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

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, gravational
waves, and cosmological models.
Statistics
Engineering students interested in a
survey of the mathematical theory of
probability and statistics should consider
the pair STAT W3105: Probability
theory and W3107: Statistical inference.
Students seeking a quicker overview
that focuses more on probability theory
should consider SIEO W4150. STAT
W4105 and W4107 are the equivalent
of W3105 and W3107, respectively; but
graduate students may not register for
W3105 and W3107. STAT W4109 (6
pts) covers the same material as W3105
and W3107 in a single semester. STAT
W4315: Linear regression models takes
W3105 and W3107 as prerequisites; like
other advanced offerings in statistics,
it covers both theory and practical
aspects of modeling and data analysis.
Advanced offerings in probability theory,
stochastic processes, and mathematical
finance generally take STAT W3105 as
a prerequisite; advanced offerings in
statistical theory and methods generally
take STAT W4107 and, in several cases,
W4315 as prerequisites; an exception
is STAT W4220: Data mining, which
has a course in computer programming
as prerequisite and STAT W3107 as
corequisite. STAT 4201 is a high-level
survey of applied statistical methods.
Please note that STAT W3000
has been renumbered as W3105 and
STAT W3659 has been renumbered as
W3107. 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 W4150x and y Introduction to
probability and statistics
3 pts. Professors Gallego, Hueter, and Wright.
Prerequisites: MATH V1101 and V1102 or the
equivalent. A quick calculus-based tour of the
fundamentals of probability theory and statistical
inference. Probabilistic models, random variables,
useful distributions, expectations, laws of large
numbers, central limit theorem. Statistical inference:
point and confidence interval estimation, hypothesis
tests, linear regression. Students seeking a more
thorough introduction to probability and statistics
should consider STAT W3105 and W3107.
STAT W2024x Applied linear regression
analysis
3 pts. Professor Lindquist.
Prerequisite: One of STAT W1001, W1111,
or W1211. Develops critical thinking and data
analysis skills for regression analysis in science
and policy settings. Simple and multiple linear
regression, nonlinear and logistic models,
random-effects models, penalized regression
methods. Implementation in a statistical package.
Optional computer-lab sessions. Emphasis on
real-world examples and on planning, proposing,
implementing, and reporting.
STAT W2025y Applied statistical methods
3 pts. Professor Whalen.
Prerequisite: STAT W2024. Classical
nonparametric methods, permutation tests;
contingency tables, generalized linear models,
missing data, causal inference, multiple
comparisons. Implementation in statistical
software. Emphasis on conducting data analyses
and reporting the results. Optional weekly
computer-lab sessions.
STAT W2026x Statistical applications and
case studies
3 pts. Professor Lindquist.
Prerequisite: STAT W2025. A sample of topics
and application areas in applied statistics.
Topic areas may include Markov processes and
queuing theory; meta-analysis of clinical trial
research; receiver-operator curves in medical
diagnosis; spatial statistics with applications in
geology, astronomy, and epidemiology; multiple
comparisons in bio-informatics; causal modeling
with missing data; statistical methods in genetic
epidemiology; stochastic analysis of neural spike
train data; graphical models for computer and
social network data.
STAT W3026x Applied data mining
3 pts. Professor Emir.
Data mining is a dynamic and fast growing field at
the interface of Statistics and Computer Science.
The emergence of massive datasets containing
millions or even billions of observations provides
the primary impetus for the field. Such datasets
arise, for instance, in large-scale retailing,
telecommunications, astronomy, computational
and statistical challenges. This course will provide
an overview of current practice in data mining.
Specific topics covered with include databases
and data warehousing, exploratory data analysis
and visualization, descriptive modeling, predictive
modeling, pattern and rule discovery, text mining,
Bayesian data mining, and causal inference. The
use of statistical software will be emphasized.
STAT W3103x Mathematical methods for
statistics
6 pts. Professor Rabinowitz.
Prerequisite: MATH V1101. A fast-paced coverage of
those aspects of the differential and integral calculus
of one and several variables and of the linear algebra
required for the core courses in the Statistics major.
The mathematical topics are integrated with an
introduction to computing. Students seeking more
comprehensive background should consider replacing
this course with MATH V1102 and V2010, and one of
COMS W1003, W1004, or W1007.
STAT W3105x Introduction to probability
3 pts. Professor Lo.
Prerequisites: MATH V1101 and V1102 or the
equivalent. A calculus-based introduction to
probability theory. A quick review of multivariate
calculus is provided. 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 W3107y Introduction to statistical
inference
3 pts. Instructor to be announced.
Prerequisite: STAT W3105 or W4105, or the
equivalent. Calculus-based introduction to the
theory of statistics. 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.
STAT W3315x Linear regression models
3 pts. Instructor to be announced.
Prerequisites: STAT W3107 (or W4150) and STAT
W3103 (or MATH V1101, V1102, and V2110).
Theory and practice of regression analysis. 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 enrollment is limited to
undergraduate students.
STAT W3997x and y Independent Research
Instructor to be announced.
Prerequisites: The permission of a member of the
department. May be repeated for credit. The student
participates in the current research of a member of
the department and prepares a report on the work.
STAT W4201x and y Advanced data analysis
3 pts. Professors Alemayehu and Liu.
Prerequisite: STAT W4315. At least one of
W4290, W4325, W4330, W4437, W4413, W4543
is recommended. This is a course on getting the
most out of data. The emphasis will be on handson
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 non-standard
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.
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engineering 2011–2012