AS/SC/ MATH 4170 6.0
GS/MATH 6900 3.0 F
plus GS/MATH 6901 3.0 W

Operations Research II

      Selected topics from game theory, decision theory, simulation, reliability theory, queuing theory, nonlinear programming, classification, pattern-recognition and prediction. Each chapter contains an optimization problem and methods and algorithms for solving it. The course is rich in examples.
      This course deals mainly with probabilistic models based on optimization. The following topics will be discussed: (a) Game Theory: how to find the best strategies in a confrontation between two players with opposite interests. (b) Decision Theory: how to act in order to minimize the loss subject to the available data. (c) Simulation: how to get representative samples from probability distributions and accurately approximate multiple integrals using random numbers. (d) Reliability Theory: how to evaluate the lifetime of a system consisting of many interacting subsystems. (e) Queueing Theory: how to assess what may happen in a system where the customers arrive randomly, wait in line, and then get served. (f) Uncertainty: how to measure uncertainty in probabilistic modelling with applications to pattern-recognition and classification.
      There is no textbook, and the lecture notes are essential. Useful books are: (a) F.S. Hillier and G.J. Liberman, Introduction to Operations Research; (b) H.A. Taha, Operations Research.
      The final grade will be based on two tests (25% each) and a final examination (50%).
      The following prerequisites indicate the sort of background in probability and statistics, in calculus of several variables, and in linear programming, needed for MATH-4170. Students missing a prerequisite need the course coordinator's permission to enrol.