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 5101 : Teaching Mathematics Practicum
This course gives new graduate student teachers a practicum experience in teaching mathematics. Mentoring on topics include instructional design, assessment methods, communication skills, and addressing the needs of diverse learners.
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, Ergodic 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 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 5V95 Special Topics in Topology-Geometry (1-3)
May be repeated for credit for a maximum of 9 semester hours.
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.