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

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.
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SEAS 2008–2009