biology. Representation, organization,structure, function and manipulation of thebiomolecular sequences of nucleic acids andproteins. The role of enzymes and gene regulatoryelements in natural biological functions aswell as in biotechnology and genetic engineering.Recombination and other macromolecular processesviewed as mathematical operations withsimulation and visualization using simple computerprogramming. This course shares lectureswith ECBM E3060, but the work requirementsdiffer somewhat.CSEE W4119x and y Computer networks3 pts. Lect: 3. Professor Misra.Corequisites: IEOR E3658 or SIEO W3600 orequivalents. Introduction to computer networksand the technical foundations of the Internet,including applications, protocols, local areanetworks, algorithms for routing and congestioncontrol, security, elementary performance evaluation.Several written and programming assignmentsrequired.CSEE W4140x or y Networking laboratory4 pts. Lect: 3. Professor Zussman.Prerequisites: CSEE W4119 or equivalent. Inthis course, students learn how to put “principlesinto practice,” in a hands-on-networking labcourse. The technologies and protocols of theInternet are covered, using equipment currentlyavailable to large Internet service providers suchas CISCO routers and end-systems. A set oflaboratory experiments provides hands-on experiencewith engineering wide-area networks andfamiliarizes students with the Internet Protocol(IP), Address Resolution Protocol (ARP),Internet Control Message Protocol (ICMP), UserDatagram Protocol (UDP) and TransmissionControl Protocol (TCP), the Domain NameSystem (DNS), routing protocols (RIP, OSPF,BGP), network management protocols (SNMP),and application-level protocols (FTP, TELNET,SMTP).ELEN E4193x or y Modern display scienceand technology3 pts. Lect: 3. Professor Kymissis.Prerequisites: Linear algebra, differentialequations, and basic semiconductor physics.Introduction to modern display systems inan engineering context. The basis for visualperception, image representation, color space,metrics of illumination. Physics of luminescence,propagation and manipulation of light in anisotropicmedia, emissive displays, and spatial lightmodulators. Fundamentals of display addressing,the Alt-Pleshko theorem, multiple line addressing.Large area electronics, fabrication, anddevice integration of commercially importantdisplay types. A series of short laboratories willreinforce material from the lectures. Enrollmentmay be limited.ELEN E4301y Introduction to semiconductordevices3 pts. Lect: 3. Professor Laibowitz.Prerequisites: ELEN E3106 or equivalent.Semiconductor physics. Carrier injection andrecombination. P-n junction and diodes: Schottkybarrier and heterojunctions, solar cells and lightemittingdiodes. Junction and MOS field-effecttransistors, bipolar transistors. Tunneling andcharge-transfer devices.ELEN E4312x Analog electronic circuits3 pts. Lect: 3. Professor Tsividis.Prerequisites: ELEN E3331 and ELEN E3801.Differential and multistage amplifiers; smallsignalanalysis; biasing techniques; frequencyresponse; negative feedback; stability criteria;frequency compensation techniques. Analoglayout techniques. An extensive design project isan integral part of the course.ELEN E4314y Communication circuits3 pts. Lect: 3. Professor Tsividis.Prerequisites: ELEN E4312. Principles of electroniccircuits used in the generation, transmission,and reception of signal waveforms, as usedin analog and digital communication systems.Nonlinearity and distortion; power amplifiers;tuned amplifiers; oscillators; multipliers and mixers;modulators and demodulators; phase-lockedloops. An extensive design project is an integralpart of the course.ELEN E4321x Digital VLSI circuits3 pts. Lect: 3. Professor Shepard.Recommended preparation: ELEN E3331, CSEEW3827, and ELEN E3106. Design and analysisof high speed logic and memory. Digital CMOSand BiCMOS device modeling. Integrated circuitfabrication and layout. Interconnect and parasiticelements. Static and dynamic techniques. Worstcasedesign. Heat removal and I/O. Yield andcircuit reliability. Logic gates, pass logic, latches,PLAs, ROMs, RAMs, receivers, drivers, repeaters,sense amplifiers.EECS E4340x Computer hardware design3 pts. Lect: 2. Lab: 3. Professor Sethumadhavan.Prerequisites: ELEN E3331 and CSEE W3827.Practical aspects of computer hardware designthrough the implementation, simulation, andprototyping of a PDP-8 processor. High-level andassembly languages, I/O, interrupts, datapathand control design, pipelining, busses, memoryarchitecture. Programmable logic and hardwareprototyping with FPGAs. Fundamentals of VHDLfor register-transfer level design. Testing andvalidation of hardware. Hands-on use of industryCAD tools for simulation and synthesis.ELEN E4401x Wave transmission and fiberoptics3 pts. Lect: 3. Professor Diament.Prerequisites: ELEN E3401 or equivalent. Wavesand Maxwell’s equations. Field energetics,dispersion, complex power. Waves in dielectricsand in conductors. Reflection and refraction.Oblique incidence and total internal reflection.Transmission lines and conducting waveguides.Planar and circular dielectric waveguides; integratedoptics and optical fibers. Hybrid and LPmodes. Graded-index fibers. Mode coupling;wave launching.ELEN E4411x Fundamentals of photonics3 pts. Lect: 3. Professor Osgood.Prerequisites: ELEN E3401 or equivalent.Planar resonators. Photons and photon streams.Photons and atoms: energy levels and bandstructure; interactions of photons with matter;absorption, stimulated and spontaneous emission;thermal light, luminescence light. Laseramplifiers: gain, saturation, and phase shift; rate147SEAS 2010–2011

148equations; pumping. Lasers: theory of oscillation;laser output characteristics. Photons in semiconductors:generation, recombination, and injection;heterostructures; absorption and gain coefficients.Semiconductor photon sources: LEDs;semiconductor optical amplifiers; homojunctionand heterojunction laser diodes. Semiconductorphoton detectors: p-n, p-i-n, and heterostructurephoto diodes; avalanche photodiodes.ELEN E4488x Optical systems3 pts. Lect: 3. Professor Bergman.Prerequisites: ELEN E3401 or equivalent.Introduction to optical systems based on physicaldesign and engineering principles. Fundamentalgeometrical and wave optics with specificemphasis on developing analytical and numericaltools used in optical engineering design. Focuson applications that employ optical systems andnetworks, including examples in holographicimaging, tomography, Fourier imaging, confocalmicroscopy, optical signal processing, fiber opticcommunication systems, optical interconnectsand networks.ELEN E4501x Electromagnetic devices andenergy conversion3 pts. Lect: 3. Professor Sen.Prerequisites: ELEN E3401. Linear and nonlinearmagnetic circuits. Electric and magnetic energystorage, loss, and transfer. Circuit behavior ofenergy storage and transfer devices. Field theoryof moving bodies. Dynamical equations of anelectromechanical system. Electromechanicaland thermo-electric sensors and actuators.Rotating electric energy converters.Superconductivity and applications.ELEN E4503x Sensors, actuators andelectromechanical systems3 pts. Lect: 3.Prerequisites: ELEN E3201 and ELEN E3401,or equivalents. Electromagnetic energystorage, loss, and transfer. Dynamics ofelectromechanical systems. Linearization ofnonlinear coupled dynamical equations andequivalent circuits. Electromechanical actuators:acoustic, IC processed micromachines.Electromechanical sensors: acoustic, pressure,and acceleration. Thermal sensors: polysiliconthermopiles and bipolar transistor temperaturesensors. Electro-optic sensors: visible light,infrared, and X-ray.ELEN E4510x or y Solar energy and smartgrid power systems3 pts. Lect: 3. Professors Kymissis and Schwartz.Prerequisites: Background in circuits. Inorganicsolar cell semiconductor physics. Single andtandem junction design. Measures of spectraland energy efficiency. Introduction to organicsolar cells and thin film inorganic cells. Batteriesand other energy storage systems. Introductionto legacy power networks: Single phase equivalentsto three-phase networks. Reactive andreal power. Equivalent circuits of synchronousmachines, transformers, and transmission lines.Smart grid technology: Control and managementof distributed solar energy and other intermittentrenewable power sources connected to legacypower networks. Microgrid concept. “Small world”networks and fault management. Communicationover power lines. Smart metering.EEME E4601y Digital control systems3 pts. Lect: 3. Professor Longman.Prerequisites: ELEN E3801 or EEME E3601, orequivalent. Real-time control using digital computers.Solving scalar and state-space differenceequations. Discrete equivalents of continuoussystems fed by holds. Z-transfer functions.Creating closed-loop difference equation modelsby Z-transform and state variable approaches.The Nyquist frequency and sample rate selection.Classical- and modern-based digital controllaws. Digital system identification.ELEN E4702x or y Digital communications3 pts. Lect: 3. Professor Cvijetic.Prerequisites: ELEN E3701 or equivalent.Digital communications for both point-to-pointand switched applications is further developed.Optimum receiver structures and transmittersignal shaping for both binary and M-ary signaltransmission. An introduction to block codes andconvolutional codes, with application to spacecommunications.ELEN E4703y Wireless communications3 pts. Lect: 3. Professor Diament.Prerequisites: ELEN E3701 or equivalent.Wireless communication systems. System designfundamentals. Trunking theory. Mobile radiopropagation. Reflection of radio waves. Fadingand multipath. Modulation techniques; signalspace; probability of error, spread spectrum.Diversity. Multiple access.ELEN E4810x Digital signal processing3 pts. Lect: 3. Professor Ellis.Prerequisites: ELEN E3801. Digital filtering intime and frequency domain, including propertiesof discrete-time signals and systems, samplingtheory, transform analysis, system structures,IIR and FIR filter design techniques, the DiscreteFourier Transform, Fast Fourier Transforms.ELEN E4815y Random signals and noise3 pts. Lect: 3.Prerequisites: IEOR E3658 or equivalent.Characterization of stochastic processes asmodels of signals and noise; stationarity, ergodicity,correlation functions, and power spectra.Gaussian processes as models of noise in linearand nonlinear systems; linear and nonlineartransformations of random processes; orthogonalseries representations. Applications to circuitsand devices, to communication, control, filtering,and prediction.CSEE W4823x or y Advanced logic design3 pts. Lect: 3. Professor Nowick.Prerequisites: CSEE W3827 or equivalent. Anintroduction to modern digital system design.Advanced topics in digital logic: controller synthesis(Mealy and Moore machines); adders andmultipliers; structured logic blocks (PLDs, PALs,ROMs); iterative circuits. Modern design methodology:register transfer level modeling (RTL);algorithmic state machines (ASMs); introductionto hardware description languages (VHDL orVerilog); system-level modeling and simulation;design examples.CSEE W4824x or y Computer architecture3 pts. Lect: 3. Professor Carloni.Prerequisites: CSEE W3827 or equivalent.Focuses on advanced topics in modern computerarchitecture, illustrated by recent casestudies. Fundamentals of quantitative analysis.Pipelined, out-of-order, and speculative execution.Superscalar, VLIW and vector processors.Embedded processors. Memory hierarchydesign. Multiprocessors and thread-level parallelism.Synchronization and cache coherenceprotocols. Interconnection networks.ELEN E4830y Digital image processing3 pts. Lect: 3.Introduction to the mathematical tools and algorithmicimplementation for representation andprocessing of digital pictures, videos, and visualsensory data. Image representation, filtering,transform, quality enhancement, restoration,feature extraction, object segmentation, motionanalysis, classification, and coding for data compression.A series of programming assignmentsreinforces material from the lectures.CSEE W4840y Embedded systems3 pts. Lect: 3.Prerequisites: CSEE W4823 or equivalent.Embedded system design and implementationcombining hardware and software. I/O, interfacing,and peripherals. Weekly laboratory sessionsand term project on design of a microprocessorbasedembedded system including at least onecustom peripheral. Knowledge of C programmingand digital logic required.ELEN E4896y Music signal processing3 pts. Lect: 3.Prerequisites: A course on discrete-time signalprocessing (at the level of ELEN E3801 or,preferably, E4810). An introductory course onthe applications of signal processing to music,suitable for seniors and first-year graduatestudents in electrical engineering, computer science,or music. Emphasis is placed on the signalprocessing operations in both recording and liveenvironments. Topics covered include audio androom acoustics; microphones and loudspeakers;A/D conversion, dithering, and digital audioformats; analog and digital audio mixers; audioeffects algorithms; sequences, samplers, andSEAS 2010–2011

effects algorithms; sequences, samplers, andDigital Audio Workstations (DAW); mastering forCD and DVD production; and sound synthesisalgorithms. Throughout the course case studiesof real systems will be examined in detail. Thecourse includes a site visit to a state-of-the-artprofessional recording facility.ELEN E4944x or y Principles of devicemicrofabrication3 pts. Lect: 3. Professor Yardley.Science and technology of conventional andadvanced microfabrication techniques for electronics,integrated and discrete components.Topics include diffusion; ion implantation,thin-film growth including oxides and metals,molecular beam and liquid-phase epitaxy; opticaland advanced lithography; and plasma and wetetching.ELEN E4998x or y Intermediate projects inelectrical engineering0 to 3 pts.Prerequisites: Instructor’s permission. May berepeated for credit, but no more than 3 totalpoints may be used for degree credit. Substantialindependent project involving laboratory work,computer programming, analytical investigation,or engineering design.ELEN E6001x-E6002y Advanced projects inelectrical engineering1–4 pts. Members of the faculty.May be repeated for up to 6 points of credit.Graduate-level projects in various areas of electricalengineering and computer science. In consultationwith an instructor, each student designshis or her project depending on the student’sprevious training and experience. Studentsshould consult with a professor in their area fordetailed arrangements no later than the last dayof registration.ELEN E6010y Systems biology: designprinciples for biological circuits4.5 pts. Lect: 3.Prerequisites: ECBM E4060 or instructor’spermission. Beyond bioinformatics, cells assystems. Metabolic networks, transcription regulatorynetworks, signaling networks. Deterministicand stochastic kinetics. Mathematical representationof reconstructed networks. Network motifs.Signal transduction and neuronal networks.Robustness. Bacterial chemotaxis and patterningin fruit fly development. Kinetic proofreading.Optimal gene circuit design. Rules for generegulation. Random networks and multipletime scales. Biological information processing.Numerical and simulation techniques. Majorproject(s) in MATLAB.EEBM E6020y Methods of computationalneuroscience4.5 pts. Lect: 3.Prerequisites: BMEB W4020 or instructor’s permission.Formal methods in computational neuroscienceincluding methods of signal processing,communications theory, information theory,systems and control, system identification andmachine learning. Molecular models of transductionpathways. Robust adaptation and integralfeedback. Stimulus representation and groups.Stochastic and dynamical systems models ofspike generation. Neural diversity and ensembleencoding. Time encoding machines and neuralcodes. Stimulus recovery with time decodingmachines. MIMO models of neural computation.Synaptic plasticity and learning algorithms. Majorproject(s) in MATLAB.BMEE E6030y Neural modeling andneuroengineering3 pts. Lect: 3. Professor Sajda.Prerequisites: APMA E3101, ELEN E3801, andBMEB W4020, or equivalent, or instructor’spermission. Engineering perspective on the studyof multiple levels of brain organization, fromsingle neurons to cortical modules and systems.Mathematical models of spiking neurons, neuraldynamics, neural coding, and biologically-basedcomputational learning. Architectures and learningprinciples underlying both artificial and biologicalneural networks. Computational modelsof cortical processing, with an emphasis on thevisual system. Applications of principles in neuroengineering;neural prostheses, neuromorphicsystems and biomimetics. Course will include acomputer simulation laboratory.ELEN E6080–6089x or y Topics in systemsbiology3 pts. Lect: 2.Prerequisites: Instructor’s permission. Selectedadvanced topics in systems biology. Content variesfrom year to year, and different topics rotatethrough the course numbers 6080 to 6089.EEBM E6090–6099x or y Topics in computationalneuroscience and neuroengineering3 pts. Lect: 2.Prerequisites: Instructor’s permission. Selectedadvanced topics in computational neuroscienceand neuroengineering. Content varies from yearto year, and different topics rotate through thecourse numbers 6090-6099.CSEE E6180x or y Modeling and performanceevaluation3 pts. Lect: 2.Prerequisites: COMS W4118 and SIEO W4150 orpermission of the instructor. Introduction to queuinganalysis and simulation techniques. Evaluationof time-sharing and multiprocessor systems.Topics include priority queuing, buffer storage, anddisk access, interference and bus contention problems,and modeling of program behaviors.ELEN E6201x Linear system theory3 pts. Lect: 3. Professor Fishler.Prerequisites: ELEN E3801 and APMA E3101,or equivalents. Abstract objects, the concepts ofstate. Definition and properties of linear systems.Characterization of linear continuous-time anddiscrete-time, fixed, and time-varying systems.State-space description; fundamental matrix, calculationby computer and matrix methods. Modesin linear systems. Adjoint systems. Controllabilityand observability. Canonical forms and decompositions.State estimators. Lyapunov’s methodand stability.ELEN E6312y Advanced analog integratedcircuits3 pts. Lect: 2.Prerequisites: ELEN E4312. Integrated circuitdevice characteristics and models; temperatureandsupply-independent biasing; IC operationalamplifier analysis and design and their applications;feedback amplifiers, stability and frequencycompensation techniques; noise in circuitsand low-noise design; mismatch in circuits andlow-offset design. Computer-aided analysis techniquesare used in homework or a design project.ELEN E6314x Advanced communicationcircuits3 pts. Lect: 2.Prerequisites: ELEN E4314 and ELEN E6312.Overview of communication systems, modulationand detection schemes. Receiver andtransmitter architectures. Noise, sensitivity,and dynamic range. Nonlinearity and distortion.Low-noise RF amplifiers, mixers, and oscillators.Phase-locked loops and frequency synthesizers.Typical applications discussed include wirelessRF transceivers or data links. Computer-aidedanalysis techniques are used in homework(s) ora design project.ELEN E6316y Analog systems in VLSI3 pts. Lect: 3.Prerequisites: ELEN E4312. Analog-digitalinterfaces in very large scale integrated circuits.Precision sampling; A/D and D/A converter architectures;continuous-time and switched capacitorfilters; system considerations. A design project isan integral part of this course.ELEN E6318x or y Microwave circuit design3 pts. Lect: 3.Prerequisites: ELEN E3331 and E3401, orequivalents. Introduction to microwave engineeringand microwave circuit design. Review oftransmission lines. Smith chart, S-parameters,microwave impedance matching, transformationand power combining networks, active andpassive microwave devices, S-parameter-baseddesign of RF and microwave amplifiers. A microwavecircuit design project (using microwaveCAD) is an integral part of the course.ELEN E6320x or y Millimeter-wave IC design3 pts. Lect: 3. Professor Krishnaswamy.Prerequisites: ELEN E3401 or equivalent, ELENE4314, and ELEN E6312. Principles behindthe implementation of millimeter-wave (30GHz-300GHz) wireless circuits and systems in siliconbasedtechnologies. Silicon-based active and149SEAS 2010–2011

150passive devices for millimeter-wave operation,millimeter-wave low-noise amplifiers, poweramplifiers, oscillators and VCOs, oscillator phasenoise theory, mixers and frequency dividers forPLLs. A design project is an integral part of thecourse.ELEN E6321y Advanced digital electroniccircuits4.5 pts. Lect: 3.Prerequisites: ELEN E4321. Advanced topics inthe design of digital integrated circuits. Clockedand non-clocked combinational logic styles.Timing circuits: latches and flip-flops, phaselockedloops, delay-locked loops. SRAM andDRAM memory circuits. Modeling and analysisof on-chip interconnect. Power distributionand power-supply noise. Clocking, timing, andsynchronization issues. Circuits for chip-to-chipelectrical communication. Advanced technologyissues that affect circuit design. The class mayinclude a team circuit design project.ELEN E6331y Principles of semiconductorphysics, I3 pts. Lect: 2.Prerequisites: ELEN E4301. Designed for studentsinterested in research in semiconductormaterials and devices. Topics include energybands: nearly free electron and tight-bindingapproximations, the k.p. method, quantitative calculationof band structures and their applicationsto quantum structure transistors, photodetectors,and lasers; semiconductor statistics, Boltzmanntransport equation, scattering processes, quantumeffect in transport phenomena, properties ofheterostructures. Quantum mechanical treatmentthroughout.ELEN E6332y Principles of semiconductorphysics, II3 pts. Lect: 2.Prerequisites: ELEN E6331. Optical propertiesincluding absorption and emission of radiation,electron-phonon interactions, radiative andphonon-mediated processes, excitons, plasmons,polaritons, carrier recombination and generation,and related optical devices, tunneling phenomena,superconductivity. Quantum mechanical treatmentthroughout, heavy use of perturbation theory.ELEN E6333y Semiconductor device physics3 pts. Lect: 2.Prerequisites: ELEN E4301 or equivalent.Physics and properties of semiconductors.Transport and recombination of excess carriers.Schottky, P-N, MOS, and heterojunction diodes.Field effect and bipolar junction transistors.Dielectric and optical properties. Optical devicesincluding semiconductor lamps, lasers, anddetectors.ELEN E6412y Lightwave devices3 pts. Lect: 2.Prerequisites: ELEN E4411. Electro-optics:principles; electro-optics of liquid crystals andphoto-refractive materials. Nonlinear optics: second-ordernonlinear optics; third-order nonlinearoptics; pulse propagation and solitons. Acoustooptics:interaction of light and sound; acoustoopticdevices. Photonic switching and computing:photonic switches; all-optical switches; bistableoptical devices. Introduction to fiber-optic communications:components of the fiber-optic link;modulation, multiplexing and coupling; systemperformance; receiver sensitivity; coherent opticalcommunications.ELEN E6413y Lightwave systems3 pts. Lect: 2.Prerequisites: ELEN E4411. Recommendedpreparation: ELEN E6412. Fiber optics. Guiding,dispersion, attenuation, and nonlinear propertiesof fibers. Optical modulation schemes. Photoniccomponents, optical amplifiers. Semiconductorlaser transmitters. Receiver design. Fiber optictelecommunication links. Nonregenerativetransmission using erbium-doped fiber amplifierchains. Coherent detection. Local area networks.Advanced topics in light wave networks.ELEN E6430x or y Applied quantum optics3 pts. Lect: 2.Prerequisites: Background in electromagnetism(ELEN E3401, ELEN E4401, ELEN E4411, orPhysics G6092) and quantum mechanics (APPHE3100, E4100, or Physics G402x). An introductionto fundamental concepts of quantum opticsand quantum electrodynamics with an emphasison applications in nanophotonic devices. Thequantization of the electromagnetic field; coherentand squeezed states of light; interactionbetween light and electrons in the language ofquantum electrodynamics (QED); optical resonatorsand cavity QED; low-threshold lasers; andentangled states of light.ELEN E6488y Optical interconnects andinterconnection networks3 pts. Lect: 2. Professor Bergman.Prerequisites: ELEN E4411 or ELEN E4488 oran equivalent photonics course. Introduction tooptical interconnects and interconnection networksfor digital systems. Fundamental opticalinterconnects technologies, optical interconnectionnetwork design, characterization, andperformance evaluation. Enabling photonictechnologies including free-space structures,hybrid and monolithic integration platforms forphotonic on-chip, chip-to-chip, backplane, andnode-to-node interconnects, as well as photonicnetworks on-chip.EEME E6601x Introduction to control theory3 pts. Lect: 3. Professor Longman.Prerequisites: MATH E1210. A graduate-levelintroduction to classical and modern feedbackcontrol that does not presume an undergraduatebackground in control. Scalar and matrix differentialequation models, and solutions in terms ofstate transition matrices. Transfer functions andtransfer function matrices, block diagram manipulations,closed-loop response. Proportional,rate, and integral controllers, and compensators.Design by root locus and frequency response.Controllability, observability. Luenberger observers,pole placement, and linear-quadratic costcontrollers.EEME E6602y Modern control theory3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: EEME E6601 or EEME E4601 orELEN E6201, or instructor’s permission. Singularvalue decomposition. ARX model and statespacemodel system identification. Recursiveleast squares filters and Kalman filters. LQR, H,linear robust control, predictive control. Learningcontrol, repetitive control, adaptive control.Liapunov and Popov stability. Nonlinear adaptivecontrol, nonlinear robust control, sliding modecontrol.ELEN E6711x Stochastic models ininformation systems4.5 pts. Lect: 3. Professor Baryshnikov.Prerequisites: IEOR E3658. Foundations: probabilityreview, Poisson processes, discrete-timeMarkov models, continuous-time Markov models,stationarity, and ergodicity. The course presentsa sample-path (time domain) treatment of stochasticmodels arising in information systems,including at least one of the following areas:communications networks (queueing systems),biological networks (hidden Markov models),Bayesian restoration of images (Gibbs fields),and electric networks (random walks).ELEN E6712x Communication theory3 pts. Lect: 3.Prerequisites: ELEN E4815, or equivalent, orinstructor’s permission. Representation of bandlimitedsignals and systems. Coherent and incoherentcommunications over Gaussian channels.Basic digital modulation schemes. Intersymbolinference channels. Fading multipath channels.Carrier and clock synchronization.ELEN E6717x Information theory3 pts. Lect: 2.Prerequisites: IEOR E3658 or a course in stochasticprocesses. Corequisites: ELEN E4815. Mutualinformation and entropy. The source codingtheorem. The capacity of discrete memorylesschannels and the noisy channel coding theorem.The rate distortion function. Discrete memorylesssources and single-letter distortion measures.Bhattacharya bounds, convolutional codes, andthe Viterbi algorithm.ELEN E6718y Algebraic coding theory3 pts. Lect: 2.Prerequisites: IEOR E3658. Elementary conceptsof error control codes. Linear blockcodes. Elements of algebra: Galois fields.Cyclic codes: BCH, Reed Solomon, Goppacodes. Coder, decoder implementation.SEAS 2010–2011

Decoding algorithms based on spectral techniques.Convolutional codes.ELEN E6761x Computer communicationnetworks I3 pts. Lect: 3. Professor Maxemchuk.Prerequisites: IEOR E3658 and CSEE W4119or equivalent, or instructor’s permission. Focuson architecture protocols and performanceevaluation of geographically distributed andlocal area data networks. Emphasis on layeredprotocols. Data link layer. Network layer: flowand congestion control routing. Transport layer.Typical Local and Metropolitan Area Networkstandards: Ethernet, DQDB, FDDI. Introductionto Internetting. Review of relevant aspects ofqueueing theory to provide the necessary analyticalbackground.ELEN E6770–6779x or y Topics intelecommunication networks3 pts. Lect: 2. Professors Sabnani, Walid, and Woo.Further study of areas such as communicationprotocols and architectures, flow and congestioncontrol in data networks, performance evaluationin integrated networks. Content varies from yearto year, and different topics rotate through thecourse numbers 6770 to 6779.ELEN E6820y Speech and audio processingand recognition4.5 pts. Lect: 3.Prerequisites: ELEN E4810 or instructor’spermission. Fundamentals of digital speech processingand audio signals. Acoustic and perceptualbasics of audio. Short-time Fourier analysis.Analysis and filterbank models. Speech andaudio coding, compression, and reconstruction.Acoustic feature extraction and classification.Recognition techniques for speech and othersounds, including hidden Markov models.CSEE E6824y Parallel computer architecture3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: CSEE W4824. Parallel computerprinciples, machine organization and design ofparallel systems including parallelism detectionmethods, synchronization, data coherence andinterconnection networks. Performance analysisand special purpose parallel machines.CSEE E6847y Distributed embedded systems3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: Any course numbered in theCOMS4110s, CSEE4800s, or ELEN4300s, orinstructor’s permission. An inter-disciplinarygraduate-level seminar on the design of distributedembedded systems. System robustness inthe presence of highly variable communicationdelays and heterogeneous component behaviors.The study of the enabling technologies (VLSIcircuits, communication protocols, embeddedprocessors, RTOSs), models of computation,and design methods. The analysis of moderndomain-specific applications including on-chipmicro-networks, multiprocessor systems, faulttolerantarchitectures, and robust deploymentof embedded software. Research challengessuch as design complexity, reliability, scalability,safety, and security. The course requiressubstantial reading, class participation and aresearch project.ELEN E6850x Visual information systems3 pts. Lect: 2.Prerequisites: ELEN E4830 or instructor’s permission.Introduction to critical image technologiesin advanced visual information systems,such as content-based image databases, videoservers, and desktop video editors. Intended forgraduate students. Topics include visual datarepresentation and compression, content-basedvisual indexing and retrieval, storage systemdesign (data placement, scheduling, and admissioncontrol), compressed video editing, and synchronizationissues of stored video/audio signals.Programming projects and final presentationsare required.ELEN E6860y Advanced digital signalprocessing3 pts. Lect: 2. Professor Nguyen.Prerequisites: ELEN E4810. This course isdesigned as an extension to ELEN E4810, withemphasis on emerging techniques in the areaof digital signal processing. Topics include multiratesignal processing, multidimensional signalprocessing, short-time Fourier transform, signalexpansion in discrete and continuous time, filterbanks, multiresolution analysis, wavelets, andtheir applications to image compression andunderstanding. Other topics may be included toreflect developments in the field.CSEE E6861y Computer-aided design ofdigital systems3 pts. Lect: 2.Prerequisites: (i) one semester of advanced digitallogic (CSEE W4823 or equivalent, or instructor’spermission); and (ii) a basic course in datastructures and algorithms (COMS W3133, 3134,3137, 3139 or 3157, or equivalent, and familiaritywith programming. Introduction to moderndigital CAD synthesis and optimization techniques.Topics include: modern digital systemdesign (high-level synthesis, register-transferlevel modeling, algorithmic state machines, optimalscheduling algorithms, resource allocationand binding, retiming), controller synthesis andoptimization, exact and heuristic two-level logicminimization, advanced multi-level logic optimization,optimal technology mapping to librarycells (for delay, power and area minimization),advanced data structures (binary decisiondiagrams), SAT solvers and their applications,static timing analysis, and introduction to testability.Includes hands-on small design projectsusing and creating CAD tools.EECS E6870x or y Speech recognition3 pts. Lect: 2.Prerequisites: Basic probability and statistics.Theory and practice of contemporary automaticspeech recognition. Gaussian mixture distributions,hidden Markov models, pronunciationmodeling, decision trees, finite-state transducers,and language modeling. Selected advanced topicswill be covered in more depth.ELEN E6880–6889x or y Topics in signalprocessing3 pts. Lect: 2. Professor Li.Prerequisites: ELEN E4810. Advanced topics insignal processing, such as multidimensional signalprocessing, image feature extraction, image/video editing and indexing, advanced digital filterdesign, multirate signal processing, adaptive signalprocessing, and wave-form coding of signals.Content varies from year to year, and differenttopics rotate through the course numbers 6880to 6889.ELEN E6900–6909x or y Topics in electricaland computer engineering3 pts. Lect: 2. Instructor to be announced.Prerequisites: Instructor’s permission. Selectedtopics in electrical and computer engineering.Content varies from year to year, and differenttopics rotate through the course numbers 6900to 6909.ELEN E6945x or y Device nanofabrication3 pts. Lect: 3.Prerequisites: ELEN E3106 and E3401, orequivalents. Recommended: ELEN E4944. Thiscourse provides an understanding of the methodsused for structuring matter on the nanometerlength: thin-film technology; lithographic patterningand technologies including photon, electron,ion and atom, scanning probe, soft lithography,and nanoimprinting; pattern transfer; self-assembly;process integration; and applications.ELEN E6950x Wireless and mobile networking, I4.5 pts. Lect: 2. Lab: 1. Professor Jelenkovic.Corequisites: ELEN E6761 or instructor’spermission. Overview of mobile and wirelessnetworking. Fundamental concepts in mobilewireless systems: propagation and fading, cellularsystems, channel assignment, power control,handoff. Examples of second-generation circuitsswitchedsystems and standards. Quantitativehomework assignments may require use of amathematical software package.ELEN E6951y Wireless and mobile networking, II3 pts. Lect: 2. Lab: 1. Professor Zussman.Prerequisites: CSEE W4119, ELEN E6761 orinstructor’s permission. Third-generation packetswitched systems, wireless LANs, mobilecomputing and communications. Study of somecurrent research topics. Quantitative homeworkassignments may require use of a mathematicalsoftware package. A project based on readingsfrom the literature will be required.151SEAS 2010–2011

152ELEN E6999 Curricular practical training1–3 pts.Prerequisites: Obtained internship and approvalfrom a faculty adviser. Only for ElectricalEngineering and Computer Engineering graduatestudents who include relevant off-campus workexperience as part of their approved program ofstudy. Final report required. May not be taken forpass/fail credit or audited.EEME E8601y Advanced topics in controltheory3 pts. Lect: 3. Not offered in 2010–2011.See entry under “Courses in MechanicalEngineering” for description.ELEN E9001x and y–E9002 Research0–6 pts. Points of credit to be approved by thedepartment.Prerequisites: submission of an outline of theproposed research for approval by the facultymember who is to supervise the work of thestudent. The research facilities of the departmentare available to qualified students interested inadvanced study.ELEN E9011x and y–E9012 Doctoral research0–6 pts.Points of credit to be approved by the department.Open only to doctoral students who havepassed the qualifying examinations. Submissionof an outline of the proposed research for theapproval of the faculty member who is to supervisethe work of the student.ELEN E9800x and y Doctoral researchinstruction3, 6, 9 or 12 pts.A candidate for the Eng.Sc.D. degree in electricalengineering must register for 12 points ofdoctoral research instruction. Registration inELEN E9800 may not be used to satisfy theminimum residence requirement for the degree.ELEN E9900x and y–9900 Doctoral dissertation0 pts.A candidate for the doctorate may be requiredto register for this course every term after thestudent’s course work has been completed, anduntil the dissertation has been accepted.COURSES IN ELECTRICALENGINEERING OFFEREDOCCASIONALLYEEHS E3900y History of telecommunications:from the telegraph to the Internet3 pts. Lect: 3.Historical development of telecommunicationsfrom the telegraphy of the mid-1800s to theInternet at present. Included are the technologiesof telephony, radio, and computer communications.The coverage includes both thetechnologies themselves and the historicalevents that shaped, and in turn were shapedby, the technologies. The historical development,both the general context and the particularevents concerning communications, is presentedchronologically. The social needs that elicitednew technologies and the consequences of theiradoption are examined. Throughout the course,relevant scientific and engineering principles areexplained as needed. These include, among others,the concept and effective use of spectrum,multiplexing to improve capacity, digital coding,and networking principles. There are no prerequisites,and no prior scientific or engineeringknowledge is required. SEAS students may notcount this course as a technical elective. Thecourse shares lectures with EEHS E4900, butthe work requirements differ somewhat.ELEN E4215y Analog filter synthesis anddesign3 pts. Lect: 3.Prerequisites: ELEN E3201 and ELEN E3801, orequivalent. Approximation techniques for magnitude,phase, and delay specifications , transferfunction realization sensitivity, passive LC filters,active RC filters, MOSFET-C filters, Gm-C filters,switched-capacitor filters, automatic tuning techniquesfor integrated filters. Filter noise. A designproject is an integral part of the course.ELEN E4302x or y Magnetic sensors andinstruments for medical imaging3 pts. Lect: 2.5, Lab: 0.5. Not offered in2010–2011.Prerequisites: ELEN E3106, ELEN E3401 orinstructor’s permission. Physics of nuclear magneticresonance (NMR) and superconductingquantum interference device (SQUID). Designand operation of superconducting DC magnet,RF receiver, Josephson junction, and integratedSQUID. Principles of biomedical sensoringsystems including Magnetic Resonance Imaging(MRI), SQUID magnetometer, and NMR spectroscopy.Medical image formation and processing.ELEN E4332y VLSI design laboratory3 pts. Lab: 3.Prerequisites: ELEN E4321 or E6316 or EECSE4340. Design of a large-scale deep submicronCMOS integrated circuit. The class may divideup into teams to work on different aspects of asingle mixed-signal circuit. The chip(s) is fabricatedfor testing the following term. Lecturescover use of computer-aided design tools, designissues specific to the project(s), and chip integrationissues.ELEN E4405x Classical nonlinear optics3 pts. Lect: 3.Prerequisites: ELEN E4401. Waves in anisotropicmedia. Maxwell’s equations and constitutiverelations. Fresnel equations. Optical waves inanisotropic crystals. Birefringence. Waves innonlinear media. Plasma model. Electro-optic,Pockels, and Kerr effects. Second harmonic generationand phase matching. Parametric amplification.Backward-wave oscillator. Acousto-opticbeam deflection and light modulation.ELEN E4420x Topics in electromagnetics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Undergraduate electromagnetictheory. Selected topics in the theory and practiceof electromagnetics, varying from year to year.Topic for current term will be available in thedepartment office one month before registration.This course may be taken more than once whentopics are different. Possible topics: microwavetheory and design (generalized waveguides,excitation and coupling of waveguides, junctions,microwave networks, periodic structures, opticalfibers); antennas (filamentary antennas, arrays,aperture radiation, system properties, patternsynthesis); electrodynamics (special relativity,radiation by charged particles, relativistic beams,free electron lasers).ELEN E4741x Introduction to biologicalsensory systems3 pts. Lect: 3. Not offered in 2010–2011.Corequisites: IEOR E3658. Introduction to visionand hearing using engineering principles. Natureof sound and light; minimum detectable energyfor human observers; excitation of the visualand hearing systems; rods, cones, and hair-cellreceptors; the experiment of Hecht, Shlaer, andPirenne; Poisson counting statistics; stimulusbasedmodeling; detection and false-alarm probabilities;de Vries-Rose square-root law; Weber’slaw; relation of sensory and communicationsystems.CSEE W4825y Digital systems design3 pts. Lect: 3.Prerequisites: CSEE W3827. Dynamic logic,field programmable gate arrays, logic designlanguages, multipliers. Special techniques formultilevel NAND and NOR gate circuits. Clockingschemes for one- and two-phase systems. Faultchecking: scan method, built-in-test. Survey oflogic simulation methods. Other topics to beadded as appropriate.ELEN E6140x Gallium arsenide materialsprocessing3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ELEN E4301 or instructor’s permission.Materials and device aspects of GaAsand compound technologies, electronic propertiesof GaAs, growth techniques (bulk and epitaxial),surface and etching properties, implantation,MESFETS, transferred electron devices, Impattdiodes, HEMTS, HBTs.ELEN E6151y Surface physics and analysis ofelectronic materials3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: Instructor’s permission. Basicphysical principles of methods of surface analysis,surfaces of electronic materials includingstructure and optical properties (auger electronspectroscopy, x-ray photoemission, ultravioletSEAS 2010–2011

photoelectron spectroscopy, electron energyloss spectroscopy, inverse photoemission, photostimulated desorption, and low energy electrondiffraction), physical principles of each approach.ELEN E6211x or y Circuit theory3 pts. Lect: 3.Prerequisites: ELEN E3331 and ELEN E3801.An axiomatic development of circuit theory.Circuit theorems, circuit topology, general methodsof circuit analysis. Normal form characterizations.Scattering characterization and sensitivityfunction. Basic network synthesis methods:immittance and transfer function realization, multiportrealization, approximation techniques.ELEN E6261y Computational methods ofcircuit analysis3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ELEN E3331 and APMA E3101.Computational algorithms for DC, transient,and frequency analysis of linear and nonlinearcircuits. Formulation of equations: state equations,hybrid equations, sparse tableaux. Solutiontechniques: iterative methods to solve nonlinearalgebraic equations; piecewise linear methods;sparse matrix techniques; numerical integrationof stiff, nonlinear differential equations, companionnetwork models; waveform relaxation.ELEN E6302x or y MOS transistors3 pts. Lect: 2.Prerequisites: ELEN E3106 or equivalent.Operation and modelling of MOS transistors.MOS two- and three-terminal structures. TheMOS transistor as a four-terminal device; generalcharge-sheet modelling; strong, moderate,and weak inversion models; short-and-narrowchanneleffects; ion-implanted devices; scalingconsiderations in VLSI; charge modelling; largesignaltransient and small-signal modelling forquasistatic and nonquasistatic operation.ELEN E6304x or y Topics in electroniccircuits3 pts. Lect: 3.Prerequisites: Instructor’s permission. State-ofthe-arttechniques in integrated circuits. Topicsmay change from year to year.ELEN E6403y Classical electromagnetic theory4.5 pts. Lect: 3.Prerequisites: One term of undergraduateelectromagnetic theory. A mathematical physicsapproach to electromagnetic phenomena.Poisson, Laplace equations; Green’s functions.Theorems of electrostatics. Multipole expansions.Energy relations and stress tensor. Maxwell’sequations in stationary and moving media. Thewave equation, energy and momentum theorems,potentials, choice of gauge.ELEN E6414y Photonic integrated circuits3 pts. Lect: 3.Photonic integrated circuits are important subsystemcomponents for telecommunications,optically controlled radar, optical signal processing,and photonic local area networks. Thiscourse will introduce the student to the devicesand the design of these circuits. Principle andmodelling of dielectic waveguides (includingsilica on silicon and InP based materials),waveguide devices (simple and star couplers),and surface diffractive elements. Numerical techniquesfor modelling circuits will be discussed,including beam propagation and finite differencecodes. Design of other devices will be discussed:optical isolators, demultiplexers.EEME E6610x Optimal control theory3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ELEN E6201 or EEME E6601.Objectives of optimal control. Continuous anddiscrete control problems. Calculus of variations:Mayer and Bolza; Pontryagin’s maximum principle.Bang-bang and singular controls. Existence of optimalcontrol. Hamilton-Jacobi theory and dynamicprogramming. Numerical methods. Optimal feedbackcontrol regulatory problems. Linear-quadratic-Gaussian estimation. Applications.EEME E6612x or y Control of nonlineardynamic systems3 pts. Lect: 3.Prerequisites: EEME E6601 or ELEN E6201 andan undergraduate controls course. Fundamentalproperties of nonlinear systems; qualitativeanalysis of nonlinear systems; nonlinear controllabilityand observability; nonlinear stability; zerodynamics and inverse systems; feedback stabilizationand linearization; sliding control theory;nonlinear observers; describing functions.ELEN E6713y Topics in communications3 pts. Lect: 3. Professor Sharony.Prerequisites: ELEN E6712 or ELEN E4702or ELEN E4703 or equivalent, or instructor’spermission. Advanced topics in communications,such as turbo codes, LDPC codes, multiusercommunications, network coding, cross-layeroptimization, cognitive radio. Content may varyfrom year to year to reflect the latest developmentin the field.ELEN E6731y Satellite communicationsystems3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: ELEN E4702. Introduction tosatellite communication, with emphasis oncharacterization and systems engineering of thetransmission channel. Power budgets, antennas,transponders, multiple access, and frequencyre-use techniques. Noise, intermodulation,interference, and propagation effects. Modulationmethods, earth terminals, and standards. Digitaltransmission and advanced systems.ELEN E6762y Computer communicationnetworks, II3 pts. Lect: 2.Prerequisites: ELEN E6761. Broadband ISDN,services and protocols; ATM. Traffic characterizationand modeling: Markov-modulated Poissonand Fluid Flow processes; application to voice,video, and images. Traffic Management in ATMnetworks: admission and access control, flowcontrol. ATM switch architectures; input/outputqueueing. Quality of service (QoS) concepts.ELEN E6763y Digital circuit switched networks3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: ELEN E6761 or instructor’s permission.Current topics in digital circuit switching:introduction to circuit switching, comparison withpacket switching, elements of telephone trafficengineering, space and time switching, callprocessing in digital circuit-switched systems,overload control mechanisms, nonhierarchicalrouting, common channel signaling, introductionto integrated services digital networks. Examplesof current systems are introduced throughout.Emphasis on modeling and quantitative performanceanalysis. Queueing models introducedwhere possible.ELEN E6781y Topics in modeling andanalysis of random phenomena3 pts. Lect: 3.Prerequisites: ELEN E6711. Recommendedpreparation: a course on real analysis andadvanced probability theory. Current methodologyin research in stochastic processes appliedto communication, control, and signal processing.Topics vary from year to year to reflectstudent interest and current developments inthe field.CSEE E6831y Sequential logic circuits3 pts. Lect: 3.Prerequisites: CSEE W3827 or any introductionto logic circuits. Generation and manipulation offlow table descriptions to asynchronous sequentialfunctions. Coding of flow tables to satisfy variousdesign criteria. Delays, races, hazards, metastability.Analysis of latches to determine key parameters.Bounds of input rates. Clocking schemesfor synchronous systems. Synthesis of self-timedsystems using 4-phase or 2-phase handshakes.CSEE E6832x or y Topics in logic designtheory3 pts. Lect: 3.Prerequisites: CSEE W3827 or any introductionto logic circuits. A list of topics for each offeringof the course is available in the department officeone month before registration. May be takenmore than once if topics are different. Iterativelogic circuits applied to pattern recognition. Finitestate machines; alternative representations,information loss, linear circuits, structure theory.Reliability and testability of digital systems.ELEN E6920x or y Topics in VLSI systemsdesign3 pts. Lect: 2. Professor Abramovici.Prerequisites: ELEN E4321. Design automation:layout, placement, and routing. Circuit simulationalgorithms and optimization of performance153SEAS 2010–2011

154and area. Multiprocessor computing systems.Verification of testing. Topics may change fromyear to year.ELEN E8701y Point processes in informationand dynamical systems3 pts. Lect: 3.Prerequisites: ELEN E6711 or equivalent.Recommended preparation: Course in measuretheory or advanced probability theory. Probabilityand point processes. Random intensity rate, martingales,and the integral representation of pointprocess martingales. Recursive estimation, thetheory of innovations, state estimate for queues.Markovian queueing networks. Hypothesistesting, the separation between filtering anddetection. Mutual information and capacity forthe Poisson-type channel. Stochastic control,dynamic programming for intensity control.ELEN E9060x or y Seminar in systemsbiology3 pts. Lect: 2.Open to doctoral candidates, and to qualifiedM.S. candidates with instructor’s permission.Study of recent developments in the field ofsystems biology.EEBM E9070x or y Seminar in computationalneuroscience and neuroengineering3 pts. Lect: 2.Prerequisites: Open to doctoral candidates andqualified M.S. candidates with instructor’s permission.Study of recent developments in computationalneuroscience and neuroengineering.ELEN E9101x or y Seminar in physicalelectronics3 pts. Lect: 2.Prerequisites: Quantum electronics and ELENE4944, or instructor’s permission. Advancedtopics in classical and quantum phenomenathat are based on ion and electron beams, gasdischarges, and related excitation sources.Application to new laser sources and microelectronicfabrication.ELEN E9201x or y Seminar in circuit theory3 pts. Lect: 2.Open to doctoral candidates, and to qualifiedM.S. candidates with instructor’s permission.Study of recent developments in linear, nonlinear,and distributed circuit theory and analysistechniques important to the design of very largescale integrated circuits.ELEN E9301x or y Seminar in electronicdevices3 pts. Lect: 2.Open to doctoral candidates, and to qualifiedM.S. candidates with instructor’s permission.Theoretical and experimental studies of semiconductorphysics, devices, and technology.ELEN E9303x or y Seminar in electroniccircuits3 pts. Lect: 2.Open to doctoral candidates, and to qualifiedM.S. candidates with instructor’s permission.Study of recent developments in electroniccircuits.ELEN E9402x or y Seminar in quantumelectronics3 pts. Lect: 2.Open to doctoral candidates, and to qualifiedM.S. candidates with instructor’s permission.Recent experimental and theoretical developmentsin various areas of quantum electronicsresearch. Examples of topics that may be treatedinclude novel nonlinear optics, lasers, transientphenomena, and detectors.ELEN E9403x or y Seminar in photonics3 pts. Lect: 2.Prerequisites: ELEN E4411. Open to doctoralcandidates, and to qualified M.S. candidateswith instructor’s permission. Recent experimentaland theoretical developments in various areas ofphotonics research. Examples of topics that maybe treated include squeezed-light generation,quantum optics, photon detection, nonlinear opticaleffects, and ultrafast optics.ELEN E9404x or y Seminar in lightwavecommunications3 pts. Lect: 2.Open to doctoral candidates, and to qualifiedM.S. candidates with instructor’s approval.Recent theoretical and experimental developmentsin light wave communications research.Examples of topics that may be treated includeinformation capacity of light wave channels,photonic switching, novel light wave networkarchitectures, and optical neural networks.ELEN E9701x or y Seminar in information andcommunication theories3 pts. Lect: 2.Open to doctoral candidates, and to qualifiedM.S. candidates with instructor’s permission.Recent developments in telecommunication networks,information and communication theories,and related topics.ELEN E9801x or y Seminar in signalprocessing3 pts. Lect: 2.Open to doctoral candidates, and to qualifiesM.S. candidates with instructor’s approval.Recent developments in theory and applicationsof signal processing, machine learning, contentanalysis, and related topics.SEAS 2010–2011

INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH313 S. W. Mudd, MC 4704, 212-854-2941www.ieor.columbia.edu155CHAIRClifford Stein326 S. W. MuddDIRECTOR: ADMINISTRATION,ACADEMIC ANDPROFESSIONALDEVELOPMENTJenny S. Mak324 S. W. MuddSTUDENT AFFAIRS MANAGERAdina Berrios BrooksDIRECTOR: UNDERGRADUATEPROGRAMSGarud IyengarDIRECTOR: MASTER OFSCIENCE PROGRAMSSoulaymane KachaniDIRECTOR: FINANCIALENGINEERING PROGRAMEmanuel DermanDIRECTOR: DOCTORALPROGRAMSDaniel BienstockDIRECTOR: EXECUTIVEEDUCATIONSoulaymane KachaniPROFESSORSDaniel BienstockMark BroadieBusiness SchoolEdward M. Coffman Jr.Electrical EngineeringEmanuel DermanAwi FedergruenBusiness SchoolGuillermo GallegoPaul GlassermanBusiness SchoolDonald GoldfarbGarud IyengarIannis KaratzasMathematicsPeter J. KolesarBusiness SchoolS. G. Steven KouKarl SigmanClifford SteinM. Suresh SundaresanBusiness SchoolGarrett van RyzinBusiness SchoolWard WhittVlihalis YannakakisComputer ScienceDavid D. YaoASSOCIATE PROFESSORSMaria ChudnovskyRama ContSoulaymane KachaniJay SethuramanASSISTANT PROFESSORSJose BlanchetVineet GoyalXuedong HeMariana Olvera-CraviotoVan Anh TruongLECTURERS IN DISCIPLINEMartin HaughAnthony WebsterADJUNCT FACULTYDavid DeRosaLeon S. GoldDavid GulleyMark HigginsAli HirsaIraj KaniAlexander KuznetsovWilliam J. LatzkoMichael D. LipkinHanan LussAllan MalzLeon M. MetzgerPeter V. NordenLucius J. RiccioMoshe RosenweinAlexander StantonLeon TatevossianLeo TilmanSheldon WeinigLarry WrightIndustrial engineering is the branchof the engineering profession that isconcerned with the design, analysis,and control of production and servicesystems. Originally, an industrial engineerworked in a manufacturing plantand was involved only with the operatingefficiency of workers and machines.Today, industrial engineers are morebroadly concerned with productivity andall of the technical problems of productionmanagement and control. They maybe found in every kind of organization:manufacturing, distribution, transportation,mercantile, and service. Theirresponsibilities range from the designof unit operations to that of controllingcomplete production and service systems.Their jobs involve the integrationof the physical, financial, economic,computer, and human componentsof such systems to attain specifiedgoals. Industrial engineering includesactivities such as production planningand control; quality control; inventory,equipment, warehouse, and materialsmanagement; plant layout; and workstationdesign.Operations research is concernedwith quantitative decision problems,generally involving the allocation andcontrol of limited resources. Such problemsarise, for example, in the operationsof industrial firms, financial institutions,health care organizations, transportationsystems, and government. Theoperations research analyst developsand uses mathematical and statisticalmodels to help solve these decisionproblems. Like engineers, they are problemformulators and solvers. Their workrequires the formation of a mathematicalmodel of a system and the analysis andprediction of the consequences of alternatemodes of operating the system.The analysis may involve mathematicaloptimization techniques, probabilisticand statistical methods, experiments,and computer simulations.Engineering management systemsis a multidisciplinary field in industrialengineering, operations research, contemporarytechnology, business, economics,and management. It providesa foundation for decision making andmanaging risks in complex systems.Financial engineering is a multidisciplinaryfield integrating financial theorywith economics, methods of engineering,tools of mathematics, and practiceof programming. The field providestraining in the application of engineeringmethodologies and quantitative methodsto finance.SEAS 2010–2011

156Current Research ActivitiesIn industrial engineering, research is conductedin the area of logistics, routing,scheduling, production and supply chainmanagement, inventory control, revenuemanagement, and quality control.In operations research, new developmentsare being explored in mathematicalprogramming, combinatorialoptimization, stochastic modeling, computationaland mathematical finance,queueing theory, reliability, simulation,and both deterministic and stochasticnetwork flows.In engineering and managementsystems, research is conducted in theareas of logistics, supply chain optimization,and revenue and risk management.In financial engineering, research isbeing carried out in portfolio management;option pricing, including exoticand real options; computational finance,such as Monte Carlo simulation andnumerical methods; as well as data miningand risk management.Projects are sponsored and supportedby leading private firms and governmentagencies. In addition, our studentsand faculty are involved in the work oftwo research and educational centers:the Center for Applied Probability (CAP),the Center for Financial Engineering(CFE), and the Computational andOptimization Research Center (CORC).These centers are supported principallyby grants from the National ScienceFoundation.The Center for Applied Probability(CAP) is a cooperative center involvingthe School of Engineering and AppliedScience, several departments in theGraduate School of Arts and Sciences,and the Graduate School of Business.Its interests are in four applied areas:mathematical and computational finance,stochastic networks, logistics and distribution,and population dynamics.The Center for Financial Engineering(CFE) at Columbia University encouragesinterdisciplinary research on financialengineering and mathematical modelingin finance and promoting collaborationbetween Columbia faculty and financialinstitutions, through the organizationof research seminars, workshops, andthe dissemination of research done bymembers of the Center.The Computational OptimizationResearch Center (CORC) at ColumbiaUniversity is an interdisciplinary groupof researchers from a variety of departmentson the Columbia campus. Itspermanent members are ProfessorsDaniel Bienstock, Don Goldfarb, GarudIyengar, Jay Sethuraman, and CliffStein, from the Industrial Engineeringand Operations Research Department,and Professor David Bayer, from theDepartment of Mathematics at BarnardCollege. Researchers at CORC specializein the design and implementation ofstate-of-the-art algorithms for the solutionof large-scale optimization problemsarising from a wide variety of industrialand commercial applications.UNDERGRADUATE PROGRAMSB.S. in Industrial EngineeringThe undergraduate program is designedto develop the technical skills and intellectualdiscipline needed by our graduatesto become leaders in industrialengineering and related professions.The program is distinctive in its emphasison quantitative, economic, computer-aidedapproaches to productionand service management problems. Itis focused on providing an experimentaland mathematical problem-formulatingand problem-solving framework forindustrial engineering work. The curriculumprovides a broad foundation inthe current ideas, models, and methodsof industrial engineering. It also includesa substantial component in the humanitiesand social sciences to help studentsunderstand the societal implications oftheir work.The industrial engineering programobjectives are:1. To provide students with the requisiteanalytical and computational skills toassess practical situations and academicproblems, formulate models ofthe problems represented or embeddedtherein, design potential solutions,and evaluate their impact;2. To prepare students for the workplaceby fostering their ability toparticipate in teams, understand andpractice interpersonal and organizationalbehaviors, and communicatetheir solutions and recommendationseffectively through written, oral, andelectronic presentations;3. To familiarize students with thehistorical development of industrialengineering tools and techniques andwith the contemporary state of theart, and to instill the need for lifelonglearning within their profession; and4. To instill in our students an understandingof ethical issues and professionaland managerial responsibilities.B.S. in Operations ResearchThe operations research program is oneof several applied science programsoffered at the School. At the undergraduatelevel, it offers basic courses inprobability, statistics, applied mathematics,simulation, and optimization as wellas more professionally oriented operationsresearch courses. The curriculumis well suited for students with an aptitudefor mathematics applications.It prepares graduates for professionalemployment as operations researchanalysts, e.g., with management consultantand financial service organizations,as well as for graduate studies in operationsresearch or business. It is flexibleenough to be adapted to the needs offuture medical and law students.B.S. in Operations Research:Engineering Management SystemsThis operations research option isdesigned to provide students withan understanding of contemporarytechnology and management. It isfor students who are interested in atechnical-management backgroundrather than one in a traditional engineeringfield. It consists of required coursesin industrial engineering and operationsresearch, economics, business, andcomputer science, intended to providea foundation for dealing with engineeringand management systems problems.Elective courses are generally intendedto provide a substantive core in at leastone technology area and at least onemanagement area.Due to the flexibility of this option, itcan incorporate the varied educationalneeds of preprofessional students interestedin law, medicine, business, andfinance. In addition, most students areencouraged to add a minor in economicsor computer science to their standardcourse schedules.SEAS 2010–2011

157B.S. in Operations Research:Financial EngineeringThe operations research concentrationin financial engineering is designed toprovide students with an understandingof the application of engineering methodologiesand quantitative methodsto finance. Financial engineering is amultidisciplinary field integrating financialtheory with economics, methodsof engineering, tools of mathematics,and practice of programming. Studentsgraduating with this concentration areprepared to enter careers in securities,banking, financial management, andconsulting industries, and fill quantitativeroles in corporate treasury and financedepartments of general manufacturingand service firms.Students who are interested inpursuing the rigorous concentration infinancial engineering must demonstrateproficiency in calculus, computer programming,linear algebra, ordinary differentialequations, probability, and statistics.Applications to the concentrationwill be accepted during the fall semesterof the sophomore year, and studentswill be notified of the departmental decisionby the end of that spring semester.The department is seeking studentswho demonstrate strength and consistencyin all the above-mentionedareas. Application to this concentrationis available online: www.ieor.columbia.edu/pages/undergraduate/financial_eng/bsfe_app.html.Undergraduate Advanced TrackThe undergraduate advanced track isdesigned for advanced undergraduatestudents with the desire to pursue furtherhigher education after graduation.Students with a minimum cumulativeGPA of 3.4 and faculty approval havethe opportunity to participate. Studentsare invited to apply to the track uponthe completion of their sophomore year.Advanced track students are required totake higher-level IEOR courses, includingthe following:IEOR E4004 instead of IEOR E3608IEOR E4106 instead of IEOR E3106IEOR E4403 instead of IEOR E4003and MATH V2500Students successfully completingthe requirements of the undergraduateadvanced track will receive recognitionon their academic record.MinorsA number of minors are available forstudents wishing to add them to theirprograms. These minors are describedstarting on page 194 of this bulletin.IEOR program students may wantto consider minors in economics orcomputer science. In addition, operationsresearch and engineering andmanagement systems majors may electto minor in industrial engineering, andindustrial engineering majors may electto minor in operations research.The department does not offer aminor in engineering management systemsor financial engineering.GRADUATE PROGRAMSThe Department of IndustrialEngineering and Operations Researchoffers courses and M.S. programs in (1)engineering management systems, (2)financial engineering, (3) industrial engineering,and (4) operations research oneither a full- or part-time basis. Graduateprograms leading to a Ph.D. or Eng.Sc.D. in industrial engineering or operationsresearch, as well as one leadingto the professional degree of IndustrialEngineer, are also available. In addition,the department and the GraduateSchool of Business offer combinedM.S./M.B.A. degree programs in industrialengineering, in financial engineering,and in operations research.All degree program applicants arerequired to take the Aptitude Tests ofSEAS 2010–2011

158the Graduate Record Examination. M.S./M.B.A. candidates are also requiredto take the Graduate ManagementAdmissions Test.A minimum grade point average of3.0 (B) in an undergraduate engineeringprogram is required for admission to theM.S. and professional degree programs.Students are expected, on entry, tohave completed courses in ordinary differentialequations, in linear algebra, andin a programming language such as Cor Java.M.S. in Engineering ManagementSystemsThe full-time M.S. in EngineeringManagement Systems (EMS) providesstudents with a curriculum that emphasizesboth technology and managementperspectives in solving problems, makingdecisions, and managing risks incomplex systems. Students pursuingthis degree program are provided witha rigorous exposure to deterministicoptimization and stochastic modeling,a basic coverage of applications in theareas of operations engineering andmanagement, and an in-depth coverageof applications in the areas of the selectedconcentration. Graduates from theprogram are expected to assume positionsas business analysts in logistics,supply chain, revenue management, andconsulting firms, and as financial analystsin risk management departmentsof investment banks, hedge funds, andcredit card and insurance firms.The requirement for the M.S. in engineeringmanagement systems degree isten 3-credit courses (two semesters offull-time study).The department requires that studentsin the program achieve grades ofB– or higher in each of the fundamentalcore courses (IEOR E4004 and IEORE4106). Poor performance in thesecourses is indicative of inadequatepreparation and is very likely to leadto serious problems in completing theprogram. In addition, students mustmaintain a cumulative GPA equivalent toa B– during every term enrolled. A studentfailing to meet these criteria may beasked to withdraw from his/her program.Required Core Courses(9 points)The department recommendsthat students complete thesecore courses during their firstterm of study:IEOR E4004 Intro to operationsresearch: deterministic modelsIEOR E4106 Introduction tooperations research: stochasticmodelsIEOR E4111 Operationsconsulting(SIEO W4150 Intro to probabilityand statistics must be taken ifstudents have not taken equivalentpreviously)M.S. in Engineering Management Systems (30 points) 1M.S. in Financial EngineeringManagement Electives(minimum 6 points) 2Choose from:The department offers a full-time M.S.in Financial Engineering. This program isintended to provide a unique technicalbackground for students interested inpursuing career opportunities in financialanalysis and risk management.In addition to the basic requirementsfor graduate study, students areexpected, on entry, to have attained ahigh level of mathematical and computerprogramming skills, particularly in probability,statistics, linear algebra, and theuse of a programming language such asC or JAVA. Work experience is desirablebut not required.The program consists of 36 points(12 courses), which can be taken over atwelve-month period of full-time studies,ECIE W4280 Corporate financeFINC B6302 Capital marketsand investmentsFINC B8301 Advanced corporatefinanceIEME E4310 The manufacturingenterpriseIEOR E4505 Operationsresearch in public policyIEOR E4510 Project managementIEOR E4550 Entrepreneurialbusiness creation for engineersIEOR E4705 Studies in operationsresearchIEOR E4721 Global CapitalMarketsIEOR E4724 Hedge FundsIEOR E4998 Managing technologicalinnovation and entrepreneurshipEngineering/Technical Electives(minimum 6 points) 2Choose from:IEOR E4000 Production managementIEOR E4210 Supply chainmanagementIEOR E4220 Demand andsupply analyticsIEOR E4403 Advanced engineeringand corporate economicsIEOR E4404 SimulationIEOR E4405 Production schedulingIEOR E4407 Game theoreticmodels of operationsIEOR E4418 Logistics and transportationmanagementIEOR E4601 Dynamic pricingand revenue optimizationIEOR E4611 Decisions modelsand applications1 All courses listed are 3 points each unless otherwise specified.2 The remaining electives can be selected from IEOR, the School of International and Public Affairs, theBusiness School, and the Departments of Economics, Mathematics, and Statistics. At least 18 points out of30 (or 33, if taking SIEO W4150) must be taken in IEOR.starting with a Part II six-week summersession (July 6–August 27, 2010).Students may elect to complete theprogram in May, August, or Decemberof the following year. The requirementsinclude eight required core courses andadditional elective courses chosen froma variety of departments or schoolsat Columbia including the GraduateSchool of Business, International Affairs,Computer Science, Statistics, andEconomics. A sample schedule is availablein the department office and on theIEOR Web site: www.ieor.columbia.edu.The eight required core courses forthe financial engineering program areIEOR E4007, IEOR E4701, IEOR E4702,IEOR E4703, IEOR E4706, IEOR E4707,IEOR E4709, and IEOR E4729.In addition, students select twoSEAS 2010–2011

semicore courses from a group ofspecialized offerings in the spring term.Electives are chosen with the approvalof an adviser.The department requires that studentsachieve grades of B– or higherin each of the four fundamental corecourses offered in the first summer.Poor performance in these courses isindicative of inadequate preparation andis very likely to lead to serious problemsin completing the program. As a result,students failing to meet this criterion willbe asked to withdraw from the program.M.S. in Industrial EngineeringThe department’s graduate programsin industrial engineering are generallyintended to enable students with industrialengineering bachelor’s degrees toenhance their undergraduate training withstudies in special fields such as productionplanning, inventory control, scheduling,and industrial economics. However,the department also offers broader master’sand professional degree programsfor engineers whose undergraduate trainingis not in industrial engineering.M.S. degree candidates are requiredto satisfy a core program of graduatecourses in production management,probability theory, statistics, simulation,and operations research. Students withB.S. degrees in industrial engineering willusually have satisfied this core in theirundergraduate programs. All studentsmust take at least 18 points of graduatework in industrial engineering and atleast 30 points of graduate studies atColumbia. Master’s degree programsmay include concentrations in:engineering and management systemsproduction and operations managementmanufacturingindustrial regulation studiesAdditional details regarding theseconcentrations are available in thedepartment office. A thesis is notrequired. Students who plan post–master’s degree studies should give dueconsideration to the course, examination,and admission requirements ofthese programs.M.S. degree programs can be takenon a part-time basis or completed inone year of full-time study.The department requires that studentsin the program achieve grades ofB– or higher in each of the fundamentalM.S. in Financial Engineering—May 2011 Completion (36 points) 1Summer SemesterFall SemesterSpring Semester(9 points) 2 (15 points) 2 (12 points) 2Required core courses:IEOR E4701 Stochastic modelsfor financial engineeringIEOR E4702 Statistical inferencefor financial engineering (1.5)IEOR E4706 Foundations offinancial engineeringIEOR E4729 Financial markets,institutions, and risk (1.5)Required core courses:IEOR E4007 Optimization forfinancial engineeringIEOR E4703 Monte CarlosimulationIEOR E4707 Continuous timefinancecore courses (IEOR E4004 and IEORE4106). Poor performance in thesecourses is indicative of inadequatepreparation and is very likely to leadto serious problems in completing theprogram. In addition, students mustmaintain a cumulative GPA equivalentto a B– during every term enrolled. Astudent failing to meet these criteriamay be asked to withdraw from his/herprogram.The professional degree of IndustrialEngineer requires a minimum of 60points of graduate credit with at least30 points beyond the M.S. degree inindustrial engineering. The complete60-point program includes (a) 30 pointscompleted in ten core courses, (b) aconcentration of at least four courses,(c) other electives and (possibly) deficiencies.A minimum of twelve courses,providing 36 points of credit, must beindustrial engineering courses takenfrom departmental course offerings or atIEOR E4709 Data analysis forfinancial engineeringElectiveChoose four from the coursesbelow, plus one other course inconsultation with faculty adviser 3 :IEOR E4500 Applications programmingfor financial engineeringIEOR E4602 Quantitative riskmanagementIEOR E4630 Asset allocationIEOR E4708 Seminar onimportant papers in financialengineeringIEOR E4710 Term structuremodelingIEOR E4718 Intro to impliedvolatility smileIEOR E4731 Credit risk andcredit derivativesDRAN B8835 Security pricingmodels1 Students may conclude the program in May, August, or December 2010. Please visit the departmentalWeb site (www.ieor.columbia.edu/pages/graduate/ms_financial_eng/index.html) for more information.2 All courses listed are for 3 credits, unless stated otherwise.3 Other courses include experimental finance, foreign exchange and related derivative instruments, hedgefund management, structured products, etc. Specific offerings may vary each term.other institutions where advanced standingis given. A thesis is not required.M.S. in Operations ResearchThe graduate program in this area isdesigned to enable students to concentratetheir studies in methodological areassuch as mathematical programming, stochasticmodels, and simulation. However,the department also has a broadly basedmaster’s degree program that enablesstudents with engineering or otherundergraduate majors that include strongmathematics preparation to completework in two terms of full-time study.M.S. degree candidates are requiredto satisfy a core set of graduate coursesin probability, statistics, linear programming,and simulation. All students mustcomplete at least 18 points of operationsresearch courses and at least 30points of graduate work at Columbia.The department considers it desirablethat students construct balanced159SEAS 2010–2011

160programs involving deterministic andstochastic models, as well as substantiveareas for application.The M.S. degree program may beconstructed to include the followingareas of focus:optimizationapplied probabilityfinancial and managerial application ofoperations researchAdditional details regarding theseconcentrations are available in thedepartment office. A thesis is notrequired. Students who plan to continuetheir studies beyond the master’s degreelevel should give due consideration tothe course, examination, and grade-pointrequirements of doctoral programs. TheM.S. degree program can be taken on apart-time basis or completed in one yearof full-time study. Students planning tocomplete this program in one year areexpected, on entry, to have completedcourses in ordinary differential equations,in linear algebra, and in a programminglanguage such as C or Java.The department requires that studentsin the program achieve grades ofB– or higher in each of the fundamentalcore courses (IEOR E4004 and IEORE4106). Poor performance in thesecourses is indicative of inadequatepreparation and is very likely to leadto serious problems in completing theprogram. In addition, students mustmaintain a cumulative GPA equivalent toa B– during every term enrolled. A studentfailing to meet these criteria may beasked to withdraw from his/her program.Joint M.S. and M.B.A.The department and the GraduateSchool of Business offer joint master’sprograms in financial engineering,industrial engineering, and operationsresearch. Prospective students forthese special programs must submitseparate applications to the School ofEngineering and Applied Science andthe Graduate School of Business and beadmitted to both schools for entranceinto the joint program.Admissions requirements are thesame as those for the regular M.S. programsand for the M.B.A. These jointprograms are coordinated so that bothdegrees can be obtained after five termsof full-time study (30 points in two termsRequired CoreCourses(12 points)Electives(18 points)OptimizationThe department recommendstaking at leastthree of the followingelective courses:Applied ProbabilityThe department recommendstaking at leastthree of the followingelective courses:Students interested infinancial and managerialapplications of operationsresearch shouldconsider taking:while registered in SEAS and 45 pointsin three terms while registered in theGraduate School of Business).Students in joint programs mustcomplete certain courses by the endof their first year of study. Students inthe IE or OR joint program should takeIEOR E4000, IEOR E4004, and SIEOW4150. If a substantial equivalent hasbeen completed during undergraduateM.S. in Operations Research (30 points)SIEO W4150 Intro to Probability and Statistics (3)IEOR E4004 Intro to OR: Deterministic Models (3)IEOR E4106 Intro to OR: Stochastic Models (3)IEOR E4004 Simulation (3)The department suggests a number of elective courses depending on areas offocus. The areas of focus include optimization, applied probability, and financial andmanagerial applications of operations research.IEOR E4000 Production and operations managementIEOR E4210 Supply chain managementIEOR E4405 Production schedulingIEOR E4418 Logistics and transportation managementIEOR E4600 Applied integer programmingIEOR E4630 Asset allocationIEOR E4000 Production and operations managementIEOR E4210 Supply chain managementIEOR E4220 Demand and supply analyticsIEOR E4407 Game theoretic models of operationIEOR E4601 Dynamic pricing and revenue managementIEOR E4602 Quantitative risk managementIEOR E4700 Intro to financial engineeringCorporate FinanceCoursesIEOR E4403 Advancedengineering & corporateeconomicsAnd at least one of:FINC B6302 Capital marketsand investmentsFINC B8301 Advancedcorporate financeECIE W4280 CorporatefinanceIEOR E4721 Globalcapital marketsDerivatives PricingCoursesIEOR E4700 Intro tofinancial engineeringAnd at least one of:IEOR E4602Quantitative riskmanagementIEOR E4630Asset allocationIEOR E4620Pricing modelsstudies, students should consult with afaculty adviser in order to obtain exemptionfrom a required course.Doctoral StudiesManagementCoursesAt least one of:IEOR E4505OR in public policyIEOR E4510Project managementIEOR E4550Entrepreneurialbusiness creation forengineersIEOR E4705Studies in ORIEOR E4998 Managingtechnological innovationThe requirements for the Ph.D. in industrialengineering and operations researchare identical. Both require the studentto pass two qualifying examinations—respectively covering stochastic andSEAS 2010–2011

deterministic models—as well as submitand defend a dissertation based onthe candidate’s original research, conductedunder the supervision of a facultymember. The dissertation work may betheoretical or computational or both.Doctoral students are also required toselect a concentration for their studiesand complete a certain amount ofcourse work in one of the followingfields: applied probability, mathematicalprogramming, financial engineering, orsupply chain management and logistics.Doctoral candidates must obtain aminimum of 60 points of formal coursecredit beyond the bachelor’s degree.A master’s degree from an accreditedinstitution may be accepted asequivalent to 30 points. A minimum of30 points beyond the master’s degreemust be earned while in residence inthe doctoral program. Detailed informationregarding the requirements for thedoctoral degree may be obtained in thedepartment office or online at www.ieor.columbia.edu/phd_ieor.html.COURSES IN INDUSTRIALENGINEERING ANDOPERATIONS RESEARCHFor up-to-date course offerings, pleasevisit www.ieor.columbia.edu.IEOR E2261x and y Introduction to accountingand finance3 pts. Lect: 3. Professor Webster.Prerequisites: ECON W1105 Principles ofEconomics. For undergraduates only. This courseis required for all undergraduate students majoringin IE, OR:EMS, OR:FE and OR. This courseexamines the fundamental concepts of financialaccounting and finance, from the perspective ofboth managers and investors. Key topics coveredinclude:principles of accrual accounting; recognizing andrecording accounting transactions; preparation andanalysis of financial statements; ratio analysis; proformaprojections; time value of money (presentvalues, future values and interest/discount rates);inflation; discounted-cash-flow (DCF) projectevaluation methods; deterministic and probabilisticmeasures of risk; capital budgeting.IEOR E3106x Introduction to operationsresearch: stochastic models3 pts. Lect: 3. Professor Whitt.Prerequisites: SIEO W3600. For undergraduatesonly. This course is required for all undergraduatestudents majoring in IE, OR:EMS, OR:FE and OR.This class must be taken during (or before) thefifth semester. Some of the main stochastic modelsused in engineering and operations research applications:discrete-time Markov chains, Poisson processes,birth and death processes and other continuousMarkov chains, renewal reward processes.Applications: queueing, reliability, inventory, andfinance. IEOR E3106 must be completed by thefifth term. Only students with special academic circumstancesmay be allowed to take these coursesin alternative semesters with the consultation ofCSA and Departmental advisers.IEOR E3402y Production inventory planningand control4 pts. Lect: 3. Recit: 1. Instructor to be announced.Prerequisites: SIEO W3600 (Probability andstatistics) and IEOR E3608 Introduction to OR:Mathematical programming. For undergraduatesonly. This course is required for all undergraduatestudents majoring in IE, OR:EMS, OR:FE and OR.This class must be taken during (or before) thesixth semester.Inventory management and productionplanning. Continuous and periodic reviewmodels: optimal policies and heuristic solutions,deterministic and probabilistic demands. Materialrequirements planning. Aggregate planning ofproduction, inventory, and work force. Multiechelonintegrated production-inventory systems.Production scheduling. Term project. Recitationsection required.SIEO W3600y Introduction to probabilityand statistics4 pts. Lect: 3. Recit: 1. Instructor to be announced.Prerequisites: Calculus. For undergraduates only.This course is required for undergraduate studentsmajoring in IE, OR:EMS, and OR. This class mustbe taken during the fourth semester. Fundamentalsof probability and statistics used in engineeringand applied science. Probability: random variables,useful distributions, expectations, law of largenumbers, central limit theorem. Statistics: point andconfidence interval estimation, hypothesis tests,linear regression. SIEO W3600 must be completedby the fourth term. Only students with special academiccircumstances may be allowed to take thesecourses in alternative semesters with the consultationof CSA and Departmental advisers. Recitationsection required.IEOR E3608x Introduction to mathematicalprogramming4 pts. Lect: 3. Recit: 1. Professor Chudnovsky.Prerequisites: MATH V2010 Linear algebra.Corequisites: COMS W3134 (or COMS W3137Data structures). For undergraduates only. Thiscourse is required for all undergraduate studentsmajoring in IE, OR:EMS, OR:FE and OR. Thisclass must be taken during (or before) the fifthsemester. Introduction to mathematical programmingmodels and computational techniques.Linear programming and the simplex method,dynamic programming, implicit enumeration forinteger programs; production planning applications.IEOR E3608 must be completed by thefifth term. Only students with special academiccircumstances may be allowed to take thesecourses in alternative semesters with the consultationof CSA and Departmental advisers.Recitation section required.IEOR E3658x Probability3 pts. Lect: 3. Professor Olvera-Cravioto.Prerequisites: Calculus. For undergraduates only.This course is required for the OR:FE concentration.This class must be taken during (or before)the third semester. Fundamentals of probabilitytheory. Distributions of one or more random variables.Moments, generating functions, law of largenumbers and central limit theorem.IEOR E3900x and y Undergraduate researchor project1–3 pts. Members of the faculty.Prerequisites: approval by a faculty memberwho agrees to supervise the work. Independentwork involving experiments, computer programming,analytical investigation, or engineeringdesign.IEOR E4000x Production and operationsmanagement3 pts. Lect: 3. Professor Gallego.Prerequisites or Corequisite: Probability theory andlinear programming. Required course for MSIE.An introduction to production management forstudents not having an industrial engineering bachelor’sdegree. Topics include deterministic inventorymodels, aggregate production planning, materialrequirements planning, forecasting, stochasticinventory models and supply chain management.Emphasis is on modeling and its implications formanagerial decisions.IEOR E4001y Design and management ofproduction and service systems3 pts. Lect: 3. Instructor to be announced.Prerequisites: IEOR E4000 or IEOR E3402. Thiscourse is required for undergraduate studentsmajoring in OR:EMS. Design and managementproblems in production and service systems:process design and capacity management, inventorysystem design and management, aggregateplanning, staff scheduling, and quality controlsystem design.IEOR E4003x Industrial economics3 pts. Lect: 3. Professor Kachani.Prerequisites: or Corequisites: probability theoryand linear programming. This course is required forall undergraduate students majoring in IE, OR:EMS,OR:FE and OR. Introduction to the economic evaluationof industrial projects. Economic equivalenceand criteria. Deterministic approaches to economicanalysis. Multiple projects and constraints. Analysisand choice under risk and uncertainty.IEOR E4004x and y–E4004 Introduction tooperations research: deterministic models3 pts. Lect: 3. Professor Sethuraman.This is a required course for MSEMS, MSIE, andMSOR students. This is also required for studentsin the Undergraduate Advanced Track. For studentswho have not studied linear programming.Some of the main methods used in IEOR applica-161SEAS 2010–2011

162INDUSTRIAL ENGINEERING: FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Linear algebra (3) 1PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)Chemistry or physics lab:PHYS C1493 (3) orPHYS W3081 (2) orCHEM C1500 (3) orCHEM C2507 (3) orCHEM C3085 (4) orCHEMISTRY(choose one course)C1403 (3) or C1404 (3) orC1604 (3.5) or C3045 (3.5)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESECON W1105 (4) and W1155 recitation (0)either semesterHUMA C1001,COCI C1101,or Global core (3–4)HUMA C1002,COCI C1102,or Global core (3–4)HUMA W1121 or W1123 (3)either semesterFIRST- ANDSECOND-YEARDEPT.REQUIREMENTSProfessional-level course (3) (see pages 12–13) IEOR E2261 (3) SIEO W3600 (4) 2COMPUTERSCIENCECOMS W1004 (Java) (3) orCOMS W1007 (Java) (3) 2andCOMS W3134 (3) orCOMS W3137 (4) 2PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.2If taking IEOR E3658, students must take STAT W3107 or W4107 to complete the SIEO W3600 requirement.tions involving deterministic models: linear programming,the simplex method, nonlinear, integerand dynamic programming.IEOR E4007x Optimization models andmethods for financial engineering3 pts. Lect: 3. Professor Iyengar.Prerequisites: Linear algebra. This course is forMSFE students only. Linear, quadratic, nonlinear,dynamic, and stochastic programming. Somediscrete optimization techniques will also beintroduced. The theory underlying the various optimizationmethods is covered. The emphasis is onmodeling and the choice of appropriate optimizationmethods. Applications from financial engineeringare discussed.CSOR E4010y Graph theory: a combinatorial view3 pts. Lect: 3.Prerequisites: Linear algebra, or instructor’s permission.An introductory course in graph theorywith emphasis on its combinatorial aspects. Basicdefinitions, and some fundamental topics in graphtheory and its applications. Topics include treesand forests graph coloring, connectivity, matchingtheory and others.IEOR E4106y Introduction to operationsresearch: stochastic models3 pts. Lect: 3. Professor Sigman.Prerequisites: SIEO W4150 or probability theory.This is a required course for MSEMS, MSIE, andMSOR students. This is also required for studentsin the Undergraduate Advanced Track. Some ofthe main stochastic models used in engineeringand operations research applications: discrete-timeMarkov chains, Poisson processes, birth and deathprocesses and other continuous Markov chains,renewal reward processes. Applications: queueing,reliability, inventory, and finance.SIEO W4150x and y–S4150 Introduction toprobability and statistics3 pts. Lect: 3. Professor Gallego.Prerequisites: Calculus. Fundamentals of probabilitytheory and statistical inference used inengineering and applied science. Probabilisticmodels, random variables, useful distributions,expectations, law of large numbers, central limitSEAS 2010–2011

INDUSTRIAL ENGINEERING: THIRD AND FOURTH YEARS163SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIMATH E1210 (3)Ordinary diff. equationsIEOR E3106 (3)Stochastic modelsREQUIREDCOURSES 1 IEOR E3608 (4)Mathematical prog.COMS W4111 (3)Database systemsIEOR E3402 (4)Production planningIEOR E4404 (4)SimulationIEOR E4003 (3)Industrial econ.IEOR E4207 (3)Human factorsIEOR E4705 (3)Studies in operationsresearchIEOR E4405 (3)Prod. schedulingIEOR E4412 (3)Quality control andmanagementIEOR E4510 (3)Project managementTECHNICALELECTIVESNONTECHELECTIVESINDUSTRIALENGINEERINGELECTIVESChoose one (3 pts.): Please consult the list on the departmental Web site: www.ieor.columbia.eduComplete 27-point requirement. See page 10 or www.engineering.columbia.edu for details.Choose two (6 pts.): IEOR E4210, IEOR E4418, or IEME E43101 Taking required courses later than the prescribed semester is not permitted.theorem. Statistical inference: point and confidenceinterval estimation, hypothesis tests, linearregression.IEOR E4207x Human factors: performance3 pts. Lect: 3. Professor Gold.This course is required for undergraduate studentsmajoring in IE. Sensory and cognitive (brain) processingconsiderations in the design, development,and operations of systems, products, and tools.User or operator limits and potential in sensing,perceiving decision making, movement coordination,memory, and motivation.IEOR E4208y Seminar in human factors design3 pts. Lect: 3. Professor Gold.Prerequisites: IEOR E4207 or instructor’s permission.This course is an elective undergraduatestudents majoring in IE. An in-depth explorationof the application potential of human factor principlesfor the design of products and processes.Applications to industrial products, tools, layouts,workplaces, and computer displays. Considerationto environmental factors, training and documentation.Term project.IEOR E4210y Supply chain management3 pts. Lect: 3. Instructor to be announced.Prerequisites: IEOR 3402, IEOR 4000 or permissionof instructor. This is a IE elective forundergraduate students majoring in IE. Majorissues in supply chain management, including,definition of a supply chain; role of inventory;supply contracts; bullwhip effect and informationsharing; vendor-managed inventories andother distribution strategies; third-party logisticsproviders; managing product variety; informationtechnology and supply chain management; internationalissues. Emphasis on quantitative modelsand analysis.IEOR E4220y Demand and supply analytics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: IEOR E4004 (or IEOR E3608), IEORE4106 (or IEOR E3608). Tools to efficiently managesupply and demand networks. Topics includeservice and inventory trade-offs, stock allocation,pricing, markdown management and contracts,timely product distribution to market while avoidingexcess inventory, allocating adequate resources tothe most profitable products and selling the rightproduct to the right customer at the right price andat the right time.IEOR E4307x Industrial forecasting3 pts. Lect: 3. Professor Wright.Prerequisites: SIEO W3600This course is required for undergraduate studentsmajoring in OR:FE and OR. Analytical techniquesand forecasting methodologies with application toindustrial problems. Evaluation and comparisonof techniques as they pertain to industrial applications.Term project.IEOR E4308x Industrial budgeting andfinancial control3 pts. Lect: 3. Instructor to be announced.Prerequisites: ENGI W2261 or accounting andfinance. Management control via the budgetingand financial processes. Topics include the preparation,evaluation, and implementation of operatingand capital budgets and review of their performance.Examples from contemporary practice.IEME E4310x The manufacturing enterprise3 pts. Lect: 3. Professor Weinig.The strategies and technologies of global manufacturingand service enterprises. Connectionsbetween the needs of a global enterprise, the technologyand methodology needed for manufacturingand product development, and strategic planningas currently practiced in industry.IEOR E4403x Advanced engineering andcorporate economics3 pts. Lect: 3. Professor Kachani.Prerequisites: probability theory and linear programmingThis course is required for students inthe Undergraduate Advanced Track. Key measuresand analytical tools to assess the financialperformance of a firm and perform the economicevaluation of industrial projects. Deterministicmathematical programming models for capital budgeting.Concepts in utility theory, game theory andreal options analysis.IEOR E4404x and y Simulation4 pts. Lect: 3. Recit: 1. Professor Olvera-Cravioto.Prerequisites: SIEO W3600 or SIEO W4150,computer programming Corequisites: IEORE3106 or IEOR E4106 This course is requiredfor all undergraduate students majoring in IE,OR:EMS, OR:FE and OR. This course is alsorequired for MSIE and MSOR. Generation of randomnumbers from given distributions; variancereduction; statistical output analysis; introductionto simulation languages; application to financial,telecommunications, computer, and productionsystems. Graduate students must register for 3points. Undergraduate students must register for4 points. NOTE: Students who have taken IEORE4703 Monte Carlo simulation may not registerfor this course for credit. Recitation sectionrequired.SEAS 2010–2011

164OPERATIONS RESEARCH: FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Linear algebra (3) 1PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)Chemistry or physics lab:PHYS C1493 (3) orPHYS W3081 (2) orCHEM C1500 (3) orCHEM C2507 (3) orCHEM C3085 (4) orCHEMISTRY(choose one course)C1403 (3) or C1404 (3) orC1604 (3.5) or C3045 (3.5)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESECON W1105 (4) and W1155 recitation (0)either semesterHUMA C1001,COCI C1101,or Global Core (3–4)HUMA C1002,COCI C1102,or Global Core (3–4)HUMA W1121 or W1123 (3)either semesterFIRST- AND SECOND-YEAR DEPT.REQUIREMENTSProfessional-level course (3) (see pages 12–13) IEOR E2261 (3) SIEO W3600 (4)COMPUTERSCIENCECOMS W1004 (Java) (3) orCOMS W1007 (Java) (3) 2andCOMS W3134 (3) orCOMS W3137 (4) 2PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.2If taking IEOR E3658, students must take STAT W3107 or W4107 to complete the SIEO W3600 requirement.IEOR E4405y Production scheduling3 pts. Lect: 3. Instructor to be announced.Prerequisites: SIEO W3600, IEOR E3608, computerprogramming. This course is required forundergraduate students majoring in IE and OR.Job shop scheduling: parallel machines, machinesin series; arbitrary job shops. Algorithms, complexity,and worst-case analysis. Effects of randomness:machine breakdowns, random processingtime. Term project.IEOR E4407x Game theoretic models ofoperations3 pts. Lect: 3. Professor Sethuraman.Prerequisites: IEOR E4004 (or IEOR E3608),IEOR E4106 (or IEOR E3106), familiarity withdifferential equations and computer programming;or instructor’s permission. This course is requiredfor undergraduate students majoring in OR:FEand OR. A mathematically rigorous study of gametheory and auctions, and their application tooperations management. Topics include introductorygame theory, private value auction, revenueequivalence, mechanism design, optimal auction,multiple-unit auctions, combinatorial auctions,incentives, and supply chain coordination withcontracts. No previous knowledge of game theoryis required.IEOR E4412y Quality control and management3 pts. Lect: 3. Professor Latzko.Prerequisites: SIEO W3600 or SIEO W4150 Thiscourse is required for undergraduate studentsmajoring in IE. Statistical methods for qualitycontrol and improvement: graphical methods,introduction to experimental design and reliabilityengineering and the relationships between qualityand productivity. Contemporary methods used bymanufacturing and service organizations in productand process design, production and delivery ofproducts and services.IEOR E4418y Logistics and transportationmanagement3 pts. Lect: 3.Prerequisites: IEOR 3608 or IEOR 4404 orpermission of instructor. Introduces quantitativetechniques and state-of-the-art practice of operationsresearch relevant to the design and both thetactical and strategic management of logistical andtransportation systems. Discusses a wide variety ofSEAS 2010–2011

OPERATIONS RESEARCH: THIRD AND FOURTH YEARS165SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIMATH E1210 (3)Ordinary diff. equationsIEOR E3106 (3)Stochastic modelsREQUIREDCOURSES 1 IEOR E3608 (4)Mathematical prog.COMS W4111 (3)Database systemsIEOR E3402 (4)Production planningIEOR E4404 (4)SimulationIEOR E4600 (3)Applied integer prog.IEOR E4003 (3)Industrial econ.IEOR E4307 (3)ForecastingIEOR E4407 (3)Game theoretic models ofoperationsIEOR E4405 (3)Prod. schedulingOPERATIONSRESEARCHELECTIVESNONTECHELECTIVESChoose four OR electives (12 pts. total):Please consult the list on the departmental Web site: www.ieor.columbia.eduComplete 27-point requirement. See page 10 or www.engineering.columbia.edu for details.1 Taking required courses later than the prescribed semester is not permitted.passenger and freight systems, including air, urbanand highway traffic, rail, and maritime systems.Explores the practice of revenue management anddynamic pricing. Through case studies, analyzessuccesses and failures in third-party logistics,postal, truck and rail pickup and delivery systems.Investigates large-scale integrated logistics andtransportation systems and studies the underlyingprinciples governing transportation planning,investment and operations.IEOR E4500y Applications programming forfinancial engineering3 pts. Lect: 3. Professor Bienstock.Prerequisites: Computer programming orinstructor’s approval This course is required forundergraduate students majoring in OR:FE. Inthis course we will take a hands-on approach todeveloping computer applications for FinancialEngineering. Special focus will be placed onhigh-performance numerical applications thatinteract with a graphical interface. In the courseof developing such applications we will learnhow to create DLLs, how to integrate VBA withC/C++ programs, and how to write multithreadedprograms. Examples of problems settings thatwe consider include simulation of stock priceevolution, tracking, evaluation and optimizationof a stock portfolio; optimal trade execution. Inthe course of developing these applications, wereview topics of interest to OR/FE in a holisticfashion.IEOR E4510y Project management3 pts. Lect: 3.Prerequisites: IEOR E4004 (or IEOR E3608).Management of complex projects and the toolsthat are available to assist managers with suchprojects. Topics include: project selection,project teams and organizational issues, projectmonitoring and control, project risk management,project resource management, and managingmultiple projects.IEOR E4550y Entrepreneurial businesscreation for engineers3 pts. Lect: 3. Instructor to be announced.Prerequisites: ENGI W2261. This course is requiredfor undergraduate students majoring in OR:EMS.Introduces the basic concepts and methodologiesthat are used by the non-engineering part of theworld in creating, funding, investing in, relating to,and operating entrepreneurial ventures. The first halfof the course focuses on the underpinning principlesand skills required in recognizing, analyzing, evaluating,and nurturing a business idea. The secondhalf focuses on basic legal knowledge necessary increating a business entity, defending your businessassets, and in promoting effective interaction withother individuals and organizations.IEOR E4600y Applied integer programming3 pts. Lect: 3. Instructor to be announced.Prerequisites: Linear programming, linear algebra,and computer programming. This course isrequired for undergraduate students majoring inOR. Applications of mathematical programmingtechniques, especially integer programming, withemphasis on software implementation. Typicalapplications: capacity expansion, network design,and scheduling.IEOR E4601y Dynamic pricing and revenuemanagement3 pts. Lect: 3. Professor Gallego.Prerequisites: SIEO W4150 and IEOR E4004.Focus on capacity allocation, dynamic pricing andrevenue management. Perishable and/or limitedproduct and pricing implications. Applications tovarious industries including service, airlines, hotel,resource rentals, etc.IEOR E4602y Quantitative risk management3 pts. Lect: 3. Instructor to be announced.Prerequisites: SIEO W4150 and IEOR E4106.Risk management models and tools; measure riskusing statistical and stochastic methods, hedgingand diversification. Examples include insurancerisk, financial risk, and operational risk. Topics coveredinclude VaR, estimating rare events, extremevalue analysis, time series estimation of extremalevents; axioms of risk measures, hedging usingfinancial options, credit risk modeling, and variousinsurance risk models.IEOR E4611y Decision models andapplications3 pts. Lect: 3.Prerequisites: For undergraduates: SIEO W3600/SIEO W4150 or equivalent and IEOR E3608/IEOR E4004 or equivalent. For graduate students:Instructor’s permission required. Corequisites:IEOR E4404 or equivalent. Introduction to deterministicand stochastic decision tools used byleading corporations and applied researchers.Real-world problems in engineering and financeare discussed.IEOR E4620x Pricing models for financialengineering3 pts. Lect: 3. Professor DeRosa.Prerequisites: IEOR E4700This course is required for undergraduate studentsmajoring in OR:FE. Characteristics of commoditiesor credit derivatives. Case study and pricing ofstructures and products. Topics covered includeswaps, credit derivatives, single tranche CDO,hedging, convertible arbitrage, FX, leverageleases, debt markets, and commodities.IEOR E4630y Asset allocation3 pts. Lect: 3. Professor Iyengar.Prerequisites: IEOR E4700. Models for pric-SEAS 2010–2011

166OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS:FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Linear algebra (3) 1PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)Chemistry or physics lab:PHYS C1493 (3) orPHYS W3081 (2) orCHEM C1500 (3) orCHEM C2507 (3) orCHEM C3085 (4) orCHEMISTRY(choose one course)C1403 (3) or C1404 (3) orC1604 (3.5) or C3045 (3.5)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESECON W1105 (4) and W1155 recitation (0)either semesterHUMA C1001,COCI C1101,or Global Core (3–4)HUMA C1002,COCI C1102,or Global Core (3–4)HUMA W1121 or W1123 (3)either semesterFIRST- ANDSECOND-YEAR DEPT.REQUIREMENTSProfessional-level course (3) (see pages 12–13) IEOR E2261 (3) SIEO W3600 (4)COMPUTERSCIENCECOMS W1004 (Java) (3) orCOMS W1007 (Java) (3) 2andCOMS W3134 (3) orCOMS W3137 (4) 2PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.2If taking IEOR E3658, students must take STAT W3107 or W4107 to complete the SIEO W3600 requirement.ing and hedging equity, fixed-income, creditderivativesecurities, standard tools for hedgingand risk management, models and theoreticalfoundations for pricing equity options (standardEuropean, American equity options, Asianoptions), standard Black-Scholes model (withmultiasset extension), asset allocation, portfoliooptimization, investments over longtime horizons,and pricing of fixed-income derivatives(Ho-Lee, Black-Derman-Toy, Heath-Jarrow-Morton interest rate model).IEOR E4700x and y Introduction to financialengineering3 pts. Lect: 3. Professor Yao.Prerequisites: IEOR E4106 or IEOR E3106. Thiscourse is required for undergraduate studentsmajoring in OR:FE. Introduction to investment andfinancial instruments via portfolio theory and derivativesecurities, using basic operations research/engineering methodology. Portfolio theory, arbitrage;Markowitz model, market equilibrium, andthe capital asset pricing model. General models forasset price fluctuations in discrete and continuoustime. Elementary introduction to Brownian motionand geometric Brownian motion. Option theory;Black-Scholes equation and call option formula.Computational methods such as Monte Carlosimulation.IEOR E4701 Stochastic models for financialengineering3 pts. Lect: 3. Instructor to be announced.Prerequisites: SIEO W4105. This course is forMSFE students only, offered during the summersession. Review of elements of probability theory,Poisson processes, exponential distribution,SEAS 2010–2011

OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS:THIRD AND FOURTH YEARS167SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIMATH E1210 (3)Ordinary diff. equationsIEOR E3106 (3)Stochastic modelsREQUIREDCOURSES 1 IEOR E3608 (4)Mathematical prog.ECON W3211 (3)MicroeconomicsIEOR E3402 (4)Production planningECON W3213 (3)MacroeconomicsCOMS W4111 (3)Database systemsIEOR E4003 (3)Industrial econ.IEOR E4404 (4)SimulationIEOR E4001 (3)Design and mgmt. of prod.and service systemsIEOR E4550Entrepren. bus. creationfor engrs.orIEOR E4998Managing technol. innov.and entrepreneurshipTECH Technical electives (12 pts. total) 2ELECTIVESMANAGEMENTNONTECHManagement electives (9 pts. total):Please consult lists posted on IEOR Web site: www.ieor.columbia.eduComplete 27-point requirement; see page 10 or www.engineering.columbia.edu for details.1 Taking required courses later than the prescribed semester is not permitted.2 At least two technical electives must be chosen from IEOR; the complete list is available at www.ieor.columbia.edu.renewal theory, Wald’s equation. Introduction todiscrete-time Markov chains and applications toqueueing theory, inventory models, branchingprocesses.IEOR E4702 Statistical inference for financialengineering1.5 pts. Lect: 1.5.Corequisites: IEOR E4701 and IEOR E4706.This course is for MSFE students only, offeredduring the summer session. The course coversbasic tools of statistical inference relevantto financial engineering. The statistical topicscovered include point estimation, maximum likelihoodestimators, confidence intervals, the deltamethod, hypothesis testing, and goodness of fittests. The financial examples include selectionbias in finance, estimation of drift and volatility inthe geometric Brownian motion model, the leptokurticfeature, and difficulties in estimating the taildistributions of asset returns.IEOR E4703x Monte Carlo simulation3 pts. Lect: 3. Professor Sigman.Prerequisites: IEOR E4701. This course is for MSFEstudents only. Multivariate random number generation,bootstrapping, Monte Carlo simulation, efficiencyimprovement techniques. Simulation outputanalysis, Markov-chain Monte Carlo. Applicationsto financial engineering. Introduction to financialengineering simulation software and exposure tomodeling with real financial data. NOTE: Studentswho have taken IEOR E4404 Simulation may notregister for this course for credit.IEOR E4705x Studies in operations research3 pts. Lect: 3. Professor Riccio.Prerequisites: IEOR E4004 (or IEOR E3608) andIEOR E4106 (or IEOR E3106). Analysis and critiqueof current operations research studies. Blood bankinventory, fire departments, police departments, andhousing operations research studies are considered.IEOR E4706 Foundations of financialengineering3 pts. Lect: 3.Prerequisites: IEOR E4701, IEOR E4702, andlinear algebra. This course is for MSFE studentsonly, offered during the summer session.Discrete-time models of equity, bond, credit, andforeign-exchange markets. Introduction to derivativemarkets. Pricing and hedging of derivativesecurities. Complete and incomplete markets.Introduction to portfolio optimization and the capitalasset pricing model.IEOR E4707x Financial engineering:continuous-time asset pricing3 pts. Lect: 3. Professor Haugh.Prerequisites: IEOR E4701. This course is forMSFE students only. Modeling, analysis, andcomputation of derivative securities. Applicationsof stochastic calculus and stochastic differentialequations. Numerical techniques: finite-difference,binomial method, and Monte Carlo.IEOR E4708y Seminar on important papers infinancial engineering3 pts. Lect: 3. Professor Derman.Prerequisites: IEOR E4703, IEOR E4706, probabilityand statistics. Selected topics of special interestto Financial Engineering M.S. students. If topicsare different then this course can be taken morethan once for credit.IEOR E4709x Data analysis for financialengineering3 pts. Lect: 3. Professor Kou.Prerequisites: Probability and IEOR E4702.Corequisites: IEOR E4706, IEOR E4707This course is for MSFE students only. Empiricalanalysis of asset prices: heavy tails, test of the predictabilityof stock returns. Financial time series: ARMA,stochastic volatility, and GARCH models. Regressionmodels: linear regression and test of CAPM, nonlinearregression and fitting of term structures.IEOR E4710y Term structure models3 pts. Lect: 3. Instructor to be announced.Prerequisites: IEOR E4706, IEOR E4707, andcomputer programming. Interest rate models andnumerical techniques for pricing and hedging interestrate contracts and fixed income securitiesIEOR E4718y Introduction to the impliedvolatility smile3 pts. Lect: 3. Professor Derman.Prerequisites: IEOR E4706, knowledge of derivativesvaluation models. During the past fifteenyears the behavior of market options prices haveshown systematic deviations from the classicBlack-Scholes model. The course examines theempirical behavior of implied volatilities, in particularthe volatility smile that now characterizes mostmarkets, the mathematics and intuition behind newmodels that can account for the smile, and theirconsequences for hedging and valuation.SEAS 2010–2011

168OPERATIONS RESEARCH: FINANCIAL ENGINEERING:FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)Linear algebra (3) 1and ODE (3)PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)Physics or chemistry lab:PHYS C1493 (3) orPHYS W3081 (2) orCHEM C1500 (3) orCHEM C2507 (3) orCHEM C3085 (4) orCHEMISTRY(choose one course)C1403 (3.5) or C1404 (3.5) orC1604 (3.5) or C3045 (3.5)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESECON W1105 (4) and W1155 recitation (0)either semesterHUMA C1001,COCI C1101,or Global Core (3–4)HUMA C1002,COCI C1102,or Global Core (3–4)HUMA W1121 or W1123 (3)either semesterFIRST- ANDSECOND-YEARDEPT.REQUIREMENTSProfessional-level course (3) (see pages 12–13)IEOR E2261 (4)and IEOR E3658 (3) or STAT W4105 (3)and STAT W3107 (3) or STAT W4107 (3)COMPUTERSCIENCECOMS W1004 (Java) (3) or COMS W1007 (Java) (3)and COMS W3134 (3) or COMS W3137 (3) 2PHYSICALEDUCATIONC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.2 Computer programming should be taken consecutively with data structures.IEOR E4720x and y–E4729 Topics inquantitative finance1.5-3 pts. Lect: 2-2.5. Professor Higgins.Prerequisites: IEOR E4700, additional pre-requisiteswill be announced depending on offering.Selected topics of interest in the area of quantitativefinance. Offerings vary each year; sometopics include: energy derivatives, experimentalfinance, foreign exchange and related derivativeinstruments, inflation derivatives, hedge fundmanagement, modeling equity derivatives in Java,mortgage-backed securities, numerical solutions ofpartial differential equations, quantitative portfoliomanagement, risk management, trade and technologyin financial markets.IEOR E4724x (Section 001) Topics inquantitative finance: hedge fund management3 pts. Lect: 3. Professor Metzger.The course covers the critical managerial aspectsand characteristics of hedge funds and its industry,including legal regulations, strategies, risk management,performance evaluation, etc.IEOR E4725y Topics in quantitative finance:numerical solutions of partial differentialequation3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: IEOR E4706 and IEOR E4707.The course covers derivations and solutions ofpartial differential equations under variety of underlyingstochastic price processes. Students willgain exposure to applications of partial differentialequations to security pricing in different financialmarkets (i.e. equity derivatives, fixed income securitiesand credit derivative markets).IEOR E4726y Topics in quantitative finance:experimental finance3 pts. Lect: 3.Prerequisites: IEOR E4706 and IEOR E4707.The course introduces concepts to proposetrading schema, organize tests via options/stock databases and carry out tests efficientlyand accurately. It exposes students to the strikingdifferences between static, thermodynamic/SDE model solutions and real (time-of-flight)pricing. They become familiar with computationalSEAS 2010–2011

OPERATIONS RESEARCH: FINANCIAL ENGINEERING:THIRD AND FOURTH YEARS169SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIREQUIREDCOURSESECON W3213 (3)MacroeconomicsIEOR E3106 (3)Stochastic modelsIEOR E3608 (4)Mathematical prog.IEOR E4003 (3)Industrial econ.IEOR E3402 (4)Production planningIEOR E4404 (4)SimulationIEOR E4700 (3)Intro. to FECOMS W4111 (3)Database systemsECON W3211 (3)MicroeconomicsIEOR E4307 (3)ForecastingIEOR E4407 (3)Game theoretic modelsof operationsIEOR E4620 (3)Pricing models for FEIEOR E4500 (3)Applications prog. for FEIEOR E4630 (3)Asset allocationECON E3412 (3)Intro. to econometricsELECTIVESFINANCIALENGINEERINGNONTECHPlease consult the list on the departmental Web site: www.ieor.columbia.eduComplete 27-point requirement; see page 10 or www.engineering.columbia.edu for detailstechniques for modeling and testing proposals fortrading strategies.IEOR E4729 Financial markets, risk, andinstitutions1.5 pts. Lect: 1.5.Corequisites: IEOR E4701, IEOR E4702, IEORE4706. This course is for MSFE students only,offered during the summer session. This corecurriculum course introduces students pursuinga graduate degree in financial engineering tothe main areas and concepts of modern finance.Topics include financial analytics; fixed incomeand equity markets; macroeconomic aspects ofinvestment decisions; portfolio and utility theories;introduction to risk management; financialcrises. The course’s objective is to provide thebroadest possible perspective on how financialtheory and real-life practice interact, preparingstudents for successful careers in the financialindustry and paving the way for in-depth studiesthat follow.IEOR E4731y Credit risk modeling and creditderivatives3 pts. Lect: 3. Instructor to be announced.Prerequisites: IEOR E4701 and IEOR E4707.Introduction to quantitative modeling of credit risk,with a focus on the pricing of credit derivatives.Focus on the pricing of single-name credit derivatives(credit default swaps) and collateralized debtobligations (CDOs). Detail topics include defaultand credit risk, multiname default barrier modelsand multiname reduced form models.IEOR E4900x and y Master’s research orproject1–3 pts. Members of the faculty.Prerequisites: approval by a faculty member whoagrees to supervise the work. Independent workinvolving experiments, computer programming,analytical investigation, or engineering design.IEOR E4998x and y Managing technologicalinnovation and entrepreneurship3 pts. Lect: 3. Professor McGourty.This is a required course for undergraduatestudents majoring in OR:EMS. Focus on the managementand consequences of technology-basedinnovation. Explores how new industries are created,how existing industries can be transformedby new technologies, the linkages between technologicaldevelopment and the creation of wealth andthe management challenges of pursuing strategicinnovation.IEOR E4999x and y Curricular practicaltraining1–2 pts. Professor Derman.Prerequisites: Obtained internship and approvalfrom faculty adviser. Only for IEOR graduate studentswho need relevant work experience as partof their program of study. Final reports required.This course may not be taken for pass/fail creditor audited.MSIE W6408y Inventory theory3 pts. Lect: 3. Not offered in 2010-2011.Prerequisites: probability theory, dynamic programming.Construction and analysis of mathematicalmodels used in the design and analysisof inventory systems. Deterministic and stochasticdemands and lead times. Optimality of (s, S)policies. Multiproduct and multiechelon systems.Computational methods.IEOR E6602y Nonlinear programming3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Ph.D.-level linear programming.Convex sets and functions, convex duality andoptimality conditions. Computational methods:steepest descent, Newton and quasi-newtonmethods for unconstrained problems, active set,penalty set, interior point, augmented Lagrangianand sequential quadratic programming methods forconstrained problems. Introduction to nondifferentiableoptimization and bundle methods.IEOR E6613x Optimization, I4.5 pts. Lect: 3. Professor Goldfarb.Prerequisites: Linear algebra. Theory and geometryof linear programming. The simplex method.Duality theory, sensitivity analysis, column generationand decomposition. Interior point methods.Introduction to nonlinear optimization: convexity,optimality conditions, steepest descent, andNewton’s method, active set, and barrier methods.IEOR E6614y Optimization, II4.5 pts. Lect: 3. Instructor to be announced.Prerequisites: Linear algebra. An introduction tocombinatorial optimization, network flows anddiscrete algorithms. Shortest path problems,maximum flow problems. Matching problems,bipartite and cardinality nonbipartite. Introductionto discrete algorithms and complexity theory:NP-completeness and approximation algorithms.SEAS 2010–2011

170IEOR E6703y Advanced financial engineering3 pts. Lect: 2. Not offered in 2010–2011.Prerequisites: Probability theory and advanced stochasticmodels at the SIEO W6501 level. Reviewof basic mathematics, including renewal theory andstochastic calculus. Martingale approach to Black-Scholes formula. Optimal stopping and Americanoptions. Pricing of continuous and discrete exoticoptions. Term structure models and pricing ofbond options. Jump diffusion models. Applications,including pricing of real and electricity options andhedging of real options.IEOR E6711x Stochastic models, I4.5 pts. Lect: 3. Professor Whitt.Prerequisites: SIEO W4105 or equivalent.Advanced treatment of stochastic modeling in thecontext of queueing, reliability, manufacturing,insurance risk, financial engineering and otherengineering applications. Review of elements ofprobability theory; exponential distribution; renewaltheory; Wald’s equation; Poisson processes.Introduction to both discrete and continuous-timeMarkov chains; introduction to Brownian motion.IEOR E6712y Stochastic models, II4.5 pts. Lect: 3. Instructor to be announced.Prerequisites: IEOR E6711 or equivalent.Continuation of IEOR E6711, covering further topicsin stochastic modeling in the context of queueing,reliability, manufacturing, insurance risk, financialengineering, and other engineering applications.Topics from among generalized semi-Markovprocesses; processes with a nondiscrete statespace; point processes; stochastic comparisons;martingales; introduction to stochastic calculus.IEOR E8100x and y Advanced topics in IEOR1–3 pts. Professors Bienstock and Iyengar.Prerequisites: Faculty adviser’s permission.Selected topics of current research interest. Maybe taken more than once for credit.IEOR E9101x and y Research1–6 pts. Members of the faculty.Before registering, the student must submit anoutline of the proposed work for approval bythe supervisor and the chair of the Department.Advanced study in a specialized field under thesupervision of a member of the department staff.This course may be repeated for credit.IEOR E9800x and y Doctoral researchinstruction3, 6, 9, or 12 pts. Members of the faculty.A candidate for the Eng.Sc.D. degree in industrialengineering or operations research must registerfor 12 points of doctoral research instruction.Registration in IEOR E9800 may not be used tosatisfy the minimum residence requirement forthe Ph.D. degree.SEAS 2010–2011

MATERIALS SCIENCE AND ENGINEERING PROGRAMProgram in the Department of Applied Physics and AppliedMathematics, sharing teaching and research with the faculty ofthe Henry Krumb School of Mines.171200 S. W. Mudd, MC 4701, 212-854-4457www.apam.columbia.eduwww.seas.columbia.edu/matsciIN CHARGE OF MATERIALSSCIENCE AND ENGINEERINGProfessor James S. Im1106 S. W. MuddIN CHARGE OF SOLID-STATESCIENCE AND ENGINEERINGProfessor Siu-Wai Chan1136 S. W. MuddProfessor Irving P. Herman208 S. W. MuddCOMMITTEE ON MATERIALSSCIENCE AND ENGINEERING/SOLID-STATE SCIENCE ANDENGINEERINGWilliam E. BaileyAssociate Professor of MaterialsScienceSimon J. BillingeProfessor of Materials ScienceLouis E. BrusProfessor of ChemistrySiu-Wai ChanProfessor of Materials SciencePaul F. DubyProfessor of Mineral EngineeringChristopher J. DurningProfessor of ChemicalEngineeringIrving P. HermanProfessor of Applied PhysicsJames S. ImProfessor of Materials ScienceChris A. MarianettiAssistant Professor of MaterialsScienceGertrude F. NeumarkHowe Professor of MaterialsScience and Engineering andProfessor of Applied Physics andApplied MathematicsRichard M. Osgood Jr.Professor of ElectricalEngineeringAron PinczukProfessor of Applied Physicsand PhysicsPonisseril SomasundaranProfessor of Mineral EngineeringYasutomo UemuraProfessor of PhysicsWen I. WangProfessor of ElectricalEngineeringChee Wei WongAssociate Professor ofMechanical EngineeringMaterials Science and Engineering(MSE) focuses onunderstanding, designing,and producing technology-enablingmaterials by analyzing the relationshipsamong the synthesis and processingof materials, their properties, and theirdetailed structure. This includes a widerange of materials such as metals, polymers,ceramics, and semiconductors.Solid-state science and engineeringfocuses on understanding and modifyingthe properties of solids from theviewpoint of the fundamental physics ofthe atomic and electronic structure.Undergraduate and graduateprograms in materials science andengineering are coordinated throughthe Materials Science and EngineeringProgram in the Department of AppliedPhysics and Applied Mathematics. Thisprogram promotes the interdepartmentalnature of the discipline and involvesthe Departments of Applied Physicsand Applied Mathematics, ChemicalEngineering and Applied Chemistry,Electrical Engineering, and Earth andEnvironmental Engineering (EEE) in theHenry Krumb School of Mines (HKSM)with advisory input from the Departmentsof Chemistry and Physics.Students interested in materials scienceand engineering enroll in the materialsscience and engineering programin the Department of Applied Physicsand Applied Mathematics. Thoseinterested in the solid-state scienceand engineering specialty enroll in thedoctoral program within Applied Physicsand Applied Mathematics or ElectricalEngineering.The faculty in the interdepartmentalcommittee constitute but a smallfraction of those participating in thisprogram, who include ProfessorsBailey, Billinge, Chan, Herman, Im,Marianetti, Neumark, Noyan, Pinczuk,and Stormer from Applied Physics andApplied Mathematics; Brus, Durning,Flynn, Koberstein, O’Shaughnessy, andTurro from Chemical Engineering; Duby,Somasundaran, and Themelis fromEEE; Heinz, Osgood, and Wang fromElectrical Engineering and Wong fromMechanical Engineering.Materials science and engineeringuses optical, electron, and scanningprobe microscopy and diffraction techniquesto reveal details of structure,ranging from the atomic to the macroscopicscale—details essential to understandingproperties such as mechanicalstrength, electrical conductivity, andtechnical magnetism. These studies alsogive insight into problems of the deteriorationof materials in service, enablingdesigners to prolong the useful life oftheir products. Materials science andengineering also focus on new ways tosynthesize and process materials, frombulk samples to ultrathin films to epitaxialheterostructures to nanocrystals.This involves techniques such as UHVsputtering; molecular beam epitaxy;plasma etching; laser ablation, chemistry,and recrystallization; and other nonequilibriumprocesses. The widespreaduse of new materials and the new usesSEAS 2010–2011

172of existing materials in electronics,communications, and computers haveintensified the demand for a systematicapproach to the problem of relatingproperties to structure and necessitatesa multidisciplinary approach.Solid-state science and engineeringuses techniques such as transportmeasurements, X-ray photoelectronspectroscopy, inelastic light scattering,luminescence, and nonlinear opticsto understand electrical, optical, andmagnetic properties on a quantummechanical level. Such methods areused to investigate exciting new typesof structures, such as two-dimensionalelectron gases in semiconductor heterostructures,superconductors, and semiconductorsurfaces and nanocrystals.Current Research ActivitiesCurrent research activities in the materialsscience and engineering programat Columbia focus on thin films andelectronic materials that enable significantadvances in information technologies.Specific topics under investigationinclude interfaces, stresses, and grainboundaries in thin films; lattice defectsand electrical properties of semiconductors;laser processing and ultrarapidsolidification of thin films; nucleation incondensed systems; optical and electricproperties of wide-band semiconductors;synthesis of nanocrystals, carbonnanotubes, and nanotechnology-relatedmaterials; deposition, in-situ characterization,electronic testing, and ultrafastspectroscopy of magnetoelectronicultrathin films and heterostructures. Inaddition, there is research in surfaceand colloid chemistry involving bothinorganic and organic materials such assurfactants, polymers, and latexes, withemphasis on materials/ environmentinteractions.The research activities in solid-statescience and engineering are describedlater in this section.Laboratory FacilitiesFacilities and research opportunitiesalso exist within the interdepartmentalMaterials Research Science andEngineering Center (MRSEC), NanoscaleScience and Engineering Center (NSEC),and Energy Frontier Research Center(EFRC), which focus on complex filmsformed from nanoparticles, molecularelectronics, and solar energy conversion,respectively. Modern clean room facilitieswith optical and e-beam lithography,thin film deposition, and surface analyticalprobes (STM, SPM, XPS) are available.More specialized equipment existsin individual research groups in solidstate engineering and materials scienceand engineering. The research facilitiesin solid-state science and engineeringare listed in the sections for each hostdepartment. Facilities, and researchopportunities, also exist within theinterdepartmental Materials ResearchScience and Engineering Center, whichfocuses on complex films composed ofnanoparticles.UNDERGRADUATE PROGRAMIN MATERIALS SCIENCE ANDENGINEERINGThis program provides the basis fordeveloping, improving, and understandingmaterials and processes forelectronic, structural, and other applications.It draws from physics, chemistry,and other disciplines to providea coherent background for immediateapplication in engineering or for subsequentadvanced study. The emphasisis on fundamentals relating atomic- tomicroscopic-scale phenomena to materialsproperties and processing, includingdesign and control of industriallyimportant materials processes. Corecourses and electives combine rigorwith flexibility and provide opportunitiesfor focusing on such areas as electronicmaterials, polymers, ceramics, biomaterials,structural materials, and metalsand mineral processing. There are alsoopportunities for combining materialsscience and engineering with interestsin areas such as medicine, business,law, or government.The unifying theme of understandingand interrelating materials synthesis,processing, structure, and propertiesforms the basis of our MSAE programand is evident in the undergraduate curriculumand in faculty research activities.These activities include work on polycrystallinesilicon for flat panel displays;high-temperature superconductors forpower transmission and sensors; semiconductorsfor laser and solar cell applications;magnetic heterostructures forinformation storage and novel computationarchitectures; electronic ceramicsfor batteries, gas sensors, and fuel cells;electrodeposition and corrosion of metals;and the analysis and design of hightemperaturereactors. Through involvementwith our research groups, studentsgain valuable hands-on experience andare often engaged in joint projects withindustrial and government laboratories.The materials science and engineeringundergraduate curriculum requires16 courses in the third and fourth years,of which four are restricted electives.This program allows students to specializein a subdiscipline of MSAE if theyso choose. Students must take twelverequired courses and four electives. Atleast two electives must be in the TypeA category, and at most two may be inthe Type B category. The Type B electivesare listed under different materialssubdisciplines for guidance. Still, somecourses listed under different categoriesmay appeal to students interested in agiven area. For example, CHEE E4252:Introduction to surface and colloidalchemistry should also be considered bystudents interested in biomaterials andenvironmental materials.Type A electives are:CHEE E4530: Corrosion of metalsMSAE E4207: Lattice vibrations and crystaldefectsMSAE E4250: Ceramics and compositesELEN E4944: Principles of device microfabricationType B electives are:BIOMATERIALSBMEN E4300: Solid biomechanicsBMEN E4301: Structure, mechanics, and adaptationof boneBMEN E4501: Tissue engineering, I: biological tissuesubstitutesELECTRONIC MATERIALSAPPH E3100: Introduction to quantum mechanicsAPPH E3300: Applied electromagnetismAPPH E4100: Quantum physics of matterAPPH E4110: Modern opticsELEN E4301: Introduction to semiconductordevicesELEN E4411: Fundamentals of photonicsENVIRONMENTAL MATERIALSEAEE E4001: Industrial ecology of Earth resourcesEAEE E4160: Solid and hazardous waste managementMECHANICAL PROPERTIES OF MATERIALSENME E3114: Experimental mechanics of solidsENME E4113: Advanced mechanics of solidsSEAS 2010–2011

ENME E4114: Mechanics of fracture and fatigueMECE E4608: Manufacturing processesSOFT MATERIALS AND SURFACESCHEE C3443: Organic chemistry (note that C3444is not allowed)CHEE E4252: Introduction to surface and colloidchemistryAPMA E4400: Introduction to biophysical modelingOTHERMSAE E3900: Undergraduate research in materialsscienceAlternative courses can be takenas electives with the approval of theundergraduate adviser. Of the 24points of elective content in the thirdand fourth years, at least 12 points ofrestricted electives approved by theadviser must be taken. Of the remaining12 points of electives allotted, asufficient number must actually betaken so that no fewer than 64 pointsof courses are credited to the thirdand fourth years. Those remainingpoints of electives are intended primarilyas an opportunity to completethe four-year, 27-point nontechnicalrequirement, but any type of coursework can satisfy them.GRADUATE PROGRAMS INMATERIALS SCIENCE ANDENGINEERINGMaster of Science DegreeCandidates for the Master of Sciencedegree follow a program of study formulatedin consultation with, and approvedby, a faculty adviser. A minimum of30 points of credit must be taken ingraduate courses within a specific areaof study of primary interest to the candidate.All degree requirements mustbe completed within five years. A candidateis required to maintain at leasta 2.5 grade point average. Applicantsfor admission are required to takethe Graduate Record Examinations.A research report (6 points of credit,MSAE E6273) is required. Specialreports (3 points of credit) are acceptablefor Columbia Video Network (CVN)students.Doctoral ProgramAt the end of the first year of graduatestudy, doctoral candidates are requiredto take a comprehensive written qualifyingexamination, which is designed totest the ability of the candidate to applycourse work in problem solving and creativethinking. The standard is first-yeargraduate level. There are two four-hourexaminations over a two-day period.Candidates in the program must takean oral examination within one year oftaking the qualifying examination. Withintwo years of taking the qualifying examination,candidates must submit a writtenproposal and defend it orally before aThesis Proposal Defense Committeeconsisting of three members of thefaculty, including the adviser. Doctoralcandidates must submit a thesis to bedefended before a Dissertation DefenseCommittee consisting of five facultymembers, including two professorsfrom outside the doctoral program.Requirements for the Eng.Sc.D. (administeredby the School of Engineeringand Applied Science) and the Ph.D.(administered by the Graduate School ofArts and Sciences) are listed elsewherein this bulletin.Areas of ResearchMaterials science and engineering isconcerned with synthesis, processing,structure, and properties of metals,ceramics, polymers, and other materials,with emphasis on understandingand exploiting relationships amongstructure, properties, and applicationsrequirements. Our graduate researchprograms encompass projects in areasas diverse as polycrystalline silicon, electronicceramics grain boundaries andinterfaces, microstructure and stressesin microelectronics thin films, oxide thinfilms for novel sensors and fuel cells,wide-band-gap semiconductors, opticaldiagnostics of thin-film processing,ceramic nanocomposites, electrodepositionand corrosion processes,magnetic thin films for giant and colossalmagnetoresistance, chemical synthesisof nanoscale materials, nanocrystals,carbon nanotubes, nanostructure analysisusing X-ray and neutron diffractiontechniques, and electronic structurecalculation of materials using densityfunctional and dynamical mean-fieldtheories. Application targets for polycrystallinesilicon are thin film transistorsfor active matrix displays and siliconon-insulatorstructures for ULSI devices.Wide-band-gap II–VI semiconductorsare investigated for laser applications.Novel applications are being developedfor oxide thin films, including uncooledIR focal plane arrays and integratedfuel cells for portable equipment. Longrangeapplications of high-temperaturesuperconductors include efficient powertransmission and highly sensitive magneticfield sensors.Thin film synthesis and processing inthis program include evaporation, sputtering,electrodeposition, and plasmaand laser processing. For analyzingmaterials structures and properties,faculty and students employ electronmicroscopy, scanning probe microscopy,cathodoluminescence and electronbeam–induced current imaging, photoluminescence,dielectric and anelasticrelaxation techniques, ultrasonic methods,magnetotransport measurements,and X-ray diffraction techniques. Facultymembers have research collaborationswith Lucent, Exxon, Philips Electronics,IBM, and other New York area researchand manufacturing centers, as well asmajor international research centers.Scientists and engineers from theseinstitutions also serve as adjunct facultymembers at Columbia. The NationalSynchrotron Light Source at BrookhavenNational Laboratory is used for high-resolutionX-ray diffraction and absorptionmeasurements.Entering students typically haveundergraduate degrees in materialsscience, metallurgy, physics, chemistry,or other science and engineeringdisciplines. First-year graduate coursesprovide a common base of knowledgeand technical skills for more advancedcourses and for research. In additionto course work, students usually beginan association with a research group,individual laboratory work, and participationin graduate seminars during theirfirst year.GRADUATE SPECIALTY INSOLID-STATE SCIENCE ANDENGINEERINGSolid-state science and engineering isan interdepartmental graduate specialtythat provides coverage of an importantarea of modern technology thatno single department can provide. Itencompasses the study of the full rangeof properties of solid materials, with173SEAS 2010–2011

174MATERIALS SCIENCE AND ENGINEERING PROGRAM:FIRST AND SECOND YEARSSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS 1 MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and ODE (3)PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)C1403 (3)C2601 (3.5)Lab W3081 (2)C1494 (3)Lab C2699 (3)CHEMISTRY(three tracks,choose one)C1403 (3.5)C1404 (3)Lab C1500 (2) either semesterC1604 (3.5)C3045 (3.5)C2507 (3)C3046 (3), Lab C2507 (3) C3545 (3)ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALELECTIVESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 (3)or W1123 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)REQUIRED TECHELECTIVES(3) Student’s choice, see list of first-and second-year technical electives(professional-level courses; see pages 12–13).COMPUTERSCIENCEPHYSICALEDUCATIONA computer language of the student’s choice at the 1000 level or higherC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1 Students with advanced standing may start the calculus sequence at a higher level.special emphasis on electrical, magnetic,optical, and thermal properties.The science of solids is concerned withunderstanding these properties in termsof the atomic and electronic structureof the materials in question. Insulators(dielectrics), semiconductors, ceramics,and metallic materials are all studiedfrom this viewpoint. Quantum and statisticalmechanics are key backgroundsubjects. The engineering aspects dealwith the design of materials to achievedesired properties and the assemblingof materials into systems to producedevices of interest to modern technology,e.g., for computers and for energyproduction and utilization.Areas of ResearchThe graduate specialty in solid-statescience and engineering includesresearch programs in the FractionalQuantum Hall Effect and electronictransport (Professor Stormer,Physics/ Applied Physics and AppliedMathematics); nonlinear optics ofsurfaces (Professor Heinz, ElectricalEngineering/ Physics); semiconductornanocrystals (Professor Brus,Chemistry/ Chemical Engineering);optics of semiconductors, includingat high pressure (ProfessorHerman, Applied Physics and AppliedMathematics); chemical physics ofsurfaces and photoemission (ProfessorOsgood, Electrical Engineering/AppliedPhysics and Applied Mathematics);molecular beam epitaxy leading tosemi- conductor devices (ProfessorWang, Electrical Engineering/AppliedPhysics and Applied Mathematics);luminescence in heavily doped wideband-gapsemiconductors (ProfessorNeumark, Henry Krumb School ofMines/Applied Physics and AppliedMathematics); and inelastic lightscattering in low-dimensional electrongases within semiconductors(Professor Pinczuk, Applied Physicsand Applied Mathematics/ Physics);large-area electronics and thin-filmtransistors (Professor Im, Henry KrumbSchool of Mines/Applied Physicsand Applied Mathematics); structuralSEAS 2010–2011

MATERIALS SCIENCE AND ENGINEERING: THIRD AND FOURTH YEARS175SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIMSAE E3103 (3)Elements of mat. sci.MSAE E3104 (3)Laboratory in mat. sci.MSAE E3156 (3)Design projectMSAE E3157 (3)Design projectREQUIREDCOURSESMSAE E 3111 (3)Thermodynamics,kinetic theory, andstatistical mechanicsENME E3113 (3) 1Mechanics of solidsMSAE E3141 (3)Processing of metalsand semiconductorsMSAE E3142 (3) 3Processing of ceramicsand polymersMSAE E4101 (3)Structural analysisof materialsMSAE E4206 (3)Electronic and magneticproperties of solidsMSAE E4202 (3)Thermodynamics andreactions in solidsMSAE E4215 (3)Mechanical behaviorof materialsELECTIVES 6 points 2 6 points 2 6 points 2 6 points 2TOTAL POINTS 15 15 15 151 Students wishing to have advance preparation for ENME E3113 may take ENME-MECE E3105: Mechanics as an elective in Semester IV.2 At least 6 of the 24 points of electives must be Type A. Another 6 points must be from the Type A and Type B elective lists.3 Juniors substitute E4132 for E3142 when offered.analysis and high Tc superconductors(Professor Chan, Henry KrumbSchool of Mines/Applied Physics andApplied Mathematics); X-ray microdiffractionand stresses (Professor Noyan,Henry Krumb School of Mines/ AppliedPhysics and Applied Mathematics);magnetic properties of thin films(Professor Bailey, Henry Krumb Schoolof Mines/Applied Physics and AppliedMathematics); the structure of nanomaterials(Professor Billinge, Henry KrumbSchool of Mines/Applied Physicsand Applied Mathematics); electronicstructure calculations of materials(Professor Marianetti, Henry KrumbSchool of Mines/ Applied Physics andApplied Mathematics); and opticalnanostructures (Professor Wong, HenryKrumb School of Mines/MechanicalEngineering).Program of StudyThe applicant for the graduate specialtymust be admitted to one of theparticipating programs: applied physicsand applied mathematics, or electricalengineering. A strong undergraduatebackground in physics or chemistry andin mathematics is important.The doctoral student must meet theformal requirements for the Eng.Sc.D. orPh.D. degree set by the department inwhich he or she is registered. However,the bulk of the program for the specialtywill be arranged in consultationwith a member of the interdepartmentalCommittee on Materials Science andEngineering/ Solid-State Science andEngineering. At the end of the first yearof graduate study, doctoral candidatesare required to take a comprehensivewritten examination concentrating onsolid-state science and engineering.The following are regarded as corecourses of the specialty:APPH E4100: Quantum physics of matterAPPH E4112: Laser physicsAPPH-MSAE E6081-E6082: Solid state physics,I and IICHEM G4230: Statistical thermodynamicsorCHAP E4120: Statistical mechanicsELEN E4301: Introduction to semiconductordevicesELEN E4944: Principles of device microfabricationELEN E6331-E6332: Principles of semiconductorphysicsELEN E6403: Classical electromagnetic theoryorPHYS G6092: Electromagnetic theory, IMSAE E4206: Electronic and magnetic propertiesof solidsMSAE E4207: Lattice vibrations and crystaldefectsMSAE E6220: Crystal physicsMSAE E6240: Impurities and defects in semiconductormaterialsMSAE E6241: Theory of solidsPHYS G6018: Physics of the solid statePHYS G6037: Quantum mechanicsCOURSES IN MATERIALSSCIENCE AND ENGINEERINGFor related courses, see also AppliedPhysics and Applied Mathematics,Chemical Engineering and AppliedChemistry, Earth and EnvironmentalEngineering, and Electrical Engineering.MSAE E1001y Atomic-scale engineering of newmaterials3 pts. Lect: 3. Professor Noyan.An introduction to the nanoscale science andengineering of new materials. The control andmanipulation of atomic structure can create newsolids with unprecedented properties. Computerhard drives, compact disc players, and liquidcrystal displays (LCDs) are explored to understandthe role of new materials in enabling technologies.Group problem-solving sessions are used todevelop understanding.MSAE E3103x Elements of materials science3 pts. Lect: 3. Professor Noyan.Prerequisites: CHEM C1404 and PHYS C1011.Atomic and crystal structures, structural defects,alloying and phase diagrams. The influence ofmicrostructure on the strength and physical propertiesof metals and alloys, semiconductors, ceramics,glasses, and polymers.MSAE E3104y Laboratory in materials science3 pts. Lect: 1. Lab: 4. Professor Marianetti.Corequisite: MSAE E3103. Metallographic specimenpreparation, optical microscopy, quantitativemetallography, hardness and tensile testing, plasticdeformation, annealing, phase diagrams, brittlefracture of glass, temperature and strain ratedependent deformation of polymers, written andoral reports.SEAS 2010–2011

176MSAE E3111x Thermodynamics, kinetictheory and statistical mechanics3 pts. Lect: 3. Professor Billinge.An introduction to the basic thermodynamics ofsystems, including concepts of equilibrium, entropy,thermodynamic functions, and phase changes.Basic kinetic theory and statistical mechanics,including diffusion processes, concept of phasespace, classical and quantum statistics, and applicationsthereof.MSAE E3141y Processing of metals andsemiconductors3 pts. Lect: 3. Professor Duby.Prerequisites: MSAE E3103 or the equivalent.Synthesis and production of metals and semiconductorswith engineered microstructures fordesired properties. Includes high-temperature,aqueous, and electrochemical processing;thermal and mechanical processing of metalsand alloys; casting and solidification; diffusion,microstructural evolution, and phase transformations;modification and processing of surfacesand interfaces; deposition and removal of thinfilms. Processing of Si and other materials forelemental and compound semiconductor-basedelectronic, magnetic, and optical devices.MSAE E3142y Processing of ceramics andpolymers3 pts. Lect: 3. Instructor to be announced.Prerequisites: MSAE E3103 or equivalent.Established and novel methods involved in theprocessing of polymers and ceramics. The fundamentalaspects of the structure and propertiesof polymers and ceramic materials; strategy inthe preparatory, synthesis,, and processing methodsfor obtaining them. Topics include polymersynthesis, elastomers, thermoplastics, thermosetmaterials, design and molding processes.Ceramics: inorganic glasses and composites,materials production and principle inorganicchemistry. Processing methodology, conditioning,drying, forming, sintering, and microstructuredevelopment. Relevant aspects of transportphenomena, colloid and sol-gel science, contemporaryissues in modern polymer and ceramicprocessing.MSAE E3156x-E3157y Design project3 pts. Members of the faculty.Prerequisites: Senior standing. May be repeatedwith the permission of the undergraduate adviser.E3156: A design problem in materials science ormetallurgical engineering selected jointly by thestudent and a professor in the department. Theproject requires research by the student, directedreading, and regular conferences with the professorin charge. E3157: Completion of the research,directed reading, and conferences, culminatingin a written report and an oral presentation to thedepartment.MSAE E3900x and y Undergraduate researchin materials science0–4 pts. Members of the faculty.This course may be repeated for credit, but nomore than 6 points of this course may be countedtoward the satisfaction of the B.S. degree requirements.Candidates for the B.S. degree may conductan investigation in materials science or carryout a special project under the supervision of thestaff. Credit for the course is contingent upon thesubmission of an acceptable thesis or final report.MSAE E4090x Nanotechnology3 pts. Lect: 3. Professor Herman.Prerequisites: APPH E3100 and MSAE E3103 ortheir equivalents with instructor’s permission. Thescience and engineering of creating materials,functional structures and devices on the nanometerscale. Carbon nanotubes, nanocrystals, quantumdots, size dependent properties, self-assembly,nanostructured materials. Devices and applications,nanofabrication. Molecular engineering,bionanotechnology. Imaging and manipulating atthe atomic scale. Nanotechnology in society andindustry. Offered in alternate years.MSAE E4101x Structural analysis of materials3 pts. Lect: 3. Professor Chan.Prerequisites or corequisite: MSAE E3103 or theinstructor’s permission. Geometry of crystals, basicdiffraction theory. X-ray diffraction. Techniques andtheory of electron microscopy. Analysis of crystalstructures and orientations. Microstructure characterizationand analysis of crystalline defects.MSAE E4132y Fundamentals of polymers andceramics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MSAE E3103 or instructor’s permission.The science and engineering of polymer,ceramic and composite inorganic materials.Fundamental aspects of structure, processing andproperties. Polymers: classification, synthesis,elastomers, thermoplastics, thermosets; ceramics:Crystal structure, morphology, classification,oxides, nitrides, carbides, silicates. Electrical,mechanical, thermal and optical properties.Common and advanced technological applications,electrical/optical devices, catalytic and environmentalapplications.MSAE E4202y Thermodynamics and reactionsin solids3 pts. Lect: 3. Professor Im.Prerequisites: Instructor’s permission. Freeenergy of phases, the relationship between phasediagrams and metastability. Thermodynamicsof surfaces and interfaces, effect of particle sizeon phase equilibria, Gibbs adsorption of soluteat interfaces, grain boundaries, surface energy.Nucleation and growth, spinodal decompositionof phases. Diffusion in metals, intermetalliccompounds and ionic crystals. Diffusion alonginterfaces.MSAE E4206x Electronic and magneticproperties of solids3 pts. Lect: 3. Professor Bailey.Prerequisites: PHYS C1401-3 or equivalent. Asurvey course on the electronic and magneticproperties of materials, oriented towards materialsfor solid state devices. Dielectric and magneticproperties, ferroelectrics and ferromagnets.Conductivity and superconductivity. Electronicband theory of solids: classification of metals,insulators, and semiconductors. Materials indevices: examples from semiconductor lasers,cellular telephones, integrated circuits, and magneticstorage devices. Topics from physics areintroduced as necessary.MSAE E4207y Lattice vibrations and crystaldefects3 pts. Lect: 3. Professor Chan.An introductory course in topics of solid state physicsother than electronics and magnetic properties.Elastic waves in solids. Phonons and lattice vibrations.Brillouin zones. Thermal properties of solids.Defects, such as point defects in metals, ioniccrystals, semiconductors, and ceramics.MSAE E4215y Mechanical behavior ofstructural materials3 pts. Lect: 3. Professor Noyan.Prerequisites: MSAE E3103. Recommendedpreparation: a course in mechanics of materials.Review of states of stress and strain andtheir relations in elastic, plastic, and viscousmaterials. Dislocation and elastic-plastic conceptsintroduced to explain work hardening, variousmaterials-strengthening mechanisms, ductility,and toughness. Macroscopic and microstructuralaspects of brittle and ductile fracture mechanics,creep and fatigue phenomena. Case studies usedthroughout, including flow and fracture of structuralalloys, polymers, hybrid materials, compositematerials, ceramics, and electronic materialsdevices. Materials reliability and fracture preventionemphasized.MSAE E4250x Ceramics and composites3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites or corequisites: MSAE E3142and MSAE E3104, or instructor’s permission.The course will cover some of the fundamentalprocesses of atomic diffusion, sintering andmicrostructural evolution, defect chemistry, ionictransport, and electrical properties of ceramicmaterials. Following this, we will examine applicationsof ceramic materials, specifically, ceramicthick and thin film materials in the areas of sensorsand energy conversion/storage devices such asfuel cells, and batteries. The course work levelassumes that the student has already taken basiccourses in the thermodynamics of materials,diffusion in materials, and crystal structures ofmaterials.MSAE E4301x and y Materials sciencelaboratory1–3 pts. Members of the faculty.Prerequisites: the instructor’s permission. Materialsscience laboratory work so conducted as to fulfillparticular needs of special students.SEAS 2010–2011

177MSAE E4990x and y Special topics inmaterials science and engineering1–3 pts. Instructor to be announced.Prerequisites: Permission of the instructor. Thiscourse may be repeated for credit. Topics andinstructors change from year to year. For advancedundergraduate students and graduate students inengineering, physical sciences, and other fields.MSAE E4999x or y–S4999 Curricularpractical training1 pt. Members of the faculty.Prerequisites: Internship and approval fromadviser must be obtained in advance. Only formaster’s students in the Department of AppliedPhysics and Applied Mathematics who may needrelevant work experience as part of their programof study. Final report required. This course may notbe taken for pass/fail or audited.MSAE E6020y Electronic ceramics3 pts. Lect: 3. Not offered in 2010–2011.Structure and bonding of ceramics and glasses.Point defects and diffusion. Electronic and ionicconduction. Dielectric, ferroelectric, magnetic, andoptical ceramics.MSAE E6081x Solid state physics, I3 pts. Lect: 3. Professor Pinczuk.Prerequisites: APPH E3100 or equivalent.Knowledge of statistical physics on the level ofMSAE E3111 or PHYS G4023 strongly recommended.Crystal structure; reciprocal lattices; classificationof solids; lattice dynamics; anharmoniceffects in crystals; stress and strain; classicalelectron models of metals; and periodic, nearlyperiodic, and more advanced analysis of electronband structure.MSAE E6082y Solid state physics, II3 pts. Lect: 3. Professor Kim.Prerequisites: MSAE E6081 or the instructor’spermission. Semiclassical and quantum mechanicalelectron dynamics and conduction; dielectricproperties of insulators; semiconductors; defects;magnetism; superconductivity; low-dimensionalstructures; and soft matter.MSAE E6091x Magnetism and magnetic materials3 pts. Lect. 3. Professor Bailey.Prerequisites: MSAE E4206, APPH E6081, orequivalent. Types of magnetism. Band theory of ferromagnetism.Magnetic metals, insulators, and semiconductors.Magnetic nanostructures: ultrathin films,superlattices, and particles. Surface magnetism andspectroscopies. High speed magnetization dynamics.Spin electronics. Offered in alternate years.MSAE E6120x Grain boundaries andinterfaces3 pts. Lect: 2. Not offered in 2010–2011Prerequisites: the instructor’s permission.Suggested background: basic knowledge ofmaterials science, dislocations and point defects.The course gives an overview of the classicapproaches in studying grain boundaries. Topicsinclude boundary geometry and structure, boundaryinteractions with crystal defects, boundariesas short-circuit diffusion paths, applications ofboundary concepts to interfaces, and roles of grainboundaries in material properties and in kineticphenomena in polycrystalline materials.MSAE E6220x Crystal physics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MSAE E4206 or instructor’spermission. The course develops the idea of atensor and applies it to stress and, together withconsiderations of crystal symmetry, to the studyof the physical constants of crystals, such as diamagneticand paramagnetic susceptibility, dielectricconstants, thermal expansivity, piezoelectricconstants, and others. The physical properties arealso studied against the background material ofMSAE E4206.MSAE E6221x Introduction to dislocationtheory3 pts. Lect: 3. Not offered in 2010–2011Prerequisites: MSAE E4215 or course in theoryof elasticity, or instructor’s permission. Point andline imperfections. Theory of dislocations. Relationbetween imperfections and structure-sensitiveproperties.MSAE E6225y Techniques in X-ray andneutron diffraction3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MSAE E4101. Crystal symmetry,diffraction, reciprocal space and Ewald sphere construction,radiation sources, analytical representationof diffraction peaks, diffraction line broadening,Fourier analysis of peak shape, texture analysis,diffraction analysis of stress and strain, diffractionanalysis of order-disorder thermal diffuse scattering,small angle scattering, instrumentation indiffraction experiments, error analysis.MSAE E6229x Energy and particle beamprocessing of materials3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MSAE E4202 or instructor’s permission.Laser-, electron-, and ion-beam modificationof materials to achieve unique microstructures andmetastable phases for electronic and structuralSEAS 2010–2011

178applications. Fundamentals of energy depositionand heat flow during laser- and electron-beamirradiation. Atomic displacement processes in ionirradiatedmaterials. Beam-induced microstructuralevolution, crystallization, surface alloying, rapidsolidification, and metastable phase formation.Review of current industrial applications.MSAE E6230y Kinetics of phase transformations3 pts. Lect: 3. Professor Im.Prerequisites: MSAE E4202 or instructor’s permission.Principles of nonequilibrium thermodynamics;stochastic equations; nucleation, growth, andcoarsening reactions in solids; spinodal decomposition;eutectic and eutectoid transformations.MSAE E6251y Thin films and layers3 pts. Lect: 3. Professor Chan.Vacuum basics, deposition methods, nucleationand growth, epitaxy, critical thickness, defectsproperties, effect of deposition procedure,mechanical properties, adhesion, interconnects,and electromigration.MSAE E6273x and y–S6273x Materialsscience reports0 to 6 pts. Members of the faculty.Formal written reports and conferences with theappropriate member of the faculty on a subject ofspecial interest to the student but not covered inthe other course offerings.MSAE E8235x and y Selected topics inmaterials science3 pts. Lect: 3. x: Professor Marianetti.This course may be repeated for credit. Selectedtopics in materials science. Topics and instructorschange from year to year. For students inengineering, physical sciences, biological sciences,and related fields.MSAE E8236y Anelastic relaxations incrystals3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: the instructor’s permission. Formaltheory of anelastic relaxation phenomena. Detailedstudy of the mechanisms of anelasticity and internalfriction in crystals, including the role of point defects,dislocations, grain boundaries, electron-phononinteractions, and ferromagnetic domain effects.MSAE E9000x and y Materials science andengineering colloquium0 pts. Professor Im.Speakers from industry are invited to speak on therecent impact of materials science and engineeringinnovations.MSAE E9259x-E9260y Research topicsin materials science and metallurgicalengineering1 pt. Lect: 1. Members of the faculty.Discussion of a group of technical papers relatedto a topic of current research interest.MSAE E9301x-S9301 Doctoral research0–15 pts. Members of the faculty.Prerequisite: Qualifying examination for doctorate.Required of doctoral candidates.MSAE E9309x and y–S9309 Proposal ofResearch for the Doctorate0–3 pts. Members of the faculty.A written report prepared by the prospective doctoralcandidate defining the proposed research forthe dissertation, and oral defense of the proposalat the time of the qualifying examinations.MSAE E9800x and y–S9800 Doctoral researchinstruction3, 6, 9, or 12 pts. Professor Im.A candidate for the Eng.Sc.D. degree must registerfor 12 points of doctoral research instruction.Registration in MECE E9800 may not be used tosatisfy the minimum residence requirement for thedegree.MSAE E9900x and y–S9900 Doctoraldissertation0 pts. Members of the faculty.A candidate for the doctorate may be required toregister for this course every term after the coursework has been completed and until the dissertationhas been accepted.SEAS 2010–2011

MECHANICAL ENGINEERING220 S. W. Mudd, MC 4703, 212-854-2965www.columbia.edu/cu/mechanical179CHAIRY. Lawrence Yao248 S. W. MuddDEPARTMENTALADMINISTRATORSandra Morris220 S. W. MuddPROFESSORSGerard H. A. AteshianRichard W. LongmanVijay ModiY. Lawrence YaoASSOCIATE PROFESSORSJames HoneJeffrey W. KysarQiao LinChee Wei WongASSISTANT PROFESSORSDaniel AttingerJung-Chi LiaoKristin MyersArvind NarayanaswamyElon TerrellSENIOR LECTURERFred StolfiADJUNCT FACULTYPejman AkbariInes BasaloKai KangMichael McGoughMohammad H. N. NaraghiElias PanidesV. T. RajanGraham WalkerMANAGER OFINSTRUCTIONALLABORATORIESRobert G. StarkMechanical engineering is adiverse subject that derivesits breadth from the need todesign and manufacture everything fromsmall individual parts/devices (e.g., microscalesensors, inkjet printer nozzles)to large systems (e.g., spacecraft andmachine tools). The role of a mechanicalengineer is to take a product froman idea to the marketplace. In order toaccomplish this, a broad range of skillsare needed. The particular skills in whichthe mechanical engineer acquires deeperknowledge are the ability to understandthe forces and the thermal environmentthat a product, its parts, or its subsystemswill encounter; design them forfunctionality, aesthetics, and the abilityto withstand the forces and the thermalenvironment they will be subjected to;determine the best way to manufacturethem and ensure they will operate withoutfailure. Perhaps the one skill that is themechanical engineer’s exclusive domainis the ability to analyze and design objectsand systems with motion.Since these skills are required for virtuallyeverything that is made, mechanicalengineering is perhaps the broadestand most diverse of engineering disciplines.Hence mechanical engineersplay a central role in such industries asautomotive (from the car chassis to itsevery subsystem—engine, transmission,sensors); aerospace (airplanes,aircraft engines, control systems forairplanes and spacecraft); biotechnology(implants, prosthetic devices, fluidicsystems for pharmaceutical industries);computers and electronics (disk drives,printers, cooling systems, semiconductortools); microelectromechanicalsystems, or MEMS (sensors, actuators,micro power generation); energy conversion(gas turbines, wind turbines, solarenergy, fuel cells); environmental control(HVAC, air-conditioning, refrigeration,compressors); automation (robots, data/image acquisition, recognition, and control);manufacturing (machining, machinetools, prototyping, microfabrication).To put it simply, mechanicalengineering deals with anything thatmoves, including the human body, avery complex machine. Mechanicalengineers learn about materials, solidand fluid mechanics, thermodynamics,heat transfer, control, instrumentation,design, and manufacturing to realize/understand mechanical systems.Specialized mechanical engineeringsubjects include biomechanics, cartilagetissue engineering, energy conversion,laser-assisted materials processing,combustion, MEMS, microfluidicdevices, fracture mechanics, nanomechanics,mechanisms, micropowergeneration, tribology (friction and wear),and vibrations. The American Societyof Mechanical Engineers (ASME) currentlylists thirty-six technical divisions,from advanced energy systems andaerospace engineering to solid wasteengineering and textile engineering.The breadth of the mechanical engineeringdiscipline allows students a varietyof career options beyond some ofthe industries listed above. Regardlessof the particular future path they envisionfor themselves after they graduate,their education would have providedthem with the creative thinking thatallows them to design an exciting productor system, the analytical tools toachieve their design goals, the ability tomeet several sometimes conflicting constraints,and the teamwork needed toSEAS 2010–2011

180design, market, and produce a system.These skills also prove to be valuable inother endeavors and can launch a careerin medicine, law, consulting, management,banking, finance, and so on.For those interested in applied scientificand mathematical aspects of thediscipline, graduate study in mechanicalengineering can lead to a career ofresearch and teaching.Current Research ActivitiesCurrent research activities in theDepartment of Mechanical Engineeringare in the areas of controls and robotics,energy and micropower generation,fluid mechanics, heat/mass transfer,mechanics of materials, manufacturing,material processing, MEMS, nanotechnology,and orthopedic biomechanics.Biomechanics and Mechanics ofMaterials. Some of the current researchin biomechanics is concerned with theapplication of continuum theories ofmixtures to problems of electromechanicalbehavior of soft biological tissues,contact mechanics, lubrication of diarthrodialjoints, and cartilage tissue engineering.(Ateshian)In the area of the mechanics of materials,research is performed to betterunderstand material constitutive behaviorat the micro- and mesolength scales.This work is experimental, theoretical,and computational in nature. The ultimategoal is to formulate constitutiverelationships that are based on physicalconcepts rather than phenomenology, asin the case of plasticity power-law hardening.In addition, the role that the constitutiverelations play in the fracture andfailure of materials is emphasized. (Kysar)In the area of molecular mechanics inbiology, mechanical effects on stem celldifferentiation is studied to understand theunderlying molecular mechanisms. Themolecular motion in living cells is monitoredto examine how the dynamics ofmolecules determine the specificity of stemcell differentiation. Mechanics of molecularmotors is studied to correlate their functionswith cell differentiation. (Liao)Control, Design, and Manufacturing.Control research emphasizes iterativelearning control (ILC) and repetitivecontrol (RC). ILC creates controllers thatlearn from previous experience performinga specific command, such as robotson an assembly line, aiming for highprecisionmechanical motions. RC learnsto cancel repetitive disturbances, suchas precision motion through gearing,machining, satellite precision pointing,particle accelerators, etc. Time optimalcontrol of robots is being studied forincreased productivity on assemblylines through dynamic motion planning.Research is also being conducted onimproved system identification, makingmathematical models from input-outputdata. The results can be the startingpoint for designing controllers, but theyare also studied as a means of assessingdamage in civil engineering structuresfrom earthquake data. (Longman)Robotics and mechanism synthesisresearch focuses on the analysis ofkinematic relationship, optimization, anddesign of linkages and spatial mechanisms,and the development of novelrobotic mechanical architectures. Thesenew robotic architectures include parallelrobots, hybrid robots, snakelike robots,and flexible and flexure-based robots.The theoretical aspects of this researchinclude applications of line geometrytools and screw theory for analysis andsynthesis of robotic devices, applicationsof actuation redundancy and kinematicredundancy for stiffness control, andapplications of algebraic geometry methodsfor robot synthesis. The appliedaspects of this research include taskbaseddesign and construction of newdevices/robots for robotic medical assistancein the surgical arena. (Simaan)In the area of advanced manufacturingprocesses and systems, currentresearch concentrates on laser materialsprocessing. Investigations are beingcarried out in laser micromachining;laser forming of sheet metal; microscalelaser shock-peening, material processingusing improved laser-beam quality.Both numerical and experimental workis conducted using state-of-the-artequipment, instruments, and computingfacilities. Close ties with industryhave been established for collaborativeefforts. (Yao)Energy, Fluid Mechanics, and Heat/Mass Transfer. In the area of energy,one effort addresses the design of flow/mass transport systems for the extractionof carbon dioxide from air. Anothereffort addresses the development ofdistributed sensors for use in micrositingand performance evaluation of energyand environmental systems. The designand testing of components and systemsfor micropower generation is part of thethermofluids effort as well as part of theMEMS effort. (Modi)In the area of fluid mechanics, studyof low-Reynolds-number chaotic flowsis being conducted both experimentallyand numerically, and the interactionswith molecular diffusion and inertia arepresently being investigated. Other areasof investigation include the fluid mechanicsof inkjet printing, drop on demand,the suppression of satellite droplets,shock wave propagation, and remediationin high-frequency printing systems.(Attinger, Modi)In the area of microscale transportphenomena, current research is focusedon understanding the transport throughinterfaces, as well as the dynamics ofinterfaces. For instance, an oscillatingmicrobubble creates a microflow patternable to attract biological cells. Highspeedvisualization is used togetherwith innovative laser measurementtechniques to measure the fluid flow andtemperature field with a very high resolution.(Attinger)In the area of nanoscale thermaltransport, our research efforts center onthe enhancement of thermal radiationtransport across interfaces separatedby a nanoscale gap. The scaling behaviorof nanoscale radiation transport ismeasured using a novel heat transfermeasurement technique based on thedeflection of a bimaterial atomic forcemicroscope cantilever. Numerical simulationsare also performed to confirmthese measurements. The measurementsare also used to infer extremelysmall variations of van der Waals forceswith temperature. This enhancement ofradiative transfer will ultimately be usedto improve the power density of thermophotovoltaicenergy conversion devices.(Narayanaswamy)Research in the area of tribology—thestudy of friction, lubrication, and wear—focuses on studying the wear damageand energy loss that is experienced inpower generation components suchas piston rings, fuel injection systems,geartrains, and bearings. Next-generationlubricants, additives, surface coatings,SEAS 2010–2011

and surface finishes are being studied inorder to determine their effects on frictionand wear. Additionally, environmentallyfriendly lubricants are also beingidentified and characterized. (Terrell)MEMS and Nanotechnology. In theseareas, research activities focus onpower generation systems, nanostructuresfor photonics, fuel cells and photovoltaics,and microfabricated adaptivecooling skin and sensors for flow, shear,and wind speed. Basic research in fluiddynamics and heat/mass transfer phenomenaat small scales also supportthese activities. (Attinger, Hone, Lin,Modi, Narayanaswamy, Wong)We study the dynamics of microcantileversand atomic force microscopecantilevers to use them as microscalethermal sensors based on the resonancefrequency shifts of vibrationmodes of the cantilever. Bimaterialmicrocantilever-based sensors are usedto determine the thermophysical propertiesof thin films. (Narayanaswamy)Research in the area of nanotechnologyfocuses on nanomaterials suchas nanotubes and nanowires and theirapplications, especially in nanoelectromechanicalsystems (NEMS). A laboratoryis available for the synthesis of carbonnanotubes and semiconductor nanowiresusing chemical vapor deposition (CVD)techniques and to build devices usingelectron-beam lithography and variousetching techniques. This effort will seekto optimize the fabrication, readout, andsensitivity of these devices for numerousapplications, such as sensitive detectionof mass, charge, and magnetic resonance.(Hone, Wong, Modi)In the area of nanoscale imaging inbiology, a superresolution microscopy(nanoscopy) system is built to break thediffraction limit of light. The superresolutionmicroscopy system is to be usedto observe molecular dynamics in livingcells. A high-speed scanning systemis designed and implemented to trackmolecular dynamics in a video rate.Control of sample motion in nanometerresolution is achieved by integratingsingle photon detection and nanopositioningsystems. (Liao)Research in the area of optical nanotechnologyfocuses on devices smallerthan the wavelength of light, for example,in photonic crystal nanomaterialsand NEMS devices. A strong researchgroup with facilities in optical (includingultrafast) characterization, device nanofabrication,and full numerical intensivesimulations is available. Current effortsinclude silicon nanophotonics, quantumdot interactions, negative refraction,dramatically enhanced nonlinearities,and integrated optics. This effort seeksto advance our understanding of nanoscaleoptical physics, enabled now byour ability to manufacture, design, andengineer precise subwavelength nanostructures,with derived applications inhigh-sensitivity sensors, high-bandwidthdata communications, and biomolecularsciences. Major ongoing collaborationsacross national laboratories, industrialresearch centers, and multiuniversitiessupport this research. (Wong)In the area of microscale power generation,efforts are dedicated to build amicromotor using acoustic energy amplifiedby a microbubble. (Attinger)Research in the area of microtribology—thestudy of friction, lubrication,and wear at the microscale—analyzesthe surface contact and adhesive forcesbetween translating and rotating surfacesin MEMS devices. Additionally,the tribological behavior between slidingmicro- and nano-textured surfaces isalso of interest, due to the prospects ofenhanced lubrication and reduced friction.(Terrell)Research in BioMEMS aims todesign and create MEMS and micro/nanofluidic systems to control themotion and measure the dynamicbehavior of biomolecules in solution.Current efforts involve modeling andunderstanding the physics of micro/nanofluidic devices and systems,exploiting polymer structures to enablemicro/nanofluidic manipulation, and integratingMEMS sensors with microfluidicsfor measuring physical properties ofbiomolecules. (Lin)Biological Engineering andBiotechnology. Active areas of researchin the musculoskeletal biomechanicslaboratory include theoretical and experimentalanalysis of articular cartilagemechanics; theoretical and experimentalanalysis of cartilage lubrication, cartilagetissue engineering, and bioreactordesign; growth and remodeling ofbiological tissues; cell mechanics; andmixture theory for biological tissues withexperiments and computational analysis(Ateshian).The Hone group is involved in anumber of projects that employ the toolsof micro- and nanofabrication towardthe study of biological systems. Withcollaborators in biology and appliedphysics, the group has developed techniquesto fabricate metal patterns on themolecular scale (below 10 nanometers)and attach biomolecules to create biofunctionalizednanoarrays. The groupis currently using these arrays to studymolecular recognition, cell spreading,and protein crystallization. ProfessorHone is a co-PI of the NIH-fundedNanotechnology Center for Mechanics inRegenerative Medicine, which seeks tounderstand and modify at the nanoscaleforce- and geometry-sensing pathwaysin health and disease. The Hone groupfabricates many of the tools used by thecenter to measure and apply force on acellular level. (Hone)In the area of molecular bioengineering,proteins are engineered to understandtheir mechanical effects on stemcell differentiation. Molecular motorsare designed and engineered computationallyand experimentally to identifykey structural elements of motor functions.Fluorescent labels are added tothe molecules of interest to follow theirdynamics in living cells and to correlatetheir mechanical characteristics with theprocess of stem cell differentiation. (Liao)Microelectromechanical systems(MEMS) are being exploited to enableand facilitate the characterization andmanipulation of biomolecules. MEMStechnology allows biomolecules to bestudied in well-controlled micro/nanoenvironmentsof miniaturized, integrateddevices, and may enable novel biomedicalinvestigations not attainable byconventional techniques. The researchinterests center on the development ofMEMS devices and systems for labelfreemanipulation and interrogation ofbiomolecules. Current research effortsprimarily involve microfluidic devices thatexploit specific and reversible, stimulusdependentbinding between biomoleculesand receptor molecules to enableselective purification, concentration,and label-free detection of nucleic acid,protein, and small molecule analytes;miniaturized instruments for label-free181SEAS 2010–2011

182characterization of thermodynamic andother physical properties of biomolecules;and subcutaneously implantableMEMS affinity biosensors for continuousmonitoring of glucose and othermetabolites (Lin).The advanced robotics and mechanismapplication lab (ARMA) is focusedon surgical intervention using novelrobotic architectures. Examples of thesearchitectures include flexible snakelikerobots, parallel robots, and cooperativerobotic systems. The current researchactivity is focused on providing saferand deeper interaction with the anatomyusing minimally invasive approaches,surgery through natural orifices, surgicaltask planning based on dexterity andperformance measures, and manipulationof flexible organs. The ongoingfunded research projects includeNIH-funded grants on designing nextgenerationrobotic slaves for incisionlesssurgical intervention (surgery throughnatural opening); minimally invasive surgeryfor the throat and upper airways;image-guided insertable robotic platformsfor less invasive surgery (surgerythat is carried out using a single incisionin the abdomen); and robotic assistancefor cochlear implant surgery (NSFfunded, Simaan).Mass radiological triage is criticalafter a large-scale radiological eventbecause of the need to identify thoseindividuals who will benefit from medicalintervention as soon as possible.The goal of the ongoing NIH-fundedresearch project is to design a prototypeof a fully automated, ultra high throughputbiodosimetry. This prototype is supposedto accommodate multiple assaypreparation protocols that allow thedetermination of the levels of radiationexposure that a patient received. Theinput to this fully autonomous system isa large number of capillaries filled withblood of patients collected using fingersticks. These capillaries are processedby the system to distill the micronucleusassay in lymphocytes, with all theassays being carried out in situ in multiwellplates. The research effort on thisproject involves the automation systemdesign and integration including hierarchicalcontrol algorithms, design andcontrol of custom built robotic devices,and automated image acquisition andprocessing for sample preparation andanalysis (Simaan, Yao).A technology that couples the powerof multidimensional microscopy (threespatial dimensions, time, and multiplewavelengths) with that of DNA arraytechnology is investigated in an NIHfundedproject. Specifically, a systemis developed in which individual cellsselected on the basis of optically detectablemultiple features at critical timepoints in dynamic processes can berapidly and robotically micromanipulatedinto reaction chambers to permit amplifiedDNA synthesis and subsequentarray analysis. Customized image processingand pattern recognition techniquesare developed, including Fisher’slinear discriminant preprocessing withneural net, a support vector machinewith improved training, multiclass celldetection with error correcting outputcoding, and kernel principal componentanalysis (Yao).Facilities for Teaching and ResearchThe undergraduate laboratories, occupyingan area of approximately 6,000square feet of floor space, are the site ofexperiments ranging in complexity frombasic instrumentation and fundamentalexercises to advanced experiments insuch diverse areas as automatic controls,heat transfer, fluid mechanics,stress analysis, vibrations, microcomputer-baseddata acquisition, and control ofmechanical systems.Equipment includes microcomputersand microprocessors, analog-to-digitaland digital-to-analog converters, lasersand optics for holography and interferometry,a laser-Doppler velocimetrysystem, a Schlieren system, dynamicstrain indicators, a servohydraulic materialtesting machine, a photoelastictesting machine, an internal combustionengine, a dynamometer, subsonic andsupersonic wind tunnels, a cryogenicapparatus, computer numerically controlledvertical machine centers (VMC),a coordinate measurement machine(CMM), and a rapid prototyping system.A CNC wire electrical discharge machine(EDM) is also available for the use ofspecialized projects for students withprior arrangement. The undergraduatelaboratory also houses experimentalsetups for the understanding and performanceevaluation of a complete smallsteam power generation system, a heatexchanger, and a compressor. Part ofthe undergraduate laboratory is a staffedmachine shop with machining tools suchas standard vertical milling machines,engine and bench lathes, programmablesurface grinder, band saw, drill press,tool grinders, and a power hacksaw.The shop also has a tig welder.A mechatronics laboratory affordsthe opportunity for hands-on experiencewith microcomputer-embedded controlof electromechanical systems. Facilitiesfor the construction and testing of analogand digital electronic circuits aid thestudents in learning the basic componentsof the microcomputer architecture.The laboratory is divided into work centersfor two-person student laboratoryteams. Each work center is equippedwith several power supplies (for lowpowerelectronics and higher powercontrol), a function generator, a multimeter,a protoboard for building circuits,a microcomputer circuit board (whichincludes the microcomputer and peripheralcomponents), a microcomputerprogrammer, and a personal computerthat contains a data acquisition board.The data acquisition system servesas an oscilloscope, additional functiongenerator, and spectrum analyzer forthe student team. The computer alsocontains a complete microcomputersoftware development system, includingeditor, assembler, simulator, debugger,and C compiler. The laboratory is alsoequipped with a portable oscilloscope,an EPROM eraser (to erase microcomputerprograms from the erasable chips),a logic probe, and an analog filter bankthat the student teams share, as well asa stock of analog and digital electroniccomponents.The department maintains a moderncomputer-aided design laboratoryequipped with fifteen Silicon Graphicsworkstations and software tools. Theresearch facilities are located withinindividual or group research laboratoriesin the department, and these facilitiesare being continually upgraded. To viewthe current research capabilities pleasevisit the various laboratories within theresearch section of the departmentWeb site. The students and staff ofthe department can, by prior arrangement,use much of the equipment inthese research facilities. Through theirparticipation in the NSF-MRSEC cen-SEAS 2010–2011

ter, the faculty also have access toshared instrumentation and the cleanroom located in the Schapiro Centerfor Engineering and Physical ScienceResearch. Columbia University’s extensivelibrary system has superb scientificand technical collections.E-mail and computing services aremaintained by Columbia UniversityInformation Technology (CUIT) (http://www.columbia.edu/cuit).UNDERGRADUATE PROGRAMThe objectives of the undergraduateprogram in mechanical engineering areas follows:The Mechanical EngineeringDepartment at Columbia University isdedicated to graduating mechanicalengineers who:1. Practice mechanical engineering in abroad range of industries2. Pursue advanced education, researchand development, and other creativeand innovative efforts in science,engineering, and technology, as wellas other professional careers3. Conduct themselves in a responsible,professional, and ethical manner4. Participate as leaders in their fields ofexpertise and in activities that supportservice and economic developmentnationally and throughout the worldHighly qualified students are permittedto pursue an honors course consistingof independent study under theguidance of a member of the faculty.Upon graduation the student maywish to enter employment in industry orgovernment, or continue with graduatestudy. Alternatively, training in mechanicalengineering may be viewed as abasis for a career in business, patentlaw, medicine, or management. Thus,the department’s undergraduate programprovides a sound foundation for avariety of professional endeavors.The program in mechanical engineeringleading to the B.S. degree is accreditedby the Engineering AccreditationCommission of the Accreditation Boardfor Engineering and Technology (ABET).Of the 21 points of elective contentin the third and fourth years, at least 12points of technical courses, including atleast 6 points from the Department ofMechanical Engineering, must be taken.Those remaining points of electives areintended primarily as an opportunityto complete the four-year, 27-pointnontechnical requirement. Consistentwith professional accreditation standards,courses in engineering scienceand courses in design must have acombined credit of 48 points. Studentsshould see their advisers for details.Fundamentals of Engineering (FE)ExamThe FE exam is a state licensing examand the first step toward becominga Professional Engineer (P.E.). P.E.licensure is important for engineersto obtain—it shows a demonstratedcommitment to professionalism and anestablished record of abilities that willhelp a job candidate stand out in thefield. Ideally, the FE exam should betaken in the senior year while the technicalmaterial learned while pursuing theundergraduate degree is still fresh in thestudent’s mind. In addition to the FEexam, achieving P.E. licensure requiressome years of experience and a secondexamination, which tests knowledgegained in engineering practice. For moreinformation, please see www.columbia.edu/cu/mechanical/misc-pages/FE_Exam.html.The Mechanical Engineering Departmentstrongly encourages all seniorsto take this exam and offers a reviewcourse covering material relevant tothe exam, including a practice exam tosimulate the testing experience. The FEexam is given in the fall and spring ofeach year. The review course is offeredin the spring semester, concludingbefore the spring exam.Integrated B.S./M.S. ProgramThe Integrated B.S./M.S. Program isopen to a select group of Columbiajuniors (excluding 3-2 combined planstudents) and makes possible the earningof both a B.S. and an M.S. degreesimultaneously. Benefits of this programinclude optimal matching of graduatecourses with corresponding undergraduateprerequisites, greater abilityto plan ahead for most advantageouscourse planning, opportunities to doresearch for credit during the summerafter senior year, and up to 6 points of4000-level technical electives from theB.S. requirement may count toward thefulfillment of the point requirement of theM.S. degree. Additional benefits includesimplified application process, no GREis required, and no reference letters arerequired. To quality for this program,your cumulative GPA should be at least3.4. This program is not applicable to3-2 students. For more information onrequirements and access to an applicationform, please visit http://www.me.columbia.edu/pages/academics/Integrated_BSMS/index.html.GRADUATE PROGRAMSMaster of Science Degree ProgramThe program leading to the Master ofScience degree in mechanical engineeringrequires completion of a minimumof 30 points of approved course workconsisting of no fewer than ten courses.A thesis based on either experimental,computational, or analytical research isoptional and may be counted in lieu ofup to 6 points of course work. In general,attainment of the degree requiresone academic year of full-time study,although it may also be undertaken ona part-time basis over a correspondinglylonger period. A minimum grade pointaverage of 2.5 is required for graduation.The M.S. degree in mechanicalengineering requires a student to takea sequence of courses that shows a“clearly discernible specialty or concentration.”In consultation with his/heradviser an M.S. student can developa concentration specifically tailored tohis/her interests and objectives, andwe refer to this as the standard track.Alternatively, M.S. students can pickfrom a set of predefined concentrations,or special tracks.Typical choices of concentration inthe standard track include such subjectsas mechanics of solids and fluids, thermodynamics,heat transfer, manufacturingengineering, robotics, kinematics,dynamics and vibrations, controls, andpower generation. Nevertheless, the followingguidelines must be adhered to:1. The sequence of courses selectedmust not be haphazard but rathershow a clearly discernible specialty.2. All courses must be at the graduatelevel, i.e., numbered 4000 orhigher, with some 6000-level courses183SEAS 2010–2011

184MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARSSTANDARD TRACKSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and APMA E2101 (3)PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)C1403 (3) 3C2601 (3.5) 3CHEMISTRYone semester lecture (3–4)C1403 or C1404 orC3045 or C1604Lab C1500 (3) 1ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALCOURSESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA W1121 orW1123 (3)HUMA C1002,COCI C1102,or Global Core (3–4)ECON W1105 (4) andW1155 recitation (0)REQUIREDTECHNICALCOURSES(3) Student’s choice, see list offirst- and second-year technical electives(professional-level courses; see pages 12–13) 2ENME-MECE E3105 (4) either semesterCOMPUTERSCIENCEPHYSICALEDUCATIONComputer language: W1003 (3) or W1004 (3) any semesterC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1 May substitute Physics Lab C1493 (3), C1494 (3), or W3081 (2).2 ELEN E1201 (see semester VI) satisfies this requirement. However, MECE E1001 is strongly encouraged.3 May substitute BIOL W2001 or higher.included.3. Every program must contain at leastone course in mathematics (APMA orMATH designators) or their equivalent,covering material beyond whatthe student has taken previously. Itshould appear early in the sequencein order to serve as a basis for thetechnical course work.4. O ut-of-department study is encouraged,but at least five courses shouldbe in mechanical engineering.Rather than apply for the standardtrack, students can apply for a specialtrack in either energy systems orin micro/nanoscale engineering. Therequirements for a special track areidentical to those of the standard track,with one exception: a special trackstudent must take at least 15 of his/her points from a list determined by aspecial track adviser in consultation witha special track advisory committee. Thename of the special track will be listedon a student’s transcript. The currentlyavailable special tracks are listed below.M.S. in Mechanical Engineering withConcentration in Energy SystemsAdvisers: Profs. Daniel Attinger andVijay ModiThe concentration in energy systemsprovides the M.S. candidate with aglobal understanding of current energychallenges. Advanced thermofluidicknowledge is provided to design andoptimize energy systems, with a strongemphasis on renewable energies.Courses related to energy and environmentalpolicy, two strong areas ofColumbia as a global university, can beintegrated into the course sequence.This concentration is a suitable prepara-SEAS 2010–2011

MECHANICAL ENGINEERING: THIRD AND FOURTH YEARSSTANDARD TRACK185SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIMECE E3018 (3)Lab IMECE E3028 (3)Lab IIMECE E3100 (3)Fluids IMECE E3408 (3)Graphics and designMECE E3038 (3)Lab IIIREQUIREDCOURSESMECE E3301 (3)ThermodynamicsMECE E3311 (3)Heat transferMECE E3409 (3)Machine designMECE E3410 (4)Engineering designENME E3105 (4) 1MechanicsMECE E4608 (3)Manufacturing proc.MECE E3601 (3)Classical control sys.ENME E3113 (3)Mechanics of solidsELEN E1201 (3.5)Intro. elec. eng.TECHNICALELECTIVES6 points 6 pointsNONTECHELECTIVES3 points 6 pointsTOTAL POINTS 2 15 15.5 15 161 Strongly recommended to be taken in Semester III or IV.2 Students must complete 128 points to graduate.tion for careers in energy productionand energy consultation.Requirements: While satisfying thegeneral mechanical engineering requirements,take at least five courses from:MECE E4211: Energy: sources and conversionMECE E4302: Advanced thermodynamicsMECE E4312: Solar thermal engineeringMECE E4314: Energy dynamics of green buildingsMECE E6100: Advanced mechanics of fluidsMECE E6104: Case studies in computational fluiddynamicsMECE E6313: Advanced heat transferAPPH E4130: Physics of solar energyEAEE E6126: Carbon sequestrationEAEE E6208: Combustion chemistry or processesINTA W4200: Alternative energy resourcesARCH A4684: Sustainable designSIPA U4727: Environmental politics and policymanagementSIPA U6060: International energy systems andbusiness structuresM.S. in Mechanical Engineering withConcentration in Micro/NanoscaleEngineeringAdvisers: Profs. James Hone and JeffKysarThe concentration in micro/nanoscaleengineering provides the M.S. candidatewith an understanding of engineeringchallenges and opportunities in microandnanoscale systems. The curriculumaddresses fundamental issues ofmechanics, fluid mechanics, optics, heattransfer, and manufacturing at small-sizescales. Application areas include MEMS,bio-MEMS, microfluidics, thermal systems,and carbon nanostructures.Requirements: While satisfying thegeneral mechanical engineering requirements,take at least five courses from:MECE E4212: Microelectromechanical systemsMECE E4213: BioMEMSMECE E6105: Transport phenomena in the presenceof interfacesMECE E6700: Carbon nanotubesMECE E6710: Nanofabrication laboratoryMECE E6720: Nano/microscale thermal transportprocessesMECE E8990: Small scale mechanical behaviorELEN E4503: Sensors, actuators, and electromechanicalsystemsELEN E6945: Device nanofabricationBMEN E4590: BioMEMS: cellular and molecularapplicationsMSAE E4090: NanotechnologyExpress M.S. ProgramThe Express M.S. Program is offered tocurrent seniors, including 3-2 students,who are enrolled in the BS program.In the Express M.S. Program, a master’sdegree can be earned seamlessly.Graduate classes are availablefor seniors to apply toward their M.S.degree and the advanced courses thatwill be taken have been designed tohave the exact prerequisites completedas an undergraduate. Other advantagesinclude the opportunity for better courseplanning and creating a streamlined setof courses more possible. Additionalbenefits include simplified applicationprocess, no GRE is required and noreference letters are required. To qualifyfor this program, your cumulative GPAshould be at least 3.4. For more informationon requirements and accessto an application, please visit www.me.columbia.edu/pages/academics/Express_MS/index.htmlDoctoral/Professional DegreeProgramsStudents who wish to continue theirstudies beyond the master’s degreeSEAS 2010–2011

186MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARSEARLY DECISION TRACKSEMESTER I SEMESTER II SEMESTER III SEMESTER IVMATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)MATH V1202 (3)and APMA E2101 (3)PHYSICS(three tracks,choose one)C1401 (3)C1601 (3.5)C2801 (4.5)C1402 (3)C1602 (3.5)C2802 (4.5)C1403 (3) 3C2601 (3.5) 3CHEMISTRYone semester lecture (3–4)C1403 or C1404 orC3045 or C1604Lab C1500 (3) 2ENGLISHCOMPOSITION(three tracks,choose one)C1010 (3)Z1003 (0)Z0006 (0)C1010 (3)Z1003 (0) C1010 (3)REQUIREDNONTECHNICALCOURSESHUMA C1001,COCI C1101,or Global Core (3–4)HUMA C1002,COCI C1102,or Global Core (3–4)REQUIREDTECHNICALCOURSES(3) Student’s choice,see list of first- andsecond-year technical ENME E3105 (4)electivesMechanics(professional-level courses;see page 12) 1ENME E3113 (3)Mechanics of solidsELEN E1201 (3.5)Intro. to elec. eng.MECE E3408 (3)Graphics and designCOMPUTERSCIENCEPHYSICALEDUCATIONComputer language: W1003 (3) or W1004 (3) any semesterC1001 (1) C1002 (1)GATEWAY LABE1102 (4) either semester1 ELEN E1201 (see semester IV) satisfies this requirement. However, MECE E1001 is strongly encouraged.2 May substitute Physics Lab C1493 (3), C1494 (3), or W3081 (2).3 May substitute BIOL W2001 or higher.level but are unwilling to embark upon aprogram of research of the kind requiredfor a doctoral degree may continue ina program leading to the professionaldegree of Mechanical Engineer (MECE).The course of study consists of a minimumof 30 points of work beyond themaster’s degree, combining courses ofan analytical nature with those emphasizingthe applied aspects of one ormore fields in mechanical engineering.For the professional degree, the studentmust have a grade point average of 3.0or better.When a student becomes a prospectivecandidate for either the Doctorof Engineering Science (Eng.Sc.D.) orDoctor of Philosophy (Ph.D.) degree,a faculty adviser is assigned whosetask is to help choose a program ofcourses, provide general advice onacademic matters, and monitor academicperformance.The doctoral candidate is expectedto attain a level of mastery in some areaof mechanical engineering, and musttherefore choose a field and concentratein it by taking the most advancedcourses offered. This choice of specialtyis normally made by the time the studenthas completed 30 points of creditbeyond the bachelor’s degree, at whichtime a complete course program isprepared and submitted to the departmentaldoctoral committee for approval.The student must maintain a grade pointaverage of 3.2 or better in graduatecourses.The department requires the prospectivecandidate to pass a qualifyingexamination. Given once a year, inJanuary, it is usually taken after the studenthas completed 30 points beyondthe bachelor’s degree. However, it maynot be delayed past the next examina-SEAS 2010–2011

MECHANICAL ENGINEERING: THIRD AND FOURTH YEARSEARLY DECISION TRACK187SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIIIMECE E3018 (3)Lab IMECE E3028 (3)Lab IIMECE E3038 (3)Lab IIIREQUIREDCOURSESMECE E3100 (3)Fluids IMECE E3311 (3)Heat transferMECE E3409 (3)Machine designMECE E3410 (4)Engineering designMECE E3301 (3)ThermodynamicsMECE E4608 (3)Manufacturing proc.MECE E3601 (3)Classical control sys.REQUIREDNONTECHNICALCOURSESHUMA W1121 orW1123 (3)ECON W1105 (4) andW1155 recitation (0)TECHNICALELECTIVESNONTECHELECTIVES3 points 3 points 6 points3 points 3 points 6 pointsTOTAL POINTS 1 15 16 15 161 Students must complete a minimum of 128 points to graduate.tion given after completion of 45 points.The examination comprises a writtentest, given in two parts over two days, inwhich questions may be selected froma broad set in all areas of mechanicalengineering and applied mathematics,devised to test the candidate’s abilityto think creatively. There is also an oralexamination based on some researchproject the student has undertaken. Acandidate who fails the examination maybe permitted to repeat it once in the followingyear.After passing the qualifying examination,the student chooses a facultymember in the pertinent area of specializationwho then serves as the researchadviser. This adviser helps select aresearch problem and supervises theresearch, writing, and defense of thedissertation. Once a specific problemhas been identified and a tentative planfor the research prepared, the studentsubmits a research proposal andpresents it to a faculty committee. Thecommittee considers whether the proposedproblem is suitable for doctoralresearch, whether the plan of attack iswell formulated and appropriate to theproblem, and whether the student isadequately prepared. It may approve theplan without reservation, or it may recommendmodifications or additions. Thisis the last formal requirement until thedissertation is submitted for approval.All doctoral students are required tosuccessfully complete four semestersof the mechanical engineering seminarMECE E9500.COURSES IN MECHANICALENGINEERINGMECE E1001x Mechanical engineering:micromachines to jumbo jets3 pts. Lect: 3. Professor Myers.Corequisites: MATH V1101 Calculus 1A. Thisintroductory course explores the role of MechanicalEngineering in developing many of the fundamentaltechnological advances on which today’ssociety depends. Students will be exposed toseveral mature and emerging technologies througha series of case studies. Topics include: airplanes,automobiles, robots, modern manufacturingmethods as well as the emerging fields of microelectromechanicalmachines (MEMS) and nanotechnology.The physical concepts that govern theoperation of these technologies will be developedfrom basic principles and then applied in simpledesign problems. Students will also be exposed tostate-of-the art innovations in each case study.MECE E3018x Mechanical engineeringlaboratory, I3 pts. Lect: 3. Professor Basalo.Experiments in instrumentation and measurement:optical, pressure, fluid flow, temperature, stress,and electricity; viscometry, cantilever beam, digitaldata acquisition. Probability theory: distribution,functions of random variables, tests of significance,correlation, ANOVA, linear regression. A lab fee of$50.00 is collected.MECE E3028y Mechanical engineeringlaboratory, II3 pts. Lect: 3. Professor Wong.Experiments in engineering and physical phenomena:aerofoil lift and drag in wind tunnels, laserDoppler anemometry in immersed fluidic channels,supersonic flow and shock waves, Rankinethermodynamical cycle for power generation, andstructural truss mechanics and analysis. A lab feeof $50.00 is collected.MECE E3038x Mechanical engineeringlaboratory, III3 pts. Lect: 3. Professor Stolfi.Mechatronic control of mechanical and electromechanicalsystems. Control of various thermodynamiccycles, including internal combustion engine(Otto cycle). Reverse engineering of an electromechanicalproduct. A lab fee of $50.00 is collected.MECE E3100x Introduction to mechanicsof fluids3 pts. Lect: 3. Professor Attinger.Prerequisites: ENME E3105. Basic continuumconcepts. Liquids and gases in static equilibrium.Continuity equation. Two-dimensional kinematics.Equation of motion. Bernoulli’s equation and applications.Equations of energy and angular momen-SEAS 2010–2011

188tum. Dimensional analysis. Two-dimensionallaminar flow. Pipe flow, laminar, and turbulent.Elements of compressible flow.ENME E3105x and y Mechanics4 pts. Lect: 4. Professor Hone.Prerequisites: PHYS C1401 and MATH V1101–MATH V1102 and MATH V1201. Elements of statics,dynamics of a particle, systems of particles,and rigid bodies.MECE E3301x Thermodynamics3 pts. Lect: 3. Professor Modi.Classical thermodynamics. Basic properties andconcepts, thermodynamic properties of puresubstances, equation of state, work, heat, the firstand second laws for flow and nonflow processes,energy equations, entropy, and irreversibility.Introduction to power and refrigeration cycles.MECE E3311y Heat transfer3 pts. Lect: 3. Professor Narayanaswamy.Steady and unsteady heat conduction. Radiativeheat transfer. Internal and external forced and freeconvective heat transfer. Change of phase. Heatexchangers.MECE E3401x Mechanics of machines3 pts. Lect: 3. Professor Lin.Prerequisites: ENME E3105 and MECE E3408.Introduction to mechanisms and machines, analyticaland graphical synthesis of mechanism, displacementanalysis, velocity analysis, accelerationanalysis of linkages, dynamics of mechanism, camdesign, gear and gear trains, and computer-aidedmechanism design.MECE E3408y Computer graphics and design3 pts. Lect: 3. Instructor to be announced.Introduction to drafting, engineering graphics, computergraphics, solid modeling, and mechanicalengineering design. Interactive computer graphicsand numerical methods applied to the solution ofmechanical engineering design problems. A laboratoryfee of $175 is collected.MECE E3409x Machine design3 pts. Lect: 3. Professor Ateshian.Prerequisites: MECE E3408. Computer-aidedanalysis of general loading states and deformationof machine components using singularity functionsand energy methods. Theoretical introduction tostatic failure theories, fracture mechanics, andfatigue failure theories. Introduction to conceptualdesign and design optimization problems. Designof machine components such as springs, shafts,fasteners, lead screws, rivets, welds. Modeling,analysis, and testing of machine assemblies forprescribed design problems. Problems will bedrawn from statics, kinematics, dynamics, solidmodeling, stress analysis, and design optimization.MECE E3410y Engineering design4 pts. Lect: 4. Professor Stolfi.Prerequisites: Senior standing. Elements of thedesign process: concept formulation, systems synthesis,design analysis optimization. Selection andexecution of a project involving the design of anactual engineering device or system. A laboratoryfee of $125 is collected.MECE E3411y Fundamentals of engineering1 pt. Lect: 3. Professor Stolfi.Prerequisites: Senior standing. Review of corecourses in mechanical engineering, includingmechanics, strength of materials, fluid mechanics,thermodynamics, heat transfer, materials andprocessing, control, and mechanical design andanalysis. Review of additional topics, includingengineering economics and ethics in engineering.The course culminates with a comprehensiveexamination, similar to the Fundamentals ofEngineering examination. This course meets thefirst 4.5 weeks only.EEME E3601x Classical control systems3 pts. Lect: 3. Professor Longman.Prerequisites: MATH E1210. Analysis and designof feedback control systems. Transfer functions;block diagrams; proportional, rate, and integralcontrollers; hardware, implementation. Routh stabilitycriterion, root locus, Bode and Nyquist plots,compensation techniques.MECE E3900x-E3901y Honors tutorial inmechanical engineering3 pts. Lect: 3. Members of the faculty.Individual study; may be selected after the firstterm of the junior year by students maintaining a3.2 grade-point average. Normally not to be takenin a student’s final semester. Course format mayvary from individual tutorial to laboratory workto seminar instruction under faculty supervision.Written application must be made prior to registrationoutlining proposed study program. Projectsrequiring machine-shop use must be approved bythe laboratory supervisor.MECE E3998x and y Projects in mechanicalengineering1-3 pts. Members of the faculty.Prerequisites: Approval by faculty member whoagrees to supervise the work. Normally not to betaken in a student’s final semester. Independentproject involving theoretical, computational,experimental or engineering design work. Maybe repeated, but no more than 3 points may becounted toward degree requirements. Projectsrequiring machine-shop use must be approved bythe laboratory supervisor.MECE E4058x and y Mechatronics andembedded microcomputer control3 pts. Lect: 3. Professor Stolfi.Prerequisites: ELEN E1201. Recommended:ELEN E3000. Enrollment limited to 12 students.Mechatronics is the application of electronicsand microcomputers to control mechanical systems.Systems explored include on/off systems,solenoids, stepper motors, DC motors, thermalsystems, magnetic levitation. Use of analog anddigital electronics and various sensors for control.Programming microcomputers in Assembly and C.A lab fee of $75.00 is collected. Lab required.MECE E4100y Mechanics of fluids3 pts. Lect: 3. Instructor to be announced.Prerequisites: MECE E3100 or equivalent. Fluiddynamics and analyses for mechanical engineeringand aerospace applications: boundary layers andlubrication, stability and turbulence, and compressibleflow. Turbomachinery as well as additionalselected topics.MECE E4211x Energy: sources andconversion3 pts. Lect: 3. Instructor to be announced.Prerequisites: MECE E3301. Energy sourcessuch as oil, gas, coal, gas hydrates, hydrogen,solar, and wind. Energy conversion systems forelectrical power generation, automobiles, propulsionand refrigeration. Engines, steam and gasturbines, wind turbines; devices such as fuel cells,thermoelectric converters, and photovoltaic cells.Specialized topics may include carbon-dioxidesequestration, cogeneration, hybrid vehicles andenergy storage devices.MECE E4212x or y Microelectromechanicalsystems3 pts. Lect: 1.5. Lab: 3. Professor Wong.MEMS markets and applications; scaling laws;silicon as a mechanical material; Sensors andactuators; micromechanical analysis and design;substrate (bulk) and surface micromachining;computer aided design; packaging; testing andcharacterization; microfluidics.MECE E4213y Biomicroelectromechanicalsystems (BioMEMS): design, fabrication, andanalysis3 pts. Lect: 3. Professor Lin.Prerequisites: MECE E3100 and MECE E3311,course in transport phenomena, or instructor’spermission Silicon and polymer micro/nanofabricationtechniques; hydrodynamic microfluidic control;electrokinetic microfluidic control; microfluidicseparation and detection; sample preparation;micro bioreactors and temperature control; implantableMEMS, including sensors, actuators and drugdelivery devices.MECE E4302y Advanced thermodynamics3 pts. Lect: 3. Professor Kang.Prerequisites: MECE E3301. Advanced classicalthermodynamics. Availability, irreversibility, generalizedbehavior, equations of state for nonidealgases, mixtures and solutions, phase and chemicalbehavior, combustion. Thermodynamic propertiesof ideal gases. Applications to automotive andaircraft engines, refrigeration and air conditioning,and biological systems.MECE E4304x Turbomachinery3 pts. Lect: 3. Professor Akbari.This course will introduce you to the basics oftheory, design, selection and applications ofturbomachinery. Turbomachines are widely usedin many engineering applications such as energyconversion, power plants, air-conditioning, pumping,refrigeration and vehicle engines, as there arepumps, blowers, compressors, gas turbines, jetengines, wind turbines etc. Applications are drawnfrom energy conversion technologies, HVAC andpropulsion. The course provides a basic understandingof the different kinds of turbomachines.SEAS 2010–2011

MECE E4305y Mechanics andthermodynamics of propulsion3 pts. Lect: 3. Professor Akbari.Prerequisites: MECE E3301x Thermodynamicsand MECE E3311y Heat transfer; MECE E4304xTurbomachinery (or instructor approval). Principlesof propulsion. Thermodynamic cycles of air breathingpropulsion systems including ramjet, scramjet,turbojet, and turbofan engine and rocket propulsionsystem concepts. Turbine engine and rocketperformance characteristics. Component andcycle analysis of jet engines and turbomachinery.Advanced propulsion systems. SEAS interdisciplinarycourse.IEME E4310x The manufacturing enterprise3 pts. Lect: 3. Professor Weinig.The strategies and technologies of global manufacturingand service enterprises. Connectionsbetween the needs of a global enterprise, the technologyand methodology needed for manufacturingand product development, and strategic planningas currently practiced in industry.MECE E4312x Solar thermal engineering3 pts. Lect: 3. Instructor to be announced.Prerequisites: MECE E3311 (Heat transfer).Fundamentals of solar energy transport: radiationheat transfer, convention, conduction andphase change processes. Heat exchangersand solar collectors: basic methods of thermaldesign, flow arrangements, effects of variableconditions, rating procedures. Solar energyconcentration. Piping Systems: series andparallel arrangements, fluid movers. Thermalresponse and management of photovoltaicenergy conversion. Solar energy storage. Solarcooling, solar thermal power and cogeneration.Applications to the design of solar thermalengineering systems.MECE E4314y Energy dynamics of greenbuildings3 pts. Lect: 3. Professor Naraghi.Prerequisites: MECE E3301 and MECE E3311.Introduction to analysis and design of heating,ventilating and air-conditioning systems. Heatingand cooling loads. Humidity control. Solar gain andpassive solar design. Global energy implications.Green buildings. Building-integrated photovoltaics.Roof-mounted gardens and greenhouses.Financial assessment tools and case studies.Open to Mechanical Engineering graduate studentsonly.MECE E4400x and y Computer laboratory access0 pts. Professor Ateshian.Sign up for this class to obtain a computer accountand access to the Department of MechanicalEngineering Computer Laboratory. A laboratory feeof $50 is collected.MECE E4404x Lubrication theory and design3 pts. Lect: 3. Professor Terrell.Prerequisites: MECE E3100. Fluid friction. Thehydrodynamic and hydrostatic theories of lubrication.Plane surfaces and thrust bearing design.Journal bearings; load-carrying capacity and temperaturerise. Principles of bearing design for efficientlubrication. Oil flow in bearings. Bearings withsemifluid lubrication. Fluid and nonfluid lubricants.Bearing materials.MECE E4430y Automotive dynamics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ENME 3105 or equivalent, recommended:ENME 3106 or equivalent. Automobiledynamic behavior is divided into three subjects:vehicle subsystems, ride, and handling. Vehiclesubsystems include: tire, steering, mechanisms,suspensions, gearbox, engine, clutch, etc.Regarding ride, vibrations and ride comfort areanalyzed, and suspension optimization of a quartercar model is treated. Regarding handling, vehicledynamic behavior on the road is analyzed, withemphasis on numerical simulations using planar aswell as roll models.MECE E4431 Space vehicle dynamics andcontrol3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: ENME-MECE E3105, ENME E4202recommended. Space vehicle dynamics and control,rocket equations, satellite orbits, initial trajectorydesigns from earth to other planets, satelliteattitude dynamics, gravity gradient stabilization ofsatellites, spin-stabilized satellites, dual-spin satellites,satellite attitude control, modeling, dynamics,and control of large flexible spacecraft.MEBM E4439x Modeling and identification ofdynamic systems3 pts. Lect: 3. Professor Chbat.Prerequisites: APMA E2101, ELEN E3801, orcorequisite EEME E3601, or permission of instructor.Generalized dynamic system modeling andsimulation. Fluid, thermal, mechanical, diffusive,electrical, and hybrid systems are considered.Nonlinear and high order systems. System identificationproblem and Linear Least Squares method.State-space and noise representation. Kalmanfilter. Parameter estimation via prediction-errorand subspace approaches. Iterative and bootstrapmethods. Fit criteria. Wide applicability: medical,energy, others. MATLAB and Simulink environments.MECE E4501y Geometrical modeling3 pts. Lect: 3. Professor Rajan.Prerequisites: COMS W1005. Relationshipbetween 3D geometry and CAD/CAM; representationsof solids; geometry as the basis of analysis,design, and manufacturing; constructive solidgeometry and the CSG tree; octree representationand applications; surface representations andintersections; boundary representation and boundaryevaluation; applied computational geometry;analysis of geometrical algorithms and associateddata structures; applications of geometrical modelingin vision and robotics.MECE E4502x Computational geometry forCAD/CAM3 pts. Lect: 3. Professor Rajan.Prerequisites: COMS W1005 FORTRAN orPASCAL. Analysis of geometric problems andthe design of efficient methodologies to obtainsolutions to these problems. Algorithms to bestudied include geometric searching, convex hulls,triangulations, Voronoi diagrams, intersections,hidden surfaces. Emphasis will be on practicalaspects of these algorithms, and on applications ofthe solutions in computer-aided product design andmanufacturing.EEME E4601y Digital control systems3 pts. Lect: 3. Professor Longman.Prerequisites: EEME E3601 or ELEN E3201. Realtimecontrol using digital computers. Solving scalarand state-space difference equations. Discreteequivalents of continuous systems fed by holds.Z-transer functions. Creating closed-loop differenceequation models by Z-transform and state variableapproaches. The Nyquist frequency and samplerate selection. Classical and modern based digitalcontrol laws. Digital system identification.MECE E4602y Introduction to robotics3 pts. Lect: 3. Instructor to be announced.Overview of robot applications and capabilities.Linear algebra, kinematics, statics, and dynamicsof robot manipulators. Survey of sensor technology:force, proximity, vision, compliant manipulators.Motion planning and artificial intelligence; manipulatorprogramming requirements and languages.MECE E4604x Product design formanufacturability3 pts. Lect: 3. Professor Walker.Prerequisites: Manufacturing process, computergraphics, engineering design, mechanical design.General review of product development process;market analysis and product system design;principles of design for manufacturing; strategyfor material selection and manufacturing processchoice; component design for machining; casting;molding; sheet metal working and inspection;general assembly processes; product design formanual assembly; design for robotic and automaticassembly; case studies of product design andimprovement.MECE E4608y Manufacturing processes3 pts. Lect: 3. Professor Yao.Prerequisites: ENME E3113 or equivalent.Processes and materials of manufacture: metalcutting, forming, stamping, forging, welding, powdermetallurgy; classification and fabricating characteristicsof metals and composites; plastics, adhesives.MECE E4609y Computer-aided manufacturing3 pts. Lect: 3. Professor Walker.Prerequisites: Introductory course on manufacturingprocesses, and knowledge of computer aideddesign, and mechanical design or instructor’s permission.Computer-aided design, free-form surfacemodeling, tooling and fixturing, computer numericcontrol, rapid prototyping, process engineering,fixed and programmable automation, industrialrobotics.MECE E4610x Advanced manufacturingprocesses3 pts. Lect: 3. Professor Yao.Prerequisites: Introductory course on manufacturingprocesses, and heat transfer, knowledge ofengineering materials, or instructor’s permission.189SEAS 2010–2011

190Principles of nontraditional manufacturing, nontraditionaltransport and media. Emphasis on laserassisted materials processing, laser material interactionswith applications to laser material removal,forming, and surface modification. Introduction toelectrochemical machining, electrical dischargemachining and abrasive water jet machining.MEBM E4702x Advanced musculoskeletalbiomechanics3 pts. Lect: 3. Professor Guo.Advanced analysis and modeling of the musculoskeletalsystem. Topics include advanced conceptsof 3D segmental kinematics, musculoskeletaldynamics, experimental measurements of jointskinematics and anatomy, modeling of muscles andlocomotion, multibody joint modeling, introductionto musculoskeletal surgical simulations.MEBM E4703y Molecular mechanics inbiology3 pts. Lect: 3. Professor Liao.Prerequisites: ENME E3105,APMA E2101, orinstructor’s permission. Mechanical understandingof biological structures including proteins, DNAand RNA in cells and tissues. Force response ofprotenis and DNA, mechanics of membranes, biophysicsof molecular motors, mechanics of proteinproteininteractions. Introduction to modeling andsimulation techniques, and modern biopohysicaltechniques such as single molecule FRET, opticaltraps, AFM, and superresolution imaging, forunderstanding molecular mechanics and dynamics.MECE E4990x or y Special topics inmechanical engineering3 pts. Lect: 3. Instructor to be announced.Prerequisites: Permission of the instructor. Topicsand Instructors change from year to year. Foradvanced undergraduate students and graduatestudents in engineering, physical sciences, andother fields.MECE E4999x, y or s Curricular practicaltraining1 pt. Professor Yao.Prerequisites: Instructor’s written approval. Onlyfor ME graduate students who need relevant internor field-work experience as part of their programof study as determined by the instructor. Writtenapplication must be made prior to registrationoutlining proposed study program. Final reportsrequired. This course may not be taken for pass/fail credit or audited. International students mustalso consult with the International Students andScholars Office.MECE E6100x Advanced mechanics of fluids3 pts. Lect: 3. Professor Panides.Prerequisites: MATH E1210 and MECE E3100.Eulerian and Lagrangian descriptions of motion.Stress and strain rate tensors, vorticity, integraland differential equations of mass, momentum,and energy conservation. Potential flow.MECE E6102y Computational heat transferand fluid flow3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MECE E3100 and MECE E3311;COMS W1005 FORTRAN. Mathematical descriptionof pertinent physical phenomena. Basics offinite-difference methods of discretization, explicitand implicit schemes, grid sizes, stability, andconvergence. Solution of algebraic equations,relaxation. Heat conduction. Incompressiblefluid flow, stream function-vorticity formulation.Forced and natural convection. Use of primitivevariables, turbulence modeling, and coordinatetransformations.MECE E6104y Case studies in computationalfluid dynamics3 pts. Lect: 3. Professor Panides.Prerequisites: APAM E4200 and MECE E6100.Corequisites: APAM E4300 and MECE E4400Hands-on case studies in computational fluiddynamics, including steady and transient flows,heat and mass transfer, turbulence, compressibleflow and multiphase flow. Identifying assumptions,computational domain selection, modelcreation and setup, boundary conditions, choiceof convergence criteria, visualization and interpretationof computed results. Taught in theMechanical Engineering Computer Laboratory withComputational Fluid Dynamics software.MECE E6105y Transport phenomena in thepresence of interfaces3 pts. Lect: 3. Professor Attinger.Prerequisites: MECE E3301, Thermodynamicsand MECE E3311, Heat transfer; MECE E4100Mechanics of fluids, or equivalent or instructor’spermission; CHEE E4252, Introduction to Surfaceand Colloid Chemistry, or the equivalent, or theinstructor’s permission. Surface energy and capillaryphenomena. Wetting and spreading of liquids,wetting line pinning and hysteresis, dynamics ofwetting. Surfactants. Bubbles: nucleation, stability,dynamics, microstreaming. Jets and Drops: generation,dynamics, stability and impact with surfaces.Measurement of transport phenomena involvinginterfaces. Interfacial transport phenomenainvolvng thermal, chemical or electrical gradients.Applications in microfluidic systems.MECE E6200y Turbulence3 pts. Lect: 3. Not offered in 2010-2011.Prerequisites: MECE E6100. Introductory conceptsand statistical description. Kinematics of randomvelocity fields, dynamics of vorticity, and scalarquantities. Transport processes in a turbulentmedium. Turbulent shear flows: deterministic andrandom structures. Experimental techniques, predictionmethods, and simulation.MEBM E6310x-E6311y Mixture theories forbiological tissues, I and II3 pts. Lect: 3. Not offered in 2010-2011.Prerequisites: MECE E6422 and APMA E4200 orequivalent. Development of governing equationsfor mixtures with solid matrix, interstitial fluid,and ion constituents. Formulation of constitutivemodels for biological tissues. Linear and nonlinearmodels of fibrillar and viscoelastic porous matrices.Solutions to special problems, such as confinedand unconfined compression, permeation, indentationand contact, and swelling experiments.MECE E6313x Advanced heat transfer3 pts. Lect: 3. Professor Naraghi.Prerequisites: MECE E3311. Corequisites: MECEE6100. Application of analytical techniques to thesolution of multidimensional steady and transientproblems in heat conduction and convection.Lumped, integral, and differential formulations.Topics include use of sources and sinks, laminar/turbulent forced convection, and natural convectionin internal and external geometries.MECE E6400y Advanced machine dynamics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MECE E3401. Review of classicaldynamics, including Lagrange’s equations.Analysis of dynamic response of high-speedmachine elements and systems, including massspringsystems, cam-follower systems, and gearing;shock isolation; introduction to gyrodynamics.MECE E6422x–E6423y Introduction to thetheory of elasticity, I and II3 pts. Lect: 3. Professor Ateshian.Corequisites: APMA E4200. Analysis of stressand strain. Formulation of the problem of elasticequilibrium. Torsion and flexure of prismatic bars.Problems in stress concentration, rotating disks,shrink fits, and curved beams; pressure vessels,contact and impact of elastic bodies, thermalstresses, propagation of elastic waves.MECE E6424x Vibrations in machines, I3 pts. Lect: 3. Professor Stolfi.Prerequisites: MECE E3401. Review of vibrationanalysis of systems and mechanisms with onedegree of freedom. Natural frequencies. Forcedvibrations. Effects of dry and viscous friction.Energy methods of Rayleigh and Ritz. Suppressionand elimination of vibration. Vibration isolation.Measuring instruments. Critical speeds in machinery.Synchronous whirl. Half-frequency whirl. Influence ofbearing characteristics on critical speeds. Effect ofgyroscopic moments. Systems with multiple degreesof freedom. Dynamic vibration absorbers. Self-tuningabsorbers of pendulum and roller types. Lagrangianequations of motion as applied to vibrating systems.General equations for transverse critical speeds ofshafts. Surging of helical springs.EEME E6601x Introduction to control theory3 pts. Lect: 3. Professor Longman.Prerequisites: MATH E1210. A graduate-levelintroduction to classical and modern feedbackcontrol that does not presume an undergraduatebackground in control. Scalar and matrix differentialequation models and solutions in terms of statetransition matrices. Transfer functions and transferfunction matrices, block diagram manipulations,closed loop response. Proportional, rate, and integralcontrollers, and compensators. Design by rootlocus and frequency response. Controllability andobservability. Luenberger observers, pole placement,and linear-quadratic cost controllers.SEAS 2010–2011

EEME E6602y Modern control theory3 pts. Lect: 3. Not offered in 2010-2011.Prerequisites: EEME E6601 or EEME E4601 orELEN E6201, or instructor’s permission. Singularvalue decomposition. ARX model and statespace model system identification. Recursiveleast squares filters and Kalman filters. LQR,Hlinear robust control, predictive control, adaptivecontrol. Liapunov and Popov stability.Nonlinear adaptive control, nonlinear robustcontrol, sliding mode control.EEME E6610y Optimal control theory3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: EEME E6601 or EEME E4601 orinstructor’s permission. Covers topics in calculus ofvariations, Pontryagin maximum principle, quadraticcost optimal control, predictive control, dynamicprogramming for optimal control, Kalman filtering,numerical methods for solution. Some applicationsdiscussed include: minimum energy subwayoperation (our solution saved 11% in tests on theFlushing Line, and the method was adopted by thetransit authority, saving many millions of dollars peryear), minimum time robot optimal controlallowing one to run assembly lines faster forincreased productivity.MECE E6614y Advanced topics in roboticsand mechanism synthesis3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Prerequisite: APMA E2101,APMA E3101, MECE E4602 (or COMS W4733).Recommended: MECE E3401 or instructor’s permission.Kinematic modeling methods for serial,parallel, redundant, wire-actuated robots and multifingeredhands with discussion of open researchproblems. Introduction to screw theory and linegeometry tools for kinematics. Applications ofhomotropy continuation methods and symbolicnumericalmethods for direct kinematics of parallelrobots and synthesis of mechanisms. Course usestextbook materials as well as a collection of recentresearch papers.MECE E6620x or y Applied signal recognitionand classification3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MATH E1210, APMA E3101,knowledge of a programming language, orpermission of instructor. Applied recognition andclassification of signals using a selection of toolsborrowed from different disciplines. Applicationsinclude human biometrics, imaging, geophysics,machinery, electronics, networking, languages,communications, and finance. Practical algorithmsare covered in signal generation, modeling,feature extraction, metrics for comparison andclassification, parameter estimation, supervised,unsupervised and hierarchical clustering andlearning, optimization, scaling and alignment,signals as codes emitted from natural sources,information, and extremely large-scale searchtechniques.MECE E6700y Carbon nanotube science andtechnology3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: Knowledge of introductory solidstate physics (e.g., PHYS G4018, APPH E6081, orMSAE E3103) or instructor’s permission. Basic scienceof solid state systems. Crystal structure, electronicand phonon band structures of nanotubes.Synthesis of nanotubes and other nanomaterials.Experimental determination of nanotube structuresand techniques for nanoscale imaging. Theoryand measurement of mechanical, thermal, andelectronic properties of nanotubes and nanomaterials.Nanofabrication and nanoelectronic devices.Applications of nanotubes.MECE E6710x or y Nanofabrication laboratory3 pts. Lect: 3. Professor Hone.Prerequisites: ELEN E6945 or Instructor’s permission.Laboratory in techniques for fabrication atthe nanometer scale. Electron-beam lithography.Plasma etching and 3D nanofabrication. Thin filmdeposition. Self-assembly and “bottom up” nanofabrication.Fabrication of and testing of completenanodevices. A lab fee of $300 is required.MECE E6720x Nano/microscale thermaltransport process3 pts. Lect: 3. Professor Narayanaswamy.Nano- and microscale origins of thermaltransport phenomena by molecules, electrons,phonons, and photons. Quantum mechanicsand statistical physics. Density of states. Kinetictheory of gases. Boltzmann transport equation(BTE), classical and quantum size effects.Landauer formalism for transport via nanostructures.Macroscopic constitutive equationsfrom BTE. Application to electronics cooling,thermoelectric and thermophotovoltaic devices,and energy conversion.MECE E8020x-E8021y Master’s thesis1–3 pts. Members of the faculty.Interpretive research in graduate areas in mechanicalengineering and engineering science.MECE E8100y Advanced topics in fluidmechanics3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: MECE E6100. This course may betaken more than once, since its content has minimaloverlap between consecutive years. Selectedtopics from viscous flow, turbulence, compressibleflow, rarefied gas dynamics, computationalmethods, and dynamical systems theory, non-Newtonian fluids, etc.EEME E8601y Advanced topics in control theory3 pts. Lect: 3. Not offered in 2010–2011.Prerequisites: EEME E6601 and EEME E4601 orinstructor’s permission This course may be takenmore than once, since the content changes fromyear to year, electing different topics from controltheory such as learning and repetitive control,adaptive control, system identification, Kalmanfiltering, etc.MECE E8990x and y Special topics inmechanical engineering3 pts. Lect: 3. Instructor to be announced.Prerequisites: Instructor’s permission. This coursemay be taken for credit more than once. The instructorfrom the Mechanical Engineering Departmentand the topics covered in the course will vary fromyear to year. This course is intended for studentswith graduate standing in Mechanical Engineeringand other engineering and applied sciences.Topic for Spring 2011: Small-scalemechanical behavior3 pts. Lect: 3. Professor Kysar.Prerequisites: ENME E3105 or equivalent; APMAE4200 or equivalent. Introduction to the mechanicalbehavior of small scale components, structuresand devices. Review of variational calculus asused to derive governing equations of beam andplate theory. Deformation and vibration of beamsand plates. Stress, deformation, and substrate curvaturein thin films. Fracture, delamination, bulging,buckling and of thin films. Equilibrium and stabilityof surfaces. Small scale mechanical characterizationincluding: nanoindentation, thin film bulge test,and electron microscopy methods.MECE E9000x-E9001y and E9002s Graduateresearch and study1–3 pts. Members of the faculty.Theoretical or experimental study or research ingraduate areas in mechanical engineering andengineering science.MECE E9500x and y Graduate seminar0 pts. Pass/fail only. Professor Liao.All doctoral students are required to completesuccessfully four semesters of the mechanicalengineering seminar MECE E9500.MECE E9800x and y Doctoral researchinstruction3, 6, 9, or 12 pts. Members of the faculty. Acandidate for the Eng.Sc.D. degree in mechanicalengineering must register for 12 points of doctoralresearch instruction. Registration in MECE E9800may not be used to satisfy the minimum residencerequirement for the degree.MECE E9900x and y Doctoral dissertation0 pts. Members of the faculty.A candidate for the doctorate may be required toregister for this course every term after his/hercourse work has been completed and until the dissertationhas been accepted.191SEAS 2010–2011

192SEAS 2010–2011

Undergraduate Minors

194UNDERGRADUATE MINORSUndergraduate minors aredesigned to allow engineeringand applied science studentsto study, to a limited extent, a disciplineother than their major. Besidesengineering minors offered by SEASdepartments, new liberal arts minors areavailable.A minor requires at least 15 pointsof credit, and no more than one coursecan be taken outside of Columbiaor met through AP or IB credit. Thisincludes courses taken through studyabroad. In SEAS departments with morethan one major program, a minor in thesecond program may be permitted, ifapproved by the department.No substitutions or changes of anykind from the approved minors arepermitted (see lists below). No appealfor changes will be granted. Pleasenote that the same courses may notbe used to satisfy the requirementsof more than one minor. No coursestaken for pass/fail may be counted fora minor. Minimum GPA for the minor is2.0. Departments outside SEAS have noresponsibility for nonengineering minorsoffered by SEAS.For a student to receive credit fora course taken while studying abroad,the department offering the minor mustapprove the course in writing, ahead ofthe student’s study abroad.Students must expect a course loadthat is heavier than usual. In addition,unforeseen course scheduling changes,problems, and conflicts may occur. TheSchool cannot guarantee a satisfactorycompletion of the minor.MINOR IN APPLIEDMATHEMATICSProspective students should consult thefirst- and second-year requirements forapplied mathematics majors to ensurethat prerequisites for the applied mathematicsminor are satisfied in the firsttwo years.Course work counting toward theapplied mathematics minor may notinclude advanced placement credits.Any substitutions for the courses listedbelow require the approval of the appliedmathematics program adviser.1. APMA E3101: Linear algebra 3.0 pointsorMATH V2010: Linear algebra 3.0 points2. APMA E3102:Partial differential equationsorMATH V3028:Partial differential equations3.0 points3.0 points3– 5. Any three of the following courses:APMA E4300:Introduction to numerical methods 3.0 pointsAPMA E4204:APMA E4101:MATH V2500:SIEO W4105:STAT W4107: Statistical inference 3.0 pointsor any other course designated APMA, MATH,STAT, IEOR, or COMS that is approved by theapplied mathematics program adviser.MINOR IN APPLIED PHYSICSProspective students should consult thefirst- and second-year requirements forapplied physics majors to ensure thatprerequisites for the applied physicsminor are satisfied in the first two years.Course work counting toward theapplied physics minor may not includeadvanced placement credits.1. APPH E4901: Seminar: problems in appliedphysics1.0 point2. PHYS W3003: Mechanics 3.0 points3. APPH E3100: Introduction to quantummechanics3.0 points4. APPH E3300: Applied electromagnetism3.0 points5. MSAE E3111: Thermodynamics, kinetic theory,and statistical mechanics3.0 points6. Two of the following courses:APPH E4010: Introduction to nuclear science3.0 pointsAPPH E4100: Quantum physics of matter3.0 pointsAPPH E4110: Modern optics 3.0 pointsAPPH E4112: Laser physics 3.0 pointsAPPH E4300: Applied electrodynamics3.0 pointsAPPH E4301: Introduction to plasma physics3.0 pointsMINOR IN ARCHITECTURE1. Studio course (choose one from thefollowing):ARCH V1020: Introduction to architecturaldesign and visual culture3.0 pointsARCH V3101: Arch representation: abstraction4.0 pointsARCH V3103: Arch representation: perception4.0 points2–4. History/theory courses (see Note below)5. Elective course (must be either an approvedsecond design studio or an additional history/theorycourse)Note: A list of the approved history/theory courses is available at the departmentaloffice each semester.SEAS 2010–2011

195MINOR IN ART HISTORY1–7. Seven courses in art history, coveringfour of the following areas: (a) ancientMediterranean, (b) medieval Europe,(c) Renaissance and baroque, (d) 18th,19th, and 20th century, and (e) non-Western.MINOR IN BIOMEDICALENGINEERINGThe Biomedical Engineering programoffers a minor in one of three tracks: (I)cellular engineering, (II) biomechanics,and (III) biomedical imaging. Studentswho wish to get a minor in biomedicalengineering should take the core BMErequirements, as well as select coursesfrom one of the three tracks, describedbelow. Participation in the minor issubject to the approval of the major programadviser.Core BME Requirements1. BIOL C2005: Introduction to molecular andcellular biology4.0 points2. BMEN E4001: Quantitative physiology, I3.0 pointsorBMEN E4002: Quantitative physiology, II3.0 pointsI. CELL AND TISSUE ENGINEERING TRACK3. CHEN E3010: Chemical engineeringthermodynamics4.0 pointsorBMEN E4210: Thermodynamics of biologicalsystems4.0 points4. BMEN E4501: Tissue engineering, I 3.0 points5. BMEN E4502: Tissue engineering, II 3.0 points6. One of the following courses:BMEN E3320: Fluid biomechanics 3.0 pointsBMEN E4570: Science and engineering of bodyfluids, I3.0 pointsECBM E3060: Introduction to genomic information3.0 pointsCHEN E3110: Transport phenomena, I4.0 pointsCHEN E4700: Principles of genomictechnologies3.0 pointsMSAE E3103: Elements of materials science3.0 pointsII. BIOMECHANICS TRACK3. BMEN E4300: Solid biomechanics 3.0 points4. BMEN E3320: Fluid biomechanics 3.0 points5– 6. Two from the following course groups:ENME E3113: Mechanics of solids 3.0 pointsENME E3161: Fluid mechanics 4.0 pointsorMECE E3301: Thermodynamics 3.0 pointsorMSAE E3111: Thermodynamics, kinetic theory,and statistical mechanics3.0 pointsIII. BIOMEDICAL IMAGING TRACK3. BMEN E4894: Biomedical imaging 3.0 points4– 5. Two from the following courses:BMEN E4430: Principles of magnetic resonanceimaging3.0 pointsBMEN E4400: Wavelet applications in biomedicalimage and signal processing3.0 pointsBMEN E4898: Phototonics 3.0 pointsBMEN E4410: Ultrasound in diagnosticimaging3.0 pointsBMEN E4420: Biomedical signal processing andsignal modeling3.0 points6. One from the following courses:ELEN E3801: Signals and systems 3.0 pointsELEN E4810: Digital signal processing3.0 pointsELEN E4830: Digital image processing3.0 pointsMINOR IN CHEMICALENGINEERINGOf the six courses required, at leastthree must have the CHEN, CHEE, orCHAP designator:1. CHEN E3100: Material and energy balances4.0 points2. CHEN E3010: Principles of chemicalengineering thermodynamics 4.0 pointsorMSAE E3111: Thermodynamics, kinetic theory,and statistical mechanics3.0 pointorMECE E3301: Thermodynamics 3.0 points3. CHEN E3110: Transport phenomena, I4.0 pointsor one of the following:EAEE E4900: Applied transport and chemicalrate phenomena3.0 pointsMECE E3100: Introduction to mechanics offluids3.0 pointsENME E3161: Fluid mechanics 4.0 points4. CHEN E4230: Reactor design and control4.0 points5– 6. Two courses from the following:Any 3000-level or higher BMCH, CHEN, CHAP,or CHEE courseAPMA E3101: Applied mathematics, I3.0 pointsAPMA E3102: Applied mathematics, II3.0 pointsBMEN E3320: Fluid biomechanics3.0 pointsBMEN E4001: Quantitative physiology, I3.0 pointsBMEN E4002: Quantitative physiology,II3.0 pointsELEN E3201: Circuit analysis 3.5 pointsELEN E3301: Electronic circuits 3.0 pointsSIEO W3600: Introduction to probabilityand statistics4.0 pointsIEOR W4105: Probability 3.0 pointsIEOR W4106: Stochastic models 3.0 pointsSEAS 2010–2011

196MSAE E3103: Elements of materials science3.0 pointsMSAE E3142: Processing of ceramics andpolymers3.0 pointsMINOR IN CIVIL ENGINEERING1. CIEN E3121: Structural analysis 3.0 pointsorENME E3161: Fluid mechanics 4.0 pointsorMECE E3100: Introduction to mechanics offluids3.0 points2. ENME E3105: Mechanics 4.0 points3. ENME E3113: Mechanics of solids 3.0 points4– 6. Electives (any three)CIEN E1201: Design of buildings, bridges, andspacecraft3.0 pointsENME E3161: Fluid mechanics 4.0 pointsENME E3114: Experimental mechanics ofmaterials4.0 pointsMECE E3414: Advanced strength of materials3.0 pointsCIEN E4332: Finite element analysis, I3.0 pointsCIEN E3125: Structural design 3.0 pointsCIEN E4241: Geotechnical engineeringfundamentals3.0 pointsCIEE E3250: Hydrosystems engineering3.0 pointsCIEE E4163: Environmental engineering:wastewater3.0 pointsCIEN E3129: Project management forconstruction3.0 pointsCIEN E4131: Principles of constructiontechniques3.0 pointsNote: At least three of the courses mustbe courses that are not required in thestudent’s major.MINOR IN COMPUTER SCIENCEStudents who pass the ComputerScience Advanced Placement Exam,either A or AB, with a 4 or 5 will receive3 points and exemption from COMSW1004. An additional elective is tobe recommended but not required.Participation in the minor is subject to theapproval of the major program adviser.For further information, please see theQuickGuide at www.cs.columbia.edu/education/undergrad/seasguide.1. COMS W1004: Introduction to computer scienceand programming in Java 3.0 points2. COMS W1007: Object-oriented programmingand design3.0 pointsorCOMS W1009: Introduction to computer science(honors)3.0 points3. COMS W3133: Data structures in C 3.0 pointsorCOMS W3134: Data structures in Java3.0 pointorCOMS W3137: Data structures and algorithms4.0 pointsorCOMS W3139: Data structures and algorithms(honors)4.0 points4. COMS W3157: Advanced programming4.0 points5. COMS W3203: Discrete mathematics 3.0 points6. COMS W3261: Computer science theory3.0 points7. CSEE W3827:Fundamentals of computer systems 3.0 pointsora 4000-level COMS technical electiveMINOR IN DANCEThe SEAS dance minor consists of five3-point courses. Please note that noperformance/choreography coursesbelow count toward the nontechrequirement for SEAS students.1– 2. Two from the following history/criticismcourses:DNCE BC 2565: World dance historyDNCE BC 2570: Dance in New York CityDNCE BC 2575: Choreography for theAmerican musicalDNCE BC 3000: From the page to thedance stageDNCE BC 3001: Western theatrical dance fromthe Renaissance to the 1960’sDNCE BC 3200: Dance in filmDNCE BC 3567: Dance in AsiaDNCE BC 3570: Latin American and CaribbeandanceDNCE BC 3574: Seminar on contemporarychoreographers and their worksDNCE BC 3576: Dance criticismDNCE BC 3577: Performing the politicalDNCE BC 3578: Traditions of African-Americandance3– 4. Two from the following performance/choreography coursesDNCE BC 2563: Dance composition formDNCE BC 2563: Dance composition: form,dance/theaterDNCE BC 2564: Dance composition: contentDNCE BC 2567: Music for danceDNCE BC 2580: Tap as an American art formDNCE BC 3565: Group forms: advanced dancecompositionDNCE BC 3590: Rehearsal and performancein dance5. One elective.MINOR IN EARTH ANDENVIRONMENTALENGINEERING1– 3. Three courses from the following:EAEE E3101: Earth resource production systems3.0 pointsEAEE E3103: Energy, minerals and materialssystems3.0 pointsEAEE E3255: Environmental control and pollutionreduction systems3.0 pointsEAEE E4001: Industrial ecology of earthresources3.0 pointsEAEE E4003: Introduction to aquatic chemistry3.0 pointsEAEE E4004: Physical processing and recoveryof solids3.0 pointsEAEE E4006: Field methods for environmentalengineering3.0 pointsEAEE E4009: GIS for resource, environmentand infrastructure management 3.0 pointsEAEE E4150: Air pollution prevention andcontrol3.0 pointsEAEE E4160: Solids and hazardous wastemanagement3.0 pointsEAEE E4200: Production of inorganicmaterials3.0 pointsEAEE E4257: Environmental data analysis andmodeling3.0 pointsEAEE E4361: Economics of Earth resourceindustries3.0 pointsEAEE E4560: Particle technology 3.0 points4– 6. Three courses from the following:CHEE E4252: Introduction to surface andcolloid chemistry3.0 pointsCHEN E3010: Principles of chemical engineeringthermodynamics3.0 pointsCHEN E3110: Transport phenomena, I4.0 pointsCHEN E4410: Environmental controltechnology3.0 pointsCIEE E3250: Hydrosystems engineering3.0 pointsCIEE E4163: Environmental engineering:wastewater3.0 pointsCIEE E4252: Environmental engineering3.0 pointsCIEE E4257: Groundwater contaminant transportand remediation3.0 pointsCIEE E4260: Urban ecology studios3.0 pointsCIEN E3141: Soil mechanics 3.0 pointsCIEN E4250: Waste containment design andpractice3.0 pointsEAEE E4190: Photovoltaic systemsengineering3.0 pointsECIA W4100: Management and development ofwater systems3.0 pointsMECE E4211: Energy: sources andconversion3.0 pointsSIEO W3600: Introduction to probability andstatistics4.0 pointsSEAS 2010–2011

MINOR IN EAST ASIAN STUDIES1–5. Any two of the survey courses onChinese, Japanese, Korean, or Tibetancivilization (ASCE V2359, V2361, V2363,V2365), plus three elective courses dealingwith East Asia. The elective coursesmay be taken in departments outsideof East Asian Languages and Cultures.The minor does not include a languagerequirement. However, one semester ofan East Asian language class may beused to fulfill one of the three electives,as long as at least two semesters of thatlanguage have been taken. Placementexams may not be used in place of thesecourses.MINOR IN ECONOMICS1. ECON W1105: Principles of economics2. ECON W3211: Intermediate microeconomicsECON W4490: Economics of the InternetECON W4500: International tradeECON W4505: International monetary theoryand policyECON W4615: Law and economicsECON W4625: Economics of the environmentECON W4750: Globalization and its risksNote: Electives may be taken only afterthe completion of both ECON W3211and W3213, with the exception ofECON W2257, which may be takenafter completion of ECON W1105.Some of the elective courses listedabove have additional prerequisites.Courses may be taken only after thecompletion of all prerequisites. Pleasesee the Columbia College bulletin forcourse descriptions and complete listsof prerequisites.MINOR IN ELECTRICALENGINEERING1. ELEN E1201: Introduction to electricalengineering3.5 points(May be replaced by a similar course or roughlyequivalent experience)2. ELEN E3201: Circuit analysis 3.5 points3. CSEE W3827: Fundamentals of computer systems3.0 points4. ELEN E3081 and ELEN E3082:Electrical engineering labs2.0 points5. ELEN E3801: Signals and systems 3.5 points6. ELEN E3106:Solid-state devices and materials 3.5 points orELEN E3401: Electromagnetics 4.0 pointsNote: Not available to computer engineeringmajors.1973. ECON W3213: Intermediate macroeconomics4. ECON W3412: Introduction to econometricsNote: W1105 is a prerequisite forW3211, W3213, and W3412. Studentsmust have completed Calculus I beforetaking W3213, Calculus III before takingW3211, and one of the introductorystatistics courses (see list) before takingW3412.5– 6. Two electives from the following:ECON W2257: Global economyECON W4280: Corporate financeECON V3025: Financial economicsECON V3265: Economics of money andbankingECON W4020: Economics of uncertainty andinformationECON W4080: Globalization, incomes andinequalityECON W4211: Advanced microeconomicsECON W4213: Advanced macroeconomicsECON W4228: Urban economicsECON G4235: Historical foundations of moderneconomicsECON W4251: Industrial organizationECON G4301: Economic growth anddevelopmentECON W4321: Economic developmentECON W4329: Economics of sustainabledevelopmentECON W4345: World economic problemsECON W4370: Political economyECON W4400: Labor economicsECON W4412: Advanced econometricsECON W4415: Game theoryECON W4438: Economics of race in the UnitedStatesECON W4457: Industrial organization of art,entertainment and communicationsECON W4465: Public economicsECON W4480: Gender and applied economics7. One from the following statistics courses(or sequence of courses):STAT W1211: Introduction to statisticsSIEO W3600: Introduction to probability andstatisticsIEOR W3658: ProbabilityandSTAT W3659 or W4107: Statistical inferenceSIEO W4150: Introduction to probability andstatisticsNotes:The statistics course must be finishedbefore taking ECON W3412, and itis recommended that students takeECON W3412 in the semester followingthe statistics course.economics minor nay count towardsfulfilling the School’s nontechnicalrequirements. However, other courses,such as ECON W3412: Introductionto econometrics, may not be appliedtoward satisfaction of the nontechnicalcourse requirements. To determinewhich economic class can counttowards the non-tech elective requirement,please consult the non-techelective section of this bulletin for furtherdetails.and an exemption for ECON W1105may use the credit toward the minor.not be applied to fulfill the requirementsof the economics minor.MINOR IN ENGINEERINGMECHANICS1. ENME E3105: Mechanics 4.0 points2. ENME E3113: Mechanics of solids 3.0 points3. ENME E3161: Fluid mechanics 4.0 pointsorMECE E3100: Mechanics of fluids 3.0 points4– 6. Electives (any two):ENME E3106: Dynamics and vibrations3.0 pointsENME E3114: Experimental mechanicsof materials4.0 pointsorMECE E3414: Advanced strengthof materials3.0 pointsCIEN E3121: Structural analysis 3.0 pointsENME E4202: Advanced mechanics 3.0 pointsENME E4113: Advanced mechanics of solids3.0 pointsENME E4114: Mechanics of fractureand fatigue3.0 pointsENME E4214: Theory of plates and shells3.0 pointsENME E4215: Theory of vibrations 3.0 pointsMECE E3301: Thermodynamics 3.0 pointsNote: At least three of the courses mustbe courses that are not required in thestudent’s major.MINOR IN ENGLISH ANDCOMPARATIVE LITERATURE1– 5. Any five courses in the EnglishDepartment with no distributionrequirement. No speech courses, only onewriting course as above and excludingENGL C1010, may be taken; total 15 points.SEAS 2010–2011

198MINOR IN ENTREPRENEURSHIPAND INNOVATIONMinimum: 15 points1– 2. Required courses:ENGI E2261: Introduction to accounting andfinance3.0 pointsandIEOR E4998: Managing technologicalinnovation and entrepreneurship 3.0 points3– 5. Electives (three additional courses fromthe list below):BMEN E3998: Projects in biomedicalengineering3.0 pointsBUSI W3021: Marketing3.0 pointsCHEN E4020: Protection of industrial andbusiness property3.0 pointsCIEN E4136: Entrepreneurship in civilengineering and construction 3.0 pointsCOMS W4444: Programming and problemsolving3.0 pointsECIE E4280: Corporate finance 3.0 pointsIEOR E4003: Industrial economics 3.0 pointsIEOR W4308: Industrial budgeting and financecontrol3.0 pointsIEOR E4403: Advanced engineering and corporateeconomics3.0 pointsIEOR E4510: Project management 3.0 pointsIEOR E4550: Entrepreneurial businesscreation for engineers3.0 pointsIEOR E4705: Studies in operations research3.0 pointsISME E4310: The manufacturing enterprise3.0 pointsSCNC W3010: Science, technology,and society3.0 pointsURBS V3310: Science and technology in urbanenvironments3.0 pointsMINOR IN FRENCH1– 2. FREN W3333: Major literary works to 18003.0 pointsandFREN W3334: Major literary workssince 18003.0 points3– 5. Three additional courses in Frenchbeyond satisfaction of the languagerequirement.MINOR IN FRENCH ANDFRANCOPHONE STUDIESRequired: 15 points beyond secondyearFrench.1– 2. FREN W3420: Introduction to French andfrancophone studies, I3.0 pointsandFREN W3421: Introduction to French and francophonestudies, II3.0 points3– 5. Three additional courses in Frenchbeyond satisfaction of the languagerequirement.MINOR IN GERMANRequired: 15 points beyond secondyearGerman.1. GERM V3001 or V3002: Advanced German, Ior II3.0 points2. GERM W3333: Introduction to Germanliterature3.0 points3. One of the period survey courses inGerman literature and culture, GERMW3442, W3443, W3444, W3445.4– 5. Two courses taken from any 3000/4000level German or CompLit-German coursestaught in German or English.MINOR IN GREEK OR LATIN1–4 . A minimum of 13 points in the chosenlanguage at the 1200-level or higher.5. 3 points in ancient history of theappropriate civilization.MINOR IN HISPANIC STUDIES1. SPAN W3300: Advanced language throughcontent3.0 points2. SPAN W3330: Introduction to the study ofHispanic cultures3.0 points3. SPAN W3349: Hispanic cultures, I: IslamicSpain through the colonial period 3.0 points4. SPAN W3350: Hispanic cultures, II:Enlightenment to the present3.0 points5. One additional 3000-level elective coursein the Department of Latin American andIberian CulturesNote: Please see the director of undergraduatestudies in the Department ofLatin American and Iberian Cultures formore information and to declare theminor.MINOR IN HISTORY1– 5. Minimum 15 points in the HistoryDepartment with no distribution or seminarrequirements. Transfer or study-abroadcredits may not be applied.MINOR IN INDUSTRIALENGINEERING1. SIEO W3600: Introduction to probability andstatistics4.0 points2. IEOR E3608: Introduction to mathematical programming4.0 points3. IEOR E3402: Production-inventory planning andcontrol3.0 points4. IEOR E4003: Industrial economics 3.0 points5– 6. Electives: Two IEOR courses of interestand approved by a faculty adviser.Note: In addition to the requiredcourses, students majoring in operationsresearch or engineering and managementsystems minoring in industrialengineering must take three industrialengineering courses that are not used tosatisfy the requirements of their major.MINOR IN MATERIALS SCIENCEAND ENGINEERING1. MSAE E3103: Elements of materials science3.0 points2– 3. Two from the following courses:MSAE E3111: Thermodynamics, kinetic theory,and statistical mechanics3.0 pointsMSAE E3141: Processing of metals and semiconductors3.0 pointsMSAE E3142: Processing of ceramics andpolymers3.0 pointsMSAE E4090: Nanotechnology 3.0 pointsMSAE E4101: Structural analysis of materials3.0 pointsMSAE E4206: Electronic and magneticproperties of solids3.0 pointsMSAE E4215: Mechanical behavior ofmaterials3.0 pointsMSAE E4250: Ceramics and composites3.0 points4– 6. Three from the following courses(other materials-related courses may beacceptable):APPH E4100: Quantum physics of matter3.0 pointsCHEE E4050: Industrial and environmentalelectrochemistry3.0 pointsCHEE E4252: Introduction to surface and colloidchemistry3.0 pointsCHEE E4530: Corrosion of metals 3.0 pointsCHEE E4620: Introduction to polymer science3.0 pointsCHEN E4630: Polymer laboratory 3.0 pointsCHEM C3443-C3444: Organic chemistry3.5 pointsELEN E4411: Fundamentals of photonics3.0 pointsELEN E4301: Introduction to semiconductordevices3.0 pointsELEN E4944: Principles of devicemicrofabrication3.0 pointsENME E4113: Advanced mechanics of solids3.0 pointsENME E4114: Mechanics of fracture and fatigue3.0 pointsMECE E4608: Manufacturing processes3.0 pointsMECE E4701: Introductory biomechanics3.0 pointsSEAS 2010–2011

MINOR IN MECHANICALENGINEERING1– 4. Any four courses from the following(equivalent substitution courses requirethe approval of the mechanical engineeringprogram adviser):MECE E3100:Introduction to mechanics of fluids 3.0 pointsor one of the following three:ENME E3161: Fluid mechanics 4.0 pointsCHEN E3110: Transport phenomena, I4.0 pointsEAEE E4900: Applied transport andchemical rate phenomena 3.0 pointsENME E3105: Mechanics 4.0 pointsMECE E3301: Thermodynamics 3.0 pointsor one of the following two:CHEN E3010: Principles of chemicalengineering thermodynamics 4.0 pointsMSAE E3111: Thermodynamics, kinetictheory, and statistical mechanics 3.0 pointsENME E3113: Mechanics of solids 3.0 pointsMECE E3408: Computer graphics and design3.0 pointsMECE E3311: Heat transfer 3.0 pointsMECE E4608: Manufacturing processes3.0 pointsMECE E3409: Computer-aided design3.0 pointsEEME E3601: Classical control systems3.0 points5– 6. Electives: Two additional mechanical engineeringcourses from either the above list orthe following (not all courses in this list aregiven every year):MECE E3401: Mechanics of machines3.0 pointsMECE E4058: Mechatronics and embeddedmicrocomputer control3.0 pointsMECE E4100: Mechanics of fluids 3.0 pointsMECE E4211: Energy: sources and conversion3.0 pointsMECE E4212: Microelectromechanical systems3.0 pointsMECE E4302: Advanced thermodynamics3.0 pointsMECE E4404: Lubrication theory and design3.0 pointsMECE E4501: Geometrical modeling 3.0 pointsMECE E4502: Computational geometry forCAD/CAM3.0 pointsEEME E4601: Digital control systems3.0 pointsMECE E4602: Introduction to robotics3.0 pointsMECE E4604: Product design formanufacturability3.0 pointsMECE E4609: Computer-aided manufacturing3.0 pointsMECE E4610: Advancedmanufacturing processes3.0 pointsMINOR IN MIDDLE EASTERN,SOUTH ASIAN, AND AFRICANSTUDIES1– 5. Five courses, to be chosen with theapproval of the MESAAS Director ofUndergraduate Studies; no elementary orintermediate language courses may becounted.MINOR IN MUSIC1. MUSI V2318-V2319: Diatonic harmony andcounterpoint, I and II6.0 points2. MUSI V1312-V1313: Introductory ear training1.0 point3. MUSI V2314: Ear training, I 1.0 point4. One course from the following:MUSI V3128: History of Western music I:Middle Ages to baroque3.0 pointsMUSI V3129: History of Western music II:classical to 20th century3.0 points5– 6. Any two electives at the 3000- or 4000-level. See also the SEAS-approved nontechnicalelectives in music (page 12).Notes:of MUSI V1002: Fundamentals ofWestern music (3.0 points).to fulfill the nontechnical electiverequirement for graduation.agedto take HUMA W1123:Masterpieces of Western music(3.0 points) from the list of nontechnicalelectives.MINOR INOPERATIONS RESEARCH1. IEOR E3106: Stochastic models 3.0 points2. SIEO W3600: Introduction to probability andstatistics4.0 points3. IEOR E3608: Introduction to mathematical programming4.0 points4. IEOR E4404: Simulation 3.0 points5– 6. Electives: Two IEOR courses of interestand approved by a faculty adviser. IEORE3402: Production-inventory planning andcontrol 3.0 points is strongly recommended.Note: In addition to the required courses,students majoring in industrial engineeringor engineering management systemsmust take three operations researchcourses that are not used to satisfy therequirements of their major.MINOR IN PHILOSOPHY1– 5. Any five courses in the PhilosophyDepartment with no distributionrequirement; total 15 points. See alsothe list of exceptions under ElectiveNontechnical CoursesNote: Please be aware that some philosophycourses may not count as nontechnicalelectives.MINOR IN POLITICAL SCIENCE1– 2. Two from the following courses:W1201: Introduction to American governmentand politics3.0 pointsW1501: Comparative politics: an introduction3.0 pointsW1601: Introduction to international politics3.0 points3– 5. Any three courses in the Political ScienceDepartment with no distribution requirement;total 9 points.MINOR IN PSYCHOLOGYFive courses required, including PSYCW1001 and courses in at least twoof the three groups listed below. (Forexample, you could select two coursesfrom Group I and two from Group IIIalong with the required W1001.) Total15 points (minimum).1. PSYC W1001: The science of psychology2– 5. Any four courses from, at a minimum, twoof the three groups below:I. PERCEPTION AND COGNITIONCourses numbered in the 2200s, 3200s,or 4200s. Also PSYC W1420, W1480, orW1490.II. PSYCHOBIOLOGY AND NEUROSCIENCEPSYC W1010:Mind, brain, and behavior 3.0 pointsCourses numbered in the 2400s, 3400s,or 4400s. Also PSYC W1440.III. SOCIAL, PERSONALITY, ANDABNORMALCourses numbered in the 2600s, 3600s,or 4600s. Also PSYC W1450 or W1455.MINOR IN RELIGION1– 5. Five courses (total 15 points), one ofwhich must be at the 2000 level.199SEAS 2010–2011

200MINOR IN SOCIOLOGY1. SOCI W1000: The social world 3.0 points2. SOCI W2200: Evaluation of evidence 3.0 points3. SOCI W3000: Social theory 3.0 points4– 5. Any two 2000-, 3000-, or 4000-level coursesoffered by the Department of Sociology;total 6 points.MINOR IN STATISTICS1. STAT W1211: Introduction to statistics (withcalculus)3.0 points2. STAT W2024: Applied linear regressionanalysis3.0 points3. STAT W2025: Applied statistical methods3.0 points4. STAT W2026: Statistical applications andcase studies3.0 points5. STAT W3026: Applied data mining 3.0 points6. EitherSTAT W3997: , orany Statistics department offering numbered4201 or above.Notes:STAT W1001, W1111, W3105 andW3107, or W4150 may be substitutedfor W1211.numbered 4201 or above may besubstituted for STAT W2024, W2025,W2026, or W3026. The minor isdesigned for students seeking practicaltraining in applied statistics;students seeking a foundation foradvanced work in probability andstatistics should consider substitutingSTAT W3105 (Introductionto Probability Models), W3107(Introduction to Statistical Inference),W3315 (Linear Regression Models),and W4606 (Elementary StochasticProcesses).MINOR IN SUSTAINABLEENGINEERINGTotal of six courses from the followinglists required with no substitutionsallowed.1– 4. Four courses from the following:EAEE E1101: Better planet by designEAEE E2002: Alternative energy sourcesCIEE/EAEE 3260: Engineering for developingcommunities,EAEE E3901: Environmental microbiologyEAEE E4001: Industrial ecology: EarthresourcesEAEE W4100: Management and developmentof water systemsAPPH E4130: Physics of solar energyEAEE E4190: Photovoltaic systems engineeringand sustainabilityMECE E4211: Energy sources and conservationenergyCIEE E4260: Urban ecology studioMECE E4312: Design of thermal systemsMECE E4314: Dynamics of green buildingsEESC W4404: Regional dynamics, climate, andclimate impacts5. One course from the following:ECON W2257: The global economyPLAN 4151: Foundations of urban economicanalysisPLAN 4304: Introduction to housingECON 4321: Economic developmentPLAN 4501: Local economic developmentplanningECON G4527: Economic organization anddevelopment of ChinaPLAN 4540: Interdisciplinary planning for healthPLAN 4579: Environmental planningPLAN 4609: Introduction to international planningECON U4737: Economics of the environment6. One course from the following:SOCI V2230: Food and the social orderSCNC W3010: Science, technology, and societySOCI W3235: Social movementsANTH V3950: Anthropology of consumptionSOCI W3960: Law, science, and societyINAF U4763: Policy analysis of development(seniors only)SEAS 2010–2011

Interdisciplinary Courses andCourses in OtherDivisions of the University

202INTERDISCIPLINARY ENGINEERING COURSESOf the following courses, somemay be requirements fordegree programs, and othersmay be taken as electives. See yourdepartmental program of study or consultwith an adviser for more information.EEHS E3900y History of telecommunications:from the telegraph to the internet3 pts. Lect: 3.Historical development of telecommunications fromthe telegraphy of the mid-1800s to the Internetat present. Included are the technologies oftelephony, radio, and computer communications.The coverage includes both the technologies themselvesand the historical events that shaped, andin turn were shaped by, the technologies. The historicaldevelopment, both the general context andthe particular events concerning communications,is presented chronologically. The social needs thatelicited new technologies and the consequencesof their adoption are examined. Throughout thecourse, relevant scientific and engineering principlesare explained as needed. These include,among others, the concept and effective use ofspectrum, multiplexing to improve capacity, digitalcoding, and networking principles. There are noprerequisites, and no prior scientific or engineeringknowledge is required. SEAS students may notcount this course as a technical elective.ENGI E1102x and y Design fundamentalsusing advanced computer technologies4 pts. Lect: 4. Professor McGourty.Core requirement for all entering SEAS students.Students learn the basics of engineering designfrom problem definition to detailed conceptualdesign. Computer technologies such as advancedthree-dimensional graphical and computationalapplications are applied in the service of authenticcommunity-based design projects, using the stateof-the-artdesign facility, the Botwinick MultimediaLearning Laboratory. Aligned with the technicalcomponents of the design, students develop collaboration,communication, problem solving, andproject management skills, as well as a life-longorientation of social responsibility and communityservice. Lab fee: $325.ENGI E2261x Introduction to accountingand finance3 pts. Lect: 3. Professor Webster.Prerequisite: ECON W1105. The concepts andmethods underlying the financial statements ofbusiness corporations. Attention to problemsof asset valuation, income determination, cashflows, and cost and profit behavior in response tochanges in the level of business activity. Analysisof selected corporate financial statements, capitalstructure, and leverage. Strategies and analyticalmethods for the evaluation of capital projects.ENGI/CHEN E4020x Safeguarding intellectualand business property3 pts. Lect: 3. Professor Pearlman.Designed for both University engineering studentsand engineers in industry to provide a broad backgroundin those aspects of the law that are mostfrequently encountered in a professional engineeringcareer. Topics include patents, protection ofknow-how, contracts, employer-employee rights,confidential relationships, unfair competition, trademarks,and the like. Principles of law are illustratedby case studies.IEOR E4998x and y Managing technologicalinnovation and entrepreneurship3 pts. Lect: 3. Professor McGourty.This course will focus on the management andconsequences of technology-based innovation.The course explores how new industries are created,how existing industries can be transformedby new technologies, the linkages between technologicaldevelopment and the creation of wealth andthe management challenges of pursuing strategicinnovation.SCNC W3010x and y Science, technology andsociety3 pts. Lect: 3. Professor McGourty.Prerequisite: Students must have declared theirconcentration/major. By investigating the scientificand technical evolution and subsequent diffusion ofcontemporary technological innovations, studentslearn how science and technology fit into thebigger picture; i.e., how technologies technicallydevelop from concept to diffusion into society, howthey work, and how they are bidirectionally relatedto social forces, cultural values, economic trends,environmental factors, and political influences. Anessential part of the course work is participation ina community-based learning project, working withlocal not-for-profit organizations.URBS V3310x Science and technology inurban environments3 pts. Lect: 3. Professor Cross.Prerequisite: Students must have declared theirconcentration/major. The course examines the roleof science and technology in urban settings, usingexamples from modern cities. It explores how technologyshapes towns and cities, and how urbanenvironments, including politics, economics, culture,and the natural environment, have influencedthe development, acceptance, and application oftechnology. An essential part of the course work isparticipation in a community-based learning project,working with local not-for-profit organizations.SEAS 2010–2011

COURSES IN OTHER DIVISIONS OF THE UNIVERSITY203This listing of courses (at left) hasbeen selected with specific engineeringprogram requirements inmind. For information on these coursesand additional courses offered by thesedepartments, please consult the bulletinsof Columbia College, the Schoolof Continuing Education, the Schoolof General Studies, and the GraduateSchool of Arts and Sciences.BIOLOGICAL SCIENCESBIOL C2005 Introductory biology I:biochemistry, genetics and molecular biology4 pts. Professors Chasin and Mowshowitz.Prerequisite: one year of college chemistry, or astrong high school chemistry background. Lectureand recitation. Recommended as the introductorybiology course for biology and related majors, andfor premedical students. Fundamental principlesof biochemistry, molecular biology, and genetics.Web site: www.columbia.edu/cu/biology/courses/c2005/BIOL C2006 Introductory biology II: cellbiology, development and physiology4 pts. Professor Mowshowitz.Prerequisites: EEEB W2001 or BIOL C2005, orthe instructor’s permission. Lecture and recitation.Recommended second term of biology for majorsin biology and related majors, and for premedicalstudents. Cellular biology and development;physiology of cells and organisms. Web site: www.columbia.edu/cu/biology/courses/c2006/BIOL W2501x or y Contemporary biologylaboratory3 pts. Lab: 3. Professor Hazen.Corequisites: strongly recommended prerequisiteor required corequisite: BIOL C2005 or F2401.Enrollment limited to 24 students per section.Attendance at the first class is mandatory. Fee$150. Emphasis on experimental techniques anddata analysis in a variety of biological disciplines.BIOC C3501 Biochemistry: structure andmetabolism4 pts. Professors Stockwell and Tong.Prerequisites: BIOL W2001 or C2005 and oneyear of organic chemistry. Lecture and recitation.Students wishing to cover the full rangeof modern biochemistry should take both BIOCC3501 and C3512. C3501 covers subject mattersin modern biochemistry, including chemicalbiology and structural biology, discussing thestructure and function of both proteins and smallmolecules in biological systems. Proteins are theprimary class of biological macromolecules andserve to carry out most cellular functions. Smallorganic molecules function in energy productionand creating building blocks for the componentsof cells and can also be used to perturb thefunctions of proteins directly. The first half of thecourse covers protein structure, enzyme kineticsand enzyme mechanism. The second half of thecourse explores how small molecules are usedendogenously by living systems in metabolic andcatabolic pathways; this part of the course focuseson mechanistic organic chemistry involved inmetabolic pathways.BUSINESSBUSI W3021x or y Marketing management3 pts. Lect: 3. Professors Lee and Netzer.Designed to provide students with an understandingof the fundamental marketing conceptsand their application by business andnon-business organizations. The goal is toexpose students to these concepts as theyare used in a wide variety of settings, includingconsumer goods firms, manufacturingand service industries, and small and largebusinesses. The course gives an overviewof marketing strategy issues, elements of amarket (company, customers, and competition),as well as the fundamental elements ofthe marketing mix (product, price, placement/distribution, and promotion).CHEMISTRYCourses of InstructionPre-engineering students should referto the First Year–Sophomore Programto determine the chemistry requirementsfor admission to particularJunior-Senior Programs. Special attentionshould be given to the requirementsfor admission to chemicalengineering, biomedical engineering,materials science and metallurgicalengineering, and other related fields.Laboratory FeeThe laboratory fee covers the cost ofnonreturnable items, chemicals, andreasonable breakage. In addition, studentsmay be charged for lab handoutsand excessive breakage, for cleaning ofequipment returned dirty, and for checkingout late.CHEM C1403x-C1404y General chemistry3.5 pts. Members of the faculty.Prerequisites: for C1403: concurrent registration inMATH V1101; for C1404: CHEM C1403 or W1403.Only students with scheduling conflicts need reportto the Chemistry Department (340 Havemeyer) duringregistration. Preparation equivalent to one yearof high school chemistry is assumed and concurrentregistration in Calculus I. Students lacking suchpreparation should plan independent study of chemistryover the summer or take CHEM F0001 beforetaking C1403. Topics include stoichiometry, states ofmatter, chemical equilibria, acids and bases, chemicalthermodynamics, nuclear properties, electronicstructures of atoms, periodic properties, chemicalbonding, molecular geometry, introduction to organicand biological chemistry, solid state and materialsscience, polymer science and macromolecularstructures, chemical kinetics, coordination chemistry,and electrochemistry. Although C1403 and C1404are separate courses, students are expected to takeboth terms sequentially. The order of presentation oftopics may differ from the order presented here, andfrom year to year. Recitation section required.SEAS 2010–2011

204CHEM C1500x or y General chemistrylaboratory3 pts. Lab: 3. Professors Hansen and Ulichny.Corequisites: CHEM C1403 or W1403. Fee: $140.An introduction to basic techniques of modernexperimental chemistry, including quantitative proceduresand chemical analysis.CHEM C1604x Second semester generalchemistry3.5 pts. Professor Flynn.Prerequisites: A grade of “B” or better in CHEMC1403 or W1403 or acceptable performance onthe Department placement exam. Corequisites:Calculus II. Topics include gases (kinetic theoryof gases); binary collision model for chemicalreactions; chemical kinetics; acid-base equilibria;thermochemistry (Thermodynamics I); spontaneousprocesses (Thermodynamics II); chemicalbonding in polyatomic molecules. Recitation sectionrequired.CHEM C2507y Intensive general chemistrylaboratory3 pts. Lab: 3. Professor Avila.Prerequisite: CHEM C1604 or C3045. Fee: $140.An introduction to basic techniques and practicesof modern experimental chemistry, includingqualitative procedures and chemical analysis. Thiscourse differs from CHEM C1500 in its emphasison instrumentation and methods.CHEM C3045x-C3046y Intensive organicchemistry for first-year students (lecture)3.5 pts. Professors Breslow and Snyder.Prerequisites: A grade of 5 on the ChemistryAdvanced Placement exam and an acceptablegrade on the Department placement exam.Not open to students who have taken othercourses in college-level chemistry. Premedicalstudents may take CHEM C3045, C3046, andC3545 to meet the minimum requirements foradmission to medical school. This course coversthe same material as CHEM C3443-C3444,but is intended for students who have learnedthe principles of general chemistry in highschool. The level of instruction is appropriatefor those who have not had a college course ingeneral chemistry. Students enrolled in CHEMC3045-C3046 are expected to enroll concurrentlyin CHEM C2507. Recitation sectionrequired.CHEM C3071y Introduction to inorganicchemistry3 pts. Lect: 3. Professor Owen.Corequisite: CHEM C3444 or C3046. Principlesgoverning the structure and reactivity of inorganiccompounds surveyed from experimental and theoreticalviewpoints. Topics include inorganic solids,aqueous and nonaqueous solutions, the chemistryof selected main group elements, transition metalchemistry, metal clusters, metal carbonyls, andorganometallic chemistry. Recitation sectionrequired.CHEM C3079x-C3080y Physical chemistry,I and II4 pts. Professors Cacciuto and Reichman.Prerequisites: CHEM C1403 and C1404, or C1604,or C3045 and C3046; PHYS V1201-V1202 isacceptable, PHYS C1401-C1402 is recommended,or the equivalent; and MATH V1101-V1102 orV1207-V1208. Recommended corequisite: CHEMC3085-C3086. Elementary but comprehensivetreatment of the fundamental laws governing thebehavior of individual atoms and molecules andcollections of them. C3079: The thermodynamicsof chemical systems at equilibrium and the chemicalkinetics of nonequilibrium systems. C3080: Thequantum mechanics of atoms and molecules, thequantum statistical mechanics of chemical systems,and the connection of statistical mechanicsto thermodynamics. Recitation section required.CHEM C3085x-C3086y Physical and analyticalchemistry laboratory4 pts. Lab: 4. Professor Avila.Prerequisites: CHEM C3085 is prerequisite forC3086. Corequisites: CHEM C3079 for CHEMC3085 and C3080 for C3080. Fee: $125 perterm. Techniques of experimental physical chemistryand instrumental analysis, including infraredand ultraviolet spectrophotometry, magnetic resonance,electroanalytical methods, calorimetry,reaction kinetics, hydrodynamic methods, andapplications of digital computers to the analysis ofexperimental data.CHEM C3098x and y Supervised independentresearch4 pts. Lab: 4. Professor Valentini.Prerequisite: the permission of the professor incharge for entrance, and the permission of thedepartmental representative for aggregate pointsin excess of 12 or less than 4. Laboratory fee:$105 per term. This course may be repeatedfor credit (see major and concentration requirements).Individual research under the supervisionof a member of the staff. Research areas includeorganic, physical, inorganic, analytical, and biologicalchemistry.CHEM C3443x-C3444y Organic chemistry(lecture)3.5 pts. Professors Cornish, Lambert, Sames,and Turro.Prerequisites: CHEM C1404 or W1404 or C1604,and C1500 or W1500. The principles of organicchemistry. The structure and reactivity of organicmolecules are examined from the standpoint ofmodern theories of chemistry. Topics includestereochemistry, reactions of organic molecules,mechanisms of organic reactions, syntheses anddegradations of organic molecules, and spectroscopictechniques of structure determination.Recitation section required.CHEM C3543x and y Organic chemistrylaboratory3 pts. Lab: 3. Professors Ghurbanyan and Ng.Prerequisites: CHEM C1500 or W1500.Corequisites: CHEM C3443 or W3343. Fee: $125.Students planning to take a full year of laboratoryshould enroll in CHEM C3543 and C3546.Techniques of experimental organic chemistry,with emphasis on understanding fundamental principlesunderlying the experiments in methodologyof solving laboratory problems involving organicmolecules.CHEM C3545x Organic chemistry laboratory3 pts. Lab: 3. Professors Ghurbanyan and Ng.Prerequisites: CHEM C3045 and C3046 andC2507. Fee: $125. The course covers the samematerial as CHEM C3543, but is intended forthose students who have taken Intensive OrganicChemistry for First-Year Students, CHEMC3045-C3046.CHEM C3546y Advanced organic chemistrylaboratory3 pts. Lab: 3. Professors Ghurbanyan and Ng.Prerequisites: CHEM C3543 or W3543 or C3545.Corequisites: CHEM C3444 or W3444. Fee: $125.A project laboratory with emphasis on complexsynthesis and advanced techniques includingqualitative organic analysis and instrumentation.EARTH AND ENVIRONMENTALSCIENCESUndergraduates in the four-year courseof study in the School of Engineeringand Applied Science may take coursesnumbered up to 4999 but may entercourses of higher numbers only if(1) the course is expressly included inthe prescribed curriculum or(2) special permission is obtainedfrom the Department of Earth andEnvironmental Sciences.EESC V1011x Earth: origin, evolution,processes, future4 pts. Lect: 3. Lab: 1. Professors Kelemen andMutter.Students who wish to take only the lectures shouldregister for V1411. What is the nature of our planetand how did it form? From geochemical and geophysicalperspectives we explore Earth’s internalstructure, its dynamical character expressed inplate tectonics, and ask if its future behavior canbe known.EESC V1030x Oceanography3 pts. Lect: 3. Professor Hoenisch.Explore the geology of the sea floor, understandwhat drives ocean currents and how ocean ecosystemsoperate. Case studies and discussionscentered on ocean-related issues facing society.EESC V1201y Environmental risks anddisasters3 pts. Lect: 3. Professor Ekstrom.Prerequisites: high school science and math. Anintroduction to risks and hazards in the environment.Different types of hazards are analyzed andcompared: natural disasters, such as tornados,earthquakes, and meteorite impacts; acute andchronic health effects caused by exposure to radia-SEAS 2010–2011

tion and toxic substances such as radon, asbestos,and arsenic; long-term societal effects due toenvironmental change, such as sea level rise andglobal warming. Emphasizes the basic physicalprinciples controlling the hazardous phenomenaand develops simple quantitative methods formaking scientifically reasoned assessments of thethreats (to health and wealth) posed by variousevents, processes, and exposures. Discussesmethods of risk mitigation and sociological, psychological,and economic aspects of risk controland management.EESC V1600x Earth resources andsustainable development3 pts. Lect: 3. Professor Kelemen.Prerequisites: none. High school chemistryrecommended. Survey of the origin and extentof mineral resources, fossil fuels, and industrialmaterials, that are non-renewable, finiteresources, and the environmental consequencesof their extraction and use, using the textbookEarth Resources and the Environment, by JamesCraig, David Vaughan and Brian Skinner. Thiscourse provides an overview but includes focuson topics of current societal relevance, includingestimated reserves and extraction costs forfossil fuels, geological storage of CO 2 , sourcesand disposal methods for nuclear energy fuels,sources and future for luxury goods such as goldand diamonds, and special, rare materials used inconsumer electronics (e.g., “Coltan,” mostly fromCongo) and in newly emerging technologies suchas superconducting magnets and rechargeablebatteries (e.g., heavy rare earth elements, mostlyfrom China). Guest lectures from economists,commodity traders and resource geologists willprovide “real world” input.EESC W3018y Weapons of mass destruction3 pts. Lect: 3. Professor Richards.Prerequisites: high school science and math.A review of the history and environmental consequencesof nuclear, chemical, and biologicalweapons of mass destruction (WMD); of how theseweapons work, what they cost, how they havespread, how they might be used, how they arecurrently controlled by international treaties anddomestic legislation, and what issues of policy andtechnology arise in current debates on WMD. Whataspects of the manufacture of WMD are easilyaddressed, and what aspects are technically challenging?It may be expected that current events/headlines will be discussed in class.EESC W4001x Advanced general geology4 pts. Lect: 3. Lab: 1. Professors Anders andScholz.Prerequisites: one semester of college-levelcalculus, physics, and chemistry. A concentratedintroduction to the solid Earth, its interior, andnear-surface geology. Intended for students withgood backgrounds in the physical sciences butnone in geology. Laboratory and field trips.EESC W4008x Introduction to atmosphericscience3 pts. Lect: 3. Professor Del Genio.Prerequisites: advanced calculus and generalphysics, or the instructor’s permission. Basic physicalprocesses controlling atmospheric structure:thermodynamics; radiation physics and radiativetransfer; principles of atmospheric dynamics; cloudprocesses; applications to Earth’s atmosphericgeneral circulation, climatic variations, and theatmospheres of the other planets.EESC W4009x. Chemical geology4 pts. Offered in alternate years. Professor Walker.Prerequisite: physical chemistry or the instructor’spermission. Thermodynamics as applied to earthsystems.EESC W4050x Global assessment andmonitoring using remote sensing3 pts. Offered in alternate years. Professor Small.Prerequisite: instructor’s permission.Recommended preparation: some college-levelphysics or math. Enrollment limited to 24 students.General introduction to fundamentals of remotesensing and image processing. Example applicationsin the Earth and environmental sciences areexplored through the analysis of remote sensingimagery in a state-of-the-art visualization laboratory.Lab required.EESC W4076y Geologic mapping3 pts. Lect: 3. Professors Anders and Walker.Field work on weekends in April and for twoweeks in mid-May, immediately following the endof examinations. Estimated expenses: $250. Theprinciples and practices of deciphering geologichistory through the observation of rocks in thefield, mapmaking, construction of geological crosssections,and short written reports.EESC W4085x Geodynamics3 pts. Lect: 3. Offered in alternate years.Professor Buck.Prerequisites: calculus, differential equations,introductory physics. An introduction to how theEarth and planets work. The focus is on physicalprocesses that control plate tectonics and the evolutionof planetary interiors and surfaces; analyticaldescriptions of these processes; weekly physicalmodel demonstrations.EESC W4113 Introduction to mineralogy4 pts. Offered in alternate years. Not offered in2010-2011.Prerequisites: introductory geology or the equivalent,elementary college physics and chemistry, orthe instructor’s permission. Elementary crystallographyand crystal structures, optical properties ofminerals, mineral associations, economic minerals.Laboratory: identification of minerals in hand specimensand use of the petrographic microscope.EESC W4230y Crustal deformation3 pts. Lect: 3. Professors Anders and Scholz.Prerequisites: introductory geology and one yearof calculus. Recommended preparation: higherlevels of mathematics. Introduction to the deformationprocesses in the Earth’s crust. Fundamentaltheories of stress and strain; rock behavior in bothbrittle and ductile fields; earthquake processes;ductile deformation; large-scale crustal contractionaland extensional events.EESC W4300x The earth’s deep interior3 pts. Lect: 3. Professor Ekstrom.Prerequisites: calculus, differential equations,one year of college physics, and EESC W4950or its equivalent. An introduction to propertiesof the Earth’s mantle, fluid outer core, and solidinner core. Current knowledge of these features isexplored, using observations of seismology, heatflow, gravity, and geomagnetism, plus informationon the Earth’s bulk composition.EESC W4600x Earth resources andsustainable development3 pts. Lect: 3. Professor Kelemen.Prerequisites: none. High school chemistry recommended.Survey of the origin and extent of mineralresources, fossil fuels, and industrial materials,that are nonrenewable, finite resources, and theenvironmental consequences of their extractionand use, using the textbook Earth Resources andthe Environment, by James Craig, David Vaughanand Brian Skinner. This course provides anoverview, but includes focus on topics of currentsocietal relevance, including estimated reservesand extraction costs for fossil fuels, geologicalstorage of CO2, sources and disposal methods fornuclear energy fuels, sources and future for luxurygoods such as gold and diamonds, and special,rare materials used in consumer electronics (e.g.,“Coltan,” mostly from Congo) and in newly emergingtechnologies such as superconducting magnetsand rechargeable batteries (e.g., heavy rare earthelements, mostly from China). Guest lecturesfrom economists, commodity traders and resourcegeologists will provide “real world” input. Requiredrecitation session.EESC W4701 Introduction to igneouspetrology4 pts. Offered in alternate years. Not offered in2010-2011.Prerequisites: introductory geology or the equivalent.Recommended preparation: EESC W4113and knowledge of chemistry. Students not enrolledin terrestrial geology may elect to write a substantialterm paper in lieu of the laboratory course.Compositional characteristics of igneous and metamorphicrocks and how they can be used as toolsto investigate earth processes. Development ofigneous and metamorphic rocks in a plate-tectonicframework.EESC W4885 The chemistry of continentalwaters3 pts. Lect: 3. Offered in alternate years. Notoffered in 2010-2011.Recommended preparation: a solid background inbasic chemistry. Introduction to geochemical cyclesinvolving the atmosphere, land, and biosphere;chemistry of precipitation, weathering reactions,rivers, lakes, estuaries, and groundwaters; stableisotopes and radioactive tracers of transport processesin continental waters.205SEAS 2010–2011

206EESC W4924 Introduction to atmosphericchemistry3 pts. Lect: 3. Offered in alternate years. Notoffered in 2010-2011.A survey of trace gas photochemistry important inthe Earth’s atmosphere. Major topics are composition,including biogenic and anthropogenic inputs,and chemical processes, including reaction kineticsand photochemistry. Specific applications totropospheric air quality, including smog, acid rain,and stratospheric ozone, including the Antarcticozone hole, are covered, with an emphasis on theresponse to anthropogenic pollutants and climatechange.EESC W4925x Principles of physicaloceanography3 pts. Lect: 3. Professor Gordon.Recommended preparation: a solid backgroundin mathematics, physics, and chemistry. Physicalproperties of seawater, water masses and their distribution,sea-air interaction influence on the oceanstructure, basic ocean circulation pattern, relationof diffusion and advection with respect to distributionof ocean properties, ocean tides and waves,turbulence, and introduction to ocean dynamics.EESC W4926y Principles of chemicaloceanography3 pts. Offered in alternate years. ProfessorsAnderson and Hoenisch.Recommended preparation: Solid backgroundin mathematics, physics, and chemistry. Factorscontrolling the concentration and distribution of dissolvedchemical species within the sea. Applicationof tracer and natural radioisotope methods tolarge-scale mixing of the ocean, the geologicalrecord preserved in marine sediments, the role ofocean processes in the global carbon cycle, andbiogeochemical processes influencing the distributionand fate of elements in the ocean.EESC W4930y Earth’s oceans andatmosphere3 pts. Lect: 3. Offered in alternate years.Professor Gordon.Recommended preparation: a good backgroundin the physical sciences. Physical properties ofwater and air. Overview of the stratification andcirculation of Earth’s oceans and atmosphere andtheir governing processes; ocean-atmosphereinteraction; resultant climate system; natural andanthropogenic forced climate change.EESC W4947y Plate tectonics3 pts. Lect: 3. Professor Abers.Prerequisites: physical geology. Prepares studentsfor research and oral exams with cross-disciplinaryanalysis of the plate-tectonic cycle. Driving forcesand mantle convection, plate kinematics, magmatism,structure, thermal and chemical evolution ofmid-ocean ridges and subduction zones, continentalrifts and collisions, and hot spots. Includesliterature readings of great debates, and emphasizesintegration of geophysical, geological andgeochemical observations and processes.EESC W4949x Introduction to seismology3 pts. Lect: 3. Offered in alternate years.Professor Menke.Prerequisites: elementary college physics andmathematics (including calculus). Basic methodsof seismogram analysis. Classification of seismicwaves and elementary theory of body waves andnormal modes. Elementary aspects of seismicprospecting, earthquake source theory, instrumentation,discrimination between explosions andearthquakes, inversion of seismic data to inferEarth structure, earthquake engineering, earthquakeinsurance and hazards mitigation, estimationof seismic risk, and earthquake prediction.HUMANITIES AND SOCIALSCIENCESFor listings of additional courses of interestto engineering students, consultthe bulletins of Columbia College; theSchool of General Studies; the GraduateSchool of Architecture, Planning, andPreservation; the Graduate School ofBusiness; and the Graduate School ofArts and Sciences.COCI C1101x-C1102y Introduction tocontemporary civilization4 pts. Lect: 4. Instructor to be announced.Taught by members of the Departments ofAnthropology, Classics, English and ComparativeLiterature, French, German, History, Middle Eastand Asian Languages and Cultures, Philosophy,Political Science, Religion, Slavic Languages,and Sociology; and members of the Society ofFellows. A study in their historical context of majorcontributions to the intellectual traditions thatunderpin contemporary civilization. Emphasis ison the history of political, social, and philosophicalthought. Students are expected to write at leastthree papers to complete two examinations, and toparticipate actively in class discussions.ECON W1105x and y Principles of economics4 pts. Professors Desai, Musatti, and Salanie.Corequisites: ECON W1155 recitation sectionwith the same instructor. How a market economydetermines the relative prices of goods, factors ofproduction, and the allocation of resources andthe circumstances under which it does it efficiently.Why such an economy has fluctuations and howthey may be controlled. Recitation section required.ENGL C1010x or y University writing3 pts. Members of the faculty.Teaches general techniques and strategies foracademic reading and writing. Students read anddiscuss a range of published essays, completeregular reading and writing exercises, write severallonger essays, and undertake a collaborativeresearch and writing project designed by the class.Students placed in C1010 whose names fall in thefirst part of the alphabet must take the course inthe fall. Students whose names fall in the secondpart of the alphabet take the course in the spring.The alphabet will be split somewhere between Kand O. The exact place for the split will be postedbefore fall registration.Global CoreThe Global Core requirement consists ofcourses that examine areas not the primaryfocus of Literature Humanities and ContemporaryCivilization and that, like other Core courses, arebroadly introductory, interdisciplinary, and temporallyor spatially expansive. Courses in the GlobalCore are organized around a set of primary textsor artifacts, which may range from texts of literatetraditions to media (e.g. film), ritual performancesor oral sources, produced in the regions of theworld in question. Global Core courses fall into twocategories: those that focus on a specific culture orcivilization, tracing its appearance and/or existenceacross a significant span of time and sometimesacross more than one present-day country orregion; and those that address several world settingsor cultures comparatively (and may includeEurope and the West), in terms of a commontheme, a set of analytic questions, or interactionsbetween different world regions. Students mustcomplete two courses from the Global Core List ofApproved Courses for a letter grade.HUMA C1001x-C1002y Masterpieces ofWestern literature and philosophy4 pts. Lect: 4. Instructor to be announced.Taught by members of the Departments ofClassics, English and Comparative Literature,French, German, Italian, Middle East and AsianLanguages and Cultures, Philosophy, Religion,Slavic Languages, and Spanish; and members ofthe Society of Fellows in the Humanities. Majorworks by over twenty authors, ranging in time,theme, and genre from Homer to Virginia Woolf.Students are expected to write at least two papers,to complete two examinations each semester, andto participate actively in class discussions.HUMA W1121x or y Masterpieces ofWestern art3 pts. Lect: 3. Instructor to be announced.Discussion and analysis of the artistic qualitiesand significance of selected works of painting,sculpture, and architecture from the Parthenon inAthens to works of the 20th century.HUMA W1123x or y Masterpieces ofWestern music3 pts. Lect: 3. Instructor to be announced.Popularly known as “Music Hum,” this course aimsto instill in students a basic comprehension ofthe many forms of the Western musical imagination.The course involves students actively in theprocess of critical listening, both in the classroomand in concerts. Although not a history of Westernmusic, the course is taught in chronologicalformat and includes masterpieces by Josquindes Prez, Monteverdi, Bach, Handel, Mozart,Haydn, Beethoven, Verdi, Wagner, Schoenberg,Stravinsky, Louis Armstrong, and Duke Ellington,among others.SEAS 2010–2011

MATHEMATICSCourses for First-Year StudentsDepending on the program, completionof Calculus III or IV satisfies the basicmathematics requirement. Normally studentswho have taken an AP Calculuscourse begin with either Calculus II orCalculus III. Refer to the AP guidelineson page 14 for placement information.The sequence ends with MATH E1210:Ordinary differential equations.Students who wish to transfer fromone calculus course to another areallowed to do so beyond the date specifiedon the Academic Calendar. Theyare considered to be adjusting theirlevel, not changing their program. Theymust, however, obtain the approval ofthe new instructor and the Center forStudent Advising before reporting to theRegistrar.MATH V1101 Calculus, I3pts. Lect: 3.Functions, limits, derivatives, introduction tointegrals.MATH V1102 Calculus, II3 pts. Lect: 3.Prerequisite: Calculus I or the equivalent. Methodsof integration, applications of integrals, series,including Taylor’s series.MATH V1201 Calculus, III3 pts. Lect: 3.Prerequisite: Calculus II or the equivalent. Vectoralgebra, complex numbers and exponential, vectordifferential calculus.MATH V1202 Calculus, IV3 pts. Lect: 3.Prerequisite: Calculus II and III. Multiple integrals,line and surface integrals, calculus of vector fields,Fourier series.MATH V1207x-V1208y Honors math A-B4 pts. Lect and recit. Professor Friedman.Prerequisite: Score of 5 on the AdvancedPlacement BC calculus exam. The second termof this course may not be taken without the first.Multivariable calculus and linear algebra from arigorous point of view.MATH E1210x or y Ordinary differentialequations3 pts. Lect: 3. Professors Kutluhan, Lauda, andOllivier.Prerequisite: MATH V1201 or the equivalent.Special differential equations of order one. Lineardifferential equations with constant and variablecoefficients. Systems of such equations. Transformand series solution techniques. Emphasis onapplications.MATH V2010 x and y Linear algebra3 pts. Lect: 3. Professors Kerzhner and Zheng.Prerequisite: MATH VI201 or the equivalent.Vector spaces, linear transformations, matrices,quadratic and hermitian forms, reduction to canonicalforms.MATH V2500x or y Analysis and optimization3 pts. Lect: 3. Professor Pinkham.Prerequisites: MATH V1102 and V1201 or theequivalent, and MATH V2010. Mathematicalmethods for economics. Quadratic forms, Hessian,implicit functions. Convex sets, convex functions.Optimization, constrained optimization, Kuhn-Tucker conditions. Elements of the calculus ofvariations and optimal control.MATH V3007y Complex variables3 pts. Lect: 3. Professor Phong.Prerequisite: MATH V1202. An elementary coursein functions of a complex variable. Fundamentalproperties of the complex numbers, differentiability,Cauchy-Riemann equations, Cauchy integraltheorem, Taylor and Laurent series, poles, andessential singularities. Residue theorem and conformalmapping.MATH V3027x Ordinary differential equations3 pts. Lect: 3. Professor Daskalopoulos.Prerequisite: MATH V1201 or the equivalent.Equations of order one, linear equations, seriessolutions at regular and singular points, boundaryvalue problems. Selected applications.MATH V3028y Partial differential equations3 pts. Lect: 3. Professor Munteanu.Prerequisite: MATH V3027 or the equivalent.Introduction to partial differential equations. Firstorderequations. Linear second-order equations,separation of variables, solution by series expansions.Boundary value problems.MATH W4032x Fourier analysis3 pts. Lect: 3. Professor Lipyanskiy.Prerequisite: MATH V1201 and linear algebra,or MATH V1202. Fourier series and integrals,discrete analogues, inversion and Poisson summation,formulae, convolution, Heisenberg uncertaintyprinciple. Emphasis on the application of Fourieranalysis to a wide range of disciplines.MATH W4041x-W4642y Introduction tomodern algebra3 pts. Lect: 3. Professor Thaddeus.The second term of this course may not be takenwithout the first. Prerequisite: MATH V1202 andV2010 or the equivalent. Groups, homomorphisms,rings, ideals, fields, polynominals, and field extensions.Galois theory.MATH W4061x-W4062y Introduction tomodern analysis3 pts. Lect: 3. Professor Gallagher.The second term of this course may not be takenwithout the first. Prerequisite: MATH V1202 or theequivalent. Real numbers, metric spaces, elementsof general topology. Continuous and differentiablefunctions. Implicit functions. Integration, change ofvariables. Function spaces. Further topics chosenby the instructor.MATH W4065x Honors complex variables3 pts. Lect: 3. Professor Friedman.Prerequisite: MATH V1207, V1208, or W4061.A theoretical introduction to analytic functions.Holomorphic functions, harmonic functions, powerseries, Cauchy-Riemann equations, Cauchy’sintegral formula, poles, Laurent series, residuetheorem. Other topics as time permits: ellipticfunctions, the gamma and zeta functions, theRiemann mapping theorem, Riemann surfaces,Nevanlinna theory.PHYSICSThe general four-term preengineeringphysics sequence consists of PHYSC1401, C1402, C1403, and C1494(laboratory); or PHYS C1601, C1602,C2601, and C2699 (laboratory).PHYS C1401x Introduction to mechanics andthermodynamics3 pts. Lect: 3. Professors Dodd and Hailey.Corequisite: MATH V1101 or the equivalent.Fundamental laws of mechanics, kinematics anddynamics, work and energy, rotational dynamics,oscillations, gravitation, fluids, temperature andheat, gas laws, the first and second laws of thermodynamics.PHYS C1402y Introduction to electricity,magnetism, and optics3 pts. Lect: 3. Professors Dodd and Hailey.Prerequisite: PHYS C1401. Corequisite: MATHV1102 or the equivalent. Electric fields, direct currents,magnetic fields, alternating currents, electromagneticwaves, polarization, geometrical optics,interference and diffraction.PHYS C1403x Introduction to classical andquantum waves3 pts. Lect: 3. Professor Brooijmans.Prerequisite: PHYS C1402. Corequisite: MATHV1201 or the equivalent. Classical waves and thewave equation, Fourier series and integrals, normalmodes, wave-particle duality, the uncertaintyprinciple, basic principles of quantum mechanics,energy levels, reflection and transmission coefficients,applications to atomic physics.PHYS C1493x Introduction to experimentalphysics3 pts. Lect: Tues., 3:10–4:00 p.m. Lab: 3hours weekly to be arranged. Instructor to beannounced.Prerequisites: PHYS C1401 and C1402.Laboratory work associated with the two prerequisitelecture courses. Experiments in mechanics,thermodynamics, electricity, magnetism,optics, wave motion, atomic and nuclear physics.(Students cannot receive credit for both PHYSC1493 and C1494.)PHYS C1494y Introduction to experimentalphysics3 pts. Lect: Tues., 3:10–4:00 p.m. Lab: 3hours weekly to be arranged. Instructor to beannounced.207SEAS 2010–2011

208Prerequisites: PHYS C1401 and C1402.Laboratory work associated with the two prerequisitelecture courses. Experiments in mechanics,thermodynamics, electricity, magnetism,optics, wave motion, atomic and nuclear physics.(Students cannot receive credit for both PHYSC1493 and C1494.)PHYS C1601x Physics, I: mechanics andrelativity3.5 pts. Lect: 2.5. Rec: 1 hour weekly to bearranged. Professor Millis.Corequisite: MATH V1102 or the equivalent.Fundamental laws of mechanics, kinematics anddynamics, work and energy, rotational dynamics,oscillations, gravitation, fluids, introduction to specialrelativity and relativistic kinematics. The courseis preparatory for advanced work in physics andrelated fields.PHYS C1602y Physics, II: thermodynamics,electricity, and magnetism3.5 pts. Lect: 3.5. Professor Hughes.Prerequisite: PHYS C1601. Corequisite:MATH V1201 or equivalent. Temperatureand heat, gas laws, the first and second lawsof thermodynamics, kinetic theory of gases,electric fields, direct currents, magnetic fields,alternating currents, electromagnetic waves.The course Is preparatory for advanced work inphysics and related fields.PHYS C2601x Physics, III: classical andquantum waves3.5 pts. Lect: 2.5. Rec: 1 hour weekly to bearranged. Professor Kim.Prerequisite: PHYS C1602 or C1402. Corequisite:MATH V1202 or equivalent. Classical wavesand the wave equation, geometrical optics,interference and diffraction, Fourier series andintegrals, normal modes, wave-particle duality,the uncertainty principle, basic principles ofquantum mechanics, energy levels, reflection andtransmission coefficients, the harmonic oscillator.The course is preparatory for advanced work inphysics and related fields.PHYS C2699y Experiments in classical andmodern physics3 pts. Lect: Tues., 3:10–4:00 p.m. Lab: 3hours weekly to be arranged. Instructor to beannounced.Prerequisites: PHYS C1601 (or C1401), C1602(or C1402), and C2601. Laboratory work associatedwith the three prerequisite lecture courses.Experiments in mechanics, thermodynamics,electricity, magnetism, optics, wave motion, atomicand nuclear physics.PHYS C2801x-C2802y Accelerated physics,I and II4.5 pts. Lect: 3.5. Rec: 1 hour weekly to bearranged. Professor Christ.Prerequisite: Advanced placement in physics andmathematics, or the equivalent, and the instructor’spermission. (A special placement meetingis held during Orientation.) This accelerated twosemestersequence covers the subject matter ofPHYS C1601, C1602, and C2601 and is intendedfor students who have an exceptionally strongbackground in both physics and mathematics. Thecourse is preparatory for advanced work in physicsand related fields. There is no accompanyinglaboratory; however, students are encouraged totake the intermediate laboratory, PHYS W3081, inthe following year.PHYS W3002y From quarks to the cosmos:applications of modern physics3.5 pts. Lect: 3.5. Not offered in 2010–2011.Prerequisites: PHYS C2601 or C2802. Thiscourse reinforces basic ideas of modern physicsthrough applications to nuclear physics, highenergyphysics, astrophysics, and cosmology. Theongoing Columbia research programs in thesefields are used as practical examples. The courseis preparatory for advanced work in physics andrelated fields.PHYS W3003x Mechanics3 pts. Lect: 3. Professor Weinberg.Prerequisite: General physics; differential andintegral calculus. Newtonian mechanics, oscillationsand resonance, conservative forces andpotential energy, central forces, noninertial framesof reference, rigid body motion, an introductionto Lagrange’s formulation of mechanics, coupledoscillators, and normal modes.PHYS W3007y Electricity and magnetism3 pts. Lect: 3. Professor Pasupathy.Prerequisite: General physics; differential andintegral calculus. Electrostatics and magnetostatics,Laplace’s equation and boundary-valueproblems, multipole expansions, dielectric andmagnetic materials, Faraday’s law, AC circuits,Maxwell’s equations, Lorentz covariance, andspecial relativity.PHYS W3008x Electromagnetic waves andoptics3 pts. Lect: 3. Professor Marka.Prerequisite: PHYS W3007. Maxwell’s equationsand electromagnetic potentials, the wave equation,propagation of plane waves, reflection and refraction,geometrical optics, transmission lines, waveguides, resonant cavities, radiation, interference ofwaves, and diffraction.PHYS W3081x or y Intermediate laboratorywork2 pts. Lab: 2. Professors Aprile and May.Primarily for junior and senior physics majors.Other majors require the instructor’s permission.May be repeated for credit by performing differentexperiments. The laboratory has 13 individualexperiments available, of which two are requiredper 2 points. Each experiment is chosen by thestudent in consultation with the instructor. Eachsection meets one afternoon per week, with registrationin each section limited by the laboratorycapacity. Experiments (classical and modern)cover topics in electricity, magnetism, optics,atomic physics, and nuclear physics.PHYS W3083y Electronics laboratory3 pts. Lab: 3. Professor Parsons.Registration is limited to the capacity of the laboratory.Corequisite or prerequisite: PHYS W3003 orW3007. A sequence of experiments in solid-stateelectronics, with introductory lectures.PHYS G4003y Advanced mechanics3 pts. Lect: 3. Instructor to be announced.Prerequisite: Differential and integral calculus,differential equations, and PHYS W3003 or theequivalent. Lagrange’s formulation of mechanics,calculus of variations and the Action Principle,Hamilton’s formulation of mechanics, rigid bodymotion, Euler angles, continuum mechanics,Introduction to chaotic dynamics.PHYS G4018y Solid-state physics3 pts. Lect: 3. Professor Uemura.Prerequisites: PHYS G4021 and G4023, or theequivalent. Introduction to solid-state physics:crystal structures, properties of periodic lattices,electrons in metals, band structure, transportproperties, semiconductors, magnetism, andsuperconductivity.PHYS G4019x Mathematical methods ofphysics3 pts. Lect: 3. Professor Blaer.Prerequisite: Differential and integral calculus.Highlights of complex analysis, differential equations,integral equations, Green’s functions, specialfunctions, Fourier and other transforms, approximationmethods, group theory and representations,differential geometry and manifolds. Emphasis isplaced on applications to physical problems.PHYS G4021x-G4022y Quantum mechanics,I and II3 pts. Lect: 3. Professor Mueller.Prerequisite: PHYS C2601 or C2802, or the equivalent.The formulation of quantum mechanics interms of state vectors and linear operators, threedimensionalspherically symmetric potentials, thetheory of angular momentum and spin, time-independentand time-dependent perturbation theory,scattering theory, identical particles. Selected phenomenafrom atomic physics, nuclear physics, andelementary particle physics are described and theninterpreted using quantum mechanical models.PHYS G4023x Thermal and statistical physics3 pts. Lect: 3. Professor Heinz.Prerequisite: PHYS G4021 or equivalent.Thermodynamics, kinetic theory, and methodsof statistical mechanics; energy and entropy;Boltzmann, Fermi, and Bose distributions; idealand real gases; blackbody radiation; chemicalequilibrium; phase transitions; ferromagnetism.PHYS G4040x General relativity3 pts. Lect: 3. Professor Beloborodov.Prerequisites: PHYS W3003 and W3007, or equivalent.Tensor algebra, tensor analysis, introductionto Riemann geometry. Motion of particles, fluid,and fields in curved spacetime. Einstein equation.Schwarzschild solution; test-particle orbits and lightbending. Introduction to black holes, gravationalwaves, and cosmological models.SEAS 2010–2011

STATISTICSEngineering students interested in asurvey of the mathematical theory ofprobability and statistics should considerthe pair STAT W3105: Probabilitytheory and W3107: Statistical inference.Students seeking a quicker overviewthat focuses more on probability theoryshould consider SIEO W4150. STATW4105 and W4107 are the equivalentof W3105 and W3107, respectively; butgraduate students may not register forW3105 and W3107. STAT W4109 (6pts) covers the same material as W3105and W3107 in a single semester. STATW4315: Linear regression models takesW3105 and W3107 as prerequisites;like other advanced offerings in statistics,it covers both theory and practicalaspects of modeling and data analysis.Advanced offerings in probability theory,stochastic processes, and mathematicalfinance generally take STAT W3105as a prerequisite; advanced offerings instatistical theory and methods generallytake STAT W4107 and, in several cases,W4315 as prerequisites; an exception isSTAT W4220: Data mining, which hasa course in computer programming asprerequisite and STAT W3107 as corequisite.STAT 4201 is a high-level surveyof applied statistical methods.Please note that STAT W3000has been renumbered as W3105 andSTAT W3659 has been renumberedas W3107. For a description of thefollowing course offered jointly by theDepartments of Statistics and IndustrialEngineering and Operations Research,see “Industrial Engineering andOperations Research.”SIEO W4150x and y Introduction toprobability and statistics3 pts. Professors Gallego, Hueter, and Wright.Prerequisites: MATH V1101 and V1102 or theequivalent. A quick calculus-based tour of the fundamentalsof probability theory and statistical inference.Probabilistic models, random variables, usefuldistributions, expectations, laws of large numbers,central limit theorem. Statistical inference: point andconfidence interval estimation, hypothesis tests,linear regression. Students seeking a more thoroughintroduction to probability and statistics should considerSTAT W3105 and W3107.STAT W2024x Applied linear regressionanalysis3 pts. Professor Lindquist.Prerequisites: One of STAT W1001, W1111,or W1211. Develops critical thinking and dataanalysis skills for regression analysis in scienceand policy settings. Simple and multiple linearregression, nonlinear and logistic models, randomeffectsmodels, penalized regression methods.Implementation in a statistical package. Optionalcomputer-lab sessions. Emphasis on real-worldexamples and on planning, proposing, implementing,and reporting.STAT W2025y Applied statistical methods3 pts. Professor Whalen.Prerequisite: STAT W2024. Classical nonparametricmethods, permutation tests; contingency tables,generalized linear models, missing data, causalinference, multiple comparisons. Implementation instatistical software. Emphasis on conducting dataanalyses and reporting the results. Optional weeklycomputer-lab sessions.STAT W2026x Statistical applications andcase studies3 pts. Professor Lindquist.Prerequisites: STAT W2025. A sample of topics andapplication areas in applied statistics. Topic areasmay include Markov processes and queuing theory;meta-analysis of clinical trial research; receiveroperatorcurves in medical diagnosis; spatialstatistics with applications in geology, astronomy,and epidemiology; multiple comparisons in bioinformatics;causal modeling with missing data; statisticalmethods in genetic epidemiology; stochasticanalysis of neural spike train data; graphical modelsfor computer and social network data.STAT W3026x Applied data mining3 pts. Professor Emir.Data Mining is a dynamic and fast growing field atthe interface of Statistics and Computer Science.The emergence of massive datasets containingmillions or even billions of observations providesthe primary impetus for the field. Such datasetsarise, for instance, in large-scale retailing, telecommunications,astronomy, computational andstatistical challenges. This course will providean overview of current practice in data mining.Specific topics covered with include databasesand data warehousing, exploratory data analysisand visualization, descriptive modeling, predictivemodeling, pattern and rule discovery, text mining,Bayesian data mining, and causal inference. Theuse of statistical software will be emphasized.STAT W3103x Mathematical methods forstatistics6 pts. Professor Rabinowitz.Prerequisites: MATH V1101. A fast-paced coverageof those aspects of the differential and integralcalculus of one and several variables and of the linearalgebra required for the core courses in the Statisticsmajor. The mathematical topics are integrated withan introduction to computing. Students seeking morecomprehensive background should consider replacingthis course with MATH V1102 and V2010, and one ofCOMS W1003, W1004, or W1007.STAT W3105x Introduction to probability3 pts. Professor Lo.Prerequisites: MATH V1101 and V1102 or theequivalent. A calculus-based introduction toprobability theory. A quick review of multivariatecalculus is provided. Topics covered include randomvariables, conditional probability, expectation,independence, Bayes’ rule, important distributions,joint distributions, moment generating functions,central limit theorem, laws of large numbers andMarkov’s inequality.STAT W3107y Introduction to statisticalinference3 pts. Instructor to be announced.Prerequisite: STAT W3105 or W4105, or theequivalent. Calculus-based introduction to thetheory of statistics. Useful distributions, law oflarge numbers and central limit theorem, pointestimation, hypothesis testing, confidence intervalsmaximum likelihood, likelihood ratio tests, nonparametricprocedures, theory of least squares, andanalysis of variance.STAT W3315x Linear regression models3 pts. Instructor to be announced.Prerequisites: STAT W3107 (or STAT W4150)and STAT W3103 (or MATH V1101, V1102,and V2110). Theory and practice of regressionanalysis. Simple and multiple regression, testing,estimation, prediction, and confidence procedures,modeling, regression diagnostics and plots,polynomial regression, colinearity and confounding,model selection, geometry of least squares.Extensive use of the computer to analyze data.Equivalent to STAT W4315 except that enrollmentis limited to undergraduate students.STAT W3997x and y Independent ResearchInstructor to be announced.Prerequisites: The permission of a member of thedepartment. May be repeated for credit. The studentparticipates in the current research of a member ofthe department and prepares a report on the work.STAT W4201x and y Advanced data analysis3 pts. Professors Alemayehu and Liu.Prerequisites: STAT W4315. At least one ofW4290, W4325, W4330, W4437, W4413, W4543is recommended. This is a course on getting themost out of data. The emphasis will be on handsonexperience, involving case studies with realdata and using common statistical packages. Thecourse covers, at a very high level, exploratorydata analysis, model formulation, goodness offit testing, and other standard and non-standardstatistical procedures, including linear regression,analysis of variance, nonlinear regression,generalized linear models, survival analysis, timeseries analysis, and modern regression methods.Students will be expected to propose a data set oftheir choice for use as case study material.STAT W4240x Data mining3 pts. Professors Madigan and Wood.Prerequisites: COMS W1003, W1004, W1005,W1007, or the equivalent. Corequisites: EitherSTAT W3105 or W4105, and either STAT W3107or W4107. Data Mining is a dynamic and fastgrowing field at the interface of Statistics andComputer Science. The emergence of massivedatasets containing millions or even billions ofobservations provides the primary impetus for the209SEAS 2010–2011

210field. Such datasets arise, for instance, in largescaleretailing, telecommunications, astronomy,computational and statistical challenges. Thiscourse will provide an overview of current researchin data mining and will be suitable for graduatestudents from many disciplines. Specific topicscovered with include databases and data warehousing,exploratory data analysis and visualization,descriptive modeling, predictive modeling,pattern and rule discovery, text mining, Bayesiandata mining, and causal inference.STAT W4290y Statistical methods in finance3 pts. Professor Pospisil.Prerequisites: STAT W3107 or W4107. A fastpacedintroduction to statistical methods used inquantitative finance. Financial applications andstatistical methodologies are intertwined in alllectures. Topics include regression analysis andapplications to the Capital Asset Pricing Model andmultifactor pricing models, principal componentsand multivariate analysis, smoothing techniquesand estimation of yield curves statistical methodsfor financial time series, value at risk, termstructure models and fixed income research, andestimation and modeling of volatilities. Hands-onexperience with financial data.STAT W4315x and y Linear regression models3 pts. Instructor to be announced.Prerequisites: STAT W3107 or equivalent, MATHV2110 or the equivalent. Corequisites: MATHV1101, V1102, and V2110. Simple and multipleregression, including testing, estimation andconfidence procedures, modeling, regressiondiagnostics and plots, polynomial regression, fixedeffects ANOVA and ANCOVA models, nonlinearregression, multiple comparisons, colinearityand confounding, model selection. Emphasis ongeometric approach to the theory and the use of astatistical package to analyze data.STAT W4325y Generalized linear models3 pts. Professor Sobel.Prerequisites: STAT W4315. Statistical methodsfor rates and proportions, ordered and nominalcategorical responses, contingency tables, oddsratios,exact inference, logistic regression, Poissonregression, generalized linear models.STAT W4330x Multilevel modelsProfessor Chen.Prerequisites: STAT W4315. Theory and practice,including model-checking, for random andmixed-effects models (also called hierarchical,multi-level models). Extensive use of the computerto analyze data.STAT W4335x Sample surveys3 pts. Professor Sobel.Prerequisites: STAT W3107 or W4107.Introductory course on the design and analysisof sample surveys. How sample surveys are conducted,why the designs are used, how to analyzesurvey results, and how to derive from first principlesthe standard results and their generalizations.Examples from public health, social work, opinionpolling, and other topics of interest.STAT W4413y Nonparametric statistics3 pts. Professor Sen.Prerequisites: STAT W3107 or W4107. Statisticalinference without parametric model assumption.Hypothesis testing using ranks, permutations, andorder statistics. Nonparametric analogs of analysisof variance. Non-parametric regression, smoothingand model selection.STAT W4437x and y Time series analysis3 pts. Professors Davis, Hernandez-del-Valle,and Hueter.Prerequisites: STAT W4315 or equivalent. Leastsquares smoothing and prediction, linear systems,Fourier analysis, and spectral estimation. Impulseresponse and transfer function. Fourier series,the fast Fourier transform, autocorrelation function,and spectral density. Univariate Box-Jenkinsmodeling and forecasting. Emphasis on applications.Examples from the physical sciences, socialsciences, and business. Computing is an integralpart of the course.STAT W4543y Survival analysisProfessor Shnaidman.Prerequisite: STAT W4315. Survival distributions,types of censored data, estimation for various survivalmodels, nonparametric estimation of survivaldistributions, the proportional hazard and acceleratedlifetime models for regression analysis withfailure-time data. Extensive use of the computer.STAT W4606x and y Elementary stochasticprocesses3 pts. Professors Brown and Hogan.Prerequisites: STAT W3105, W4105, or equivalent.Review of elements of probability theory. Poissonprocesses. Renewal theory. Wald’s equation.Introduction to discrete and continuous timeMarkov chains. Applications to queueing theory,inventory models, branching processes.STAT W4635y Stochastic Processes forFinance3 pts. Professor Vecer.Prerequisites: STAT W3105, W4105, or equivalent.This course covers theory of stochasticprocesses applied to finance. It covers conceptsof Martingales, Markov chain models, Brownianmotion. Stochastic Integration, Ito’s formula as atheoretical foundation of processes used in financialmodeling. It also introduces basic discrete andcontinuous time models of asset price evolutionsin the context of the following problems in finance:portfolio optimization, option pricing, spot rate interestmodeling.STAT W4840x Theory of interest3 pts. Professor Rajah.Prerequisites: MATH V1101 or equivalent.Introduction to the mathematical theory of interestas well as the elements of economic and financialtheory of interest. Topics include rates of interestand discount; simple, compound, real, nominal,effective, dollar (time)-weighted; present, current,future value; discount function; annuities; stocksand other instruments; definitions of key termsof modern financial analysis; yield curves; spot(forward) rates; duration; immunization; and shortsales. The course will cover determining equivalentmeasures of interest; discounting; accumulating;determining yield rates; and amortization.SEAS 2010–2011

Campus and Student Life

212CAMPUS LIFEThe Fu Foundation School ofEngineering and Applied Scienceattracts and admits an exceptionallyinteresting, diverse, and multiculturalgroup of students, and it takes stepsto provide a campus environment thatpromotes the continued expansion ofeach student’s ideas and perspectives.Starting with the residence halls,in which nearly all first-year undergraduatestudents live, the Universityassigns rooms to both Engineering andColumbia College undergraduate students,ensuring that all students will liveeither with or near a student attendingthe other program.Once students have moved intotheir new campus home they will findthemselves part of a residential systemthat offers undergraduates a networkof social and academic support.Designed to make students aware ofthe vast number of social and academicopportunities available to them at theUniversity, these networks provide anumbrella of comprehensive advising tohelp students articulate and realize theirgoals while at Columbia. More informationabout the residence halls canbe found in the chapter “Housing andResidence Life” in this bulletin.DIVISION OFSTUDENT AFFAIRSUndergraduate life is not confined to theclassroom. A blend of academic, educational,social, and cocurricular activitiescontributes to the Columbia experience.While The Fu Foundation Schoolof Engineering and Applied Science islarge enough to support a wide varietyof programs, it is also small enough topromote the close interaction amongstudents, faculty, and administration thathas created a strong sense of communityon campus.With its mission of providing a widerange of services designed to enhancethe student experience from the timeof admission through graduation, theDivision of Student Affairs is the hub ofundergraduate student life. Admissions,Financial Aid and EducationalFinancing, Center for Student Advising,Residential Programs, Office ofMulticultural Affairs, Parent and FamilyPrograms, Office of Judicial Affairs andCommunity Standards, Events andCommunications, Student and AlumniPrograms, Student Development andActivities, and Office of Student GroupAdvising are integral components of theDivision. The integrated efforts of theseunits assures that individual studentsreceive support in both their academicand cocurricular pursuits. The Division ofStudent Affairs is responsible for assistingstudents in all matters beyond actualcourse instruction, helping to create aspecial spirit on campus and a sense ofcommunity for students.CENTER FORSTUDENT ADVISING403 Lerner Hall, 212-854-6378Mail Code 1201www.studentaffairs.columbia.edu/csacsa@columbia.eduThe Center for Student Advising reflectsthe mission of the University in strivingto support and challenge the intellectualand personal growth of its studentsand by creating a developmental,diverse, and open learning environment.Individually and collaboratively,each center: demicadvisement, exploration, andcounseling alstudies, study abroad, and majordeclaration and completion, as well asvarious leadership, career, graduateschool, and research opportunities;refers to additional campus resources to meet the unique developmentalneeds of each class and to enhancecommunity among students, faculty,and administrators tionregarding University polices, procedures,resources, and programs take responsibility in making informeddecisionsEach student is assigned to an advisingdean who advises in his or her academicarea of interest. When a studentdeclares a major, a faculty member isappointed to guide him or her for the nexttwo years. Advising deans regularly referstudents to their academic departmentsto receive coordinated expert advice intheir engineering course selections.Preprofessional AdvisingThe Office of Preprofessional Advisingworks closely with the Center forStudent Advising and with the Centerfor Career Education to provide informationfor students who plan a career inlaw or the health professions. The OfficeSEAS 2010–2011

213advises and assists students throughouttheir four years, but works most closelywith students during their applicationyear and with alumni who apply foradmission after graduation. Informationsheets, forms, and helpful resources areavailable in the Office of PreprofessionalAdvising. Students will work with theiradvising deans as primary preprofessionaladvisers; these advisers will beinstrumental in writing committee evaluationsfor some professional schools.COMMUNITY DEVELOPMENTThe Community Development teamworks to foster a vibrant and welcomingundergraduate community throughorganizational advising, leadership development,advocacy, diversity education,civic engagement, and community programming.The team includes the Officeof Student Development and Activities,the Office of Multicultural Affairs, theOffice of Student Group Advising, andthe Office of Residential Programs.Knowing that students’ learning continuesbeyond the classroom, ColumbiaUniversity strongly encourages studentsto become involved in programs andactivities to enhance their educationalexperience and personal growth. A widearray of student organizations addressesboth student interests and professionalconcerns, including the arts, politics,identity, culture, and religion. Joiningsuch groups offers an exciting anddynamic opportunity to develop leadershipskills that will serve students wellthroughout their lives.Student OrganizationsPrograms and activities at Columbiaare shaped primarily by students whoassume leadership and volunteer positionsin hundreds of organizationsacross the campus. The EngineeringStudent Council and its associated classcouncils are the elected representativebody of undergraduates with The FuFoundation School of Engineering andApplied Science. Its members representstudent interests on committees andprojects addressing a wide range ofissues facing the Columbia communityand help shape the quality of life forColumbia students.Working in conjunction with theStudent Council, the Activities Boardat Columbia (ABC), Student GoverningBoard (SGB), Inter-Greek Council (IGC),Community Impact (CI), Club Sports,and Interschool Governing Board (IGB)oversee the management and funding ofover 300 student organizations.The ABC provides governance formore than 160 recognized student organizations,including cultural organizations,performance-based and theatricalgroups, media and publications groups,competition and special interests groupsand pre-professional organizations andsocieties. The pre-professional organizationsand societies are of special interestto engineering students. These societiesreflect the range of academic disciplinesand interests to be found among studentsand include the Asian-AmericanSociety of Engineers, National Society ofBlack Engineers, the Society of WomenEngineers, the American Institute ofAeronautics and Astronautics, and theBiomedical Engineering Society, just toname a few.The SGB provides governance forapproximately 100 recognized studentorganizations that are faith-based, spiritual,political, activist, and humanitarianand that encourage open interreligiousand political dialogue at ColumbiaUniversity’s Morningside campus. TheInterSchool Governing Board recognizesstudent organizations whose membershipspans across the various undergraduateand graduate schools.For more information on the Inter-Greek Council (IGC), see ResidentialPrograms, below. For more information onClub Sports, see Intercollegiate AthleticsProgram (page 216), and for more informationon Community Impact see Officeof the University Chaplain (page 215). Allthe governing groups provide networking,leadership, and professional developmentopportunities for students.Columbia University graduate studentscan participate in and enjoyhundreds of diverse, University-affiliatedsocial, religious, cultural, academic,athletic, political, literary, professional,public service, and other organizations.At SEAS, graduate students are encouragedto become active members of theEngineering Graduate Student Council(EGSC). The EGSC is a recognizedgroup that consists of representativesfrom each of the nine academic departmentsat SEAS. The objectives of theEGSC are to foster interaction amonggraduate engineering students, to serveas a voice for graduate engineering students,and to sponsor social and educationalevents of interest to the graduateengineering community.SEAS 2010–2011

214Office of Student Developmentand ActivitiesThe Office of Student Development andActivities (SDA) provides programs andservices designed to support a widerange of co-curricular activities that helpbuild a sense of community, supportresponsible student governance andstudent group involvement, and furtherstudents’ leadership development andpersonal growth.Student Development and Activitiesstaff members advise student organizationsrecognized through the ActivitiesBoard of Columbia (ABC), as well asthe student governments of The FuFoundation School of Engineering andApplied Science and Columbia College.SDA serves as resources for eventplanning, organizational leadership,and budgeting. The Office of StudentDevelopment and Activities offers leadershiptraining workshops and helpsnetworking among student leaders andadministrative offices. In addition, theSDA administers the Urban New YorkProgram, the New Student OrientationProgram, the Columbia UrbanExperience Program, and the ColumbiaOutdoor Orientation Program.OrientationAll new students are required to participatein an orientation program thatis designed to acquaint them with theUniversity and its traditions, the administrationand faculty of The Fu FoundationSchool of Engineering and AppliedScience, upperclass students, and NewYork City. The New Student OrientationProgram (NSOP) for new undergraduatestudents begins the week prior tothe start of the fall semester. NSOP isintended to assist all new students withthe transition to college life.Orientation is busy, exciting, and alot of fun, but it is also a week in whichimportant academic decisions are made.Scheduled into the program are informationsessions and opportunities to meetwith academic advisers. Through largegroup programs and small group activities,students will be introduced to facultymembers, deans, resident advisers, andother students. NSOP includes walkingtours of New York City, social events,and information sessions on Universityservices and co-curricular opportunities.During NSOP, new students have thecampus to themselves. This provides studentswith a unique opportunity to makefriends and settle into life at Columbiabefore classes begin.Undergraduate students may e-mailnsop@columbia.edu or call 212-854-5808 for additional information on NSOP.Orientation for graduate students isscheduled during the week prior to thebeginning of each semester. For moreinformation on orientation for graduatestudents, contact the Office of GraduateStudent Services.Office of Student Group AdvisingThe Office of Student Group Advising(OSGA) is committed to supporting theprogramming of our faith-based, spiritual,political, activist, and humanitarianstudent organizations. In reaching tofulfill this commitment, OSGA providesprogramming in leadership skills,program development, and organizationalmanagement to all undergraduatestudent organizations recognized bythe Student Governing Board (SGB)and organizations recognized by theInterschool Governing Board (IGB).OSGA assists students in their developmentas individuals, community members,and leaders.Issues of social responsibility andcivic engagement are central to themission of OSGA and the student organizationsthat OSGA supports. OSGAstrives to encourage open dialogueat Columbia University’s MorningsideCampus and seeks to find connectionsamong student groups. The Officeof Student Group Advising works toenhance the undergraduate educationalexperience by fostering a dynamic andenriching University community, supportingresponsible student governanceand co-curricular activities, and offeringprograms and opportunities focusedon civic and community engagement.Through advising, the office encouragescritical thinking and the free exchange ofideas by all of the student organizationsit supports.Office of Multicultural AffairsThe Office of Multicultural Affairs isdevoted to promoting a just societyand exploring issues of interculturalismand diversity within and beyondthe Columbia University community. Bypromoting forums that address diversityissues, self-discovery takes place alongwith a greater awareness and appreciationof cultural history within andbetween communities on campus. Weendeavor to empower students, faculty,and staff with the tools to be able tosuccessfully navigate their environmentsand thus be able to positively changeand impact the community at large.Programs and services provided byMulticultural Affairs include the ColumbiaMentoring Initiative, a program connectingincoming students with returningstudents, and returning studentswith alumni; Respecting Ourselves andOthers Through Education (ROOTED),a peer diversity faciliation program;Dessert and Discussion, the signaturelecture series; and the InterculturalHouse (ICH), a unique residential experiencethat is supportive of MulticulturalAffairs’ social justice goals.Residential ProgramsThe Residential Programs staff,supervised by the Assistant Dean ofCommunity Development and ResidentialPrograms, includes 8 professional staff,13 graduate students, and 130 undergraduateswho contribute to the growth,well-being, and personal and intellectualdevelopment of students. The staffstrives to enhance the quality of residentiallife by cultivating an atmosphere conduciveto educational pursuits and thedevelopment of community within thestudent body. These contributions forman integral part of a Columbia educationby stimulating mutual understanding andby fostering an atmosphere based onthe appreciation of the differences andsimilarities characterizing such a diversecultural community.The undergraduate student staff,resident advisers (RAs), and communityadvisers (CAs) serve as role models fortheir residents. They facilitate discussionsabout community standards, providecommunity building programs, andserve as a resource for the residents.Their RAs/CAs serve as the front line ofa layered on-call system and are trainedto respond to the variety of issues thatemerge in community life. As backup,they have graduate assistants (GAs),associate directors (ADs), and a deanon-duty.SEAS 2010–2011

The Faculty-in-Residence Programallows students, alumni, and faculty tomeet formally and informally throughoutthe year. Faculty members in residencein three residence halls invite studentsto dine in their apartments; organizespecial programs around issues of interest;provide opportunities for academicgrowth and challenges within the residencehalls; and help students establishlinks with major cultural, political, andprofessional institutions in New YorkCity. In addition, the faculty member inresidence partners with the SEAS alumnioffice to provide opportunities for studentsto network and gain exposure to avariety of careers.Begun in fall 2006, the GatewayResidential Initiative allows SEASfirst-years, sophomores, juniors, andseniors to live together clustered in theLiving Learning Center (LLC) housed inHartley and Wallach Halls. This initiativeseeks to bridge the academic and cocurricularexperience for SEAS students.Mentorship between students, connectionamong the class years, and alumniinteraction are the foundations for thesuccess of the program.Fraternities and SororitiesFraternities and sororites have brownstonesnear the campus and some ofthe organizations without brownstoneshave a suite within the residence halls.There is a full-time Assistant Director forGreek Life and Leadership Development.The InterGreek Council (IGC) is theself-governing student organization thatprovides guidelines and support to thethree Greek councils: The InterfraternityCouncil (IFC), Panhellenic Council, andMulticutural Greek Council (MGC). Thereare thirty-three recognized Greek organizationswhose membership totals overone thousand undergraduates.Fraternity and sorority members sharein service, scholastic, philanthropic, cultural,and leadership experiences. Thisactive and vibrant community adds tothe diversity of the residential experience.OFFICE OF JUDICIAL AFFAIRSAND COMMUNITY STANDARDSThe Office of Judicial Affairs was createdto assist students in the maintenance ofa safe, honest, and responsible campuscommunity. To achieve this goal, theOffice of Judicial Affairs partners withvarious offices on campus to createprograms designed to educate studentsregarding the potential impact of theiractions on both their individual livesand the community at large. In addition,the Office of Judicial Affairs works withstudent groups to facilitate the developmentof skills and processes studentscan use to hold each other accountablewhen they encounter inappropriatebehavior. The Office of Judicial Affairsand Community Standards also holdsstudents accountable for inappropriatebehavior through the Dean’s Disciplineprocess when necessary.OFFICE OF THEUNIVERSITY CHAPLAINColumbia is home to a community ofscholars, students, and staff from manydifferent religious backgrounds. TheOffice of the University Chaplain ministersto their individual faiths and supports individualspirituality, while promoting interreligiousunderstanding. The UniversityChaplain oversees the work of the UnitedCampus Ministries—a fellowship ofmore than twenty religious life advisersrepresenting specific faith traditions. TheUniversity Chaplain also fosters learningthrough spiritual, ethical, religious,political, and cultural exchanges andhosts programs on matters of justice,faith, and spirituality. Through these andother means, the Office of the UniversityChaplain cultivates interfaith and interculturalawareness.The University Chaplain is availablefor confidential pastoral counseling toindividuals, couples, and families in theColumbia University community. TheOffice of the University Chaplain mayalso assist with private ceremonies suchas weddings, christenings, and memorialservices. We warmly welcome yourinterest, questions, and participation.For more information, please call theEarl Hall Center at 212-854-1474 or212-854-6242 or visit www.columbia.edu/cu/earl/.LERNER HALLColumbia’s new student center, LernerHall, officially opened in the fall of 1999.Located on the southwest corner ofcampus, this 225,000-square-foot studentcenter was designed by BernardTschumi, the former Dean of Columbia’sGraduate School of Architecture,Planning and Preservation. Architecturalfeatures of Lerner Hall, such as the glassfacade and ramps, allow the campusto clearly view the activities within thebuilding, and offer those within Lernerscenic views of the campus.Undergraduate students are likely tovisit Lerner to check the mail from the7,000 student mailboxes located alongthe ramps. Students may check theire-mail in Lerner’s computer center orby plugging in their laptop computersat one of Lerner’s Ethernet-outfittedlounges. Students will also visit Lernerto interact with one another in variousways. They may strategize and planevents with their student organizations inone of the student club offices, or in themeeting rooms designated for studentclub usage. Students may also meetfriends in one of Lerner’s two dininglocations, for an event in the auditorium,in various lounges, or in one of the building’smultipurpose spaces that are idealfor exercise classes.In addition to providing spaces forstudent interaction, Lerner is home to theColumbia University Bookstore. Lerneralso features retail services, includinga travel agency, a copy center, and anelectronic banking center. Included inthe building are orchestra/band rehearsaland art exhibition spaces, and variousadministrative offices (Student Affairs,Student Services, Residential Programs,Judicial Affairs, Multicultural Affairs, Officeof Student Group Advising, Center forStudent Advising, Financial Aid, andEducational Financing). These officesalso include Student Development andActivities, the Double Discovery Center,Columbia TV, WKCR, Disability Services,and Counseling and PsychologicalServices.OFFICE OF GRADUATESTUDENT SERVICESThe Office of Graduate Student Servicesat The Fu Foundation School ofEngineering and Applied Science is integralto the School’s teaching, research,and service mission, and works toenhance the educational opportunitiesavailable to students. This Officeprovides leadership for the integrationof educational programs and services215SEAS 2010–2011

216that enhance recruitment, retention, andquality of campus life for graduate studentsat SEAS. It strives to demonstratesensitivity and concern in addressing theneeds of the School’s population. TheOffice is dedicated to providing serviceto prospective, new, and continuing studentspursuing a graduate education inengineering or applied science.INTERCOLLEGIATE ATHLETICSPROGRAMColumbia has a long tradition of successin intercollegiate athletics, and TheFu Foundation School of Engineeringand Applied Science has always beenan active participant in these programs.While Columbia’s intercollegiate athleticsprogram is governed by Ivy Leagueregulations, Columbia is also a memberof the National Collegiate AthleticAssociation. Columbia sponsors men’svarsity teams in baseball, basketball,cross-country, fencing, football, golf,rowing (heavyweight and lightweight),soccer, squash, swimming and diving,tennis, track and field (indoor and outdoor),and wrestling.Women in all undergraduate divisionsof Columbia and in BarnardCollege compete together as membersof University-wide athletic teams. Thearrangement, called a consortium underNCAA rules, is one of only three in thenation and the only one on a DivisionI level. Currently, there are women’svarsity teams in archery, basketball,cross-country, fencing, field hockey,golf, lacrosse, rowing, soccer, softball,squash, swimming and diving, tennis,track and field (indoor and outdoor), andvolleyball.Columbia’s commitment to successin intercollegiate sporting competitionhas been matched by the determinationof alumni and administrators toupgrade the University’s athletic facilities.The Baker Field Athletics Complex,a few miles up the Hudson River on thenorthern tip of Manhattan, has beencompletely rebuilt and expanded. Thecomplex features Lawrence A. WienStadium, a precast concrete footballstadium capable of seating 17,000spectators; an Olympic-quality synthetictrack; a 3,500-seat soccer stadium;Robertson Field, home of the baseballprogram; and softball and field hockeyvenues. At Columbia’s Dick SavittTennis Center at the Baker AthleticsComplex there are six cushioned hardtennis courts, all of which are coveredby a state-of-the-art air dome for winteruse. The Remmer and 1929 Boathouseincludes a three-bay shell house, completewith an upper level that includesan erg and weight room.Columbia’s Dodge Physical FitnessCenter draws thousands of studentseach day for recreation, physical educationclasses, intramural play, clubcompetition, and varsity sport contestsand practices. The Center houses mostindoor sports and is available to all registeredstudents. Major athletic facilitieson campus include two full-size gymnasiumsfor basketball, volleyball, andbadminton; eight squash and handballcourts; the eight-lane Uris pool withthree diving boards; a fully equippedthree-level exercise and weight roomfacility; two aerobic dance/martial artsrooms; a fencing room; a wrestlingroom; an indoor running track; and twofully equipped saunas.Eligibility for Intercollegiate AthleticsAny student in the Engineering Schoolwho is pursuing the undergraduateprogram or an approved combined programtoward a first degree is eligible forintercollegiate athletics. To be eligible forathletic activities, the student must: degree credit degree as defined by the NCAA, theIvy League, and Columbia University.These criteria are monitored by theDirector of Compliance and certifiedby the Office of the Registrar. more than eight terms for the bachelor’s degreeQuestions about athletic eligibility shouldbe referred to the appropriate academicadviser or the Director of Compliancein the Department of IntercollegiateAthletics and Physical Education.Recreational ProgramsIn addition to the voluntary courses(see page 13), the Department ofIntercollegiate Athletics and PhysicalEducation offers a comprehensiveIntramural and Club Sports Program.Through intramurals, students have theopportunity to participate in both individualand team sports. Individual activitiesfunction through tournaments, whileteam activities feature both league andtournament competition. Club sports aredesigned to allow groups of individualswho share a common athletics interestto organize and collectively pursue thisactivity. Clubs are organized on recreational,instructional, and competitivelevels. Activities range from organizedinstruction to intercollegiate and tournamentcompetition. A list of the intramuralactivities and sports clubs as well as allinformation regarding the program canbe obtained in the Office of Intramuralsand Club Sports, 331 Dodge FitnessCenter or on the Web site at www.gocolumbialions.com.CAMPUS SAFETYAND SECURITYColumbia University prepares an annualsecurity report, which is available to allcurrent and prospective employees andstudents. The report includes statisticsfor the three previous years concerningreported crimes that occurred oncampus, in certain off campus buildingsor property owned or controlledby Columbia University, and on publicproperty within, or immediately adjacentto and accessible from, the campus.The report also includes institutional policiesconcerning campus security, suchas policies concerning sexual assault,and other matters. You can obtain acopy of this report by contacting theDirector of Administration and Planning,Public Safety at 212-854-3815 or byaccessing the following Web site:www.columbia.edu/cu/publicsafety/SecurityReport.pdf.SEAS 2010–2011

STUDENT SERVICES217UNIVERSITY HOUSINGUndergraduate HousingThe residence halls are an importantfocus for campus life outside the classroom,with the University housing morethan 95 percent of the undergraduatepopulation in residence halls on ornear the campus. A trained ResidentialPrograms staff lives with the studentsin the halls. They work to create anatmosphere conducive to educationalpursuits and the development of communityamong the diverse student body.Throughout the year the ResidentialPrograms staff presents programs in theresidence halls and off campus that areboth social and educational.Columbia guarantees housing forall undergraduate students (excepttransfers) who have filed their intentto reside on campus by the stateddeadline and who have continuouslyregistered as full-time students. Eachspring, continuing students participate ina room-selection process to select theiraccommodations for the next academicyear. Students who take an unauthorizedleave of absence are placed onthe non-guaranteed wait list upon theirreturn and are on the wait list for eachsubsequent year.A variety of residence hall accommodationsare available to Columbiastudents. Carman, John Jay, Wien,Furnald, McBain, Schapiro, Harmonyand Broadway Residence Halls aretraditional corridor-style residence halls,and all but Wien, John Jay, and Carmanhave kitchens on each floor. EastCampus, 47 Claremont, Hartley-WallachLiving Learning Center, Hogan, River,Ruggles, 600 West 113th Street, Watt,and Woodbridge offer suite-style living,and all have kitchens. All residence hallrooms are either single or double. Singleand double rooms are available in allhalls except Carman, which has onlydoubles, and Hogan, which is all singles.The residence halls are alsohome to a variety of Special InterestCommunities. These communities providean opportunity for students with acommon interest to live together anddevelop programs in their area of interest.The themes may vary from year toyear. The current communities includeCasa Latina, Metta House, Pan AfricanHouse, Community Health House, TheSymposium House, and others. Firstyearstudents are not eligible to live inSpecial Interest Communities but arewelcome to attend events.Upperclass Columbia students alsohave the option of living in Brownstones,Greek organizations, and certainBarnard College halls. Rooms are chosenby a room selection process, whichtakes place each spring.For more information, please visitthe housing Web site atwww.columbia.edu/cu/housingGraduate HousingGraduate students have a number ofhousing opportunities in the MorningsideHeights neighborhood. The three mainsources are University ApartmentHousing (UAH), International House,and off-campus listings. UAH operatesColumbia-owned apartments anddormitory-style suites in the Morningsidearea within walking distance of the campus.For further information, see UAH’sWeb site at www.columbia.edu/cu/ire.International House, a privately ownedstudent residence near the campus, hasaccommodations for about five hundredgraduate students, both internationaland American, who attend various areacolleges and universities. It provides asupportive and cross-cultural environmentwith many activities and resources,and it is conveniently located two blocksfrom the Engineering building. For moreinformation, write or call: InternationalHouse, 500 Riverside Drive, New York,NY 10027; 212-316-8400; or checktheir Web site at www.ihouse-nyc.org.There are also a number of offcampushousing opportunities. TheUniversity operates Off-Campus HousingAssistance (OCHA), which lists roomsand apartments in rental properties notowned or operated by the University.Only students with a valid ID or admissionacceptance letter are permitted touse the facility. OCHA is open throughoutthe winter and summer vacationperiods except academic holidays.Students should call 212-854-2773 foroffice hours. OCHA also operates a Webpage at www.columbia.edu/cu/ire/ocha.There is also a list of alternative housingopportunities maintained by the Office ofGraduate Student Services in 524 S. W.Mudd. Students are sent the AlternativeHousing flyer in their orientation packets.UAH applications are sent along withacceptance packets from the Office ofGraduate Student Services. They arealso available in the Office of GraduateStudent Services and the UAH Office.You can also seek additional informationSEAS 2010–2011

218on the Columbia Students Page: www.columbia.edu/cu/students. Graduatehousing through UAH is processed forthe fall and spring terms only. Summersublets are also available through individualreferrals. The UAH Office maintainsan active listing for those interested.Due to the growing demand forhousing, graduate housing is no longerguaranteed, but every effort is madeto accommodate you. It is critical thatyou submit your housing application assoon as possible and that you follow theinstructions in your acceptance packet.Housing applications received after theset date are not guaranteed housing.The order of priority for selection is:graduate fellowship recipients, Zone 1students (those who live further than250 miles from campus), and then Zone2 students (those who live between 50and 250 miles from campus). All continuingstudents and applications fromZone 3 areas (within 50 miles) are automaticallyplaced on a waiting list.UAH-approved students can beginviewing apartments and moving in duringthe last week of August for the fallterm, and early January for the springterm. Students will be properly notified ofGraduate Orientation and Registration,which are generally held the week beforethe first day of class. If a student needsto move in earlier, proper documentationfrom the department in support of therequest is necessary.DINING SERVICESFirst-Year StudentsAll first-year students in residence arerequired to enroll in one of two diningplans, each of which is comprised of avarying number of meals served in JohnJay Dining Hall, Ferris Booth Commons,or JJ’s Place, and Dining Dollars, whichcan be used at the 12 dining locationson campus.First-Year Dining Plans 2010–20111. 19 meals per week and 75 DiningDollars per term, plus 15 floatingmeals and 6 faculty meals2. 15 meals per week and 125 DiningDollars per term, plus 10 floatingmeals and 6 faculty mealsThe dining plans are transacted throughColumbia’s ID Card, called the ColumbiaCard, which serves as a convenient wayto enjoy dining all over campus withoutcarrying cash.MealsThe meals portion of the dining planenables students to help themselvesto unlimited servings of food servedin John Jay Dining Hall, Ferris BoothCommons, or JJ’s Place. The hours ofoperations for these locations offers diningoptions for breakfast, lunch, dinner,and late-night, with continuous diningfrom 7:30 a.m. to midnight.Dining DollarsIn addition to meals, Dining Dollars comprisethe other portion of the first-yeardining plan. Each Dining Dollar is equalto one dollar and operates as a decliningbalance account, much like a debit card.Columbia Dining Services maintainstwelve dining facilities conveniently locatedon campus. Each of the locationsaccepts Dining Dollars, an alternative tocash payment that is accessed by theColumbia Card (student ID card).With Dining Dollars, students willenjoy the ease and flexibility of cashlesstransactions as well as the savings ofsales tax on all food purchases. DiningDollars will roll over from year to yearuntil graduation.SEAS 2010–2011

Upperclass and Graduate StudentsMany upperclass and graduate studentswho dine on campus open a DiningDollars account; however, some chooseto enroll in an upperclass/graduate studentdining plan.Dining Services offers four plans—allare accessed by the Columbia Cardand can be used for meals in John JayDining Hall, Ferris Booth Commons, orJJ’s Place.The hours of operations forthese locations offers dining options forbreakfast, lunch, dinner, and late-night,with continuous dining from 7:30 a.m.to midnight.Upperclass, GS, and Graduate DiningPlans 2010–2011A. 14 meals per week and 200 DiningDollars per term, plus 15 floatingmeals and 6 faculty mealsB. 175 meals and 200 Dining Dollars perterm, plus 6 guest mealsC. 100 meals and 125 Dining Dollars perterm, plus 4 guest mealsD. 75 meals and 75 Dining Dollars perterm, plus 2 guest mealsKosher Dining PlanAll students who participate in a diningplan, including first-year, upperclass,General Studies, or graduate students,are eligible for the Columbia KosherDining Plan. Signing up for this diningplan allows access to a restrictedkosher area within John Jay DiningHall as well as Express Meals to go.CU kosher meals can also, for anadditional charge, be exchanged fora kosher meal at Barnard’s HewittHall (kosher to kosher only). To signup, the student selects a plan fromeither the First Year Dining Plan orthe Upperclass Dining Plan options,according to the student’s status, thenelects to enroll in the Kosher DiningPlan. The addition of the KosherDining Plan adds 10 percent to thecost of the selected plan. Visit theH&D Customer Service Center in 118Hartley Hall (enrollment allowed at anypoint throughout the term) to sign up.Locations/Menus/HoursLocations, menus, and hours of allcampus dining facilities can be found atwww.columbia.edu/cu/dining.HEALTH SERVICES ANDSTUDENT HEALTH INSURANCEHealth Services at Columbia providesintegrated and accessible services andprograms that support the well-being ofthe campus community and the personaland academic development of students.There are more than 100 individuals atHealth Services to meet students’ healthneeds, including medical providers,nutritionists, disability specialists, healtheducators, therapists, psychiatrists, peercounselors, student personnel, supportstaff, and administrative professionals.The programs and services are arrangedin five departments:Primary Care Medical Services(PCMS) provides routine and urgentmedical care, as well as sexual health,reproductive and gynecological services,travel medicine, LGBTQ healthcare, confidential HIV testing andimmunizations. Through the OpenCommunicator function, students canmake appointments online and viewtheir primary care provider information(bios and photos are availableonline). When Primary Care is closed,a clinician-on-call can provide telephoneadvice about urgent medicalconditions. John Jay Hall, 3rd and 4thfloors.Counseling and Psychological Services(CPS) offers short-term individual counseling,couples counseling, student lifesupport groups, and medication consultation.Students are encouraged tomake appointments and to select a CPSclinician (bios and photos are availableonline). When CPS is closed, a clinicianon-callcan provide telephone adviceabout urgent mental health concerns.Alfred Lerner Hall, 8th floor.Alice! Health Promotion Program connectsstudents with information andresources, and supports healthy attitudesand behaviors within the campuscommunity. Alice! provides interactivetrainings, runs “Go Ask Alice!,” a healthquestion-and answer Internet resource(www.goaskalice.columbia.edu), andleads a range of health initiatives forColumbia students. Wien Hall, 1st floor.Office of Disability Services (ODS)coordinates reasonable accommodationsand support services includingassistive technology, networking groups,academic skills workshops, and learningspecialists. Students seeking reasonableaccommodations or support servicesfrom ODS are required to register withthe office and provide disability documentationbefore receiving services.Registration and documentation guidelinesare available online. Alfred LernerHall, 7th floor.Sexual Violence Prevention andResponse Program (SVPRP) supportsstudents in healing from sexual and relationshipviolence, as well as educatesstudents about consent and coercionto promote a respectful and safe campus.Through innovative programmingand community collaboration, SVPRPempowers students to make informeddecisions, and take action to end sexualand relationship violence. Alfred LernerHall, Room 301.All Health Services programs adhereto strict standards of confidentiality incompliance with federal and state laws.Your Health at ColumbiaColumbia students have access tohealth care through on-campus programsand services, and insuranceplans for off-campus health care andservices. The coverage provided bythe Health Service Program and theColumbia Student Health Insurance Plan(or a comparable insurance plan) worktogether to help meet your health careneeds. To meet the insurance requirement,students must confirm their enrollmentin the Columbia Student MedicalInsurance Plan or provide proof of comparablecoverage.Health Service Program covers oncampusservices provided by the HSCdepartments listed above. The HealthService Program also provides supplementalcoverage for emergency healthcare, outpatient chemical dependencytreatment, and outpatient mental healthcare. The Health Service Program ismandatory for all full-time students, andthe fee will automatically appear on students’E-bill.Columbia Student Medical InsurancePlan (Columbia Plan) covers off-campusmedical services. The plan has twolevels: Comprehensive and Basic. Allfull-time students are automatically219SEAS 2010–2011

220enrolled in and billed for the Basic levelof the Columbia Plan, but may upgradeto the Comprehensive level of the planduring designated enrollment periods.Students may request a waiver fromthe Columbia Plan by providing proofof comparable insurance coverage(alternate plans must meet Columbia’scriteria for comparable coverage, availableonline). Part-time students may alsoenroll in the Columbia Plan. To confirm,upgrade or request a waiver, visit theHealth Services Web site at www.health.columbia.edu.Immunization RequirementsMeningococcal Meningitis DecisionNew York State public health lawrequires that students taking six or morepoints receive information from their institutionsabout meningococcal meningitisand the vaccine that protects againstmost strains of the disease that canoccur on university campuses. Columbiastudents must make an informed decisionabout being vaccinated and certifytheir decision online. Full instructions aregiven online, and the process takes twoto three minutes to complete. Studentsmust formally indicate their decisionabout being vaccinated before they willbe permitted to register for classes.Certify your meningitis decision onlinebefore registration begins.Measles, Mumps, and Rubella (MMR)New York State public health lawrequires that students taking 6 ormore points provide documentationof immunity to measles, mumps, andrubella (MMR) before their first termof study. There are several ways todocument immunity. In all cases, theColumbia University MMR form must becompleted and submitted to the HealthServices at Columbia ImmunizationOffice in Wien Hall, first floor, Suite108B, no later than the specifieddeadline, listed on the Health ServicesWeb site, www.health.columbia.edu. The blood test to determine ifMMR immunization is necessary canbe obtained at Primary Care MedicalServices. There is a fee for this service.If you have any questions aboutthese requirements, please e-mail hsenrollment@columbia.eduor visit www.health.columbia.edu.Immunizations RecommendationsHealth Services at Columbia recommendsthat all students be properlyimmunized against or have immunity tothe following: hepatitis B (three-doseseries), varicella (chicken pox, two-doseseries), tetanus, and all routine childhooddiseases. These immunizationsare available at Primary Care MedicalServices. Students enrolled in the HealthService Program are not charged forthe following vaccines when administeredat Primary Care Medical Services:MMR, Hepatitis A, Hepatitis B, HepatitisCombination A and B, Tetanus-Diphtheria, and Tetanus-Diphtheria-Pertussis. For all other vaccinations,students will be charged for the cost ofthe vaccine. Vaccinations are availableto students not enrolled in the HealthService Program for a minimal fee. Formore information, please check online atwww.health.columbia.edu.Contact Health Services at Columbiawww.health.columbia.edu212-854-2284Clinician-on-Call(After hours urgent health concerns)212-854-9797Insurance and ImmunizationQuestionswww.health.columbia.eduE-mail: hs-enrollment@columbia.eduOn-Campus Emergency ResourcesCAVA (Ambulance): 212-854-5555Rape Crisis/Anti-Violence Support Center:212-854-HELP, 212-854-WALKPublic Safety: 212-854-5555SEAS 2010–2011

Scholarships, Fellowships,Awards, and Prizes

222SCHOLARSHIPS, FELLOWSHIPS, AWARDS, AND PRIZESANNUAL GIFT FELLOWSHIPSAND SCHOLARSHIPSEach year the University receives gifts ofmoney, some of which are renewals, forfellowships and scholarships. The fellowshipsand scholarships made available inrecent years as a result of such gifts are:Asian Columbia Alumni AssociationScholarship (1999)General financial aid for Asian students.Kingsley R. Chin Scholarship (2009)Gift of Dr. Kingsley R. Chin (1989) tobenefit needy and deserving undergraduatesstudying biomedical engineering.Columbia-Whitman MemorialScholarshipAwarded from time to time to a WhitmanCollege preengineering junior for study inthe Columbia Engineering School towardthe B.S. degree. Maximum value: fulltuition and fees for the academic year.The holder may apply for renewal.Con Edison Minority and FemaleScholarship ProgramTo aid deserving and promising minorityor female students from within the ConEdison service territory who will be pursuinga career in engineering, by providinga renewable scholarship of at least$1,500 and a job internship. Financialneed must be demonstrated.Consolidated Natural Gas CompanyFellowshipFor graduate students in chemical engineeringand applied chemistry.DuPont FellowshipIn chemical engineering.Everard A. Elledge MemorialScholarship (1985)Gift of Carol G. Elledge, in memory ofEverard A. Elledge (1942).Ioannou Scholarship (1999)Donated by Constantine and CeciliaIoannou, Constantine D & B, Ltd.Awarded to a deserving undergraduate,preference given to a Greek-Americanstudent.Moses and Hannah MalkinScholarship Fund Gift (2004)Gift of Moses and Hannah Malkin for anundergraduate engineering scholarship.Monsanto Chemical CompanyScholarshipOpen to students in Barnard College,Columbia College, and the EngineeringSchool who are pursuing a program ofstudy in chemical engineering or directedtoward it.Louis Morin Scholars and Fellows(2000)Gift of the Louis Morin Charitable Trust.Designated for Jewish undergraduates,Ph.D.’s, and postdocs.The National Action Council forMinorities in Engineering Inc.Incentive Grants ProgramRenewable grants ranging from $250to $2,500 for minority students in goodacademic standing who continue tohave financial need. These awardssupplement the funds a student raisesthrough work, family, schools, foundations,and government grant programs.New York Chapter of the AmericanSociety for Metals ScholarshipIn metallurgy.Procter and Gamble FellowshipIn chemical engineering and appliedchemistry.Benjamin A. Tarver Jr. Memorial Fund(2002)Gifts of Benjamin A. Tarver Sr. and variousdonors in memory of Benjamin A.Tarver Jr. (2004), who passed away onApril 8, 2002.Ullian Family Scholarship (2008)Gift of Arthur and Dorothy Ullian(Parents, Class of 2008) to benefitdeserving undergraduates at ColumbiaEngineering.The Weinig Scholars Program at theSchool of Engineering and AppliedScience (1995)For engineering students who are ofhigh academic achievement.Westmoreland Davis FellowshipFor male graduate students from Virginia.ENDOWED SCHOLARSHIPSAND GRANTSCvi Abel Memorial Scholarship (2003)Gift of Jack Abel.Aigrain Family Scholarship (2008)Gift of Jacques and Nicolleta Aigrain,parents, Class of 2008.SEAS 2010–2011

223Walter H. Aldridge (1936)Gift of Walter H. Aldridge.Alvey-Ferguson CompanyScholarship (1948)Gift of the Alvey-Ferguson Company.Erwin H. Amick Memorial Scholarship(1970)Gift of various donors for students in chemicalengineering and applied chemistry.Nathaniel Arbiter Scholarship (1985)Gift of various donors in honor ofProfessor Nathaniel Arbiter for graduateand undergraduate students in theHenry Krumb School of Mines in thefollowing specializations in order of preference:mineral beneficiation, mines, andphysical metallurgy.Attardo Scholarship (1999)For needy and deserving students in theFu Foundation School of Engineeringand Applied Science. Gift of Michael J.Attardo (1963).Jee Yin and Choi Heung AuScholarship Fund (2002)Gift of Michael M. Au (1990) to supportundergraduate scholarships at The FuFoundation School of Engineering andApplied Science, with a preference to begiven to needy and deserving studentswho have graduated from StuyvesantHigh School in New York City.Frank and Harriet Ayer Scholarship(1977)Bequest of Frank A. Ayer. Graduatesof Deerfield Academy are given firstpreference.Cesare Barbieri Scholarship (1953)Gift of Cesare Barbieri Fund.William S. Barstow Scholarship (1935)Gift of William S. Barstow.Edwin D. Becker Scholarship Fund(1993)Gift of Edwin D. Becker (1956).Preference is given to students from theRocky Mountain states.John E. Bertram MemorialScholarship (1990)Gift of Mrs. Lucy Bertram and friendsin honor of John E. Bertram. Awardedto students in electrical engineering orcomputer science.Jerry and Evelyn Bishop Scholarship(1984)Gift of Jerry (1942) and Evelyn Bishopfor students in the Combined PlanProgram. Preference is given to studentsin the program who attended ColumbiaCollege.Paul H. Blaustein Scholarship (1994)Gift of Barbara Blaustein, StaceyBlaustein Divack and Joshua Divack.Philip P. Bonanno Scholarship (1999)Donated by Philip P. Bonanno (1955),Fidelity Investments Charitable Gift Fund.Awarded to a deserving undergraduate.Cornelius A. Boyle Scholarship (1962)Bequest of Cornelius A. Boyle.Lauren Breakiron Fund (1999)For a student continuing in The FuFoundation School of Engineering andApplied Science. Preference given toUnited States citizens. Gift of Lauren P.Breakiron (1956).Edwin W. and Mary ElizabethBright Scholarship in MechanicalEngineering (1985)Gift of Edwin W. (1942) and MaryElizabeth Bright. Awarded to a deservingmechanical engineering student who is anative-born U.S. citizen.Lewis G. Burnell MemorialScholarship (2001)Gift of Roger W. Burnell in memory ofhis father, Lewis G. Burnell. Incometo award an annual scholarship to aneedy and deserving undergraduatestudent in The Fu Foundation School ofEngineering and Applied Science.Burns and Roe, Arthur J. FiehnScholarship (1989)Gifts from various donors in memory ofArthur J. Fiehn (1946).Michael and Charo BykhovskyScholarship (2001)Gift of Michael Bykhovsky (1983) to supportneedy and deserving undergraduatestudents.Byron Fellowship (1980)Bequest of Verna and Oscar Byron(1914).Samuel J. Clarke Scholarship (1960)Bequest of Agnes Robertson Clarke.Class of 1885 (1910)Gift of the Class of 1885 School ofMines in commemoration of the twentyfifthanniversary of their graduation.SEAS 2010–2011

224Class of 1889 (1939)Gift of the Class of 1889 College andEngineering.Class of 1900 (1940)Gift of the Class of 1900 College andEngineering.Class of 1902 (1952)Gift of the Class of 1902 College andEngineering.Class of 1906 (1940)Gift of the Class of 1906 in honor ofFrank D. Fackenthal (1906).Class of 1907 (1937)Gift of the Class of 1907. Preference isgiven to sons and descendants of classmembers.Class of 1909 (1959)Gift of the Class of 1909 in honor ofJohn J. Ryan.Class of 1913 (1963)Gift of the Class of 1913 in commemorationof the fiftieth anniversary of theirgraduation.Class of 1914 (1937)Gift of the Class of 1914 College andEngineering for a pre-engineering orprearchitecture student.Class of 1950 Endowed Scholarship(2000)Gift of members of the Class of 1950 incommemoration of the fiftieth anniversaryof their graduation. Awarded to adeserving undergraduate.Class of 1951 Endowed Scholarship(2001)Gift of members of the Class of 1951 incommemoration of the fiftieth anniversaryof their graduation. Awarded to adeserving undergraduate.Class of 1952 Endowed Scholarship(2002)Established by Alexander Feiner to beawarded to a deserving undergraduate.Hugo Cohn Scholarship (1984)Awarded annually with preference givento electrical engineering students. Gift ofHugo Cohn (1909).Herbert J. Cooper Scholarship (1999)Gift of Mrs. Deborah Cooper and theEstate of Herbert J. Cooper (1946).Awarded to a deserving undergraduate.Milton L. Cornell Scholarship (1958)Gift of various donors in memory ofMilton L. Cornell.Paul and Lillian Costallat Scholarship(1972)Gift of Paul and Lillian Costallat.Frederick Van Dyke CruserScholarship (1980)Bequest of Maude Adelaide Cruser. Forstudents in chemical engineering withfinancial need.Cytryn Family Endowed Scholarship(2002)Gift of the Cytryn Family Fund to providefinancial aid to deserving undergraduates.Frank W. Demuth Scholarship (1965)Bequest of Frank W. Demuth (1914).Freda Imber Dicker EndowedScholarship Fund (2000)Gift of Dr. Stanley Dicker (1961) in honorof the hundredth anniversary of hismother’s birth (March 5, 1900).Jack Dicker Endowed Scholarship(2003)Gift of Dr. Stanley Dicker (1961) in honorof his father, to support a deservingjunior or senior in the Department ofBiomedical Engineering.James and Donna Down Scholarship(1997)Gift of James (1973) and Donna Downto be awarded annually to a deservingminority undergraduate who has demonstratedacademic achievement.Stancliffe Bazen Downes Scholarship(1945)Bequest of Bezena Treat DownesMerriman in honor of her brother, for astudent in civil engineering.Brooke Lynn Elzweig Scholarship(2002)Gift of Gary Elzweig (1977). Income tosupport an annual scholarship for adeserving undergraduate student withhigh financial need.Jack B. Freeman Scholarship (1994)Supports an undergraduate at SEASwho also plays varsity baseball. Gift ofJack B. Freeman (1955).Pier-Luigi Focardi Scholarship (1964)Bequest of Clara G. Focardi.Ford/EEOC ScholarshipDesignated for minorities and women.Preference is given to Ford employees,their spouses, or children.Z. Y. Fu Scholarship (1993)Gift of The Fu Foundation for undergraduatescholarship support for the Schoolof Engineering and Applied Science.General Motors ScholarshipDesignated for minorities and women.Preference is given to General Motorsemployees, their spouses, or children.Ben and Ethelyn GeschwindEndowed Scholarship (2004)Gift of Benjamin and Ethelyn (1984)Geschwind. Awarded to a deservingundergraduate in the School ofEngineering.Alger C. Gildersleeve Scholarship(1955)Bequest of Josephine M. Gildersleeve, inhonor of Alger G. Gildersleeve (1889).Frederick A. Goetze Scholarship (1960)Gift of William A. Baum, in honor ofthe former Dean of the School ofEngineering.Sarah E. Grant Memorial Scholarship(1997)Gift of Geoffrey T. (1982) and AnnetteM. Grant in memory of their daughter,Sarah, to be awarded annually to adeserving undergraduate who has demonstratedacademic achievement.Adam R. Greenbaum MemorialScholarship FundEstablished in memory of Adam R.Greenbaum by his parents, relatives,and friends following his death inFebruary 2001, when he was a sophomore.The scholarship is given to aSEAS sophomore who was named tothe Dean’s List as a first-year, as Adamwas, with a preference to students fromNew Jersey and New York.SEAS 2010–2011

Luther E. Gregory Scholarship (1963)Bequest of Luther E. Gregory (1893).Robert Gross Fund (1999)Gifts of friends of Robert Gross.For anapplied physics student.Wallace K. Grubman-GrahamScholarship (1998)Gift of Wallace Grubman (1950) and theGrubman Graham Foundation to supportan undergraduate student in chemicalengineering.Lawrence A. Gussman Scholarship(1987)Gift of Lawrence Gussman (1938).Awarded annually to students studyingcomputer science.Haight Family Scholarship (2004)Gift of Deborah E. Haight (2000).Awarded to a talented and deservingundergraduate.Ralph W. Haines Scholarship (2002)Gift of Ralph W. Haines (1969) forneedy and deserving students in The FuFoundation School of Engineering andApplied Science.A. A. Halden Scholarship (1962)Established by bequests from DorothyC. Halden and Barbara Schwartz inmemory of Alfred A. Halden.The Hamann Scholarship (1970)Bequest of Adolf M. Hamann (1910).Alfred M. and Cornelia H. HaringScholarship (1965)Gift of the Aeroflex Foundation for anannual scholarship in the School of Mines.H. Field Haviland Scholarship Fund(1988)Scholarships to be awarded equallybetween The Fu Foundation School ofEngineering and Applied Science andColumbia College. Bequest of Henry F.Haviland (1902).Harold T. Helmer Scholarship (1965)Bequest of Harold T. Helmer.David Bendel Hertz College/Engineering Interschool Scholarship(1989)Gift of David B. Hertz (1939). Awardedin alternate years to the College andto the Engineering School to a studentelecting to receive a B.A. from ColumbiaCollege and a B.S. from The FuFoundation School of Engineering andApplied Science.Edward Gurnee Hewitt Scholarship(1980)Bequest of Mary Louise Cromwell.Prentice Hiam Memorial Scholarship(2007)Gift of Atul Khanna (1983). Preferencegiven to international students.James T. Horn Scholarship (1938)Gift of Sarah L. and Mary T. Horn, inmemory of their brother, James T. Horn(1884).Richard and Janet Hunter Scholarship(2000)Gift of Richard (1967) and Janet Hunter.Scholarship awarded to 3-2 programparticipants entering the School ofEngineering and Applied Science, withprefereces given to graduates fromWhitman College.Jonathan Lewis Isaacs MemorialScholarship (2001)This scholarship was endowed in 2001by Gary F. Jonas ’66 and Jonathan L.Isaacs ’66 as the Future EntrepreneursScholarship to acknowledge the thirtyfifthanniversary of their graduation fromColumbia School of Engineering andApplied Science. On April 30, 2003,Mr. Isaacs died at the young age offifty-seven, and the scholarship wasthen renamed in his memory by Gary F.Jonas, with the support of Jon’s wife,Charlotte Isaacs.Sheldon E. Isakoff EndowedScholarship Fund (2000)Gift of Sheldon E. (1945) and AnitaIsakoff. Awarded to a deserving chemicalengineering undergraduate.Alfred L. Jaros Memorial Scholarship(1967)Gift of various donors, in memory ofAlfred L. Jaros (1911).Cavalier Hargrave Jouet Scholarship(1941)Bequest of Belinda Hearn Jouet, inmemory of C. H. Jouet (1882).Alfred E. Kadell Scholarship (1995)Bequest of the Estate of Alfred E. Kadell(1921).Wayne Kao Scholarship (1988)Awarded annually to undergraduate students.Gift of Mabel C. Kao in memoryof Wayne Kao (1949).Stanley A. and Minna KrollScholarship for Engineering andComputer Science (1987)Gift of Stanley A. Kroll (1928). For undergraduateswho are studying electricalengineering or computer science.Henry Krumb Scholarship (1945)Gift of Henry Krumb for annual scholarshipsin mining engineering, metallurgy,and ore dressing.Jacob Kurtz Memorial Scholarship(1982)Gift of Kulite Semiconductor Products,Inc., and Kulite Tungsten, for undergraduates,preferably studying in the fieldsof metallurgy or solid-state physics. Inmemory of Jacob Kurtz (1917).Ronald A. Kurtz Scholarship Fund(1990)Gift of Kulite Tungsten.Lahey Scholarship (1932)Bequest of Richard Lahey.Charles and Sarah LappleScholarship (2004)Bequest from the Estate of CharlesE. Lapple and Sarah V. Lapple to beused to provide scholarships to deservingundergraduate students in The FuFoundation School of Engineering andApplied Science. The students receivingthe scholarship shall be designatedLapple Scholars.Frank H. Lee Memorial Scholarshipfor Combined Plan Students (1986)Awarded annually to a student in theCombined Plan Program in honor ofProfessor Frank H. Lee.Leung Endowed Scholarship (2006)Gift of Lawrence Leung. Awarded annuallyto a deserving undergraduate.James F. Levens Scholarship (1973)Bequest of Ola Levens Poole for studentsin chemical engineering andapplied chemistry.225SEAS 2010–2011

226George J. Lewin Scholarship (1965)Gift of George J. Lewin (1917) andfriends. Preference given to hearingimpairedstudents.Alvin and Richard H. LewisScholarshipGift of Alvin and Helen S. Lewis in memoryof their son, Richard Lewis (1963).James M. and Elizabeth S. LiEndowed Scholarship (2006)Gift of James (1968, 1970, 1976) andElizabeth Li. Awarded to students majoringin industrial engineering and operations.Robert D. Lilley Memorial Scholarshipand Fellowship (1988)For students who are in their final yearof the 3-2 Combined Plan Program andwho have a commitment to communityservice.Bruce and Doris Lister EndowedScholarship (2000)Gift of Bruce A. Lister (1943, 1947) tosupport a needy and deserving undergraduatestudent in The Fu FoundationSchool of Engineering and AppliedScience.Anna Kazanjian and Guy LongobardoScholarship (2007)Gift of Anna Kazanjian (1949, 1952) andGuy (1949, 1950, 1962) Longobardo.Preference given to students studyingmechanical engineering.Donald D. MacLaren Scholarship(1995)For an undergraduate student whois studying biochemical engineering.Established by Donald D. MacLaren(1945).Manelski Family Scholarship (2004)Gift of Darren E. Manelski (1991) tosupport needy and deserving studentsof The Fu Foundation School ofEngineering and Applied Science.Ernest Marquardt Scholarship (1968)Bequest of Ernest Marquardt (1912).Louis F. Massa Scholarship (1952)Bequest of Louis F. Massa (1890).Ralph Edward Mayer Scholarship(1924)Contributed by friends in memory ofProfessor Ralph Edward Mayer.Henry Michel Scholarship (2005)Gift of Mrs. Mary-Elizabeth Michelin memory of Henry Michel (1949).Scholarship awarded to deservingundergraduate students with preferencegiven to civil engineering majors.Stuart Miller Endowed Scholarship inEngineering (2003)Gift of Stuart Miller, to be used to providesupport for an undergraduate engineeringstudent.John K. Mladinov Scholarship (1994)Gift of Barbara P. Mladinov in honor ofher husband, John K. Mladinov (1943).Awarded to a deserving undergraduatewith a minor in liberal arts.Frank C. Mock and FamilyScholarship (1987)Bequest of Frank C. Mock (1913). Forstudents in electrical engineering withfinancial need.New Hope Foundation Scholarship(2006)Gift of Lee and Margaret Lau. Awardedto a deserving undergraduate withpreference to students from Ontario,Canada, or mainland China.A. Peers Montgomery MemorialScholarship (1990)Gift of the family of A. PeersMontgomery (1926).John J. Morch Scholarship (1963)Bequest of John J. Morch.Seeley W. Mudd Scholarship (1958)Gift of the Seeley W. Mudd Foundation.Several awarded annually for maintenance,not for tuition. Recipient must bea U.S. citizen, and his or her grandfathermust have been born a U.S. citizen.Special application required.Mary Y. Nee Endowed Scholarship(2008)Gift of Mary Yuet-So Nee (1984).Frederick Noel Nye Scholarship(1971)Bequest of Frederick Noel Nye (1927).Parker Family Endowed Scholarship(2001)Gift of Peter D. Parker (1972, 1974).Income to award an annual scholarshipto a needy and deserving undergraduatestudent in The Fu Foundation School ofEngineering and Applied Science.Robert I. Pearlman Scholarship (1989)Gift of Robert I. Pearlman (1955).Awarded annually to students in theSchool of Engineering and AppliedScience. Preference is given to studentsfrom single-parent households.Robert Peele Scholarship (1925)Gift of E. E. Olcott (1874).Brainerd F. Phillipson Scholarship(1936)Gift of an anonymous donor in memoryof Brainerd F. Phillipson.Andre Planiol Scholarship (1967)Bequest of Andre Planiol for a studentfrom France.Roy Howard Pollack Scholarship (1998)Bequest of Roy Howard Pollack to beused for scholarships for junior or seniorstudents in The Fu Foundation School ofEngineering and Applied Science.Polychrome-Gregory HalpernScholarshipFor graduate and undergraduate studentsin chemical engineering andapplied chemistry.Professor William H. ReinmuthScholarship (1988)Gift of Curtis Instruments, Inc., awardedin alternate years to Columbia Collegeand the Engineering School. Preferencewill be given to college students studyingchemistry and to engineeringstudents studying electrochemistry.Established in honor of Professor WilliamH. Reinmuth.Brenda and Dave Rickey EndowedScholarship Fund (2008)Gift of David (1979) and Brenda Rickey(Parent, Class of 2008) to benefit undergraduatestudents from California.SEAS 2010–2011

Kevin T. Roach Endowed Scholarship(2003)Gift of Kevin T. Roach (1977). Incometo provide tuition assistance to undergraduatestudents in engineering atColumbia University.The Frederick Roeser Fund forStudent Aid (1934)An annual loan to help pay educationalexpenses, which is awarded to studentschosen by the Committee on Scholarships.The amount is individually determinedand is to be repaid only if andwhen the student can do so withoutpersonal sacrifice. Repayments go intothe Frederick Roeser Research Fund forresearch in physics and chemistry.Edgar Lewisohn Rossin Scholarship(1949)Bequest of Edgar L. Rossin, to providea scholarship for students in miningengineering.Harry B. Ryker (1947)Bequest of Miss Helen L. Ryker inmemory of her brother, Harry BensonRyker (1900).Thomas J. Sands EndowedScholarship Fund (2001)Gift of Thomas J. Sands to support ascholarship for a needy and deservingundergraduate student at The FuFoundation School of Engineering andApplied Science.Peter K. Scaturro Scholarship Fund(1997)Gift of Peter K. Scaturro (1982, 1985)to be used to support scholarships tostudents in SEAS or Columbia College,with preference given to scholarathletesfrom Archbishop Molloy H.S. inBriarwood, Queens, NY.Norman A. Schefer Scholarship (1999)Gift of Norman A. Schefer (1950) andFay J. Lindner Foundation. Awardedannually to a deserving and talented studentat the School of Engineering.Samuel Y. Sheng Scholarship (2007)Gift of Samuel Y. Sheng (1951), LaurenWong Sheng (1976), Kent Sheng, andJean Sheng. Awarded to students whodemonstrate academic excellence.Mark Schlowsky-Fischer Scholarship(2005)Gift of George Schlowsky (1965) inmemory of Mark Schlowsky-Fischer(1997). Scholarship awarded to deservingundergraduate students with preferencegiven to computer science majors.Ralph J. Schwarz Scholarship (1993)Gift of the Class of 1943 and otherdonors in memory of Ralph J. Schwarz(1943). To be awarded to academicallyoutstanding students who require financialaid.David C. and Gilbert M. SerberMemorial Scholarship (1950)Gift of the Serber family, for a studentin civil engineering, in honor of DavidSerber (1896).Varsha H. Shah Scholarship (2003)Gift of Hemant and Varsha Shah tosupport undergraduate female minoritystudents.Jared K. Shaper ScholarshipFor deserving and qualified candidatesfor degrees in engineering.Edith Shih Interschool ScholarshipFund (2008)Gift of Edith Shih, Esq. (TeachersCollege 1977–1978).Silent Hoist and Crane Company(1950)Gift of the Silent Hoist and CraneCompany.David W. Smyth Scholarship (1957)Bequest of Mrs. Millicent W. Smyth,in memory of her husband, David W.Smyth (1902).Gene F. Straube Fund (2007)Gift of Gene F. Straube (SEAS 1950, CC1949). The fund shall provide scholarshipsto undergraduate students whograduated from a high school or prepschool in northern California, and whoare pursing studies in electrical engineering,computer engineering, or computerscience.Steve Tai and Kin-Ching WuEndowed Scholarship Fund (2001)Gift of Steve Tai (1980) for an annualscholarship to a needy and deservingundergraduate student at The FuFoundation School of Engineering andApplied Science.Tai Family Scholarship (2003)Gift of Timothy Tai to be used to supportAsian students demonstrating financialneed and outstanding academicpotential, with preference given to HongKong, Taiwanese, mainland Chinese,and Chinese-American applicants foradmission. A T. Tai Family Scholar willbe named in a first-year class, and withsuitable academic achievement andcontinuing need, would retain that honoruntil graduation.Grace C. Townsend Scholarship(1941)Bequest of Miss Grace C. Townsend.Theodosios and Ekaterine TypaldosEndowed Scholarship Fund (2000)Gift of Andreas (1969) and ReneeTypaldos and the CommunityFoundation of New Jersey. Awarded todeserving undergraduates. Preference isgiven to Greek-American students.Upton FellowshipFor the children of employees of D.C. Heath and Company of Lexington,Massachusetts.Valeiras Family Scholarship (2009)Gift of Horacio and Amy Valeiras(Parents, Class of 2009) to supportneedy and deserving undergraduatestudents.Kenneth Valentine MemorialScholarship (1986)Bequest of Julia H. Valentine, in memoryof Kenneth Valentine (1914). Awardedannually with preference given to studentsin chemical engineering.Frank Vanderpoel Scholarship (1936)Bequest of Frank Vanderpoel.William E. Verplanck Scholarship(1957)Gift of Mrs. T. Bache Bleecker andEdward F. Verplanck (1912) in memoryof their father, William E. Verplanck(1876).Arnold Von Schrenk Scholarship (1943)Bequest of Mrs. Helen von Schrenk inmemory of her husband, Arnold vonSchrenk.227SEAS 2010–2011

228George Wascheck ScholarshipBequest of George Wascheck (1926).J. Watumull Scholarship (1989)For students in the Graduate Schoolof Arts and Sciences and in theEngineering School who are of EastIndian ancestry.Wells and Greene ScholarshipBequest of Josephine Wells Greene.Herbert A. Wheeler Scholarship (1923)Gift of Herbert A. Wheeler.Frederick C. Winter Scholarship(1966)Gift of various donors in memory ofFrederick C. Winter (1943).William F. Wurster Scholarship (1974)Awarded to a student of chemical engineeringand applied chemistry. Gifts ofWilliam F. Wurster (1913).Robert H. and Margaret H. WyldScholarshipGift of Robert H. (1904) and MargaretH. Wyld.Max Yablick Memorial Scholarship(1986)Bequest of Max Yablick (1914).Awarded annually with preference givento graduates of Hebrew day schoolsand to students in the Combined PlanProgram with Yeshiva University.Theresa Ann Yeager MemorialScholarship (1983)Gift of the family of Theresa Ann Yeager(1981) to support a woman who isenrolled in The Fu Foundation School ofEngineering and Applied Science.FELLOWSHIPSH. Dean Baker Fellowship (1982)Awarded to support deserving graduatestudents in mechanical engineering.Boris A. Bakhmeteff ResearchFellowship in Fluid MechanicsProvides a stipend for the academicyear, with tuition exemption to bearranged by the recipient’s department,to a candidate for a doctoral degree inany department at Columbia Universitywhose research is in fluid mechanics.Quincy Ward Boese FellowshipsPredoctoral fellowships awarded annuallyto students studying under the Facultyof Engineering and Applied Science.Roy S. Bonsib Memorial Fellowship(1957)Awarded to worthy students for advancedstudy or research in engineering.Arthur Brant Fellowship (1997)Gift of Arthur Brant. Awarded to graduatestudents of the Henry Krumb School ofMines in the field of applied geophysics.Samuel Willard Bridgham-WilliamPetit Trowbridge FellowshipA combined fellowship awarded annuallyfor research.William Campbell Fellowships forEncouraging Scientific ResearchFour or five fellowships awarded annuallyfor research in the general field of metals.Robert A.W. and Christine S. CarletonFellowships in Civil EngineeringFellowships awarded to graduatestudents in the Department of CivilEngineering and Engineering Mechanics.Chiang Chen Fellowship (2004)Chiang Chen Industrial CharityFoundation. Awarded to students inmechanical engineering.Professor Bergen Davis FellowshipGift of Dr. Samuel Ruben. To beawarded to a student in chemical engineeringand applied chemistry upon therecommendation of the senior professorin chemical engineering active in electrochemistryresearch.George W. Ellis FellowshipsAwarded annually for graduate study inany division of the University. Open tograduate students who are residents ofthe state of Vermont or who have beengraduated from a Vermont college oruniversity.Michael Frydman EndowedFellowship (2000)To support a fellowship to a deservingmaster’s student in the financial engineeringprogram of the Department ofIndustrial Engineering and OperationsResearch.Robert F. Gartland FellowshipAwarded annually for graduate study inthe Department of Industrial Engineer-ingand Operations Research. Preference isgiven to students who are native-bornU.S. citizens and who intend to pursue acareer in business or finance.GEM FellowshipThe GEM fellowship provides African-Americans, Hispanic Americans, andNative Americans access to graduateeducation. The fellowship includestuition, fees, a stipend, and a paid summerinternship. Applicants for this fellowshipmust be engineering or appliedscience majors.Governor’s Committee onScholarship AchievementOne year awards based on financialneed. Renewal is based on academicprogress, financial need, and availabilityof funds. The student applies directly tothe GCSA; the awards are matched bythe School and are not in supplement toinitial School awards.Carl Gryte Fellowship (2007)Gift from friends of Professor CarlCampbell Gryte. Awarded to needy anddeserving graduate students.Daniel and Florence GuggenheimFellowshipsTwo fellowships for the study of engineeringmechanics in the Institute ofFlight Structures.M. D. Hassialis Memorial Fellowship(2002)Gift of former students of the late KrumbProfessor Emeritus Hassialis. Awarded tograduate students of the Henry KrumbSchool of Mines in the field of Earthresources economics and management.Higgins FellowshipsFellowships awarded annually to firstyeargraduate students.Leta Stetter Hollingworth FellowshipAwarded annually to women who aregraduates of the University of Nebraska,with preference given to those who wereborn in Nebraska or received their earliereducation there. Holders are eligible toapply for reappointment for one year. Agift of Harry L. Hollingworth in memoryof his wife.SEAS 2010–2011

Edward J. Ignall Research FellowshipAwarded annually to encourage andhelp support the research activities of agraduate student in the Department ofIndustrial Engineering and OperationsResearch who is selected by the departmentchair. Gift of family, friends, andformer students in memory of ProfessorEdward J. Ignall.George M. Jaffin FellowshipAwarded for graduate study andresearch leading to the Ph.D. degreein orthopedic biomechanics by theDepartment of Bioengineering of theHospital for Joint Diseases, OrthopedicInstitute, and the Department ofMechanical Engineering. It carries tuitionexemption and a twelve-month stipendof up to $10,000.Herbert H. Kellogg Fellowship (1988)Funded by former students and friendsof Professor Emeritus H. H. Kellogg andthe generous contribution of ProfessorKellogg. Awarded to graduate studentsof the Henry Krumb School of Minesin the field of mineral engineering andchemical metallurgy.Otto Kress Fellowship (1990)Bequest of Mrs. Florence T. Kress inmemory of her husband, Otto Kress.Awarded to postgraduate students.Henry Krumb FellowshipsAnnual fellowships in mining engineering,metallurgy, and ore dressing.John F. T. Kuo Fellowship (1992)Established by Dr. I. J. Won and otherstudents of Professor Emeritus Kuofor the support of graduate students inapplied geophysics.Charles and Sarah Lapple Fellowship(2004)Bequest of Charles (1936, 1937) andSarah Lapple. Awarded to supportdeserving students in the Department ofChemical Engineering.Kuo and Grace Li MemorialFellowship (1993)Gift from the Li Foundation Inc. Awardedto deserving graduate students interestedin mining, mineral resources, metallurgy,and materials science.Ralph H. McKee Fellowship (1979)Bequest of Ralph H. Mckee. Income tobe used for fellowships and/or scholarshipsin the fields of mathematics orchemical engineering.Benjamin Miller Memorial FellowshipAwarded to a graduate student in theDepartment of Industrial Engineering andOperations Research. Preference will begiven to students concerned with workin government-industry regulatory policy,procurement procedures and traderegulations.Nichoplas FellowshipDesignated for male students of Greekextraction or born in Greece and graduatedfrom any Greek college or university.Recipients will be eligible to receivebenefits for not more than two years.Anthony Pesco Fellowship (2006)Gift of Dr. Anthony Pesco (1982, 1983,1987) to support graduate students inthe Chemical Engineering Departmentwho wish to pursue careers in academia.Piyasombatkul Fellowship (2007)Gift from Mr. and Mrs. ChatchaiPiyasombatkul. Preference for studentsfrom Southeast Asia or PresidentialFellow candidates.Presidential DistinguishedFellowshipsThese fellowships are awarded annuallyto selected incoming Ph.D., Eng.Sc.D., and master’s/Ph.D. students.Fellowships include tuition plus anannual stipend of $24,000 for up tofour years, including three months ofsummer research. All applications foradmission are considered for these newfellowships.Queneau Fellowship FundDonated by Bernard R. Queneau.Awarded to a deserving graduate studentin the Department of Earth andEnvironmental Engineering.David M. Rickey Endowed Fellowship(2000)Gift of David M. Rickey (1979). Awardedto students studying electrical engineeringunder the holder of the David M.Rickey Professorship.Lydia C. Roberts GraduateFellowshipsAwarded annually. Open to personsborn in Iowa who have been graduatedfrom an Iowa college or university.In addition to the stipend, the fellow isreimbursed the cost of traveling oncefrom Iowa to New York City and back.Special provisions: holders may notconcentrate their studies in law, medicine,dentistry, veterinary medicine, ortheology, and each holder must, whenaccepting the award, state that it is hisor her purpose to return to Iowa for atleast two years after completing studiesat Columbia; holders are eligible forreappointment.Leo Rubinstein Endowed Fellowship(2005)Bequest of Leo Rubinstein (1963) andgift of Frederick Rubinstein. Awardedto deserving students studying appliedmathematics or industrial design.Frank E. Stinchfield Fellowship inOrthopedic BiomechanicsAwarded for graduate study andresearch in the Department ofMechanical Engineering through theOrthopedic Research Laboratory ofthe Department of Orthopedic Surgery,College of Physicians and Surgeons, itcarries tuition exemption and a twelvemonthstipend of up to $15,000.Nickolas and Liliana ThemelisFellowship in Earth andEnvironmental Engineering (2000)Gift of Nickolas and Liliana Themelis.Theodore and Jennifer TsungFellowshipGift of Theodore T. Tsung (1982).Awarded for graduate study in theDepartment of Electrical Engineering.Christian R. Viros FellowshipAll French citizens and French nationalsare eligible to apply. This fellowship ismade possible by the generosity of Mr.Viros, a 1975 graduate of SEAS. The fellowshipwill include tuition and an annualstipend of $10,000.Erwin S. and Rose F. WolfsonMemorial Engineering Fellowship(1979)Gift of Erwin S. and Rose F. Wolfson.229SEAS 2010–2011

230MEDALS AND PRIZESAmerican Society of Civil EngineersAssociate Member Forum AwardAwarded annually to that member of thegraduating class in civil engineering whohas been most active in promoting theaims of the Society.American Society of Civil EngineersRobert Ridgeway AwardAwarded to the senior showing the mostpromise for a professional career in civilengineering.American Society of MechanicalEngineersIn recognition of outstanding effortsand accomplishments on behalf of theAmerican Society of Mechanical EngineersStudent Section at Columbia University.The Applied Mathematics FacultyAwardAwarded to an outstanding senior in theapplied mathematics program.The Applied Physics Faculty AwardAwarded to an outstanding graduatingsenior in the applied physics program.Edwin Howard Armstrong MemorialAwardsAwarded by the Faculty of ElectricalEngineering to one outstanding graduatingsenior and one outstanding candidatefor the M.S. degree, to honor thelate Edwin Howard Armstrong, professorof electrical engineering and noted inventorof wideband FM broadcasting, theregenerative circuit, and other basic circuitsof communications and electronics.Theodore R. Bashkow AwardA cash award presented to a computerscience senior who has excelled inindependent projects. This is awardedin honor of Professor Theodore R.Bashkow, whose contributions as aresearcher, teacher, and consultanthave significantly advanced the art ofcomputer science.Charles F. Bonilla MedalThe Bonilla Medal is an award for outstandingacademic merit. It is presentedannually to that student in the graduatingclass in the Department of ChemicalEngineering who best exemplifies thequalities of Professor Charles F. Bonilla.The Tullio J. Borri ’51 Award in CivilEngineeringA certificate and cash prize presentedannually by the Department of CivilEngineering and Engineering Mechanicsto a senior for outstanding promise ofscholarly and professional achievementin civil engineering. This award hasbeen made possible by gifts from thestockholder/employees and the boardof directors of the Damon G. DouglasCompany, a New Jersey-based generalcontractor, in appreciation of Mr. Borri’smany years of dedicated service andvisionary leadership as chairman andpresident.Computer Engineering UndergraduatePrizeAwarded each year by vote of the computerengineering faculty to an outstandingsenior in the computer engineeringprogram.The Computer Science DepartmentAward of ExcellenceA $200 cash prize to the student whohas demonstrated outstanding ability inthe field of computer science.Edward A. Darling Prize inMechanical EngineeringEstablished in 1903 by a gift from thelate Edward A. Darling, formerly superintendentof Buildings and Grounds; acertificate and $100 cash prize awardedannually to the most faithful and deservingstudent of the graduating class inmechanical engineering.Adam J. Derman Memorial PrizeEstablished in 1989 by family andfriends in memory of Adam J. Derman,a member of SEAS class of 1989 and agraduate student in the Department ofIndustrial Engineering and OperationsResearch. A certificate and cash prizeawarded annually by the Department ofIndustrial Engineering and OperationsResearch to a member of the graduatingclass who has demonstrated exceptionalability to make computer-orientedcontributions to the fields of industrialengineering and operations research.The William L. Everitt Student AwardsOf ExcellenceGiven to two students who rank in thetop 10 percent of their class, have anactive interest in telecommunications,and are active in a professional organization.Zvi Galil Award for Improvement inEngineering Student LifeGiven annually to the student group thatmost improves engineering student lifeduring the academic year. Establishedin honor of Zvi Galil, dean of the Schoolfrom 1995 to 2007.Jewell M. Garrelts AwardAwarded to an outstanding graduatingsenior who will pursue graduate studyin the department that was so long andsuccessfully shepherded by ProfessorJewell M. Garrelts. This award is madepossible by gifts from alumni and friendsof Professor Garrelts and from theGarrelts family in honor of an outstandingengineer, educator, and administrator.Stephen D. Guarino MemorialAward in Industrial Engineering andOperations Research (2003)A certificate and cash prize establishedby a gift from Roger Guarino (1951) inmemory of his son. To be awarded toone outstanding senior in the IndustrialEngineering and Operations ResearchDepartment who, in the opinion of thefaculty and Board of Managers of theColumbia Engineering School AlumniAssociation, has been active in undergraduateactivities and has displayedleadership, school spirit, and scholarshipachievement.Wlliam A. Hadley Award inMechanical EngineeringEstablished in 1973 by Lucy Hadley inmemory of her husband. The award ismade annually in the form of a certificateand cash to that student in the graduatingclass in mechanical engineeringwho has best exemplified the ideals ofcharacter, scholarship, and service ofProfessor William A. Hadley.Thomas “Pop” Harrington MedalPresented annually to the student whobest exemplifies the qualities of characterthat Professor Harrington exhibited duringhis forty years of teaching. The medalis made possible by Dr. Myron A. Coler.SEAS 2010–2011

Yuen-huo Hung and Chao-chin HuangAward in Biomedical EngineeringThis award has been endowed tohonor the grandfathers of ProfessorClark T.Hung in the Department ofBiomedical Engineering. His paternalgrandfather,Yuen-huo Hung, was asurgeon in Taipei who was renownedfor his practice of medicine and for hiscompassion toward patients. ProfessorHung’s maternal grandfather, ChaochinHuang, was a famous politicianin Taiwan who dedicated his life tothe citizens of his country, serving asmayor of Taipei, speaker ofthe TaiwanProvincial Assembly, and consul generalto the United States. This award is givento a graduating doctoral student in theDepartment of Biomedical who embodiesthe collective attributes of thesedistinguished individuals.This studentwill have demonstrated great potentialfor making significant contributions tothe fields of biomedical engineeringand public health, and for serving as anambassador of biomedical engineering.Illig MedalEstablished in 1898 by a bequest fromWilliam C. Illig, E.M., 1882, and awardedby the faculty to a member of the graduatingclass for commendable proficiencyin his or her regular studies.Eliahu I. Jury AwardEstablished 1991 for outstandingachievement by a graduate student inthe areas of systems communication orsignal processing.Charles Kandel AwardMedal and cash prize presented annuallyby the Columbia Engineering SchoolAlumni Association to that memberof the graduating class who has bestpromoted the interests of the Schoolthrough participation in extracurricularactivities and student-alumni affairs.The Andrew P. Kosoresow MemorialAward for Excellence in Teaching andServiceAwarded each year by the Departmentof Computer Science to up to threecomputer science students for outstandingcontributions to teaching in thedepartment and exemplary service tothe department and its mission.Dongju Lee Memorial AwardEstablished in 2005 by family and friendsin memory of Dongju Lee (DJ), graduatestudent in the Department of CivilEngineering and Engineering Mechanics,1999–2003. A certificate and cash prizeawarded annually by the department toa doctoral student specializing in geotechnical/geoenvironmentalengineeringand of outstanding promise for a careerin research and academia.Sebastian B. Littauer AwardEstablished in 1979 in honor of ProfessorLittauer, a certificate and cash prizepresented annually by the Departmentof Industrial Engineering and OperationsResearch to a senior for outstandingpromise of scholarly and professionalachievement in operations research.Mechanical Engineering Certificateof MeritIn recognition of excellence in undergraduatestudies.Henry L. Michel Award in CivilEngineeringEstablished by the Columbia EngineeringSchool Alumni Association in memoryof Henry M. Michel (1949), who builtParsons Brinkerhoff and MacDonaldinto one of the world’s leading engineeringcompanies. A certificate andcash prize is presented annually bythe Department of Civil Engineeringand Engineering Mechanics to a studentor group of students in the CivilEngineering Department who demonstrateoutstanding promise of leadershipand professional achievement in civil andconstruction engineering. The award isin support of a project with emphasis onthe construction industry in which thestudents participate.Paul Michelman Award for ExemplaryService to the Computer ScienceDepartmentThis award is given to a Ph.D. studentin computer science who hasperformed exemplary service to thedepartment, devoting time and effortbeyond the call to further the department’sgoals. It is given in memory ofDr. Paul Michelman ’93, who devotedhimself to improving our departmentthrough service while excelling as aresearcher.Mindlin Scholar in Civil Engineeringand Engineering MechanicsThis award will be made each year toa graduate student in the Departmentof Civil Engineering and EngineeringMechanics in recognition of outstandingpromise of a creative career in researchand/or practice. This award is madepossible by gifts of friends, colleagues,and former students of ProfessorRaymond D. Mindlin, and, above all,by the Mindlin family. It is intended tohonor the Mindlin brothers, Raymond,Eugene, and Rowland, who excelled intheir respective scientific fields of engineeringresearch, engineering practice,and medical practice.Millman AwardA certificate and prize, in honor of JacobMillman, awarded to two of the mostoutstanding teaching assistants for theacademic year.Russell Mills AwardPresented to a computer science majorfor excellence in computer science inmemory of Russell C. Mills, a Ph.D.candidate in computer science whoexemplified academic excellence byhis boundless energy and intellectualcuriosity.The Moles’ Student Award in CivilEngineeringAwarded to the student in engineeringwhose academic achievement andenthusiastic application show outstandingpromise of personal developmentleading to a career in construction engineeringand management.The James F. Parker Memorial Award(Mechanical Engineering DesignAward)James F. Parker served and representedColumbia engineering students as theirdean from 1975 to 1984. He also distinguishedhimself in the pursuit and analysisof two-dimensional art. In recognition ofhis special combination of talents and theirintegration, the School of Engineering andApplied Science salutes the graduate studentwho has distinguished her- or himselfas a designer. A person of creative andinnovative inclination receives the JamesParker Medal, as evidenced by outstandingperformance in courses integratingengineering analysis and design.231SEAS 2010–2011

232Robert Peele PrizeA prize of $500 awarded from time totime to that member of the graduatingclass in mining engineering who hasshown the greatest proficiency in his orher course of studies.Claire S. and Robert E. Reiss PrizeGift of Robert Reiss, InterVentionalTechnologies Inc. Awarded to a graduatingsenior in biomedical engineeringjudged by faculty most likely to contributesubstantially to the field.Francis B. F. Rhodes PrizeEstablished in 1926 by Eben ErskineOlcott of the Engineering Class of 1874,in memory of his classmate, FrancisBell Forsyth Rhodes, School of Mines,1874, and awarded from time to timeto the member of the graduating classin materials science and metallurgicalengineering who has shown the greatestproficiency in his or her course of study.School of Engineering and AppliedScience Scholar/Athlete AwardPresented from time to time by theOffice of the Dean to that graduatingstudent who has distinguished himself orherself as a varsity athlete and scholar.School of Engineering StudentActivities AwardThis award is presented to an undergraduatedegree candidate in The FuFoundation School of Engineering andApplied Science who by virtue of his orher willingness, energy, and leadershiphas significantly contributed to the cocurricularlife of the School.Robert Simon Memorial PrizeThe Robert Simon Memorial Prize wasestablished in 2001 to honor RobertSimon, a Columbia alumnus who spenta lifetime making valuable contributionsto computational and mathematicalsciences, and is awarded annually bythe Department of Applied Physics andApplied Mathematics to the doctoralstudent who has completed the mostoutstanding dissertation. Should no dissertationqualify in a given year, the prizemay be awarded to either the most outstandingstudent who has completed aMaster of Science degree in the departmentor to the most outstanding graduatingsenior in the department.Richard Skalak Memorial PrizeThe Richard Skalak Memorial Prize wasfounded in recognition of the pioneeringcontributions of Richard Skalak to thedevelopment of the biomedical engineeringprogram at Columbia University.Dr. Skalak was an inspirational teacherand scholar who taught students andcolleagues to appreciate the value ofbroad interactions between engineeringand medicine, particularly in the fields ofcardiovascular mechanics, tissue engineering,and orthopedics. The RichardSkalak Memorial Prize is awarded annuallyto a senior biomedical engineeringstudent who exemplifies the qualitiesof outstanding engineering scholarshipand breadth of scientific curiosity thatform the basis for lifelong learning anddiscovery.George Vincent Wendell MemorialMedalEstablished in 1924 by the friends in thealumni and faculty of the late ProfessorGeorge Vincent Wendell to honor andperpetuate his memory; a certificate andmedal awarded annually by choice ofthe class and the faculty to that memberof the graduating class who best exemplifieshis ideals of character, scholarship,and service.RESIDENCE HALLSCHOLARSHIPSClass of 1887 Mines ResidenceScholarshipAwarded annually to a third-year degreecandidate, with preference given todescendants of members of the Class of1887 Mines.Class of 1896 Arts and MinesScholarshipAwarded annually to a degree candidatein Columbia College, the EngineeringSchool, or the Graduate School ofArchitecture and Planning, with preferencegiven to descendants of membersof the Class of 1896 Arts and Mines.Class Of 1916 College andEngineering FundGift of the Class of 1916 College andEngineering.SEAS 2010–2011

University and School Policies,Procedures, and Regulations

234ACADEMIC PROCEDURES AND STANDARDSREGISTRATION ANDENROLLMENTRegistration is the mechanical processthat reserves seats in particular classesfor eligible students. It is accomplishedby following the procedures announcedin advance of each term’s registrationperiod.Enrollment is the completion of theregistration process and affords the fullrights and privileges of student status.Enrollment is accomplished by the paymentor other satisfaction of tuition andfees and by the satisfaction of otherobligations to the University.Registration alone does not guaranteeenrollment; nor does registrationalone guarantee the right to participatein class. In some cases, students willneed to obtain the approval of theinstructor or of a representative ofthe department that offers a course.Students should check this bulletin, theirregistration instructions, the Directory ofClasses, and also with an adviser for allapprovals that may be required.To comply with current and anticipatedInternal Revenue Service mandates,the University requires all students whowill be receiving financial aid or paymentthrough the University payroll systemto report their Social Security numberat the time of admission. Newly admittedstudents who do not have a SocialSecurity number should obtain onewell in advance of their first registration.International students should consultthe International Students and ScholarsOffice, located at 524 Riverside Drive(212-854-3587), for further information.Special billing authorization isrequired of all students whose bills areto be sent to a third party for payment.Students who are not citizens of theUnited States and who need authorizationfor special billing of tuition and/orfees to foreign institutions, agencies, orsponsors should go to the InternationalStudents and Scholars Office with twocopies of the sponsorship letter.University RegulationsEach person whose enrollment hasbeen completed is considered a studentof the University during the term forwhich he or she is enrolled unless hisor her connection with the University isofficially severed by withdrawal or forother reasons. No student enrolled inany school or college of the Universityshall at the same time be enrolled inany other school or college, either ofColumbia University or of any other institution,without the specific authorizationof the dean or director of the school orcollege of the University in which he orshe is first enrolled.The privileges of the University arenot available to any student until enrollmenthas been completed. Students arenot permitted to attend any Universitycourse for which they are not officiallyenrolled or for which they have not officiallyfiled a program unless they havebeen granted auditing privileges.The University reserves the right towithhold the privileges of registration andenrollment or any other University privilegefrom any person who has outstandingfinancial, academic, or administrativeobligations to the University.Continuous registration until completionof all requirements is obligatory foreach degree. Students are exemptedfrom the requirement to register continuouslyonly when granted a voluntaryor medical leave of absence by theirCommittee on Academic Standing (forundergraduate students) or the Office ofGraduate Student Services (for graduatestudents).Registration InstructionsRegistration instructions are announcedin advance of each registration period.Students should consult these instructionsfor the exact dates and times ofregistration activities. Students mustbe sure to obtain all necessary writtencourse approvals and advisers’ signaturesbefore registering. Undergraduatestudents who have not registered fora full-time course load by the end ofthe add period will be withdrawn fromthe School, as will graduate studentswho have not registered for any coursework by the end of the add period.International students enrolled in graduatedegree programs must maintain fulltimestatus until degree completion.DEGREE REQUIREMENTS ANDSATISFACTORY PROGRESSUndergraduateUndergraduate students are required tocomplete the School’s degree requirementsand graduate in eight academicterms. Full-time undergraduate registrationis defined as at least 12 semestercredits per term. However, in order tocomplete the degree, students must beaveraging 16 points per term. StudentsSEAS 2010–2011

235may not register for point loads greaterthan 21 points per term without approvalfrom the Committee on AcademicStanding.To be eligible to receive the Bachelorof Science degree, a student mustcomplete the courses prescribed in afaculty-approved major/program (orfaculty-authorized substitutions) andachieve a minimum cumulative gradepointaverage (GPA) of 2.0. While theminimum number of academic credits is128 for the B.S. degree, some programsof the School require a greater numberof credits in order to complete all therequirements. Undergraduate engineeringdegrees are awarded only to studentswho have completed at least 60points of course work at Columbia. Nocredit is earned for duplicate courses,including courses that are taken pass/failthe first time and the final grade is a P.Undergraduates in the programsaccredited by the EngineeringAccreditation Commission of the ABET(chemical engineering, civil engineering,Earth and environmental engineering,electrical engineering, and mechanicalengineering) satisfy ABET requirementsby taking the courses in prescribedprograms, which have been designedby the departments so as to meet theABET criteria.AttendanceStudents are expected to attendtheir classes and laboratory periods.Instructors may consider attendance inassessing a student’s performance andmay require a certain level of attendancefor passing a course.GraduateA graduate student who has matriculatedin an M.S. program or is a special studentis considered to be making normalprogress if at the completion of 9 credits,he or she has earned a cumulativeGPA of 2.5. Candidates in the Doctorof Engineering Science (Eng.Sc.D.) andprofessional programs are expected toachieve a 3.0 grade point average at thecompletion of 9 points of course work.Thereafter, graduate students areconsidered to be making minimumsatisfactory progress if they successfullycomplete at least 75 percent ofall courses they have registered for ascandidates for the degree with gradesof C– or better. Students placed onacademic probation because of theirgrades are nonetheless consideredto be making minimum satisfactoryprogress for their first term on probation(see chapter “Academic Standing,”following). Degree requirements formaster’s and professional degrees mustbe completed within five years; thosefor the doctoral degrees must be completedwithin seven years. A minimumcumulative grade-point average of 2.5(in all courses taken as a degree candidate)is required for the M.S. degree; aminimum GPA of 3.0 is required for theprofessional degree and the Doctor ofEngineering Science (Eng.Sc.D.) degree.The minimum residence requirement foreach Columbia degree is 30 points ofcourse work completed at Columbia.Changes in RegistrationA student who wishes to drop or addcourses or to make other changes in hisor her program of study after the add/drop period must obtain the signatureof his or her adviser. A student whowishes to drop or add a course in hisor her major must obtain departmentapproval. The deadline for making programchanges in each term is shown inthe Academic Calendar. After this date,undergraduate students must petitiontheir Committee on Academic Standing;graduate students must petition theOffice of Graduate Student Services.For courses dropped after these dates,no adjustment of fees will be made.Failure to attend a class without officiallydropping the class will result in a gradeindicating permanent unofficial withdrawal(UW).Transfer CreditsUndergraduate students may obtainacademic credit toward the B.S. degreeby completing course work at otheraccredited institutions. Normally, thiscredit is earned during the summer. Tocount as credit toward the degree, acourse taken elsewhere must have anequivalent at Columbia and the studentmust achieve a grade of at least B.The institution must be an accreditedfour-year college. To transfer credit, astudent must obtain prior approval fromhis or her adviser and the departmentbefore taking such courses. A coursedescription and syllabus should befurnished as a part of the approval process.Courses taken before the receiptof the high school diploma may notbe credited toward the B.S. degree. Amaximum of 6 credits may be creditedtoward the degree for college coursestaken following the receipt of a highschool diploma and initial enrollment.SEAS 2010–2011

236Master degree students are not eligiblefor transfer credits.Students possessing a conferredM.S. degree may be awarded 2 residenceunits toward their Ph.D., as wellas 30 points of advanced standingtoward their Ph.D. or Eng.Sc.D. withdepartmental approval.ExaminationsMidterm examinations: Instructors generallyschedule these in late October andmid-March.Final examinations: These are givenat the end of each term. The MasterUniversity Examination Schedule isavailable online and is confirmed byNovember 1 for the fall term and April1 for the spring term. This schedule issent to all academic departments andis available for viewing on the ColumbiaWeb site. Students should consult withtheir instructors for any changes to theexam schedule. Examinations will notbe rescheduled to accommodate travelplans.Note: If a student has three finalexaminations scheduled during one calendarday, as certified by the Registrar,an arrangement may be made withone of the student’s instructors to takethat examination at another, mutuallyconvenient time during the final examinationperiod. This refers to a calendarday, not a twenty-four-hour time period.Undergraduate students unable to makesuitable arrangements on their ownshould contact their adviser. Graduatestudents should contact the Office ofGraduate Student Services.Transcripts and CertificationsFor information on the Federal FamilyEducation Rights and Privacy Act(FERPA) of 1974, please visit http://facets.columbia.edu—Essential Policiesfor the Columbia Community. Informationon obtaining University transcripts andcertifications will be found as a subheadunder Essential Resources.Report of GradesStudents are notified by e-mail whengrades are submitted. Grades can thenbe viewed the following day by usingthe Student Services Online featurelocated on the Student Services homepage at www.columbia.edu/students. Ifyou need an official printed report, youmust request a transcript (please seeTranscripts and Certifications above).All graduate students must have acurrent mailing address on file with theRegistrar’s Office.Transcript NotationsThe grading system is as follows: A,excellent; B, good; C, satisfactory;D, poor but passing; F, failure (a finalgrade not subject to re-examination).Occasionally, P (Pass) is the only passingoption available. The grade-pointaverage is computed on the basis of thefollowing index: A=4, B=3, C=2, D=1,F=0. Designations of + or – (used onlywith A, B, C) are equivalent to 0.33 (i.e.,B+=3.33; B–=2.67). Grades of P, INC,UW, and MU will not be included in thecomputation of the grade-point average.The mark of R (registration credit; noqualitative grade earned): not acceptedfor degree credit in any program. Rcredit is not available to undergraduatestudents. In some divisions of theUniversity, the instructor may stipulateconditions for the grade and report afailure if those conditions are not satisfied.The R notation will be given only tothose students who indicate, upon registrationand to the instructor, their intentionto take the course for R, or who,with the approval of the instructor, filewritten notice of change of intention withthe Registrar not later than the last dayfor change of program. Students wishingto change to R credit after this dateare required to submit the Dean’s writtenapproval to the Registrar. A coursewhich has been taken for R credit maynot be repeated later for examinationcredit. The mark of R is automaticallygiven in Doctoral Research Instructioncourses.The mark of UW: given to studentswho discontinue attendance in a coursebut are still officially registered for it, orwho fail to take a final examination withoutan authorized excuse.The mark of INC (incomplete): grantedonly in the case of incapacitatingillness as certified by the Health Servicesat Columbia, serious family emergency,or circumstances of comparable gravity.Undergraduate students requeston INC by filling out the IncompleteRequest Form with their advising dean.The deadline is the last day of class inthe semester of enrollment. Studentsrequesting an INC must gain permissionfrom both the Committee on AcademicStanding (CAS) and the instructor.Graduate students should contact theirinstructor. If granted an INC, studentsmust complete the required workwithin a period of time stipulated by theinstructor but not to exceed one year.After a year, the INC will be automaticallychanged into an F or contingencygrade.The mark of YC (year course): a markgiven at the end of the first term of acourse in which the full year of workmust be completed before a qualitativegrade is assigned. The grade given atthe end of the second term is the gradefor the entire course.The mark of CP (credit pending):given only in graduate research coursesin which student research projectsregularly extend beyond the end of theterm. Upon completion, a final qualitativegrade is then assigned and creditallowed. The mark of CP implies satisfactoryprogress.The mark of MU (make-up examination):given to a student who has failedthe final examination in a course butwho has been granted the privilege oftaking a second examination in an effortto improve his or her final grade. Theprivilege is granted only when there is awide discrepancy between the qualityof the student’s work during the termand his or her performance on the finalexamination, and when, in the instructor’sjudgment, the reasons justify amake-up examination. A student maybe granted the mark of MU in only twocourses in one term, or, alternatively,in three or more courses in one term iftheir total point value is not more than 7credits. The student must remove MUby taking a special examination administeredas soon as the instructor canschedule it.The mark of P/F (pass/fail): this gradingoption is designed to allow studentsto extend their academic inquiry intonew areas of study. No course takenfor pass/fail may be used to satisfy astudent’s program and degree requirements.The P/F option does not counttoward degree requirements for graduatestudents.SEAS 2010–2011

Credit for InternshipsStudents who participate in noncompensatedoff-campus internshipsmay have the internships noted on theirtranscripts. Approval for this notationmay be obtained from your adviser.Formal notification from the employeris required. Graduate students maypetition the office of Graduate StudentServices for this notation.Name ChangesStudents may change their name ofrecord only while currently enrolled inthe University. There is no charge forthis service, but students must submita name change affidavit to the StudentService Center. Affidavits are availablefrom this office. When you graduate orcease to enroll in the University, yourname of record is considered final andmay not be changed unless you enrollagain at the University.GRADUATIONColumbia University awards degreesthree times during the year: in February,May, and October. There is one commencementceremony in May. Only studentswho have completed their requirementsfor the degree may participate ingraduation ceremonies.Application or Renewal ofApplication for the DegreeIn general, students pick up and file anapplication for a degree at their schoolsor departments, but there are severalexceptions. Candidates for Master ofScience and professional degrees maypick up and file their application for thedegree with the Diploma Division, 210Kent Hall, or through the Registrar’sWeb site: http://registrar.columbia.edu/registrar-forms/application-degree-orcertificate.Candidates for doctoral andMaster of Philosophy degrees shouldinquire at their departments but mustalso follow the instructions of theDissertation Office, 107 Low Library.General deadlines for applyingfor graduation are November 1 forFebruary, December 1 for May, andAugust 1 for October. (When a deadlinefalls on a weekend or holiday, the deadlinemoves to the next business day.)Doctoral students must deposit theirdissertations two days before the aboveconferral dates in order to graduate.Students who fail to earn the degreeby the conferral date for which theyapplied must file another application fora later conferral date.DiplomasThere is no charge for the preparationand conferral of an original diploma.If your diploma is lost or damaged,there will be a charge of $100 fora replacement diploma. Note thatreplacement diplomas carry thesignatures of current University officials.Applications for replacement diplomasare available on our Web site: http://registrar.columbia.edu/registrar-forms/application-replacement-diploma.Any questions regarding graduationor diploma processing should beaddressed to diplomas@columbia.edu.237SEAS 2010–2011

238ACADEMIC STANDINGACADEMIC HONORSDean’s ListTo be eligible for Dean’s List honors, anundergraduate student must achievea grade-point average of 3.5 or betterand complete at least 15 graded creditswith no incompletes. UWs, or gradeslower than C.Honors Awarded with the DegreeAt the end of the academic year, aselect portion of the candidates for theBachelor of Science degree who haveachieved the highest academic cumulativegrade-point average are accordedLatin honors. Latin honors are awardedin three categories (cum laude, magnacum laude, and summa cum laude) tono more than 25 percent of the graduatingclass, with no more than 5 percentsumma cum laude, 10 percent magnacum laude, and 10 percent cum laude.Honors are awarded on the overallrecord of graduating seniors who havecompleted a minimum of four semestersat Columbia. Students may not apply forhonors.ACADEMIC MONITORINGThe Fu Foundation School ofEngineering and Applied ScienceCommittee on Academic Standingdetermines academic policies and regulationsfor the School except in certaininstances when decisions are made bythe faculty as a whole. The Committeeon Academic Standing is expectedto uphold the policies and regulationsof the Committee on Instruction anddetermine when circumstances warrantexceptions to them.The Office of Graduate StudentServices will monitor the academic progressof graduate students in consultationwith the departments.Academic performance is reviewedby advisers at the end of each semester.The Committee on Academic Standing,in consultation with the departments,meets to review undergraduate gradesand progress toward the degree.Indicators of academic well-being aregrades that average above 2.0 eachterm, in a coordinated program of study,with no incomplete grades.Possible academic sanctions include: C– or below in any corescience course; low points towarddegree completion Students will beplaced on academic probation if theymeet any of the conditions below:– fall below a 2.0 GPA in a givensemester– have not completed 12 points successfullyin a given semester– are a first-year student and havenot completed chemistry, physics,University Writing, Gateway Lab,and calculus during the first year– receive a D, F, UW, or unauthorizedIncomplete in any first-year/sophomorerequired courses– receive a D, F, UW, or unauthorizedIncomplete in any course requiredfor the major– receive straight C’s in the core sciencecourses (chemistry, calculus,physics) Students whoare already on probation and fail tomeet the minimum requirements asstated in their sanction letter Students who arealready on probation, fail to meet theminimum requirements as stated intheir sanction letter, and are far belowminimum expectations; this action istypically made when there are signs ofsevere academic difficulty. Students who have a historyof not meeting minimum requirementswill be dismissed from The FuFoundation School of Engineering andApplied Science.MEDICAL LEAVE OF ABSENCEA medical leave of absence for anundergraduate student is granted by theCommittee on Academic Standing to astudent whose health prevents him or herfrom successfully pursuing full-time study.Undergraduates who take a medical leaveof absence are guaranteed housing upontheir return. A medical leave of absencefor a graduate student is granted by theOffice of Graduate Student Services, soplease consult with this office for moreinformation. Documentation from a physicianor counselor must be provided beforesuch a leave is granted. In order to applyfor readmission following a medical leave,a student must submit proof of recoveryfrom a physician or counselor. A medicalleave is for a minimum of one year andcannot be longer than two years. If thestudent does not return within the twoyeartime frame, they will be permanentlywithdrawn from the School. During thecourse of the leave, students are not permittedto take any courses for the purposeof transferring credit and are not permittedSEAS 2010–2011

239to be on the campus. For the completepolicy, consult your advising dean.VOLUNTARY LEAVEOF ABSENCEA voluntary leave of absence may begranted by the Committee on AcademicStanding to undergraduate studentswho request a temporary withdrawalfrom The Fu Foundation School ofEngineering and Applied Science for anon-medical reason. Students consideringa voluntary leave must discuss thisoption in advance with their advisingdean. Voluntary leaves are granted for aperiod of one calendar year only; VLOAswill not be granted for one semester,or for more than one year. Studentsmust be in good academic standing atthe time of the leave, and must be ableto complete their major and degree ineight semesters. Students may not takecourses for transferable credit while onleave. Finally, students who choose totake voluntary leaves are not guaranteedhousing upon return to the University.International students should contactthe International Students and ScholarsOffice to ensure that a leave will notjeopardize their ability to return to SEAS.LEAVE FOR MILITARY DUTYPlease refer to Military Leave of AbsencePolicy in Essential Policies for theColumbia Community (http://facets.columbia.edu) for recent updates regardingleave for military duty.INVOLUNTARY LEAVEOF ABSENCE POLICYThe Dean of Students or his/her designeemay place a student on an involuntaryleave of absence for reasons of personalor community safety. This processwill be undertaken only in extraordinarycircumstances when there is compellinginformation to suggest that the studentis engaging in or is at heightened riskof engaging in behavior that could leadto serious injury to others, includingas a result of physical or psychologicalillness. In addition, the involuntaryleave process may be initiated if, basedon an individualized assessment fromCounseling and Psychological Servicesor other University personnel, it is determinedthat there is a significant risk thatthe student will harm him/herself, andthat the risk cannot be eliminated orreduced to an acceptable level throughreasonable and realistic accommodationsand/or on-campus supports.This policy will not be used in lieu ofdisciplinary actions to address violationsof Columbia University rules, regulations,or policies. A student who has engagedin behavior that may violate rules, regulations,or policies of the University communitymay be subject to the Dean’sDiscipline Process of his/her particularschool. A student may be required toparticipate in the disciplinary process forhis/her school coincident with placingthe student while on an involuntary leaveof absence. A student who is placed onan involuntary leave of absence while onacademic and/or disciplinary status willreturn on that same status.Before an involuntary leave is considered,efforts may be made to encouragethe student to take a voluntary medicalleave of absence. These proceduresare described in the Medical Leave ofAbsence Policy on page 238. A readmissionprocess may still be required ofa student electing a voluntary medicalleave to determine his/her readinessto return to school. A student will notbe deemed ready to return to school ifreturning may increase the risk of selfharmand/or harm to others.International students are advisedthat an involuntary leave of absence willlikely affect their student visa status andshould consult with the InternationalStudents and Scholars Office (ISSO).When safety is an immediate concern,the Dean of Students or his/herdesignee may remove a student fromthe campus pending final decision onan involuntary leave. If this action isdeemed necessary, the student will begiven notice of the removal. An opportunityto be heard by the Dean of Studentsand, if desired, appeal the final decisionwill be provided at a later time.For the complete policy and guidelines,consult your advising dean in theCenter for Student Advising.REQUIRED MEDICAL LEAVEFOR STUDENTS WITHEATING DISORDERSWith eating disorders, a medical leave issometimes necessary to protect the safetyof a student. Usually this is becausethe student’s illness is advanced enoughto require hospitalization or intensive daytreatment beyond the scope of Universitymedical and psychological resources. ASEAS 2010–2011

240medical leave is also sometimes deemednecessary when an individual student’seating disorder has negatively impactedthe integrity of the University’s learningenvironment.Before an involuntary medical leaveis considered, efforts will be made toencourage the student to take a voluntarymedical leave, thus preserving, tothe extent possible, confidentiality andprivacy. The policy will be invoked onlyin extraordinary circumstances, when astudent is unable or unwilling to requesta voluntary medical leave of absence.For the complete policy and guidelines,consult your advising dean in theCenter for Student Advising.READMISSIONStudents seeking readmission to The FuFoundation School of Engineering andApplied Science must submit evidencethat they have achieved the purposes forwhich they left. Consequently, specificreadmission procedures are determinedby the reasons for the withdrawal. Furtherinformation for undergraduate studentsis available in the Center for StudentAdvising. Graduate students should seethe Office of Graduate Student Services.Students applying for readmissionshould complete all parts of the appropriatereadmission procedures by June1 for the autumn term or October 1 forthe spring term.SEAS 2010–2011

POLICY ON CONDUCT AND DISCIPLINE241LIFE IN THEACADEMIC COMMUNITYThe Fu Foundation School of Engineeringand Applied Science within ColumbiaUniversity is a community. Admitted students,faculty, and administrators cometogether and work through committeesand other representative bodies to pursueand to promote learning, scholarlyinquiry, and free discourse. As in anycommunity, principles of civility and reasonedinteraction must be maintained.Thus, methods for addressing social aswell as academic behaviors exist.RULES OFUNIVERSITY CONDUCTRules of University Conduct are includedunder University Regulations in EssentialPolicies for the Columbia Community(http://facets.columbia.edu).DISCIPLINEThe continuance of each student uponthe rolls of the University, the receiptof academic credits, graduation, andthe conferring of the degree are strictlysubject to the disciplinary powers of theUniversity.Although ultimate authority on mattersof student discipline is vested inthe Trustees of the University, the Deanof the School and his staff are givenresponsibility for establishing certainstandards of behavior for SEAS studentsbeyond the regulations included in theStatutes of the University and for definingprocedures by which discipline willbe administered.We expect that in and out of theclassroom, on and off campus, eachstudent in the School will act in an honestway and will respect the rights ofothers. Freedom of expression is anessential part of University life, but itdoes not include intimidation, threats ofviolence, or the inducement of others toengage in violence or in conduct whichharasses others. We state emphaticallythat conduct which threatens or harassesothers because of their race, sex,religion, disability, sexual orientation, orfor any other reason is unacceptableand will be dealt with very severely. Ifeach of us at Columbia can live up tothese standards, we can be confidentthat all in our community will benefit fullyfrom the diversity to be found here. Anyundergraduate student who believes heor she has been victimized should speakwith an adviser in the Center for StudentAdvising, a member of the ResidentialPrograms staff, or a member of theOffice of Judicial Affairs and CommunityStandards; graduate students shouldspeak with an officer in the Office ofGraduate Student Services.While every subtlety of proper behaviorcannot be detailed here, examplesof other actions that would subject astudent to discipline are: or in dealings with University officials,including members of the faculty the health or safety of others damaging, or stealing property galdrugs request of a University official; failureto respond to the legitimate requestof a University official exercising his orher duty others Conduct” (copies of which are availablein 406 Low Library and otherlocations mentioned above) halls as outlined in the “Guide toLiving”; this also applies to all fraternityand sorority housing Assault Policy University Information Technology(CUIT) policies and procedures notes (whether taken in class by astudent or distributed to the classby an instructor), syllabi, exams, orcontent on a University or individualfaculty member Web site that is notaccessible to anyone outside of theUniversity community on campus or operating any businesson campus without authorization fromthe Associate Dean of Career ServicesDISCIPLINARY PROCEDURESMany policy violations that occur in theResidence Halls rules are handled bythe Associate Directors of ResidentialPrograms. Some serious offenses arereferred directly to the Office of JudicialAffairs and Community Standards.Violations in University ApartmentHousing are handled by building managersand housing officials. Some incidentsare referred directly to the School’shousing liaison in the Office of GraduateStudent Services.Most violations of rules concerningfraternities or sororities as organizationsare handled by the Assistant Director ofGreek Life and Leadership. Some seriousoffenses are referred directly to theSEAS 2010–2011

242Office of Judicial Affairs and CommunityStandards.In matters involving rallies, picketing,and other mass demonstrations,the Rules of University Conduct outlinesprocedures.The Office of Judicial Affairs (locatedwithin the Division of Student Affairs)is responsible for all disciplinary affairsconcerning undergraduate students thatare not reserved to some other body.The Office of Graduate Student Servicesis responsible for all disciplinary affairsconcerning graduate students that arenot reserved to some other body.Dean’s Discipline Process forUndergraduate StudentsThe purpose of the Dean’s Disciplineprocess is twofold. First, it is usedto determine the accused student’sresponsibility for the alleged violation(s)of SEAS or University policy(ies). In addition,it is an opportunity for the studentto engage in a meaningful conversationregarding his or her role as a memberof the Columbia community. The Dean’sDiscipline process is not an adversarialprocess, nor is it a legalistic one, andtherefore the technical rules of evidenceapplicable to civil and criminal courtcases do not apply.After a complaint is received a studentmay be removed from housing and/or placed on interim suspension by theStudent Affairs staff if it is determined thatthe student’s behavior makes his or herpresence on campus a danger to the normaloperations of the institution, or to thesafety of himself or herself or others or tothe property of the University or others.When a complaint is received, theOffice of Judicial Affairs and CommunityStandards determines whether Dean’sDiscipline is an appropriate response orif the complaint should be referred elsewhere.If Dean’s Discipline is to occur,a student is informed in writing of thecomplaint made against him/her and ofthe next step in the process. At the hearing,at least two members of the staff ofthe Dean of Student Affairs present theaccused student with the information thatsupports the allegation that he/she hasviolated SEAS or University policy(ies).The student is then asked to respondand will be given an opportunity to presentinformation on his or her behalf.At the conclusion of the hearing, thehearing administrators will make a determination,based on all of the informationavailable to them, regarding whether theaccused student is responsible for theviolation(s). The standard of proof thatthe hearing administers will use to makethis determination is the preponderanceof the evidence standard. This standardallows for a finding of responsibility ifthe information provided shows that itis more likely than not that a violationof Columbia policy(ies) occurred. If thestudent is found responsible, the degreeof seriousness of the offense and thestudent’s previous disciplinary record,if any, will determine the severity of thesanction that will be issued. The studentwill be notified of the outcome of thehearing in writing.A student found responsible aftera hearing has the right to request anappeal of the decision and the resultingsanctions. There are three grounds uponwhich an appeal of the decision maybe made. A student found responsiblefor the violation of Columbia policy(ies)may request a review of the decisionif (1) the student has new information,unavailable at the time the hearing;(2) the student has concerns with theprocess that may change or affect theoutcome of the decision; or (3) thestudent feels that the sanction issuedis too severe. The request for reviewmust be made in writing to the individualindicated in the decision letter and mustbe received within ten calendar days(or as indicated in the hearing outcomeletter) after the student receives noticeof the hearing outcome. For more informationabout the discipline process forundergraduate students, please visit theOffice of Judicial Affairs and CommunityStandards Web site (www.studentaffairs.columbia.edu/judicialaffairs).Discipline Processfor Graduate StudentsWhen sufficient evidence exists, a studentis charged with a particular offenseand a hearing is scheduled. Present ata hearing for graduate students are thecharged student and at least two membersof the Office of Graduate StudentServices staff. At the hearing, the studentis presented with the evidencethat supports the accusation againsthim or her and is asked to respond toit. The student may then offer his orher own evidence and suggest otherstudents with whom the deans or theirdesignee might speak. On the basis ofthe strength of the evidence and thestudent’s response, the deans or theirdesignee reach a determination andnotify the student of their decision afterthe hearing. The student can be exonerated,found guilty of the accusations,or found not guilty due to insufficientevidence; if he or she is found to havecommitted an infraction, the penalty canrange from a warning to disciplinary probationto suspension or dismissal. Thestudent may also be barred from certainUniversity facilities or activities. Anaccused student has the right to appeala decision that results from a disciplinaryhearing. The appeal must be made inwriting within the time period specified inthe letter regarding the decision, and tothe person specified in the letter.ConfidentialityIn general, under University policy andfederal law, information about Dean’sDisciplinary proceedings against astudent is confidential and may not bedisclosed to others. A limited exceptionto this principle is that the outcome ofDean’s Disciplinary proceedings alleginga crime of violence may be disclosedboth to the accuser and the accused.ACADEMIC DISHONESTYAcademic dishonesty includes but is notlimited to intentional or unintentional dishonestyin academic assignments or indealing with University officials, includingfaculty and staff members.Here are the most common types ofacademic dishonesty: or ideas belonging to another, withoutproperly citing or acknowledging thesource) assignment an assignment has already been used for anothercourseSEAS 2010–2011

mentsand exams exams or other assignments withoutpermissionA student alleged to have engaged inacademic dishonesty will be subject tothe Dean’s Discipline process.Students found responsible foracademic dishonesty may face reportsof such offenses on future recommendationsfor law, medical, or graduateschool. The parents or guardians ofstudents found responsible may also benotified.ACADEMIC INTEGRITYAcademic integrity defines a universityand is essential to the mission ofeducation. At Columbia students areexpected to participate in an academiccommunity that honors intellectual workand respects its origins. In particular, theabilities to synthesize information andproduce original work are key componentsin the learning process. As such,academic dishonesty is one of the mostserious offenses a student can commitat Columbia and can be punishable bydismissal.Students rarely set out with the intentof engaging in academic dishonesty.But classes are challenging at Columbia,and students will often find themselvespressed for time, unprepared for anassignment or exam, or feeling that therisk of earning a poor grade outweighsthe need to be thorough. Such circumstanceslead some students to behavein a manner that compromises the integrityof the academic community, disrespectstheir instructors and classmates,and deprives them of an opportunity tolearn. In short, they cheat. If you everfind yourself in such circumstances,you should immediately contact yourinstructor and your adviser for advice.Just keep in mind how hard you haveworked to get to this point in your academiccareer, and don’t jeopardize yourColumbia education with a moment ofunwise decision making.The easiest way to avoid the temptationto cheat in the first place is toprepare yourself as best you can. Hereare some basic suggestions to help youalong the way: deem as academic dishonesty andtheir policy on citation and group collaboration. about assignments with instructors asearly as possible. edits of assignments and begin preparationin advance. people’s opinions and theories bycarefully citing their words and alwaysindicating sources. such as the advising centers andCounseling and PsychologicalServices, if you are feeling overwhelmed,burdened, or pressured. pletionof assignments is prohibitedunless specified by the instructor.Plagiarism andAcknowledgment of SourcesColumbia has always believed thatlearning to write effectively is one of themost important goals a college studentcan achieve. Students will be asked todo a great deal of written work while atColumbia: term papers, seminar andlaboratory reports, and analytic essaysof different lengths. These papers playa major role in course performance, butmore important, they play a major role inintellectual development. Plagiarism, theuse of words, phrases, or ideas belongingto another, without properly citing oracknowledging the source, is consideredone of the most serious violationsof academic integrity and is a growingproblem on university campuses.One of the most prevalent forms ofplagiarism involves students using informationfrom the Internet without propercitation. While the Internet can provide awealth of information, sources obtainedfrom the Web must be properly cited justlike any other source. If you are uncertainhow to properly cite a source of informationthat is not your own, whether fromthe Internet or elsewhere, it is criticalthat you do not hand in your work untilyou have learned the proper way to usein-text references, footnotes, and bibliographies.Faculty members are available tohelp as questions arise about proper citations,references, and the appropriatenessof group work on assignments. Youcan also check with the UndergraduateWriting Program. Ignorance of propercitation methods does not exonerate onefrom responsibility.Personal Responsibility, FindingSupport, and More InformationA student’s education at ColumbiaUniversity is comprised of two complementarycomponents: a mastery overintellectual material within a disciplineand the overall development ofmoral character and personal ethics.Participating in forms of academic dishonestyviolates the standards of ourcommunity at Columbia and severelyinhibits a student’s chance to grow academically,professionally, and socially. Assuch, Columbia’s approach to academicintegrity is informed by its explicit beliefthat students must take full responsibilityfor their actions, meaning you willneed to make informed choices insideand outside the classroom. Columbiaoffers a wealth of resources to helpstudents make sound decisions regardingacademics, extracurricular activities,and personal issues. If you don’t knowwhere to go, see your class dean.243SEAS 2010–2011

244ESSENTIAL POLICIES FOR THE COLUMBIA COMMUNITYThis bulletin is intended for theguidance of persons applyingfor or considering applicationfor admission to Columbia Universityand for the guidance of Columbiastudents and faculty. The bulletin setsforth in general the manner in whichthe University intends to proceed withrespect to the matters set forth herein,but the University reserves the right todepart without notice from the terms ofthis bulletin. The bulletin is not intendedto be and should not be regarded as acontract between the University and anystudent or other person.Valuable information to help students,faculty, and staff understand someof the policies and regulations of theUniversity can now be found in EssentialPolicies for the Columbia Communityon the following Web site: http://facets.columbia.edu. This document replacespolicies formerly published in the appendixof FACETS (Facts About ColumbiaEssential to Students) and includes thefollowing: Policy under the Federal Family EducationalRights and Privacy Act (FERPA) of1974, as Amended of University Conduct) Nondiscrimination Policies Procedure the Federal Bureau of Investigation’sUniform Crime Reporting Program Medical Leave for Students withEating Disorders – Disability Services– Ombuds Office– Transcripts and Certifications Columbia CommunitySEAS 2010–2011

STUDENT GRIEVANCES, ACADEMIC CONCERNS, AND COMPLAINTS245The following procedures are part ofa process to ensure that student concernsabout experiences in the classroomor with faculty are addressed in aninformed and appropriate manner.Due to the size and diverse nature ofour scholarly community, each schoolmaintains its own processes for addressingissues raised by students, includingtheir concerns about experiences in theclassroom or with faculty at their school.Experience has shown that most studentconcerns are best resolved in a collaborativeway at the school level. The FuFoundation School of Engineering andApplied Sciences (SEAS) offers severalinformal paths for students to use, asdescribed in this statement.If a student’s concerns are notsatisfied through this process, or if thestudent believes that a direct complaintto the Dean is more appropriate, formalgrievance procedures are availablethrough the Vice Dean of the School.These procedures should be used forcomplaints about SEAS faculty. For thosefaculty who are not members of SEAS,the student should consult the proceduresof the school in which they serve.For academic complaints relatingto SEAS faculty, these procedures, likethose of other schools, provide for afinal appeal to the University Provost.The procedures under item A do nottake the place of the grievance proceduresalready established to addressdisputes over grades, academic dishonesty,or issues of behavioral concernsas they relate to student conduct (seeitem B). They also should not be usedwhen students believe that they havebeen the victim of sexual harassment ordiscrimination (see item C) or that facultyhave engaged in scholarly or scientificmisconduct (see item D).We welcome students’ thoughtson ways to clarify or enhance theseprocedures. If you are an Engineeringstudent, please e-mail Vice Dean MortonFriedman at friedman@columbia.edu.A. COMPLAINTS ABOUT FAC-ULTY AND STAFF ACADEMICMISCONDUCTIn fulfilling their instructional responsibilities,faculty are expected to treat theirstudents with civility and respect. They“should make every effort to be accurateand should show respect for the rights ofothers to hold opinions differing from theirown. They should confine their classesto the subject matter covered by thecourse and not use them to advocateany cause” (2000 Faculty Handbook).A fuller description of faculty rights andobligations may be found in the FacultyHandbook. Students who feel that membersof the Engineering faculty have notmet those obligations may take the followingsteps (the procedure below alsoapplies to complaints against instructionaland administrative staff):Students are encouraged to seeka resolution to their complaints aboutfaculty misconduct by talking directlywith the faculty member. If they feeluncomfortable handling the situationin this manner, they may ask for helpfrom a departmental faculty mediator,who will assist students with complaintsabout faculty members, other academicpersonnel, or administrators.The name of the faculty mediator isposted in the department office and onthe departmental Web page. Studentsmay also ask the department chairor administrator to direct them to thefaculty mediator. The faculty mediatortries to resolve any issue by informalmeetings with the student and others,including faculty as seems appropriate.Students who are dissatisfied with theoutcome may request a meeting withthe department chair. The chair willreview the mediator’s recommendationand seek informally to resolve the student’scomplaint. the University’s Ombuds Officer, whoserves as an informal, confidentialresource for assisting members of theUniversity with conflict resolution. TheOmbuds Officer provides information,counseling, and referrals to appropriateUniversity offices and will alsomediate conflicts if both parties agree.The Ombuds Officer does not havethe authority to adjudicate disputesand does not participate in anyformal University grievance proceedings.Further information on theOmbuds Office may be found atwww.columbia.edu/cu/ombuds ingif informal mediation fails. Thegrievance procedures students shouldfollow will depend upon the schoolwithin which the faculty memberis appointed and the nature of thealleged misconduct.If the faculty member holds anappointment in SEAS, the student mayuse the procedures described belowto address the issues listed below. Ifthe faculty member belongs to anotherschool, students must use the procedureof that school. They may, however,ask for help from the departmentalfaculty mediator, chair, and the School’sdeans in identifying and understandingthe appropriate procedures.Conduct that is subject to formalgrievance procedure includes:SEAS 2010–2011

246 an instructional setting for the rights ofothers to hold opinions differing fromtheir own; instructional setting to pressure studentsto support a political or socialcause; and instructional setting that adverselyaffects the learning environment.Formal grievance procedure atSEASIf the informal mediation mentionedabove failed, the student should composeand submit to the Vice Dean of theSchool a written statement documentingthe grievance and should also include adescription of the remedy sought. Thisshould be done no later than 30 workingdays after the end of the semester inwhich the grievance occurred.The Vice Dean will review the complaintto determine if a grievance hearingis warranted. If so, the Vice Dean willconvene an ad hoc committee consistingof the Assistant Dean for GraduateStudent Services (graduate students) orthe Associate Dean of Student Affairs(undergraduate students), who acts aschair; a faculty member chosen by theVice Dean; and a student chosen by oneof the student councils (an undergraduateor a graduate student to correspondto the status of the student grieving).The faculty member is given thestudent’s letter of complaint and invitedto submit a written response. TheCommittee reviews both statementsand is given access to any other writtendocuments relevant to the complaint. Itwill normally interview both the grievantand the faculty member and may, at itsdiscretion, ask others to provide testimony.The merits of the grievance areevaluated within the context of Universityand SEAS school policy.The investigative committee servesin an advisory capacity to the Dean ofthe School. It is expected to completeits investigation in a timely manner andsubmit a written report to the Dean, whomay accept or modify its findings andany recommendations it may have madeto remedy the student’s complaint. TheDean will inform both the student and thefaculty member of his decision in writing.The committee ordinarily conveneswithin 10 working days of receivingthe complaint from the Vice Dean andordinarily completes its investigationand sends the Dean its report within 30working days of convening. The Deannormally issues his or her decision within30 working days of receiving the committee’sreport.The Dean may discipline facultymembers who are found to have committedprofessional misconduct. Anysanctions will be imposed in a mannerthat is consistent with the University’spolicies and procedures on faculty discipline.In particular, if the Dean believesthat the offense is sufficiently seriousto merit dismissal, he or she can initiatethe procedures in Section 75 ofthe University Statutes for terminatingtenured appointments, and nontenuredappointments before the end of theirstated term, for cause.Either the student or the facultymember may appeal the decision of theDean to the Provost. Findings of fact,remedies given the student, and penaltiesimposed on the faculty member areall subject to appeal. A written appealmust be submitted to the Provost within15 working days of the date of the letterinforming them of the Dean’s decision.Normally, the Provost will take nolonger than 30 working days to evaluatean appeal. The Provost usually confineshis or her review to the written recordbut reserves the right to collect informationin any manner that will help to makehis or her decision on the appeal.The Provost will inform both thestudent and the faculty member of hisor her decision in writing. If the Provostdecides that the faculty member shouldbe dismissed for cause, the case issubject to further review according tothe procedures in Section 75 of theUniversity Statutes, as noted above.Otherwise the decision of the Provost isfinal and not subject to further appeal.All aspects of an investigation of astudent grievance are confidential. Theproceedings of the grievance committeeare not open to the public. Only thestudent grievant and the faculty memberaccused of misconduct receive copiesof the decisions of the Dean and theProvost. Everyone who is involved with theinvestigation of a grievance is expected torespect the confidentiality of the process.B. DISPUTES OVERGRADES OR OTHERACADEMIC EVALUATIONSThe awarding of grades and all otheracademic evaluations rests entirely withthe faculty. If students have a concernrelating to a particular grade or otherassessment of their academic work,the student first should speak with theinstructor of the class to understandhow the grade or other evaluation wasderived and to address the student’sspecific concern.If the students do not feel comfortablespeaking with the class instructorabout the matter, they should thenbring the issue to the attention of theirclass dean (undergraduate students) ordepartment chair (graduate students).If the students are unable thus toresolve the matter to their satisfactionand believe that a procedural issue isinvolved, they should bring the matter tothe attention of the Vice Dean. The ViceDean will work with the student and thefaculty to determine whether there hasbeen a procedural breach and if so, takeimmediate steps to remedy the matter. Ifthe Vice Dean, together with appropriatefaculty other than the instructor, decidesthat there is no need for further action,the student will be informed and thedecision will be final.C. DISCRIMINATION AND SEX-UAL HARASSMENTIf the alleged misconduct involvesdiscrimination and sexual harassment,a student should file a complaintwith the Associate Provost for EqualOpportunity and Affirmative Action. Theprocedures for handling such complaintsare described in the statementDiscrimination and Sexual HarassmentPolicy and Procedure.D. SCIENTIFIC ORSCHOLARLY MISCONDUCTComplaints against the School’s facultythat allege scientific or scholarlymisconduct are evaluated using otherprocedures. These are contained in theColumbia University Institutional Policyon Misconduct in Research.SEAS 2010–2011

Directory of University Resources

248COLUMBIA UNIVERSITY RESOURCE LISTADMISSIONS (GRADUATE)See Graduate Student ServicesADMISSIONS (UNDERGRADUATE)212 Hamilton, 212-854-2522Mail Code 2807www.studentaffairs.edu/admissionsJessica Marinaccio, Dean ofUndergraduate AdmissionsPeter Johnson, Director of Admissionspvj1@columbia.eduJoanna May, Director of Outreach andAdmissions Operationsjm2638@columbia.eduMeaghan McCarthy, Director, VisitorsCentermm3359@columbia.eduAlice Huang, Senior Associate Directorah704@columbia.eduDiane McKoy, Senior Associate Directordm18@columbia.eduJames Minter, Senior Associate Directorjm35@columbia.eduADVISING CENTERSSee Center for Student AdvisingALICE!, COLUMBIA UNIVERSITY’SHEALTH EDUCATION PROGRAMSee Health Services at ColumbiaCENTER FOR CAREER EDUCATIONEast Campus, Lower Level212-854-5609Mail Code 5727www.careereducation.columbia.educareereducation@columbia.eduCENTER FOR STUDENT ADVISING403 Lerner Hall, 212-854-6378Mail Code 1201www.studentaffairscolumbia.edu/csacsa@columbia.eduMonique Rinere, Dean of AdvisingLavinia Lorch, Senior Assistant Deanlel52@columbia.eduAndrew Plaa, Senior Assistant Deanap50@columbia.eduSunday Coward, Assistant Deansfc15@columbia.eduNathaniel Wood, Jr., Assistant Deannw4@columbia.eduCOLUMBIA COLLEGE AND SCHOOLOF ENGINEERING AND APPLIEDSCIENCE CORE CURRICULUMPROGRAM OFFICESCenter for the Core Curriculum202 Hamilton, 212-854-2453Mail Code 2811Roosevelt Montás, Director of theCenter for the Core Curriculum andAssociate Dean of Academic Affairsrm63@columbia.eduArt Humanities826 Schermerhorn, 212-854-4505Mail Code 5517Professor Johnathan K. Crary, ChairMusic Humanities621 Dodge, 212-854-3825Mail Code 1813Professor Susan Boynton, ChairContemporary Civilization202 Hamilton, 212-854-2453Mail Code 2811Professor Michael Stanislawski, ChairLiterature Humanities202 Hamilton, 212-854-2453Mail Code 2811Professor Gareth Williams, ChairAll inquiries concerning Lit Hum shouldbe directed to the Center for CoreCurriculum (listed above).University WritingWriting CenterUndergraduate Writing Program310 Philosophy, Mail Code 4995212-854-3886Nicole Wallack, Acting Directoruwp@columbia.edu (for general inquiries)writingcenter@columbia.edu (for WritingCenter)COLUMBIA VIDEO NETWORK540 S. W. Mudd, 212-854-8210Mail Code 4719Grace Chung, Executive DirectorCOMMUNITY DEVELOPMENTOffice of Multicultural Affairs515 Lerner, 212-854-4809Mail Code 2601Intercultural Resource Center552 West 114th Street, 212-854-0720MC 5755Melinda Aquino, Associate Dean ofMulticultural Affairsma2398@columbia.eduSEAS 2010–2011

249Marta Esquilin, Senior AssociateDirector/Manager of IRCmee2009@columbia.eduOffice of Residential Programs515 Lerner, 212-854-6805Mail Code 4205Cristen Scully Kromm, Assistant Deanfor Community Development andResidential Programscs867@columbia.eduHikaru Kozuma, Director of ResidentialProgramshk2134@columbia.eduDarleny Cepin, Associate Director ofResidential Programs—West Campusdec23@columbia.eduAdam Fertmann, Associate Director ofResidential Programs—The Blockaf2461@columbia.eduScott Helfrich, Associate Director ofResidential Programs—Living LearningCenter (LLC)sh2409@columbia.eduDeb Pawlikowski, Associate Director ofResidential Programs—South Fielddp2309@columbia.eduKristen Sylvester, Associate Director ofResidential Programs—East Campusks2696@columbia.eduVictoria Lopez-Herrara, AssistantDirector of Greek Life and LeadershipDevelopmentvl2165@columbia.eduOffice of Student Development andActivities515 Lerner, 212-854-3611Mail Code 2601Robert Taylor, Executive Directorrt316@columbia.eduCynthia Jennings, Director of NewStudent Orientation and Class YearProgrammingcj2186@columbia.eduTailisha Gonzalez, Manager of StudentDevelopment and Activities Leadershipin Programstg164@columbia.eduBenjamin Young, Director ofBroadcasting and Operations (WKCR-FM)by10@columbia.eduDavis Milch, Manager of Media,Performing Arts, and PublicationsProductiondm2422@columbia.eduOffice of Student Group Advising505 Lerner, 212-854-4196Mail Code 2609Todd Smith, Associate Dean of StudentAffairs/Student Group Advisingts2488@columbia.eduJason Anthony, Associate Directorjla2108@columbia.eduWalter Rodriguez, Associate Directorwr2174@columbia.eduCOMPUTING SUPPORT CENTERHelpdesk Support Center202 Philosophy, Mail Code 4926212-854-1919askcuit@columbia.eduMailing Address401 Watson, Mail Code 6001COUNSELING ANDPSYCHOLOGICAL SERVICESSee Health Services at ColumbiaDEAN OF COLUMBIA COLLEGE208 Hamilton, 212-854-2441Mail Code 2805Michele M. Moody-Adams, Dean ofthe CollegeKathryn Yatrakis, Dean of Academic Affairskby1@columbia.eduDINING SERVICESSee Housing and DiningOFFICE OF DISABILITY SERVICESSee Health Services at ColumbiaEARL HALL/ST. PAUL’S CHAPEL212-854-6242, Mail Code 2008Jewelnel Davis, University Chaplain212-854-1493chaplain@columbia.eduDIVISION OF STUDENT AFFAIRSDEAN’S OFFICE: COLUMBIACOLLEGE AND THE FUFOUNDATION SCHOOL OFENGINEERING AND APPLIEDSCIENCE601 Lerner212-854-2446Mail Code 2607Kevin G. Shollenberger, Dean of StudentAffairs and Associate Vice President forUndergraduate Student Lifecc69@columbia.eduSEAS 2010–2011

250Susan Tucker, Assistant Manager tothe Deanst2509@columbia.eduKathryn Wittner, Associate Dean ofStudent Affairs/Student and AlumniProgramskb4@columbia.eduEQUAL OPPORTUNITY ANDAFFIRMATIVE ACTION OFFICE103 Low Library, 212-854-5511Mail Code 4333Susan Rieger, Associate Provostsr534@columbia.eduFINANCIAL AID AND EDUCATIONALFINANCING (UNDERGRADUATE)618 Lerner, 212-854-3711Mail Code 2802Daniel Barkowitz, Dean of Financial Aidand Associate Dean of Student AffairsKathryn Tuman, DirectorPamela Mason, Senior AssociateDirector of Financial Aid and Admissionspm520@columbia.eduJosé Carlos Rivera, Associate Directorjcr38@columbia.eduEvangelia Nonis, Assistant Directoredn1@columbia.eduFINANCIAL AID (GRADUATE)Federal Financial Aid(Loans, Work Study)Financial Aid and Educational Financing615 Lerner, 212-854-3711Mail Code 2802Jacqueline Perez, Associate Directorjg363@columbia.eduMarjorie Ortiz, Assistant Directormo2219@columbia.eduInstitutional Financial Aid(Grants, Fellowships, Assistantships)Graduate Student Services524 S. W. Mudd, 212-854-6438Mail Code 4708Jocelyn Morales, Admissions Officerjm2388@columbia.eduGRADUATE STUDENT SERVICES524 S. W. Mudd, 212-854-6438Mail Code 4708Tiffany M, Simon, Assistant Deantms26@columbia.eduJocelyn Morales, Admissions Officerjm2388@columbia.eduJonathan Stark, Student Affairs Officerirs2139@columbia.eduHEALTH SERVICES AT COLUMBIAwww.health.columbia.edu212-854-2284Enrollment/Immunization OfficeWien Hall, 212-854-7210Mail Code 3712Emergency Medical Services (CAVA)212-854-5555 or 99 from a campus phoneGay Health Advocacy Project (GHAP),including HIV Testing212-854-7970Student Medical Insurance PlanAdministrators: Chickering BenefitPlanning Insurance Agency, Inc.1-800-859-8471www.aetnastudenthealth.comTravel Medicine Clinic (CU on the Road):212-854-2284Alice!, Columbia University’sHealth Promotion ProgramWien Hall, 212-854-5453Mail Code 3711www.alice.columbia.eduPresents a wide range of health educationand skill-building programs, includingGo Ask Alice!, a health questionand-answerInternet service.Counseling and PsychologicalServicesLerner, 8th floor, 212-854-2878Mail Code 2606Individual, couple, and group counselingfor emotional stress, emergency consultation,and referral, as well as skill-buildingworkshops and outreach programs.www.health.columbia.edu/docs/about_us/cps.htmlOffice of Disability Services700 Lerner, Voice: 212-854-2388TDD: 212-854-2378Mail Code 2605Coordinates services, programs, andpolicies to support and arrange appropriateaccommodations for studentswith disabilities.Office for the Disciplinary Procedurefor Sexual AssaultWien Hall, 212-854-1717Mail Code 3717Helen Arnold, Managerhva2002@columbia.eduSexual Violence Prevention andResponse112 Hewitt (Barnard Quad)Business Line: 212-854-436624-hour Peer Advocates:212-854-WALK (9255)Peer Counselors (7 days a week):212-854-HELP (4357)Provides services and support tosurvivors of sexual assault, relationshipviolence, childhood sexual abuse, andother forms of violence, and assistanceto the friends and loved ones of survivors.HOUSING AND DININGCustomer Service Center118 Hartley, 212-854-2775Mail Code 3003Office of Dining Services102 Wallach, 212-854-2782Mail Code 3001eats@columbia.eduOffice of Housing Services125 Wallach, 212-854-2946Mail Code 3003housing@columbia.eduINTERCULTURAL RESOURCECENTER (IRC)See Community DevelopmentINTERNATIONAL STUDENTS ANDSCHOLARS OFFICE524 Riverside Drive, Suite 200SEAS 2010–2011

212-854-3587Mailing Address: 2960 Broadway,Mail Code 5724Patrick Gallagher, Director ofUndergraduate Studiespxg@math.columbia.eduJames F. McShane, Vice President forPublic Safetyjfm2112@columbia.edu251Sarah Taylor, Acting DirectorJUDICIAL AFFAIRS ANDCOMMUNITY STANDARDS607 Lerner, 212-854-1389Mail Code 4205LIBRARIESButler Library Information234 Butler, 212-854-2271Mail Code 1121Engineering Library (Monell)422 S. W. Mudd, Mail Code 4707Circulation: 212-854-2976Reference: 212-854-3206Fax: 212-854-3323MATH/SCIENCE DEPARTMENTSBiological Sciences600 Fairchild, 212-854-4581Mail Code 2402Deborah Mowshowitz, Director ofUndergraduate Programsdbm2@columbia.eduwww.columbia.edu/cu/biologyChemistry344 Havemeyer, 212-854-2202Mail Code 3174James J. Valentini, Director ofUndergraduate Studiesjjv1@columbia.eduEarth and Environmental Sciences106 Geoscience, Lamont-DohertyEarth Observatory, 845-365-8550Nicholas Christie-Blick, Codirector ofUndergraduate Studiesncb@ldeo.columbia.edu845-709-2320Walter C. Pitman, Codirector ofUndergraduate Studiespitman@ldeo.columbia.edu845-365-8397Mathematics410 Mathematics, 212-854-2432Mail Code 4426Physics704 Pupin, Mail Code 5255212-854-3348Jeremy Dodd, Director ofUndergraduate Studiesdodd@phys.columbia.eduStatistics1255 Amsterdam AvenueRoom 1005, 212-851-2132Mail Code 4690Daniel Rabinowitz, Director ofUndergraduate Studiesdan@stat.columbia.eduOFFICE OF STUDENT GROUPADVISINGSee Community DevelopmentOMBUDS OFFICE600 Schermerhorn Ext., 212-854-1234Mail Code 5558PHYSICAL EDUCATION ANDINTERCOLLEGIATE ATHLETICSDodge Physical Fitness Center212-854-2548Mail Code 1931Ken Torrey, Chair, Physical Education212-854-4001kwt1@columbia.eduJacqueline Blackett, Senior AssociateAthletics Director/SWA212-854-2544jpb3@columbia.eduAcademic and personal advising forvarsity athletes.PRIMARY CARE MEDICAL SERVICESSee Health Services at ColumbiaPUBLIC SAFETY OFFICE111 Low Library212-854-2797 (24 hours a day)Mail Code 4301publicsafety@columbia.eduCAMPUS EMERGENCIES: Fromon-campus Rolm phones dial 99 for fire,security, ambulance, or any crimeproblem; off-campus: 212-854-5555Escort Service: 212-854-SAFEREGISTRAR210 KentMail Code 9202John Carter, Deputy Registrar212-854-1458jpc11@columbia.eduJennifer Caplan, Associate Registrar212-854-5596jc12@columbia.eduJames Cunha, Assistant Registrar212-854-1454jhc4@columbia.eduBrady Sloan, Associate Registrar212-854-8112bps44@columbia.eduLenore Hubner, Assistant Registrar212-854-3240lah2@columbia.eduMelbourne Francis, Assistant Registrar212-854-7528mef2@columbia.eduRESIDENTIAL PROGRAMSSee Community DevelopmentSEXUAL VIOLENCE PREVENTIONAND RESPONSESee Health Services at ColumbiaSTUDENT DEVELOPMENTAND ACTIVITIESSee Community DevelopmentSTUDENT SERVICE CENTER205 Kent, 212-854-4400Mail Code 9206Cashiering: 212-854-1518For quick answers to your questions,visit: askus.columbia.edu.SEAS 2010–2011

252COLUMBIA UNIVERSITYTHE MORNINGSIDE CAMPUS & ENVIRONSSEAS 2010–2011

THE MORNINGSIDE HEIGHTS AREA OF NEW YORK CITY253SEAS 2010–2011

254INDEXAAcademic Advising. See Center forStudent Advisingacademic calendar, inside back coveracademic community, conductexpected in, 241academic concerns, grievances, andcomplaints, student, 245–246academic discipline, 241–243academic dishonesty, 242–243academic honors, 238academic integrity, 243academic monitoring, 238academic procedures and standards,234–237academic progress, satisfactory,26–27, 234–237academic standing, 238–240Accreditation Board for Engineeringand Technology (ABET), 18, 86,139, 183Activities Board at Columbia (ABC),213, 214addresses of Columbia Universitydepartments and resources, 248–252administrative officers, lists of,46, 52–54admissionsgraduate, 37–38, 248undergraduate, 21–23, 248advanced placement, 13–14, 22advanced standing, of transferstudents, 22–23advising centers. See Center forStudent AdvisingAlice! Columbia University’s HealthPromotion Program, 219, 250Alumni Representative Committee, 23Ambrose Monell Engineering Library, 7American College Testing (ACT)examinations, 22American Language Program (ALP), 37annual gift fellowships andscholarships, list of, 222applicationsfor degrees, 237graduate, 37prerequisite tests, 21–22process for, 21undergraduate, 21–22applied chemistry. See ChemicalEngineering, Department ofapplied mathematicscourses in, 68–70minor in, 194applied physicscourses in, 66–68minor in, 194Applied Physics and AppliedMathematics, Department of,58–70,current research activities, 58–59graduate programs, 65–66laboratory facilities, 59–61specialty areas, 63–65undergraduate programs, 61–65architecture, minor in, 194art history, minor in, 194assault, sexual, policy on, 244assistantships, 42Associate Provost for EqualOpportunity and Affirmative Action,250athletic programs, 13, 216attendance, 235BBachelor of Science degree (B.S.),17–18Baker Field Athletics Complex, 216Barnard Education Program, 19bioinductive and biomimetic materials,program in, 90Biological Sciences, Department of, 251courses for engineering students, 203biomedical engineeringcourses in, 75–82minor in, 195Biomedical Engineering, Departmentof, 71–82graduate program, 74–75undergraduate program, 72–74biophysics and soft matter physics,program in, 84Bookstore, Columbia University, 215Botwinick Multimedia LearningLaboratory, 6, 12Business, Graduate School ofcourses for engineering students,203joint programs with, 33, 128, 160Business/farm information, 29CC. Prescott Davis Scholars, 22cable TV service, 7calendaracademic, inside back coverfor graduate admissions, 37–38campus life, 212–216campus safety and security, 216career counseling, 7–8SEAS 2010–2011

255Center for Applied Probability (CAP), 156Center for Career Education (CCE),7–8, 44, 248Center for Financial Engineering, 156Center for Infrastructure Studies, 96Center for Life Cycle Analysis (LCA), 124Center for Student Advising,212–213, 248Center for Sustainable Use ofResources (SUR), 124Certificate of Professional Achievementprogram, 36, 65certification of enrollment, 236Chapel, St. Paul’s, 215, 250Chaplain, University, Office of the, 215chemical engineeringcourses in, 90–93minor in, 195–196Chemical Engineering, Department of,83–93current research activities, 84facilities and laboratories, 84–85graduate program, 87–90undergraduate program, 85–87Chemistry, Department of, 251courses for engineering students,203–204facilities and laboratories, 85civil engineeringcourses in, 100–103minor in, 196Civil Engineering and EngineeringMechanics, Department of,94–104current research activities, 94–95facilities and laboratories, 95–96graduate programs, 99–100undergraduate programs, 96–99classesattendance at, 235registration and enrollment in,234classrooms, electronic, 6Club Sports, 213College Scholarship Service (CSS)PROFILE Form, 28colleges and universities, in CombinedPlan program, 16–17Columbia Arts Experience, 7Columbia Bartending Agency andSchool of Mixology, 7Columbia Card (ID card), 218Columbia College and engineeringstudents, 212–216Columbia Comprehensive EducationalFinancing Plan, 44Columbia Dining Dollars, 218Columbia Experience Overseas (CEO), 7Columbia Genome Center (CGC), 84Columbia Microelectronic SciencesLaboratories, 138Columbia Panel on Discrimination andSexual Harassment, 244Columbia Student Enterprises (CSE), 7Columbia Universitycampuses, schools, affiliations, andresearch facilities, 5–8history of, 2–4maps of campus, 252, 253New York City roots of, 5policy, procedures, and regulations,234–246Provost, 246reservation of rights, 244resources, phone numbers, ande-mail addresses, list of, 248–252visits and tours, 23Web site, 6Columbia University Bookstore, 215Columbia University Grant (CUG)program, 28Columbia University InformationTechnology (CUIT), 6–7Columbia University Libraries, 7Columbia University’s Health PromotionProgram (Alice!), 219, 250Columbia University Tutoring andTranslation Agency, 7Columbia Video Network (CVN),35, 36, 248application to, 36Columbia Water Center, 124Combined Plan programs, 16–17, 23commencement ceremony, 237Committee on Academic Standing,232, 234, 238Committee on Instruction, 238Community Impact, 213complaints, academic concerns, andgrievances, student, 245–246Computational and OptimizationResearch Center (CORC), 156computer accounts, obtaining, 6Computer Engineering Program, 105–109graduate program, 107–109undergraduate program, 105–107computer kiosks, public, 6computer labs and clusters, 6–7computer sciencecourses in, 115–122minor in, 196Computer Science, Department of,110–122laboratory facilities, 110–111SEAS 2010–2011

256graduate programs, 114–115undergraduate program, 111–114computer security resources, 7computing facilities, University, 6–7Computing Support Center, 249conductexpected in the academiccommunity, 241unacceptable, subject to discipline,241–243Core Curriculum of ColumbiaUniversity, 4program offices, 248Counseling and Psychological Services(CPS), 219, 250coursesfor pro fessions other thanengi neering, 18–19interdisciplinary engineering, 202key to listings, 56–57in other divisions of the University,of interest to engineering students,203–210in SEAS departments. See individualdepartmentsCourseWorks, 6credit, points of, required for degreegraduate, 32–35, 235undergraduate, 10–16, 17–19,234–235Ddamages, payment for, 25, 40dance, minor in, 196Dean’s discipline, 242Dean’s List, 238Degree Audit Reporting System(DARS), 17degreesapplication for, 237doctoral, requirements, 34–35,235, 237See also individual degreesDining Dollars, 218dining facilities, locations, 219Dining Services, 218–219, 251diplomas, 237direct loans, 43Disability Services, University Office of,219, 244, 250discipline, academic, 241–243Dean’s, 242procedures for administering, 242discriminationand sexual harassment policy andprocedure, 244dishonesty, academic, 242–243disputes over grades or other academicevaluations, 246distance education. See ColumbiaVideo NetworkDivision of Student Affairs, 212, 242,250Doctor of Engineering Science (Eng.Sc.D.), 34–35Doctor of Philosophy (Ph.D.), 34–35Dodge Physical Fitness Center, 216dual degreewith the School of Journalism, incomputer science, 33, 115See also joint programsEEarl Hall Center, 215, 250Early Decision program, 21Earth and environmental engineeringcourses in, 129–136minor in, 196Earth and Environmental Engineering,Department of (DEEE), 123–136graduate programs, 127–129joint degree programs, 128research centers, 124–126scholarshihps, fellowships, andinternships, 126undergraduate program, 126–127See also Henry Krumb School ofMinesEarth and Environmental Engineering(EEE) program, 123–124Earth and Environmental Sciences,Department of (Columbia College),251courses for engineering students,204–206Earth Engineering Center (EEC), 124Earth resources engineering program,127–129East Asian studies, minor in, 197economicsminor in, 197electrical engineeringcourses in, 146–154minor in, 197Electrical Engineering, Department of,137–154B.S./M.S. program, 141–142concentration options in the M.S.program, 144–145graduate programs, 142–145laboratory facilities, 138research activities, 138undergraduate program, 138–142electronic classrooms, 6Electronic Data Service (EDS), 7e-mailaddresses of Columbia Universityresources and staff, 248–252as service of CUIT, 6–7emergency resources, 220emeriti and retired officers, list of, 52–53employment, student, 28, 44endowed scholarships and grants,list of, 222–228Engineer of Mines (professionaldegree), 129Engineering Accreditation Commission(EAC), 18engineering courses, interdisciplinary,202Engineering, School of. See FuFoundation School of Engineeringand Applied ScienceEngineering Graduate Student Council(EGSC), 213engineering management systemsgraduate program in, 158undergraduate program in, 156engineering mechanicscourses in, 103–104graduate program in, 97–98minor in, 197undergraduate program in, 98See also Civil Engineeringand Engineering Mechanics,Department ofengineering societies, 213engineering studentsand campus life, 212–216courses for, offered by otherUniversity divisions, 203–210interdisciplinary courses for, 202See also studentsEngineering Student Council, 213English and comparative literature,minor in, 197English proficiency requirement, 37SEAS 2010–2011

enrollment, 234certification of, 236entrepreneurship and innovation, minorin, 198environmental health engineering,concentration in, 127, 128Environmental Tracer Group, 124–125Equal Opportunity and AffirmativeAction, Office of, 240, 244examinations, midterm and final, 237Ffacultyand staff academic misconduct,complaints about, 245–246lists of, 46–52members-at-large, list of, 52romantic relationships withstudents, 244Faculty in Residence, 215family contributions to educationalcosts, 26Family Educational Rights and PrivacyAct (FERPA), 236, 244federal financial aid, 27–28, 43–44Federal Graduate PLUS Loan, 43federal income tax returns, 30Federal Pell Grants, 28Federal Perkins Loan, 43Federal Stafford Loan, 43Federal Supplemental EducationalOpportunity Grants (SEOG), 28Federal Work-Study Program (FWS), 28feesgraduate, 39–40refunds of, 25, 40undergraduate, 24–25See also paymentsfellowships, 42lists of, 222, 228–229financial aidaward packages, 27–28eligibility for, 26–27employment and, 28, 44federal, 28–30, 43to graduate students, 41–44, 250how to apply for, 28–30private programs, 44state, 43tax withholding from, for nonresidentaliens, 30to undergraduate students, 26–30,250Financial Aid and EducationalFinancing, Office of, 26, 41, 44, 250financial engineeringgraduate program in, 158–159joint programs in, 160undergraduate program in, 157First Year–Sophomore Program courserequirementsnontechnical, 10–12professional-level, 12–13technical, 124-2 Combined Plan B.S. program,16, 234-2 Combined Plan M.S. program,16, 23, 33fraternities and sororities, 215Free Application for Federal StudentAid (FAFSA), 28–29, 41–42, 43Frenchand francophone studies, minor in,198minor in, 198Fu Foundation School of Engineeringand Applied Science, The (SEAS)courses. See individual departmentsDean of, 241department and course codes, 56–57departments and programs, 58–191faculty and administration, 46–54history of, 2–4resources and facilities, 5–8Vice Dean of, 246See also Columbia UniversityFundamentals of Engineering (FE)exam, 183GGateway Residential Initiative, 215genomic engineering, program in, 88–90German, minor in, 198grade-point average (GPA), 236grades, report of, 236grading system, explained, 236graduate courses, taking as anundergraduate, 17Graduate Engineering Student LoanRequest Form, 41Graduate Record Examination (GRE),37Graduate Student Services, Office of,241, 242, 250graduate programs, 32–35admission to, 37–38applying to, 37–38planning and approval, 32prerequisites for admission to, 32See also individual programsgraduate studentsdegree requirements for, 235, 237discipline process for, 242financial aid for, 41–44, 250housing, 217–218special students as, 35, 38tuition and fees, 39–40graduation, 237grants and scholarships, 28endowed, list of, 222–228graphics, courses in, 104Greek or Latin, minor in, 198grievance procedures, 240, 246grievances, academic concerns, andcomplaints, student, 245–246Hharassing or threatening behavior, 244harrassmentdiscriminatory, 244sexual, 244Harriman Institute, Special Studieswith, 34health insurance, 24, 39. See alsoStudent Medical Insurance PlanHealth Service Program, 219Health Services at Columbia,219–220, 250Henry Krumb School of Mines (HKSM),123. See also Earth and EnvironmentalEngineering, Department ofHigher Education Opportunity Program(HEOP), 22Hispanic studies, minor in, 198history, minor in, 198holidays, religious, 244honors, academic, 238housing, University and off-campus,217–219. See also residence hallsHumanities and Social Sciences,Department of, courses forengineering students, 207257SEAS 2010–2011

258Iimmunization requirements, 220income tax returns, 29industrial engineeringcourses in, 161–170graduate programs in, 157–161joint programs, 33, 160minor in, 198undergraduate programs in,156–157Industrial Engineering and OperationsResearch, Department of, 157–170current research activities, 156graduate programs, 157–161undergraduate programs, 156–157Inside New York, 7Institute of Flight Structures, 96institutional grants, 42Insurance, Student Medical Plan, 219integrated waste management,concentration in, 128integrity, academic, 243Intercollegiate Athleticseligibility for, 216programs in, 216interdisciplinary engineering courses,202interfacial engineering and electrochemistry,program in, 90Inter-Greek Council, 213International and Public Affairs,School of, joint programs with, 19International English Language TestingSystem, 22International Research Center forClimate Prediction (IRI), 125International Students and ScholarsOffice (ISSO), 8, 234Internet access, 6Interschool Governing Board, 213, 214internships, 237interviews, of undergraduateapplicants, 23Intramural and Club Sports Program,216JJohn Jay Dining Hall, 218joint programswith the Graduate School ofBusiness, in Earth resourcesengineering, 33, 128with the Graduate School ofBusiness, in financial engineering, 160with the Graduate School ofBusiness, in industrial engineering,33, 160with the Graduate School ofBusiness, in operations research,33, 160with the School of International andPublic Affairs, 19with the School of Law, 19See also dual degree.Judicial Affairs and CommunityStandards, Office of, 215, 241–242Junior-Senior programs, 17–19Llaboratory charges, 24–25, 40Langmuir Center for Colloids andInterfaces (LCCI), 125Latin, Greek or, minor in, 198Law, School of, joint programs with, 19leave(s) of absenceinvoluntary, 239medical, 234, 238, 239military, 239voluntary, 234, 239Lenfest Center for Sustainable Energy,125Lerner Hall, 215libraries, 7LibraryWeb, 7lightwave (photonics) engineering,concentration in, 145LionSHARE, 7–8loans, student, 43MManager of the Disciplinary Procedurefor Sexual Assault, 250maps of Columbia Morningside Heightscampus, 252, 253marks. See grading systemMaster of Science degree (M.S.),32–34materials science and engineeringcourses in, 175–178minor in, 198Materials Science and Engineeringprogram (MSE), 123, 171–178current research activities, 172graduate programs, 173graduate specialty in solid-statescience and engineering, 173–175interdepartmental committee and,171laboratory facilities, 172undergraduate program, 172–173Mathematics, Department ofcourses for engineering students,207meal plans. See dining plansMechanical Engineer (professionaldegree), 185–187mechanical engineeringcourses in, 187–191minor in, 199Mechanical Engineering, Departmentof, 179–191current research activities, 180–182facilities for teaching and research,182–183graduate programs, 183–187undergraduate program, 183medals and prizes, list of, 230–232media engineering, concentration in,144–145medical care and insurance, 219–220Medical College Admissions Test(MCAT), 18medical leave of absence,234, 238–239medical physics, graduate programin, 65Metallurgical Engineer (professionaldegree), 129microelectronic circuits, concentrationin, 145microelectronic devices, concentrationin, 145Middle East, South Asian, and AfricanStudies, minor in, 199military leave of absence, 239minors, academic, 18, 194–200misconductacademic, complaints about facultyand staff, 245–246scientific or scholarly, 246sexual. See assault, sexualmonthly payment plan, 28Morningside Heights campus, 6maps of, 252, 253Multicultural Affairs, 214SEAS 2010–2011

multimedia networking, concentrationin, 144musicinstruction courses, 13minor in, 199Nnames, student, change of, 237National Opportunity Program (NOP),22New Student Orientation Program(NSOP), 214New York City, 5New York Stateinitial certification in adolescenceeducation, 19Tuition Assistance Program (TAP),28, 43Noncustodial Parent’s Statement Form,29nondiscriminatory policies, equaleducational opportunity andstudent, 244nontechnical requirements, 10–12NSF-Columbia MRSEC sharedfacilities, 85OOff-Campus Housing Assistance(OCHA), 217officers of SEASlist of, 46, 53retired, list of, 52–53Ombuds Office, 244, 245Ombuds Officer, 245operations researchcourses in, 161–170graduate program in, 157–161joint programs with the GraduateSchool of Business, 33, 160minor in, 199undergraduate programs in, 156–157See also Industrial Engineering andOperations Research, Department ofoptical and laser physics, graduateprogram in, 66orientation, 214PPanel on Discrimination and SexualHarassment, 244Parent Loans for UndergraduateStudents (PLUS), 28parentscontributions to educational costs, 26noncustodial, financial statement of,29paymentsfinancing options, 28timely and overdue, 24, 39See also feesPell Grants, 28Perkins Loans, 43personal expenses of students, 24, 39philosophy, minor in, 199physical education, 13and intercollegiate athletics, 216Physical Education, Intercollegiate and,Department of, 216Physics, Department of,courses for engineering students,207–208plagiarism, 243plasma physics, graduate program in, 66Plasma Physics Laboratory, 59–61political science, minor in, 199polymers and soft materials, scienceand engineering of, program in, 87pre-law program, 19pre-med program, 18preprofessional advising, 18–19, 212–213Primary Care Medical Services, 230–232printing facilities, 7prizes, medals and, list of, 230–232professional degree programs, 34professions other than engineering,SEAS programs in preparation for,18–19psychological, counseling and,services, 219psychology, minor in, 199Public Safety, Office of, 216RRape Crisis/Anti-Violence SupportCenter, 250readmission, 240recreational programs, 216refunds of tuition and fees, 25, 40registered programs (with New YorkState Department of Education),19–20registrar, 251–252See also Student Service Centerregistration, 234changes in, 235regulations, University, official,234, 244religion, minor in, 199religious holidays, 244report of grades, 236residence hall scholarships, list of, 232residence halls, 214–215, 217–219violation of rules of, 241Residence Units, and the Ph.D., 34Residential Programs, 214–215resources, Columbia University, list of,248–252Respecting Ourselves and OthersThrough Education (ROOTED), 214Romantic Relationship AdvisoryStatement, 244romantic relationships, faculty/staff andstudent, 244Rules of University Conduct, 241Ssafety and security, campus, 216St. Paul’s Chapel, 215sanctions, for academic dishonesty,242–243SAT tests, 22scholarshipsannual gift fellowships and, list of,222and grants, 28and grants, endowed, list of, 222–228residence hall, list of, 232School of Engineering (SEAS). See FuFoundation School of Engineeringand Applied Sciencescience and engineering of polymersand soft materials, program in, 87SEAS. See Fu Foundation School ofEngineering and Applied Sciencesecondary school preparation, recommendedfor first-year students, 21security resources, computer, 6Senior Advisement Center. See JuniorSenior Academic Advising Center259SEAS 2010–2011

260Sexual Assault, Manager of theDisciplinary Procedure for, 244sexual assault policy and procedures,244Sexual Violence Prevention andResponse Program, 219Social Security number, registrationand, 234sociology, minor in, 200solid-state physics, graduate programin, 66solid-state science and engineeringareas of research, 174graduate specialty in, 173–175sororities, fraternities and, 215Special Interest Communities, 217special student status, 35, 38sports, 13, 216. See alsophysical educationstaff, romantic relationships withstudents, 244Stafford Loans, 43Statistics, Department of,courses for engineering students,209–210statistics, minor in, 200Student Advising, Center for,212–213Student Affairs, Division of, 212, 242Student and Alumni MentoringPrograms, 214Student Development and Activities(SDA), 214Student Financial Services. SeeStudent Service CenterStudent Governing Board (SGB), 214student grievances, academicconcerns, and complaints, 245–246Student Group Advising, Office of,213student loans, 43–44Student Medical Insurance Plan, 219student organizations, 213student records, rights pertaining to,236Student Service Center, 252student services, 217–220studentsand campus life, 212–216contributions of, to educationalcosts, 26employment and earnings of, 28, 44international, 8, 42–43name changes of, 237new, orientation for, 214personal expenses of, 24, 39romantic relationships with facultyor staff, 244special, status, 35, 38transfer, 22–23, 38See also engineering students;graduate students; undergraduatesstudy abroad, 14–15summer courses at other institutions,235–236summer earnings, 26sustainable energyand materials, concentration in, 127concentration in, 127sustainable engineering, minor in, 200systems biology, concentration in, 145TTau Beta Pi, 17tax withholding, on tuition aid tononresident alien students, 30teacher certification, obtaining, 19telecommunications engineering,concentration in, 144telephone and cable TV services, 7telephone Helpdesk, 6telephone numbers of ColumbiaUniversity departments andresources, 248–252Test of English as a Foreign Language(TOEFL), 22, 37tests, preadmission, 21–223-2 Combined Plan B.A./B.S.program, 16–17, 23transcripts, 235–236transfer credits, 235–236transfer students, 22–23, 38tuitiongraduate, 39–40refunds of, 25, 40undergraduate, 24–25Tuition Assistance Program (TAP),New York State, 28, 43tutoring, 7UUndergraduate Research InvolvementProgram (URIP), 10undergraduatesapplications and admissions of,21–23degree requirements for, 10, 234–235financial aid for, 26–30housing for, 217minor programs for, 194–200programs in SEAS for, 10–20tuition and fees of, 24–25See also studentsUnited Campus Ministries, 215University Apartment Housing (UAH),217–218University Chaplain, Office of the, 215University Panel on Discrimination andSexual Harassment, 244University regulations, official,234, 244VVeteran Affairs, Department of, 43veterans, educational benefits for, 43Vice Dean, 246visual arts courses, 13WWaste to Energy Research andTechnology Council, 125water resources and climate risks,concentration in, 127wireless and mobile communications,concentration in, 145wireless network, 6–7women’s athletics, 216Work-Study Payroll Office, 28SEAS 2010–2011

Academic Calendar 2010–2011The following Academic Calendar was correct and complete when complied; however, the University reserves the right torevise or amend it, in whole or in part, at any time. Information on the current Academic Calendar may be obtained in theStudent Service Center, 205 Kent, 212-854-4330. It is also available on the Registrar’s Web site: www.columbia.edu/cu/registrar.AUTUMN TERM 2010August30–Sept. 6SeptemberNew student orientation program.3 Registration by appointment for first-yearstudents.6 Labor Day. University holiday.7 First day of classes.7–10, 13–17 Change of program by appointment.17 Last day to (1) register for academic credit,(2) change course programs, (3) submitwritten notice of withdrawal from theautumn term to the Dean of StudentAffairs for full refund of tuition and specialfees. No adjustment of fees for individualcourses dropped after this date.30 Last day to confirm, update, or request awaiver from the Student MedicalInsurance Plan.October20 October degrees conferred.21 Midterm date.November1 Academic holiday. Last day to apply forFebruary degrees.2 Election Day. University holiday.15–19 Registration by appointment for spring2011.18 Last day to drop individual courses withoutacademic penalty. Last day to change agrading option.25–26 Thanksgiving holidays.December1 Last day to apply for May degrees.13 Last day of classes.14–15 Study days.16–23 Final examinations.24–Jan. 17 Winter holidays.SPRING TERM 2011January11–14 Registration by appointment for all classes.17 Birthday of Martin Luther King Jr.University holiday.18 First day of classes.18–21, 24–28 Change of program by appointment.28 Last day to (1) register for academic credit,(2) change course programs, (3) submitwritten notice of withdrawal from thespring term to the Dean of StudentsAffairs for full refund of tuition and specialfees. No adjustment of fees for individualcourses dropped after this date.February1 Last day to confirm, update, or request awaiver from the Student MedicalInsurance Plan.9 February degrees conferred.March7 Midterm date.14–18 Spring holidays.24 Last day to drop individual courses withoutacademic penalty. Last day to changegrading option.April11–15 Registration by appointment for fall 2011.May2 Last day of classes.3–5 Study days.5 Last day for continuing students toapply for financial aid for the 2011–2012academic year.6–13 Final examinations.TBABaccalaureate Service.TBAEngineering Class Day.18 2011 University Commencement.

The Fu Foundation School of Engineering and Applied Science500 West 120th StreetNew York, New York 10027