2009-2010 Bulletin – PDF - SEAS Bulletin - Columbia University

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OPERATIONS RESEARCH: FINANCIAL ENGINEERING:
FIRST AND SECOND YEARS
SEMESTER I SEMESTER II SEMESTER III SEMESTER IV
MATHEMATICS
MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Linear algebra (3) 1
and ODE (3)
PHYSICS
(three tracks, choose one)
CHEMISTRY
(choose one course)
ENGLISH
COMPOSITION
(three tracks, choose one)
Physics or chemistry lab:
C1401 (3) C1402 (3) PHYS C1493 (3) or
C1601 (3.5) C1602 (3.5) PHYS W3081 (2) or
C2801 (4.5) C2802 (4.5) CHEM C1500 (3) or
CHEM C2507 (3) or
CHEM C3085 (4) or
C1403 (3.5) or C1404 (3.5) or
C1604 (3.5) or C3045 (3.5)
C1010 (3)
Z1003 (0) C1010 (3)
Z0006 (0) Z1003 (0) C1010 (3)
REQUIRED
NONTECHNICAL
ELECTIVES
ECON W1105 (4) and W1155 recitation (0)
either semester
HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102,
or Global Core (3–4) or Global Core (3–4)
HUMA W1121 or W1123 (3)
either semester
FIRST- AND SECOND-
YEAR DEPT.
REQUIREMENTS
Professional-level course (3) (see pages 12–13)
ENGI E2261 (4)
and SIEO W3658 (3) or SIEO W4105 (3)
and STAT W3659 (3) or STAT W4107 (3)
COMPUTER
SCIENCE
PHYSICAL
EDUCATION
GATEWAY LAB
C1001 (1) C1002 (1)
E1102 (4) either semester
COMS W1004 (Java) (3) or COMS W1007 (Java) (3)
and COMS W3134 (3) or COMS W3137 (3) 2
1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.
2 Computer programming should be taken consecutively with data structures.
optimality conditions. Computational methods:
steepest descent, Newton and quasi-Newton
methods for unconstrained problems, active set,
penalty set, interior point, augmented Lagrangian
and sequential quadratic programming methods
for constrained problems. Introduction to nondifferentiable
optimization and bundle methods.
IEOR E6603x Combinatorial optimization
Lect: 2.5. 3 pts. Not given in 2009–2010.
Prerequisites: IEOR E6613 and E6614. Algorithms
for matching problems. Introduction to matroids;
polyhedral combinatorics. Complexity theory and NP
completeness. Perfect graphs and the ellipsoid method.
IEOR E6606y Advanced topics in network flows
Lect: 3. 3 pts. The faculty.
Prerequisite: Knowledge of elementary graph
algorithms and computational complexity, equivalent
to IEOR E6605, or COMS W4203 and W4231.
Analysis of algorithms and their complexity for a
variety of network routing problems. Topics: overall
minimum cuts, minimum cost network flows, flows
with losses and gains, parametric flows, dynamic
flows, multicommodity flows and applications.
IEOR E6608x Integer programming
Lect: 2. 3 pts. The faculty.
Prerequisite: IEOR E6613 or the equivalent.
Theoretical and algorithmical aspects of integer
programming (IP). Theoretical topics: structure
of the set of feasible solutions of an IP problem,
integral polyhedra, totally unimodular matrices,
totally dual integral systems, Lovasz’s lattice
reduction method, and Lenstra’s IP algorithm.
Algorithmical topics to center on branch and
bound algorithms and the ‘‘facet’’ approach to
cutting-plane algorithms.
IEOR E6609y Dynamic programming
Lect: 3. 3 pts. Instructor to be announced.
Prerequisite: IEOR E4701 or E4106 or the equivalent.
General discrete time deterministic, dynamic
programming, discrete time-parameter finite branching,
Markov decision chains, team decisions, certainty
equivalence, continuous time-parameter
Markov branching decision processes. Applications
SEAS 2009–2010