Current version - Indiana University South Bend

IU SOUTH BEND COURSE DESCRIPTIONS 4357
MATH-M 551
MATH-M 560
MATH-M 562
MATH-M 565
MATH-M 571
performance of interconnected systems,
including use of block diagrams, Bode
plots, Nyquist criterion, and Lyapunov
functions; optimal control, bang-bang
control; discrete and digital control.
MARKETS AND ASSET PRICING (3 cr.)
P: Two courses from the following:
MATH-M 301, MATH-M 311, MATH-M
343, MATH-M 365, MATH-M 447.
Interest theory; introduction to theory
of options pricing; Black-Scholes theory
of options; general topics in finance as
the time value of money, rate of return
of an investment, cash-flow sequence,
utility functions and expected utility
maximization, mean variance analysis,
optimal portfolio selection, and the
capital assets pricing model; topics in
measurement of interest.
APPLIED STOCHASTIC PROCESSES (3 cr.)
P: MATH-M 301, MATH-M 463 or
MATH-M 365, or consent of instructor.
Simple random walk as approximation
of Brownian motion. Discrete-time
Markov chains. Continuous-time Markov
chains; Poisson, compound Poisson, and
birth-and-death chains; Kolmogorov’s
backward and forward equations; steady
state. Diffusions as limits of birth-anddeath
processes. Examples drawn from
diverse fields of application.
STATISTICAL DESIGN OF EXPERIMENTS (3 cr.)
P: MATH-M 365, MATH-M 466, or
consent of instructor. Latin square,
incomplete blocks, and nested designs.
Design and analysis of factorial
experiments with crossing and nesting
of factors, under fixed, random, and
mixed effects models, in the balanced
case. Blocking and fractionation of
experiments with many factors at two
levels. Exploration of response surfaces.
analysis of variance (3 cr.)
P: MATH-M 466 and some matrix
algebra. General linear hypothesis.
Least squares estimation. Confidence
regions. Multiple comparisons. Analysis
of complete layouts. Effects of departures
from underlying assumptions. Analysis of
covariance.
ANAlysis of numerical methods I (3 cr.)
P: CSCI-C 101, MATH-M 301, MATH-M
311, or consent of instructor. R: MATH-M
343. Solution of systems of linear equations,
elimination and iterative methods, error
analyses, eigenvalue problems; numerical
methods for integral equations and
MATH-M 572
MATH-M 574
MATH-M 575
MATH-M 576
MATH-M 577
ordinary differential equations; finite
difference, finite element, and Galerkin
methods for partial differential equations;
stability of methods.
ANAlysis of numerical methods ii (3 cr.)
P: MATH-M 343, MATH-M 571. Solution of
systems of linear equations, elimination and
iterative methods, error analyses, eigenvalue
problems; numerical methods for integral
equations and ordinary differential
equations; finite difference, finite element,
and Galerkin methods for partial differential
equations; stability of methods.
applied regression analysis (3 cr.)
P: MATH-M 466 or MATH-M 365 or
MATH-M 261. Least square estimates
of parameters; single linear regression;
multiple linear regression; hypothesis
testing and confidence intervals in linear
regression models; testing of models, data
analysis and appropriateness of models;
optional topics about nonlinear regression,
i.e., logistic regression, Poisson regression,
and generalized linear regression models. I
simulation modeling (3 cr.)
P: MATH-M 209 or MATH-M 216;
MATH-M 365, MATH-M 463, or CSCI-C
455; CSCI-C 101. The statistics needed to
analyze simulated data; examples such
as multiple server queuing methods,
inventory control, and exercising stock
options; variance reduction variables
and their relation to regression analysis.
Monte Carlo method, Markov chain, and
the alias method for generating discrete
random variables.
forecasting (3 cr.)
P: MATH-M 301, MATH-M 365, or
MATH-M 466. Forecasting systems,
regression models, stochastic forecasting,
time series, smoothing approach to
prediction, model selection, seasonal
adjustment, Markov chains, Markov
decision processes, and decision analysis.
OPERATIONS RESEARCH: modeling
APPROACH (3 cr.)
P: MATH-M 209, MATH-M 212, MATH-M
216, or MATH-M 301. Mathematical
methods of operations research used
in the biological, social, management
sciences. Topics include modeling, linear
programming, the simplex method,
duality theory, sensitivity analysis, and
network analysis. Credit not given for
both MATH-M 577 and MATH-M 447.