# 5000 Level - Electives

**MTH 5100 - **Teaching Mathematics

This course aims to equip graduate student in mathematics with pedagogical strategies and techniques for teaching mathematics effectively in various settings. Topics covered include instructional design, assessment methods, communication skills, and addressing the needs of diverse learners. (1 credit)

**MTH 5316 - Linear Algebra and Matrix Theory **

Prerequisite(s): MTH 3312. M

Matrix calculus, eigenvalues and eigenvectors, canonical forms, orthogonal and unitary transformations, and quadratic forms. Applications of these concepts. A course project is required and will be specified by the professor at the beginning of the course.

**MTH 5325 - Theory of Differential Equations **

Prerequisite(s): MTH 3325 and 5323.

Initial value problems for ordinary differential equations: existence, uniqueness, continuous dependence, stability analysis, oscillation theory, general linear systems, phase plane analysis, limit cycles and periodic solutions. Topics of current interest in dynamical systems.

**MTH 5326 - Theory of Partial Differential Equations **

Prerequisite(s): MTH 5324 and 5325.

Linear and quasilinear first order equations; shocks, characteristics, the Cauchy problem, elliptic, hyperbolic, and parabolic equations, maximum principles, Dirichlet problem, operators, Sobolev spaces, distributions.

**MTH 5332 - Algebraic Topology II **

Prerequisite(s): MTH 5331.

Cohomology theory, homology with coefficients, homological algebra, Kunneth theorem, duality in manifolds.

**MTH 5340 - Differential Geometry **

Prerequisite(s): MTH 4327, 5316, and 5330.

Differentiable manifolds, submanifolds, vector fields, tensor fields, integration on manifolds, Riemannian geometry.

**MTH 5344 - Probability Theory **

Prerequisite(s): MTH 5323.

Topics include the law of large numbers, central limit theorems, random walks, martingales, Markov chains, Egodic theorems, and Brownian motion.

**MTH 5345 - Functional Analysis **

Prerequisite(s); MTH 5324.

Banach spaces, Hilbert spaces, linear operators, and spectral theory.

**MTH 5351 - Applications of Complex Analysis **

Prerequisite(s): MTH 5350.

Poisson summation, Mellin transformation, zeta function of Riemann, special functions, zeta functions associated with eigenvalue problems, heat kernel, asymptotic expansion of the heat kernel, meromorphic structure of zeta functions, theta functions, elliptic functions.

**MTH 5375 - Linear Programming **

Prerequisite(s): MTH 2311 or consent of instructor.

Introduction to the theory and applications of linear programming, including the simplex algorithm, duality, sensitivity analysis, parametric linear programming, integer programming, with applications to transportation and allocation problems and game theory. A course project is required and will be specified by the professor at the beginning of the course.

**MTH 5376 - Nonlinear Programming **

Theory and algorithms for the optimization of unconstrained problems including gradient and Quasi-Newton methods; and constrained problems to include feasible direction methods, Lagrange multipliers, and Karush-Kuhn-Tucker conditions. Students must have a knowledge of linear algebra, third-semester calculus.

**MTH 5390 - Special Problems in Mathematics **

Project course for the project option in the M.S. degree.

**MTH 5V91 - Special Topics in Algebra for Graduates 1 to 3 sem. hrs. **

May be repeated for credit with instructor's consent.

**MTH 5V92 - Special Topics in Analysis for Graduates 1 to 3 sem. hrs. **

May be repeated for credit with instructor's consent.

**MTH 5V93 - Special Topics in Mathematics for Education Students 1 to 3 sem. hrs. **

Prerequisite(s): Consent of departmental chair and the course instructor.

May be repeated for credit for a maximum of nine semester hours if under different topics. Maximum 9 sem. hrs. MTH 5V96 - Special Topics in Graph Theory Prerequisite(s): Consent of instructor. Introduction to graph theory; Euler tours, matching, connectivity, planar graphs, coloring, random graphs. Additional topics may vary by semester.

**MTH 5V96 - Special Topics in Graph Theory**

Prerequisite(s): Consent of instructor.

Introduction to graph theory; Euler tours, matching, connectivity, planar graphs, coloring, random graphs. Additional topics may vary by semester.