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
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,
Operations Research; (b) H.A. Taha,
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.
Prerequisite:AS/SC/MATH 2010 3.0 or
AS/SC/MATH 2015 3.0 or AS/SC/AK/MATH 2310 3.0;
AS/SC/MATH 1132 3.0 or AS/SC/AK/MATH 2030 3.0;
AS/SC/AK/MATH 3170 6.0; or permission
of the course coordinator.
ExclusionAS/MATH 4570 6.0.
Coordinator: Silviu Guiasu