2008-2009 Bulletin â PDF - SEAS Bulletin - Columbia University

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200 PHYSICS The general four-term pre-engineering physics sequence consists of PHYS C1401, C1402, C1403, and C1494 (laboratory); or PHYS C1601, C1602, C2601, and C2699 (laboratory). PHYS C1401x Introduction to mechanics and thermodynamics Lect: 3 pts. Professors Dodd and Tucks. Corequisite: MATH V1101 or the equivalent. Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, temperature and heat, gas laws, the first and second laws of thermodynamics. PHYS C1402y Introduction to electricity, magnetism, and optics Lect: 3 pts. Professors Dodd and Hughes. Prerequisite: PHYS C1401. Corequisite: MATH V1102 or the equivalent. Electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves, polarization, geometrical optics, interference and diffraction. PHYS C1403x Introduction to classical and quantum waves Lect: 3 pts. Professor Brooijmans. Prerequisite: PHYS C1402. Corequisite: MATH V1201 or the equivalent. Classical waves and the wave equation, Fourier series and integrals, normal modes, wave-particle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, applications to atomic and nuclear physics. PHYS C1493x Introduction to experimental physics Lab and lecture: 3 pts. Lect: 1 hour weekly to be arranged. Lab: 3 hours weekly to be arranged. Instructor to be announced. Prerequisites: PHYS C1401 and C1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, and wave motion. (Students cannot receive credit for both PHYS C1493 and C1494.) PHYS C1494y Introduction to experimental physics Lab and lecture: 3 pts. Lect: 1 hour weekly to be arranged. Lab: 3 hours weekly to be arranged. Instructor to be announced. Prerequisites: PHYS C1401, C1402, and C1403. Laboratory work associated with the three prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic and nuclear physics. (Students cannot receive credit for both PHYS C1493 and C1494.) PHYS C1601x Physics I: mechanics and relativity Lect: 3.5 pts. Rec: 1 hour weekly to be arranged. Professor Zajc. Corequisite: MATH V1102 or the equivalent. Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, introduction to special relativity and relativistic kinematics. The course is preparatory for advanced work in physics and related fields. PHYS C1602y Physics II: thermodynamics, electricity, and magnetism Lect: 3.5 pts. Rec: 1 hour weekly to be arranged. Professor Zajc. Prerequisite: PHYS C1601. Corequisite: MATH V1201 or the equivalent. Temperature and heat, gas laws, the first and second laws of thermodynamics, kinetic theory of gases, electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves. The course is preparatory for advanced work in physics and related fields. PHYS C2601x Physics III: classical and quantum waves Lect: 3.5 pts. Rec: 1 hour weekly to be arranged. Professor Marka. Prerequisite: PHYS C1602 or C1402. Corequisite: MATH V1202 or the equivalent. Classical waves and the wave equation, geometrical optics, interference and diffraction, Fourier series and integrals, normal modes, wave-particle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, the harmonic oscillator. The course is preparatory for advanced work in physics and related fields. PHYS C2699y Experiments in classical and modern physics Lab and lecture: 3 pts. Lect: 1 hour weekly to be arranged. Lab: 3 hours weekly to be arranged. Instructor to be announced. Prerequisites: PHYS C1601 (or C1401), C1602 (or C1402), and C2601. Laboratory work associated with the three prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic and nuclear physics. PHYS C2801x-C2802y Accelerated physics, I and II Lect: 4.5 pts. Rec: 1 hour weekly to be arranged. Professor Cole. Prerequisite: advanced placement in physics and mathematics, or the equivalent, and the instructor’s permission. (A special placement meeting is held during Orientation.) This accelerated twosemester sequence covers the subject matter of PHYS C1601, C1602, and C2601 and is intended for students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, PHYS W3081, in the following year. PHYS W3002y From quarks to the cosmos: applications of modern physics Lect: 3.5 pts. Rec: 1 hour weekly to be arranged. Instructor to be announced. Prerequisites: PHYS C2601 or C2802. This course reinforces basic ideas of modern physics through applications to nuclear physics, highenergy physics, astrophysics, and cosmology. The ongoing Columbia research programs in these fields are used as practical examples. The course is preparatory for advanced work in physics and related fields. PHYS W3003x Mechanics Lect: 3 pts. Professor Blaer. Prerequisite: general physics; differential and integral calculus. Newtonian mechanics, oscillations and resonance, conservative forces and potential energy, central forces, noninertial frames of reference, rigid body motion, an introduction to Lagrange’s formulation of mechanics, coupled oscillators, and normal modes. PHYS W3007y Electricity and magnetism Lect: 3 pts. Professor Nicolis. Prerequisite: general physics; differential and integral calculus. Electrostatics and magnetostatics, Laplace’s equation and boundary-value problems, multipole expansions, dielectric and magnetic materials, Faraday’s law, AC circuits, Maxwell’s equations, Lorentz covariance, and special relativity. PHYS W3008x Electromagnetic waves and optics Lect: 3 pts. Professor Marka. Prerequisite: PHYS W3007. Maxwell’s equations and electromagnetic potentials, the wave equation, propagation of plane waves, reflection and refraction, geometrical optics, transmission lines, wave guides, resonant cavities, radiation, interference of waves, and diffraction. PHYS W3081x or y Intermediate laboratory work Lab: 2 pts. Professors May, Aprile, and Uemura. Primarily for junior and senior physics majors. Other majors require the instructor’s permission. May be repeated for credit by performing different experiments. The laboratory has 13 individual experiments available, of which two are required per 2 points. Each experiment is chosen by the student in consultation with the instructor. Each section meets one afternoon per week, with registration in each section limited by the laboratory capacity. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics. SEAS 2008–2009
PHYS G4003y Advanced mechanics Lect: 3 pts. Professor Pontón. Prerequisite: differential and integral calculus, differential equations, and PHYS W3003 or the equivalent. Lagrange’s formulation of mechanics, calculus of variations and the Action Principle, Hamilton’s formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics. PHYS G4018y Solid-state physics Lect: 3 pts. Professor Uemura. Prerequisite: PHYS G4021, G4022, G4023 or the equivalent. Introduction to solid-state physics: crystal structures, properties of periodic lattices, electrons in metals, band structure, transport properties, semiconductors, magnetism, and superconductivity. PHYS G4019x Mathematical methods of physics Lect: 3 pts. Professor Aleiner. Prerequisite: differential and integral calculus. Highlights of complex analysis, differential equations, integral equations, Green’s functions, special functions, Fourier and other transforms, approximation methods, group theory and representations, differential geometry and manifolds. Emphasis is placed on applications to physical problems. PHYS G4021x-G4022y Quantum mechanics, I and II Lect: 3 pts. Professor Mueller. Prerequisite: PHYS C2601 or C2802, or the equivalent. The formulation of quantum mechanics in terms of state vectors and linear operators, three-dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, identical particles. Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models. PHYS G4023x Thermal and statistical physics Lect: 3 pts. Professor Heinz. Prerequisite: PHYS G4021 or the equivalent. Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism. PHYS G4040x General relativity Lect: 3 pts. Professor Beloborodov. Prerequisites: PHYS G4003 and W3007. Tensor algebra, tensor analysis, introduction to Riemann geometry. Motion of particles, fluid, and fields in curved spacetime. Einstein equation. Schwarzschild solution; test-particle orbits and light bending. Introduction to black holes, gravitational waves, and cosmological models. STATISTICS For a description of the following course offered jointly by the Departments of Statistics and Industrial Engineering and Operations Research, see ‘‘Industrial Engineering and Operations Research’’: SIEO W4150: Introduction to probability and statistics STAT W3105x Introduction to probability 3 pts. Instructor to be announced. Prerequisites: MATH V1101 and V1102 or the equivalent. This course is an introduction to probability specially designed for sophomore and junior students. Emphasis is on conceptual understanding and problem solving. Students require slightly less mathematical background than required for STAT W4105. A quick review of multivariate calculus is provided. This course satisfies the prerequisite for STAT W3659/W4107. Topics covered include random variables, conditional probability, expectation, independence, Bayes’ rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers, and Markov’s inequality. STAT W3107 y Introduction to statistical inference 3 pts. Instructor to be announced. Prerequisite: STAT W3000, or SIEO W3658 or STAT W4105, or the equivalent. Principles of statistical inference. Population parameters, sufficient statistics. Basic distribution theory. Point and interval estimation. Method of maximum likelihood. Method of least squares, regression. Introduction to the theory of hypothesis testing. Likelihood ratio tests. Nonparametric procedures. Statistical design theory. Applications to engineering, medicine, natural and social sciences. STAT W3659y Statistical inference 3 pts. Instructor to be announced Prerequisite: STAT W3000 or W4105, or the equivalent. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals, maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares, and analysis of variance. General Education Requirement: Quantitative and Deductive Reasoning (QUA). STAT W4105 x and y Probability 3 pts. Instructor to be announced. Prerequisites: MATH V1101 and V1102 or the equivalent and STAT W1111 or W1211. Corequisite: MATH V1201 or the equivalent, or the instructor’s permission. This course can be taken as a single course for students requiring knowledge of probability or as a foundation for more advanced courses. It is open to both undegraduate and master students. This course satisfies the prerequisite for W3659 and W4107. Topics covered include combinatorics, conditional probability, random variables and common distributions, expectation, independence, Bayes’ rule, joint distributions, conditional expectations, moment generating functions, central limit theorem, laws of large numbers, characteristic functions.General Education Requirement: Quantitative and Deductive Reasoning (QUA). STAT W4201x and y Advanced data analysis 3 pts. D. Alemayehu and instructor to be announced. Prerequisite: A one-term introductory statistics course. This is a course on getting the most out of data. The emphasis will be on hands-on experience, involving case studies with real data and using common statistical packages. The course covers, at a very high level, exploratory data analysis, model formulation, goodness-of-fit testing, and other standard and nonstandard statistical procedures, including linear regression, analysis of variance, nonlinear regression, generalized linear models, survival analysis, time series analysis, and modern regression methods. Students will be expected to propose a data set of their choice for use as case study material. STAT W4109x Probability and statistical inference 6 pts. Instructor to be announced. Combines STAT W4105 and W4107. STAT W4290 y Statistical methods in finance 3 pts. Instructor to be announced. Prerequisites: STAT W4105 and W4107. This is a master-level course introducing statistical methodologies in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures, with several research topics being introduced through problems in a term project. Lecture notes by the instructor will be distributed. The course will cover linear regression with applications to single and multifactor pricing models, multivariate analysis and their applications in Markowitz’s portfolio management, estimation and modeling of volatilities, calculation of value-at-risk, nonparametric methods with applications to option pricing and interest rate markets. STAT W4315x and y Linear regression models 3 pts. Instructor to be announced. Prerequisites: STAT W3000 or the equivalent and STAT W3659 or the equivalent. Corequisites: MATH V1101, V1102, and V2110. Simple and multiple regression, including testing, estimation and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, fixed effects ANOVA and ANCOVA models, nonlinear regression, multiple comparisons, co-linearity and confounding, model selection. Emphasis on geometric approach to the theory and computer use to analyze data. 201 SEAS 2008–2009
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The Fu Foundation School of Enginee
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A MESSAGE FROM THE DEAN The great s
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About the School and University
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3 trical section of the Navy’s Bu
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5 Beyond its schools and programs,
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THE COLUMBIA UNIVERSITY LIBRARIES T
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Undergraduate Studies
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11 to engage in ethical, analytic,
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APAM E1601y Introduction to computa
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• take a language or literature c
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State University of New York, Genes
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agreements with forty-one other sta
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UNDERGRADUATE ADMISSIONS 21 Office
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Subject Tests are required only if
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25 research work are required to me
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Graduate Studies
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33 statements covering these specia
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GRADUATE ADMISSIONS 37 Office of Gr
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GRADUATE TUITION, FEES, AND PAYMENT
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FINANCIAL AID FOR GRADUATE STUDY 41
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and Applied Science are automatical
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Faculty and Administration
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47 Xi Chen Professor of Civil Engin
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Richard W. Longman Professor of Mec
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Alan C. West Samuel Ruben-Peter G.
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APPLIED MATHEMATICS: THIRD AND FOUR
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BIOMEDICAL ENGINEERING 351 Engineer
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BIOMEDICAL ENGINEERING: THIRD AND F
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ELECTRICAL ENGINEERING 1300 S. W. M
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members of multi-disciplinary teams
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THE MORNINGSIDE HEIGHTS AREA OF NEW
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253 career counseling, 7 Career Res
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English and comparative literature,
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monthly payment plan, 28 Morningsid
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NOTES 259 SEAS 2008-2009
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2008-2009 Bulletin â PDF - SEAS Bulletin - Columbia University