# Mathematics (MATH) 4000-level

**4320. Advanced Calculus. 3(3-0)**

Partial differentiation, Lagrange multipliers, Leibnitz's rule, multiple integrals, vector analysis, infinite series, uniform convergence and Fourier series.

**4321. Real Variables. 3(3-0)**

The real number system, its structure and properties. Properties of real functions and sequences, including uniform continuity and the Cauchy criterion. Introduction to the theory of sets. Theory and application of the derivative. Introductory concepts of function spaces, norms, and metrics.

Prerequisite: 6 semester hours of advanced mathematics, including MATH 3325.

**4340. Modern Algebra. 3(3-0)**

Properties of the integers: divisibility, prime factorization, and congruences. Integral domains, rings, and fields. Groups, permutations, and cosets. A historical development of these topics is included. Not applicable for credit in the physical sciences or engineering.

Prerequisite: MATH 3325.

**4341. Linear Algebra and Matrix Theory. 3(3-0)**

Vector spaces and their linear subspaces. Representation of linear transformations by matrices. Normal forms, eigenvalues, special transformations and applications.

Prerequisite: 6 semester hours of advanced mathematics.

**4342. Algebraic Structure. 3(3-0)
** An intensive axiomatic study of groups, rings, polynomial rings, fields and modules, along with their principal substructures. Emphasis on classification and structure theorems.

Prerequisite: 6 semester hours of advanced mathematics.

**4351. Mathematical Theory of Games. 3(3-0)**

Introduction of game theory. Topics include: combinatorial and strategic games, backward induction payoffs, cooperative and non-cooperative games, mixed strategies, equilibria, repeated games and finite automata, common knowledge and incomplete information, the prisoners dilemma. Selected applications to economics, biology, computer science and political science. Prerequisite: MATH 3340 or consent of instructor.

**4370. Vector Analysis. 3(3-0)**

Vector algebra and geometry. Scalar and vector products. Vector functions and motion in polar coordinates. Scalar and vector fields with applications to line and surface integrals.

Prerequisites: MATH 3415 and MATH 3320 or equivalent.

**4371. The Laplace Transformation and its Applications. 3(3-0)**

An introduction to the theory of the Laplace Transformation. Applications to the solution of ordinary and partial differential equations, integral equations, difference equations, and integro-differential equations. An introduction to other types of integral transformations.

Prerequisites: MATH 3415 and MATH 3320.

**4372. Mathematics for Physics and Engineering I. 3(3-0)**

Infinite series, matrix methods, vector analysis, applied multivariate calculus, and Fourier series.

Prerequisites: MATH 3415 and MATH 3320.

**4373. Applications of Matrix Methods. 3(3-0)**

Matrices and their inverses, determinants, eigenvalues and eigenvectors, Jordan canonical forms. Applications to simultaneous linear equations, matrix calculus an linear differential equations.

Prerequisites: MATH 3415 and MATH 3320.

**4374. Numerical Analysis. 3(3-0)**

The mathematical formation of the concepts in numerical analysis. These concepts include the theory of errors, roots of equations, interpolation, linear systems of equations, numerical differentiation and integration, and solutions of ordinary differential equations.

Prerequisites: MATH 3415 and MATH 3320.

**4390. (Formerly MATH 3390) Selected Topics in Mathematics. 3(3-0)**

Different topics will be covered at varying times. May be repeated for credit with consent of the instructor.

Prerequisite: 3 semester hours of advanced mathematics.

**4399. Capstone Experience in Mathematics. 3(3-0)**

Designed to integrate mathematical standards and skills of mathematics majors. Students will demonstrate their ability to organize and synthesize mathematical knowledge; and design, implement, and present an advanced project in mathematics or mathematics education.

Prerequisite: Senior standing in mathematics.

This page was last updated on: November 05, 2014