Current version - Indiana University South Bend

3563 IU SOUTH BEND COURSE DESCRIPTIONS
MATH-M 448
MATH-M 451
Mathematical Models and
Applications 2 (3 cr.)
P: MATH-M 447. Formation and study of
mathematical models used in the biological,
social, and management sciences.
Mathematical topics include games,
graphs, Markov and Poisson processes,
mathematical programming, queues, and
equations of growth. Suitable for secondary
school teachers. II (odd years)
the Mathematics of finance (3 cr.)
P: Two courses from the following
MATH-M 301, MATH-M 311, MATH-M
343, MATH-M 365, MATH-M 447,
MATH-M 463. 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.
I (even years)
MATH-M 463 INTRODUCTION TO PROBABILITY THEORY 1
(3-4 cr.)
C: MATH-M 311. The meaning of probability.
Random experiment, probability models,
combinatoric techniques, conditional
probability, independence. Random
variables, distributions, densities,
expectation, moments, transformation of
random variables. Important discrete and
continuous distributions. Multivariate
distributions, correlations. Moment
generating functions, laws of large
numbers, central limit theorem, normal
approximation. I
MATH-M 466
INTRODUCTION TO MATHEMATICAL
STATISTICS (3 cr.)
P: MATH-M 463. Theory of sampling
distribution, Chebyshev’s inequality,
convergence in probability. Estimation
theory, maximum likelihood estimators,
method of moments, goodness of
point estimators, confidence intervals.
Hypothesis testing, power function,
error types, likelihood ratio tests. Nonparametric
methods. Regression. Analysis
of variance. Sufficient statistics. Bayesian
estimation, asymptotic distribution of
maximum likelihood estimators. II
MATH-M 467 advanced statistical techniques 1
(3 cr.)
P: MATH-M 466 or consent of
instructor. Statistical techniques of
wide application, developed from the
least-squares approach: fitting of lines
and curves to data, multiple regression,
analysis of variance of one- and two-way
layouts under various models, multiple
comparison.
MATH-M 468 advanced statistical techniques 2
(3 cr.)
P: MATH-M 466 or consent of instructor.
Analysis of discrete data, chi-square tests
of goodness of fit and contingency tables,
Behrens-Fisher problem, comparison of
variances, nonparametric methods, and
some of the following topics: introduction
to multivariate analysis, discriminant
analysis, principal components.
MATH-M 471
MATH-M 472
MATH-M 491
MATH-M 546
Numerical Analysis 1 (3 cr.)
P: MATH-M 301, MATH-M 311, CSCI-C
101, or consent of instructor. R: MATH-M
343. Numerical solutions of nonlinear
equations; interpolation, including finite
difference and splines; approximation,
using various Hilbert spaces; numerical
differentiation and integration; direct
methods for linear systems; iterative
techniques in matrix algebra. Knowledge
of a programming language such as C,
C++, or Fortran is a prerequisite of this
course. I (odd years)
Numerical Analysis 2 (3 cr.)
P: MATH-M 471 and MATH-M 343.
Numerical solutions of nonlinear
systems; solution of ordinary differential
equations: initial-value problems,
boundary-value problems; computation
of eigenvalues and eigenvectors;
introduction of numerical solutions for
partial differential equations.
PUTNAM EXAMINATION SEMINAR (1 cr.)
P: MATH-M 211 or MATH-M 215, or
consent of instructor or department
chair. The Putnam Examination is a
national mathematics competition for
college undergraduates at all levels of
study. It is held in December each year.
This problem seminar is designed to help
students prepare for the examination.
May be repeated twice for credit. I
Control theory (3 cr.)
P: MATH-M 301, MATH-M 343. This
course is an introduction to the analysis
of feedback control systems. Topics may
include: modeling of physical, biological,
and information systems using linear
and nonlinear differential equations;
state=space description of systems;
frequency and time domains; linear
dynamic control systems; stability and
P = Prerequisite, R = Recommended, C = Concomitant, VT = Variable Title
I = fall semester, II = spring semester, S = summer session(s)