# Courses

**AMS 507 Introduction to Probability **

The topics include sample spaces, axioms of probability, conditional probability and
independence, discrete and continuous random variables, jointly distributed random
variables, characteristics of random variables, law of large numbers and central limit
theorem, Markov chains. Note: Crosslisted with HPH 696.

Fall, 3 credits, ABCF grading

AMS 507 webpage

**AMS 540 Linear Programming **

Formulation of linear programming problems and solutions by simplex method. Duality,
sensitivity analysis, dual simplex algorithm, decomposition. Applications to the transportation
problem, two-person games, assignment problem, and introduction to integer and nonlinear
programming. This course is offered as both MBA 540 and AMS 540.

Prerequisite: A course in linear algebra

3 credits, ABCF grading

AMS 540 webpage

**AMS 542 Analysis of Algorithms **

Techniques for designing efficient algorithms, including choice of data structures,
recursion, branch and bound, divide and conquer, and dynamic programming. Complexity
analysis of searching, sorting, matrix multiplication, and graph algorithms. Standard
NP-complete problems and polynomial transformation techniques. This course is offered
as both AMS 542 and CSE 548.

Spring, 3 credits, ABCF grading

AMS 542 webpage

**AMS 544 Discrete and Nonlinear Optimization **

Theoretical and computational properties of discrete and nonlinear optimization problems:
integer programming, including cutting plane and branch and bound algorithms, necessary
and sufficient conditions for optimality of nonlinear programs, and performance of
selected nonlinear programming algorithms. This course is offered as both MBA 544
and AMS 544.

Prerequisite: AMS 540 or MBA 540

3 credits, ABCF grading

AMS 544 webpage

**AMS 545 Computational Geometry **

Study of the fundamental algorithmic problems associated with geometric computations,
including convex hulls, Voronoi diagrams, triangulation, intersection, range queries,
visibility, arrangements, and motion planning for robotics. Algorithmic methods include
plane sweep, incremental insertion, randomization, divide-and-conquer, etc. This course
is offered as both AMS 545 and CSE 555.

Spring, 3 credits, ABCF grading

AMS 545 webpage

**AMS 546 Network Flows **

Theory of flows in capacity-constrained networks. Topics include maximum flow, feasibility
criteria, scheduling problems, matching and covering problems, minimum-length paths,
minimum-cost flows, and associated combinatorial problems. This course is offered
as both MBA 546 and AMS 546.

Spring, 3 credits, ABCF grading

AMS 546 webpage

**AMS 547 Discrete Mathematics **

This course introduces such mathematical tools as summations, number theory, binomial
coefficients, generating functions, recurrence relations, discrete probability, asymptotics,
combinatorics, and graph theory for use in algorithmic and combinatorial analysis.
This course is offered as both CSE 547 and AMS 547.

Spring, 3 credits, ABCF grading

AMS 547 webpage

**AMS 550 Operations Research: Stochastic Models **

Includes Poisson processes, renewal theory, discrete-time and continuous-time Markov
processes, Brownian motion, applications to queues, statistics, and other problems
of engineering and social sciences. This course is offered as both MBA 550 and AMS
550.

Prerequisite: AMS 507 or equivalent

Spring, 3 credits, ABCF grading

AMS 550 webpage

**AMS 552 Game Theory I **

Elements of cooperative and noncooperative games. Matrix games, pure and mixed strategies,
and equilibria. Solution concepts such as core, stable sets, and bargaining sets.
Voting games, and the Shapley and Banzhaff power indices. This course is offered as
both ECO 604 and AMS 552.

Prerequisite: Admission to graduate AMS program or permission of instructor

0-3 credits, ABCF grading

AMS 552 webpage

**AMS 553 Simulation and Modeling **

A comprehensive course in formulation, implementation, and application of simulation
models. Topics include data structures, simulation languages, statistical analysis,
pseudorandom number generation, and design of simulation experiments. Students apply
simulation modeling methods to problems of their own design. This course is offered
as CSE 529, AMS 553, and MBA 553.

Prerequisite: CSE 214 or equivalent; AMS 310 or 507 or equivalent; or permission of
instructor

Spring, 3 credits, ABCF grading

AMS 553 webpage

**AMS 554 Queuing Theory **

Introduction to the mathematical aspects of congestion. Birth and death processes.
Queues with service priorities and bulk-service queues. Analysis of transient- and
steady-state behavior. Estimation of parameters. Applications to engineering, economic,
and other systems. This course is offered as both MBA 554 and AMS 554.

3 credits, ABCF grading

AMS 554 webpage

**AMS 555 Game Theory II **

Refinements of strategic equilibrium, games with incomplete information, repeated
games with and without complete information, and stochastic games. The Shapley value
of games with many players, and NTU-values. This course is offered as both ECO 605
and AMS 555.

Spring, 0-3 credits, ABCF grading

AMS 555 webpage

**AMS 556 Dynamic Programming **

Stochastic and deterministic multistage optimization problems. Stochastic path problems.
Principle of optimality. Recursive and functional equations. Method of successive
approximations and policy iteration. Applications to finance, economics, inventory
control, maintenance, inspection, and replacement problems. This course is offered
as both MBA 556 and AMS 556.

Prerequisite: MBA/AMS 550 or MBA/AMS 558

3 credits, ABCF grading

AMS 556 webpage

**AMS 569 Probability Theory I **

Probability spaces and sigma-algebras. Random variables as measurable mappings. Borel-Cantelli
lemmas. Expectation using simple functions. Monotone and dominated convergence theorems.
Inequalities. Stochastic convergence. Characteristic functions. Laws of large numbers
and the central limit theorem. This course is offered as both AMS 569 and MBA 569.

Prerequisite: AMS 504 or equivalent

AMS 569 webpage

3 credits, ABCF grading