# Mathematics (MATH)

**MATH 5305** Graduate Research Project **3 SCH** **(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 and Plan III students. Prerequisite: departmental approval.

**MATH 5306** Thesis **3 SCH** **(3)**

Designed for thesis option students. The course requires completion of thesis research. Prerequisite: departmental approval. May be repeated for maximum of 6 semester hours.

**MATH 5310** Foundations of Mathematics **3 SCH** **(3)**

**MATH 5321** Real Analysis **3 SCH** **(3)**

Lebesgue integration and Lebesgue measure. LP spaces. Differentiability properties of monotone functions.

**MATH 5322** Complex Analysis **3 SCH** **(3)**

**MATH 5323** Partial Differential EQ **3 SCH** **(3)**

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.

**MATH 5340** Matrix Methods Linear Models **3 SCH** **(3)**

**MATH 5341** Abstract Algebraic Theories **3 SCH** **(3)**

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.

**MATH 5360** Analytic Decision Theory **3 SCH** **(3)**

Introduction to mathematical decision theory and game theoretic analysis. Classification 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** Adv Math for Physics and Eng I **3 SCH** **(3)**

Complex variable methods, concepts of the theory of distributions, eigen-value problems in partial differential equations, special functions and finite-dimensional vector spaces. Prerequisites: 9 semester hours of advanced mathematics including MATH 3315 and MATH 3320 or the equivalent. Laboratory fee, $5.

**MATH 5373** Adv Math for Physics and EN II **3 SCH** **(3)**

Infinite-dimensional vector spaces, Green's functions, variational problems, traveling waves and perturbation methods. Prerequisite: MATH 5372 or the equivalent. Laboratory fee, $5.

**MATH 5374** Numerical Analysis **3 SCH** **(3)**

Underlying principles of numerical analysis. Topics include: finite differences and interpolation, numerical differentiation and integration, solving algebraic and transcendental equations, computations with matrices, the method of lease squares, and numerical solutions of differential equations. Attention is given to the solutions of problems using computer. Prerequisite: MATH 4341 or equivalent.

**MATH 5375** Tensor Analy with Applications **3 SCH** **(3)**

**MATH 5376** Lin and Dynam Prog and Decisn **3 SCH** **(3)**

**MATH 5390** Advanced Topics in Math **1-3 SCH** **(1-3)**

Different areas of advanced mathematics with emphasis on rigor, critical reasoning and the concept of proof. May be repeated as topic changes.

**MATH 5394** Spec Topics in Mathematics **1-3 SCH** **(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.