Mathematics (MATH)

503. Vector Calculus (3).  Vectors, tensors, differential forms, covariant differentiation, curvature and elementary differential geometry. Prerequisite(s): MATH 301.  Notes: Offered on request.

509. Real Analysis I (3).  Topics in the study of functions of a real variable, including limits, continuity, differentiability, sequences, series. Prerequisite(s): MATH 522.  Notes: Offered in spring.

520. Foundations of Geometry (3).  Topics in Euclidean and non-Euclidean geometry, including incidence geometry, congruence, similarity, area theorems, circles and spheres.  Prerequisite(s): MATH 300.  Notes: Offered in fall.

522. Elements of Set Theory and Introduction to Topology (3).  Fundamentals of set theory and point-set topology, including functions, Cartesian products, topological spaces, open and closed sets, metric spaces, connected and compact spaces.  Prerequisite(s): MATH 300 and MATH 301.  Notes: Offered in fall.

535. Numerical Analysis (3).  Analysis of algorithms, including polynomial approximation of real functions, numerical differentiation and integration and manipulation of matrices.  Prerequisite(s): MATH 300 and 301 or permission of chair, Department of Mathematics.  Notes: Offered on demand.

541. Probability and Statistics I (3).  Probability theory from an axiomatic viewpoint, including combinatorics, discrete and continuous random variables and multivariate distributions.  Prerequisite(s): MATH 302.  Notes: Offered in fall.

542. Probability and Statistics II (3).  Statistical inference from a mathematical viewpoint, including the central limit theorem, point and interval estimation and regression.  Prerequisite(s): MATH 541.  Notes: Offered alternate years in spring.

543. Introduction to Stochastic Processes (3).  A survey of stochastic processes and their applications to probabilistic modeling. Topics will include discrete and continuous time Markov processes, Poisson process and time-series analysis.  Prerequisite(s): MATH 300 and 541.  Notes: Offered spring of alternate years.

545. Statistical Theory and Methods II (3).  Analysis of linear models, including both regression and ANOVA models. Contingency tables are also studied.  Prerequisite(s): MATH 541.  Notes: Offered alternate years in spring.

546. Applied Statistics for the Sciences (3).  Survey of statistical methodology applied to problems from the sciences with emphasis on the area of Health and Human Nutrition. Statistical tests will be reviewed and applied to current issues.  Prerequisites): MATH 141 or permission of instructor.  Notes: Offered in fall and summer.

547. Introduction to Categorical Models (3).  An introduction to the analysis of categorical data. Topics will include methods for comparison of binomial proportions, r x c contingency tables and logistic and log linear modeling.  Prerequisite(s): MATH 542.  Notes: Offered spring of alternate years..

550. Special Topics in Mathematics (3:3:0).  In-depth study of a mathematical topic.  Prerequisite(s): Permission of instructor. May be retaken for additional credit once for each topic.

551. Algebraic Structures (3).  Theory of rings and fields, with special attention to PID's, UFD's, Euclidean domains and modules.  Prerequisite(s): MATH 351 or equivalent.  Notes: Offered alternate years in fall.

553. Theory of Numbers (3).  Divisibility, primes, congruences, special functions, continued fractions and rational approximations.  Prerequisite(s): MATH 351 or equivalent.  Notes: Offered spring of alternate years.

575. Optimization Techniques II (3:3:0).  A continuation of MATH 375.  Areas of study include mathematical modeling, integer programming, combinatorial optimization and network algorithms.  Prerequisite(s):  MATH 375.  Notes:  Offered at variable times.

610. Real Analysis II (3).  Continuation of MATH 509, including the following topics: Riemann-Stieltjes integration, uniform convergence, Ip and Lp spaces, the Stone-Weirstrass theorem and the implicit function theorem.  Prerequisite(s): MATH 509.  Notes: Offered in fall.

615. Measure Theory I (3).  Course includes studies in limit supremum, limit infimum, Borel sets, outer measure, Lebesgue measure, Littlewood's principles, Riemann and Lebesgue integration, monotone functions and the differentiation of an integral.  Prerequisite(s): MATH 610 or permission of chair, Department of Mathematics.  Notes: Offered on request.

617. Measure Theory II (3).  Course includes integration theory and differentiation of integrals on abstract measure spaces, general convergence theorems, signed measures and the radon-nikodym theorem.  Prerequisite(s): MATH 615 or permission of chair, Department of Mathematics.  Notes: Offered on request.

649. Nonparametric Statistics (3).  A survey of current nonparametric techniques. Topics will include the sign test, runs test, Wilcoxon rank-sum test and the Kruskal Wallace test.  Prerequisite(s): MATH 542.  Notes: Offered on request.

650. Selected Topics in Mathematics (3).  An in-depth examination of a particular topic in graduate mathematics. Selections may be from the areas of algebra, probability and statistics, analysis or geometry.  Prerequisite(s): MATH 302, 351 and 541 or equivalent; and permission of instructor.  Notes: May be retaken for additional credit.

655. Advanced Linear Algebra (3).  Theory of linear transformations and their applications.  Prerequisite(s): MATH 300, 351 or equivalent.  Notes: Offered on request.

656. Topics in Module Theory (3).  Introduction to modules and operations on sub modules including quotient modules, direct sums, free modules and basic homological algebra.  Prerequisite(s): MATH 551 or permission of chair, Department of Mathematics.  Notes: Offered on request.

681. Microcomputers and Scientific Calculators (3).  Programming and use of microcomputers and graphing calculators (Casio, HP and TI) with special attention to algebraic manipulation, calculus, matrix and vector operations and statistical computation.  Notes: Offered in summer and on request.