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

OPERATIONS RESEARCH: FINANCIAL ENGINEERING:
THIRD AND FOURTH YEARS
165
SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII
IEOR E3608 (4) IEOR E3402 (4) IEOR E4307 (3) IEOR E4500 (3)
Mathematical prog. Production planning Forecasting Applications prog. for FE
REQUIRED
COURSES
IEOR E3106 (3) IEOR E4404 (4) IEOR E4407 (3) IEOR E4630 (3)
Stochastic models Simulation Game theoretic models Asset allocation
of operations
IEOR E4003 (3) IEOR E4700 (3) ECON E3412 (3)
Industrial econ. Intro. to FE IEOR E4620 (3) Intro. to econometrics
Pricing models for FE
ECON W3213 (3) COMS W4111 (3)
Macroeconomics
Database systems
ECON W3211 (3)
Microeconomics
ELECTIVES
FE TECH
NONTECH
Please consult the list on the departmental Web site: www.ieor.columbia.edu
Complete 27-point requirement; see page 11 or www.engineering.columbia.edu for details
include capital budgeting, portfolio selection, inventory
control, systems reliability, and maximization
of expected utility with constant risk posture.
IEOR E6610x Approximation algorithms
Lect: 2. 3 pts. Not given in 2009–2010.
Prerequisites: Basic knowledge of linear programming
and analysis of algorithms or combinatorial
optimization. The design and analysis of efficient
algorithms for providing near-optimal solutions to
NP-hard problems. Classic algorithms and recent
techniques for approximation algorithms.
IEOR E6611x Semidefinite and second-order
cone programming
Lect: 2. 3 pts. Professor Iyengar.
Duality theory for semidefinite programming
(SDP) and second-order cone programming
(SOCP). Jordan algebras and symmetrical cones.
Formulating engineering problems such as robust
linear programming, truss design, filter design,
and antenna design as SDPs and SOCPs. SDP
and SOCP approximations for combinatorial optimization
problems.
IEOR E6612 Robust optimization
Lect: 2. 3 pts. Professor Iyengar.
Prerequisites: Linear algebra (APMA E3101 or
the equivalent) and optimization (IEOR E6613 or
the equivalent). Robust convex optimization problems,
reformulating robust problems as nominal
problems, computational techniques. Adjustably
robust optimization. Chance constrained problems
and robust chance constrained problems.
Applications from portfolio optimization, truss
design, inventory theory, revenue management,
dynamic programming, etc.
IEOR E6613x Optimization, I
Lect: 3. 4.5 pts. Professor Goldfarb.
Prerequisite: Linear algebra. Theory and geometry
of linear programming. The simplex method.
Duality theory, sensitivity analysis, column generation
and decomposition. Interior point methods.
Introduction to nonlinear optimization: convexity,
optimality conditions, steepest descent and
Newton's method, active set and barrier methods.
IEOR E6614y Optimization, II
Lect: 3. 4.5 pts. Professor Stein.
Prerequisite: Linear algebra. An introduction to
combinatorial optimization, network flows and
discrete algorithms. Shortest path problems, maximum
flow problems. Matching problems, bipartite
and cardinality nonbipartite. Introduction to
discrete algorithms and complexity theory:
NP-completeness and approximation algorithms.
IEOR E6702x Reliability theory
Lect: 2. 3 pts. Not given in 2008–2009.
Prerequisites: IEOR E4701 or E4106, and SIEO
W4150. An overview of the techniques available
to formulate the reliability structure of a problem,
to model the various element probabilities, to estimate
parameters of element probability distributions
based on data, and to unite these steps to
obtain the reliability function of a system.
IEOR E6703x Advanced financial engineering
Lect: 2. 3 pts. Professor Kou.
Prerequisites: IEOR E4106 or E4701, and SIEO
W4150. Review of basic mathematics, including
renewal theory and stochastic calculus.
Martingale approach to Black-Scholes formula.
Optimal stopping and American options. Pricing
of continuous and discerete exotic options. Term
structure models and pricing of bond options.
Jump diffusion models. Applications, including
pricing of real and electricity options and hedging
of real options.
IEOR E6704y Queueing theory and applications
Lect: 2. 3 pts. Professor Sigman.
Prerequisite: IEOR E4106 or E4701. Introduction
to congestion and related stochastic models.
Topics include birth and death models, measures
of performance, Little’s Law, conservation law,
PASTA, work in system, service disciplines and
priorities, regenerative processes, stability and
stationary distributions, approximations and
bounds. Examples from telecommunications,
production, inventory, and computer science.
IEOR E6706y Queueing networks
Lect: 2. 3 pts. Professor Yao.
Prerequisite: IEOR E4106 or E4701. An
introduction to the analysis of queuing networks.
Applications to computer and communication systems.
The course covers reversibility, local balance,
open and closed network models, computational
procedures, and other related topics.
SEAS 2009–2010