# Graduate Mathematics (MATH) Courses

**5305. Graduate Research Project. 3**

A Graduate Research Project must be completed and submitted to the Graduate

Office for a grade to be assigned, otherwise IP notations are recorded. This course is

specifically designed for Plan II students.

Prerequisite: departmental approval.

**5306. Thesis. 3**

This course is for Plan I students. The course requires 6 hours of grades, the first 3

hours consisting of completion of a thesis proposal and the last 3 hours consisting of

completion of the thesis. Completion of the thesis proposal is a prerequisite in the last

3 hours of thesis.

**5321. Real Analysis. 3(3-0)**

Lebesgue integration and Lebegue measure, LP spaces, Differentiability properties of

monotone functions.

**5322. Complex Analysis. 3(3-0)**

The complex field, topology of the complex plane, analytic functions, conformal mappings,

power series, integration, residues.

**5323. Partial Differential Equations. 3(3-0)**

An introduction to the fundamental notions and/or methods in the theory of partial differential

equations. Includes Fourier series, the wave equation, the potential equation, and the heat

equation.

**5324. Functional Analysis. 3(3-0)**

Metric spaces and their properties; Function spaces and mapping; Contraction mapping,

existence, and uniqueness theorems for differential equations; Selected topics from functional

analysis: Stone-Weierstrass Theorem, semi-continuity, Banach spaces.

Prerequisite: 12 semester hours of advanced mathematics, including MATH 4321 or the

equivalent.

**5340. Matrix Methods for Linear Models. 3(3-0)**

Common matrix methods in statistical applications, including eigenvalues and

eigenvectors: the Moore-Penrose inverse; matrix differentiation; the

distribution of quadratic forms.

Prerequisites: MATH 3340 and STAT 4303 or equivalents.

**5341. Abstract Algebraic Theories. 3(3-0)**

Groups and their generalizations, Homomorphism and isomorphism theorem; Direct sums and

products; Linear spaces and representations; Field extensions and Galois groups.

Prerequisite: MATH 4340 or its equivalent.

**5360. Analytic Decision Theory. 3(3-0)**

Introduction to mathematical decision theory and game theoretic analysis. Classifications

of games, definitions in game theory, sequential-/simultaneous-move games, pure and

mixed strategies, equilibrium concepts and matrix games.

Prerequisite: MATH 3340 or equivalent.

**MATH 5372. Advanced Mathematics for Physics and Engineering I. 3(3-0)**

Complex variable methods, concepts of the theory of distributions, eigen-value problems in partial

differential equations, special functions, and finite-dimensional vector spaces.

Prerequisite: 9 semester hours of advanced mathematics, including MATH 3415 and MATH 3320

or the equivalent. Laboratory fee $5.00.

**5373. Advanced Mathematics for Physics and Engineering II. 3(3-0)**

Infinite-dimensional vector spaces, Green's functions, variational problems, traveling waves,

and perturbation methods.

Prerequisite: MATH 5372 or the equivalent. Laboratory Fee $5.00

**5390. Advanced Topics in Mathematics. V:1-3**

Different areas of advanced mathematics with emphasis on rigor, critical reasoning, and the

concept of proof.

May be repeated for a maximum of 6 semester hours of credit as topic changes.

**5394. Special Topics in Mathematics. V:1-3**

Topics in mathematics which are of interest to persons in diverse disciplines and occupations.

May be repeated as topic changes. Not applicable for credit in the physical sciences, mathematics,

or engineering. Laboratory fee, $5.00.

This page was last updated on: November 16, 2017