# Graduate Course Descriptions

MATH 5301: Number Theory

A graduate-level study of the theory of numbers, including divisibility, prime numbers, factorization, the Euclidean algorithm, congruences, the Chinese Remainder Theorem, Diophantine equations, quadratic residues, quadratic reciprocity, and other topics to be selected by the instructor.

MATH 5305: Set Theory

Mathematical logic, detailed and rigorous study of set theory, introduction to axiomatic systems, examination of real number systems.

MATH 5306: Topology

Study of metric spaces and topological spaces with emphasis on compactness, covering properties, separation, and metrization.

Prerequisite: MATH 3345 or equivalent.

MATH 5311: Advanced Engineering Mathematics

Advanced mathematical concepts needed in the study of engineering. Topics: partial differential equations, Fourier analysis, complex analysis, and optimization.

Prerequisite: Ordinary differential equations (MATH 3305 or equivalent) and linear algebra (MATH 3203 or equivalent).

MATH 5321: Topics in Combinatorics

Study of a specialized topic in combinatorics. Topics may include algebraic combinatorics, combinatorial game theory, generating functions, representation theory, or related topics.

MATH 5322: Graph Theory

A graduate-level survey of graph theory. Topics may include simple graphs, digraphs, connectivity, graph colorings, planar graphs, matchings, graph isomorphisms, graph polynomials, Eulerian graphs, algebraic graph theory, or other fundamental concepts in graph theory.

MATH 5331: Algebra I

Basic structure, substructure, morphisms, and quotient structures in the categories of groups, rings, and modules.

Prerequisite: MATH 3336 or equivalent.

MATH 5332: Algebra II

A continuation of the study of algebraic structures. Emphasis is given to groups, rings, modules, vector spaces, and fields.

Prerequisite: MATH 5331.

MATH 5333: Topics in Algebra

Topics may include group actions, p-groups, Galois theory, polynomial rings, field theory, vector spaces, modules over a PID, algebraic geometry, homological algebra, representation theory. Course may be repeated when content changes.

Prerequisite: MATH 5331.

MATH 5341: Real Analysis I

Topics include set theory, real number system, Lebesgue measure, the Lebesgue integral, differentiation and integration, and classical Banach spaces.

Prerequisite: MATH 4341 or equivalent.

MATH 5342: Real Analysis II

Study of generalized measure and integration. Topics may include the Fubini-Tonelli theorem, the Radon-Nikodym theorem and its consequences, an introduction to Banach and Hilbert spaces, and applications to Fourier analysis.

Prerequisite: MATH 5341.

MATH 5343: Topics in Analysis

Study of selected advanced topics in real, complex, or functional analysis. Course may be repeated when content changes.

Prerequisite: MATH 5341.

MATH 5351: Mathematical Probability

Axiomatic development of probability, distributions, mathematical expectation, moments, and generating functions.

Prerequisite: MATH 3345 or equivalent.

MATH 5352: Mathematical Statistics

Study of the mathematical basis of statistical analysis with emphasis given to sampling, distributions, testing hypotheses, interval estimation, and multivariate analysis.

Prerequisite: MATH 5351.

MATH 5381: Applied Mathematics I

Ordinary differential equations, partial differential equations, dynamical systems, complex variables, spectral theory, transformations, and modeling.

Prerequisites: MATH 3203 and MATH 3305 or consent of the instructor.

MATH 5382: Applied Mathematics II

A continuation of the study of applied mathematics, MATH 5381. Emphasis is given to modeling and solving problems in the physical sciences.

Prerequisite: MATH 5381.

MATH 5383: Topics in Applied Mathematics

An exploration of various topics in applied and computation mathematics. Materials covered may include mathematical modeling, optimization and control theory, game theory, mathematical physics, and mathematical biology. Course may be repeated when content changes.

Prerequisite: MATH 5381.

MATH 5390 & 5391: Selected Topics in Mathematics

Topics are selected to meet the needs of students and vary from semester to semester. Courses may be repeated when the content changes.

Prerequisite: Consent of department chair.

MATH 5395: Research

Research methodology in mathematics, requires individual research, and culminates in a written report.

Prerequisite: Completion of 15 graduate credit hours of mathematics and consent of instructor.

MATH 5396: Thesis

Student research that culminates in the completion of a formal thesis.

Prerequisite: MATH 5395 and appointment of a thesis advisor.

MATH 5199–5399: Independent Study

Independent study in specific areas of mathematics not covered by organized courses. A maximum of six credit hours of independent study courses may be applied toward a graduate degree.

Prerequisite: Consent of department chair.