2011-2012 Bulletin â PDF - SEAS Bulletin - Columbia University

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190 undergraduate minors Undergraduate minors are designed to allow engineering and applied science students to study, to a limited extent, a discipline other than their major. Besides engineering minors offered by Columbia Engineering departments, liberal arts minors are available. A minor requires at least 15 points of credit, and no more than one course can be taken outside of Columbia or met through AP or IB credit. This includes courses taken through study abroad. In Engineering departments with more than one major program, a minor in the second program may be permitted, if approved by the department. No substitutions or changes of any kind from the approved minors are permitted (see lists below). No appeal for changes will be granted. Please note that the same courses may not be used to satisfy the requirements of more than one minor. No courses taken for pass/fail may be counted for a minor. Minimum GPA for the minor is 2.0. Departments outside the Engineering School have no responsibility for nonengineering minors offered by Engineering. For a student to receive credit for a course taken while studying abroad, the department offering the minor must approve the course in writing, ahead of the student’s study abroad. Students must expect a course load that is heavier than usual. In addition, unforeseen course scheduling changes, problems, and conflicts may occur. The School cannot guarantee a satisfactory completion of the minor. Minor in Applied Mathematics Prospective students should consult the first- and second-year requirements for applied mathematics majors to ensure that prerequisites for the applied mathematics minor are satisfied in the first two years. Course work counting toward the applied mathematics minor may not include advanced placement credits. Any substitutions for the courses listed below require the approval of the applied mathematics program adviser. 1. APMA E3101: Linear algebra (3) or MATH V2010: Linear algebra (3) 2. APMA E3102: Partial differential equations (3) or MATH V3028: Partial differential equations (3) 3–5. Three of the following courses: APMA E4300: Intro to numerical methods (3) APMA E4204: Func of complex variable (3) APMA E4101: Intro to dynamical systems (3) MATH V2500: Analysis and optimization (3) SIEO W4105: Intro to probablity and statistics (3) STAT W4107: Statistical inference (3) or any other course designated APMA, MATH, STAT, IEOR, or COMS that is approved by the applied mathematics program adviser Minor in Applied Physics Prospective students should consult the first- and second-year requirements for applied physics majors to ensure that prerequisites for the applied physics minor are satisfied in the first two years. Course work counting toward the applied physics minor may not include advanced placement credits. 1. APPH E4901: Problems in applied physics (1) 2. PHYS W3003: Mechanics (3) 3. APPH E3100: Intro to quantum mechanics (3) 4. APPH E3300: Applied electromagnetism (3) 5. MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3) 6. Two of the following courses APPH E4010: Intro to nuclear science (3) APPH E4100: Quantum physics of matter (3) APPH E4110: Modern optics (3) APPH E4112: Laser physics (3) APPH E4300: Applied electrodynamics (3) APPH E4301: Intro to plasma physics (3) Minor in Architecture 1. Studio: One of the following courses ARCH V1020: Intro to architectural design and visual culture (3) ARCH V3101: Abstraction (4) ARCH V3103: Perception (4) 2–4. History/theory courses (see Note below) 5. Elective: must be either an approved second design studio or an additional history/theory course Note: A list of the approved history/theory courses is available at the departmental office each semester. Minor in Art History 1–7. Seven courses in art history, covering four of the following areas: (a) ancient Mediterranean, (b) medieval Europe, (c) Renaissance and baroque, (d) 18th, 19th, and 20th century, and (e) non- Western Minor in Biomedical Engineering The Biomedical Engineering program offers a minor in one of three tracks: (I) cellular engineering, (II) biomechanics, and (III) biosignals and biomedical imaging. Students who wish to get a minor in biomedical engineering should engineering 2011–2012
take the core BME requirements, as well as select courses from one of the three tracks, described below. Participation in the minor is subject to the approval of the major program adviser. Core BME Requirements 1. BIOL C2005: Intro biology, I (4) 2. BMEN E4001: Quantitative physiology, I (3) or BMEN E4002: Quantitative physiology, II (3) I. Cell and Tissue Engineering Track 3. CHEE E3010: Prin of chemical engineering thermodynamics (4) or BMEN E4210: Thermodyn of bio systems (4) or MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3) or MECE E3301: Thermodynamics (3) 3. CHEN E3110: Transport phenomena, I (3) or EAEE E4900: Applied transport and chemical rate phenomena (3) or MECE E3100: Intro to mech of fluids (3) or ENME E3161: Fluid mechanics (4) 4. CHEN E4230: Reaction kinetics and reactor design (3) 1. COMS W1004: Intro to computer science and programming in Java (3) 2. COMS W1007: Obj-oriented prog and design (3) 3. COMS W3133: Data structures in C (3) or COMS W3134: Data structures in Java (3) or COMS W3137: Data structures and algorithms (4) 4. COMS W3157: Advanced programming (4) 5. COMS W3203: Discrete mathematics (3) 191 4. BMEN E4501: Tissue engineering, I (3) 5. BMEN E4502: Tissue engineering, II (3) 6. One of the following courses: BMEN E3320: Fluid biomechanics (3) BMEN E4570: Sci and eng of body fluids (3) ECBM E3060: Intro to genomic info (3) CHEN E3110: Transport phenomena, I (3) CHEN E4700: Prin of genomic technologies (3) MSAE E3103: Elements of mat sci (3) II. Biomechanics Track 3. BMEN E4300: Solid biomechanics (3) 4. BMEN E3320: Fluid biomechanics (3) 5–6. Two from the following course groups: ENME E3113: Mechanics of solids (3) ENME E3161: Fluid mechanics (4) or MECE E3301: Thermodynamics (3) or MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3) III. biosignals and Biomedical Imaging Track 3. BMEN E4894: Biomedical imaging (3) 4–5. Two of the following courses: BMEN E4430: Prin of magnetic resonance imaging (3) BMEE E4400: Wavelet applications in biomedical image and signal processing (3) BMEN E4898: Biophototonics (3) BMEN E4410: Ultrasound in diagnostic imaging (3) BMEN E4420: Biomedical signal processing and signal modeling (3) 6. One of the following courses: ELEN E3801: Signals and systems (3.5) ELEN E4810: Digital signal processing (3) ELEN E4830: Digital image processing (3) Minor in Chemical Engineering Of the six courses required, at least three must have the CHEN, CHEE, or CHAP designator: 1. CHEN E3100: Mat and energy balances (4) 2. CHEE E3010: Prin of chemical engineering thermodynamics (3) 5–6. Two of the following courses: Any 3000-level or higher BMCH, CHEN, CHAP, or CHEE course APMA E3101: Linear algebra (3) APMA E3102: Partial differential equations (3) BMEN E3320: Fluid biomechanics (3) BMEN E4001: Quantitative physiology, I (3) BMEN E4002: Quantitative physiology, II (3) ELEN E3201: Circuit analysis (3.5) ELEN E3331: Electronic circuits (3) SIEO W3600: Intro to probability and statistics (4) IEOR W4105: Probability (3) IEOR W4106: Stochastic models (3) MSAE E3103: Elements of mat sci (3) MSAE E3142: Ceramics and polymers (3) Minor in Civil Engineering 1. CIEN E3121: Structural analysis (3) or ENME E3161: Fluid mechanics (4) or MECE E3100: Intro to mech of fluids (3) 2. ENME E3105: Mechanics (4) 3. ENME E3113: Mechanics of solids (3) 4–6. Electives: Three of the following courses: CIEN E1201: Design of buildings, bridges, and spacecraft (3) ENME E3161: Fluid mechanics (4) ENME E3114: Exp mechanics of materials (4) MECE E3414: Adv strength of materials (3) ENME E4332: Finite element analysis, I (3) CIEN E3125: Structural design (3) CIEN E4241: Geotech eng fundamentals (3) CIEE E3250: Hydrosystems engineering (3) CIEE E4163: Environ eng: wastewater (3) CIEN E3129: Project mgmt for construction (3) CIEN E4131: Prin of construction tech (3) Note: At least three of the courses must be courses that are not required in the student’s major. Minor in Computer Science Students who pass the Computer Science Advanced Placement Exam, either A or AB, with a 4 or 5 will receive 3 points and exemption from COMS W1004. An additional elective is to be recommended but not required. Participation in the minor is subject to the approval of the major program adviser. For further information, please see the QuickGuide at www.cs.columbia.edu/ education/undergrad/seasguide. 6. COMS W3261: Comp science theory (3) 7. CSEE W3827: Fund of computer systems (3) or a 4000-level COMS technical elective Minor in Dance The dance minor consists of five 3-point courses. Please note that no performance/choreography courses below count toward the nontech requirement for Engineering students. 1–2. History/criticism: Two of the following: DNCE BC2565: World dance history DNCE BC2570: Dance in New York City DNCE BC2575: Choreography for the American musical DNCE BC3000: From the page to the dance stage DNCE BC3001: Western theatrical dance from the Renaissance to the 1960s DNCE BC3200: Dance in film DNCE BC3567: Dance in Asia DNCE BC3570: Latin American and Caribbean dance DNCE BC3574: Seminar on contemporary choreographers and their works DNCE BC3576: Dance criticism DNCE BC3577: Performing the political DNCE BC3578: Traditions of African-American dance 3–4. Performance/choreography: Two of the following: DNCE BC2563: Dance composition: form DNCE BC2564: Dance composition: content DNCE BC2567: Music for dance DNCE BC2580: Tap as an American art form DNCE BC3565: Composition: collaboration and the creative process DNCE BC3590: Rehearsal and performance in dance 5. One elective Minor in Earth and Environmental Engineering 1–3. Three of the following courses: EAEE E3103: Energy, minerals, and mat syst (3) EAEE E3255: Environmental control and pollution reduction systems (3) EAEE E4001: Industrial ecology of Earth res (3) EAEE E4003: Intro to aquatic chemistry (3) EAEE E4004: Physical processing and recovery of solids (3) engineering 2011–2012
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Bulletin 2011 -2012
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Bulletin 2011 -2012
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a message from the dean As students
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About the School and University
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3 After receiving a master’s degr
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Resources and Facilities 5 A Colleg
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• CourseWorks is the University c
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Undergraduate Studies
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students improve their ability to e
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transistors, first order RC and RL
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possible overseas destinations and
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more than 68 transfer points toward
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Programs Registered with the New Yo
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Applicants may submit results of th
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Undergraduate Tuition, Fees, and Pa
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financial aid for undergraduate stu
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family’s financial situation. Con
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Graduate Studies
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statements covering these special r
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33 Completion of Requirements The r
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graduate admissions 35 Office of Gr
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Graduate tuition, fees, and payment
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financial aid for graduate study 39
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esearch assistantships, readerships
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Faculty and Administration
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45 Xi Chen Associate Professor of E
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S. G. Steven Kou Professor of Indus
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Tiffany Shaw Assistant Professor of
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Enders Robinson Maurice Ewing and J
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Departments and Academic Programs
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55 IEOR INAF INTA MATH MEBM Industr
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techniques based on the theory of g
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Applied Physics: Third and Fourth Y
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Applied mathematics: Third and Four
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are determined in consultation with
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APPH E4110x Modern optics 3 pts. Le
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squares method, pseudo-inverses, si
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iomedical engineering 351 Engineeri
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of courses in mathematics, physics,
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iomedical engineering. Up to 12 poi
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iomedical engineering Program: Thir
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BMEN E4420y Biomedical signal proce
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BMEN E6400x Analysis and quantifica
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chemical nature of things and provi
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and broad-ranging nature of the deg
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chemical engineering: Third and Fou
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principles, environmental sciences,
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systems are treated next (dominant
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civil engineering and engineering m
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Program Objectives In developing an
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civil engineering: Third and Fourth
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engineering mechanics: Third and Fo
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and leadership on the part of engin
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ENME E4363y Multiscale computationa
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computer engineering program: first
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computer engineering program: first
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Computer Science 450 Computer Scien
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Track 2: Systems Track The systems
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computer science: Third and Fourth
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CSEE W3827x and y Fundamentals of c
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EECS E4340x Computer hardware desig
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COMS E61xx course and/or COMS W4444
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COMS E6902x and y Thesis 1-9 pts. A
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Engineer, and the doctorate degrees
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Scholarships, Fellowships, and Inte
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earth and environmental engineering
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sludge or cake that must be dispose
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theory and practical aspects of dat
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EAEE E4241x Solids handling and tra
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permission. Critical discussion of
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engineering. Details on those progr
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electrical engineering: Third and F
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Page 167 and 168: operations research: Third and Four
Page 169 and 170: OPERATIONS RESEARCH: engineering ma
Page 171 and 172: OPERATIONS RESEARCH: FINANCIAL engi
Page 173 and 174: applications. Review of elements of
Page 175 and 176: Current Research Activities Current
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Page 179 and 180: Chemistry, Earth and Environmental
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Page 189 and 190: mechanical engineering: third and f
Page 191 and 192: prescribed design problems. Problem
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Page 195: Undergraduate Minors
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Page 205 and 206: EESC V1201y Environmental risks and
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Page 211 and 212: Campus and Student Life
Page 213 and 214: Preprofessional Advising The Office
Page 215 and 216: three Greek councils: The Interfrat
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Page 219 and 220: Upperclass and Graduate Students Ma
Page 221 and 222: Scholarships, Fellowships, Awards,
Page 223 and 224: Class of 1900 (1940) Gift of the Cl
Page 225 and 226: James M. and Elizabeth S. Li Endowe
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Page 231: time to that member of the graduati
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240 C. Discrimination and sexual ha
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242 columbia university resource li
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244 Medical Services John Jay Hall,
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246 The Morningside Heights Area of
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248 Center for Career Education (CC
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250 See also payments fellowships,
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252 parents contributions to educat
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254 notes engineering 2011-2012
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256 notes engineering 2011-2012
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500 West 120th Street New York, New
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