Note: Multivariable calculus and a course in proof techniques or its equivalent or permission by the Chair of the Department are required prerequisites for all graduate mathematics courses.
Discrete Mathematics (3) 

Topics include counting techniques such as Pigeonhole Principle, permutations, combinations, binomial coefficients, inclusionexclusion, and relations and graphs. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. 

Graph Theory (3) 

The elements of graph theory including: trees; bipartite, chordal and planar graphs; graph coloring; graph traversals; and flows This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. Prerequisites: Permission of instructor. 

Numerical Analysis (3) 

This course covers topics including finite differences, interpolation, numerical integration and differentiation, solutions of equations of one variable, linear systems, and numerical solutions of ordinary differential equations. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. 

Real Analysis I (3) 

A study of the real number system, completeness, limits, continuity, sequences, differentiation, and the Riemann integral. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. 

Real Analysis II (3) 

A study of sequences and series of functions, series, and a continuation of the integral to include the Fundamental Theorem of Calculus. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. Prerequisite: MTH 4424 or MTH 5524. 

Complex Analysis (3) 

A study of complex numbers, elementary functions and their mappings, complex limits and power series, analytic functions, integrals, contour integral, and Cauchy integral formula. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. 

Number Theory (3) 

This course covers divisibility, congruences, prime numbers, Fermat’s theorem, Diophantine equations, number theoretic functions, quadratic reciprocity. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. 

Abstract Algebra I (3) 

A study of properties of the integers, modular arithmetic. Elementary theory of groups, finite groups, subgroups, cyclic groups, permutation groups. Group isomorphisms and homomorphisms. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. Prerequisite: MTH 3331. 

Abstract Algebra II (3) 

This course covers the elementary theory of rings, polynomial rings, divisibility, unique factorization domains. Integral domains, ideals, factor rings, divisibility in integral domains. Elementary theory of fields. Extension fields. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. Prerequisite: MTH 4441 or MTH 5541. 

Topology (3) 

An introduction to metric and topological spaces and associated topics, separation axioms, compactness, and connectedness. This course contains additional graduatelevel content equivalent to a onehour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. 

Modern Topics in Mathematics (3) 

An investigation of current topics in mathematics that are generally not covered in regularly offered graduate courses in the mathematics graduate curriculum. Prerequisites will be determined by the topic under investigation. 

Metric Education for Elementary Teachers (3) 

A study of the materials and methods program of instruction with workshops in selected school systems. Prerequisite: Admission by permission of instructor. 

History of Mathematics (3) 

The course is designed to acquaint the secondary mathematics teacher with the historical development of mathematics with particular attention given to the techniques of the period studied. 

Advanced Discrete Mathematics (3) 

This course is a study of discrete mathematical structures and associated conceptswhich may include graphs and hypergraphs, Boolean Algebra, modeling computationproperties of these structures and their applications. Prerequisite: MTH 4412, MTH 5512 or permission of instructor. 

Advanced Topology (3) 

Generalization of such topics as functions, continuous functions, open, closed, compact and connected sets, arbitrary topological spaces. Prerequisites: MTH 4424 or 5524, MTH 4426 or 5526 or permission of instructor 

Mathematical Models (3) 

An introduction to the modeling process. Students will practice creative and empirical model constructions, analyze models and do independent model research. Application using paired data will be included. 

Advanced Concepts of Algebra (3) 

This course covers topics including rings and fields, polynomial rings and factorization, and Galois theory. Prerequisite: MTH 4442 or 5542 or permission of instructor 

Foundations of Mathematics (3) 

A study of the axiomatic nature of mathematics, theory of sets, cardinal and ordinal numbers, continuum hypothesis and axiom of choice. 

Applied Combinatorics (3) 

This course includes topics from computational aspects of discrete optimization problems from graph, hypergraph and combinatorial design theory. These aspects include complexity, algorithms for solving such problems, and their contemporary applications. 

Specialized Study in Area of Mathematics (3) 

A study of a problem or problems using research techniques. Selection of problem must be approve by student’s adviser, instructor under whom the study is to be made, and the appropriate director of the Graduate School or Dean of Arts and Sciences. Note: Total credit for any combination of enrollments in these courses may not exceed six semester hours. See semester hour limits listed under Course Restrictions in General Regulations section. 

Design Theory (3) 

Latin Squares, mutually orthogonal latin squares, orthogonal and perpendicular arrays, Steiner triple systems, block designs, difference sets, and finite geometries. Topics of current interest and research in combinatorial design theory will be explored. (areas may include: latin squares, embeddings, enclosings, Wilson’s constructions, quadruple systems, Hadamard designs, graph designs, orthogonal arrays, and computational models. Prerequisite: MTH 4412 or MTH 4420 or permission of instructor. 

NonEuclidean Geometry (3) 

A study of nonEuclidean geometries with emphasis given to their logical development. 

Advanced Linear Algebra (3) 

A study of linear and orthogonal transformations, orthogonal and unitary matrices, numerical linear algebra, and applications. Spectral theory and duality. Prerequisite: MTH 3331 or permission of instructor 

Advanced Concepts of Analysis (3) 

A study from the classical theory of point sets in Euclidean space and the theory of functions of one or more real variables to topology, continuous functions, and Lebesgue integral and the Henstock integral. Prerequisites: MTH 4425 or MTH 5525 

Trends in Technology and Problem Solving in Secondary Mathematics Instruction (3) 

A comprehensive study of contemporary teaching strategies that incorporate current technologies and effective problem solving approaches for use by the mathematics educator in the modern secondary school mathematics program. Emphasis will be placed upon the effective use of calculators, writing, and computer software in the mathematics curriculum. 

Research in Education (3) 

A study of a variety of research and evaluations methods in the teaching of mathematics. A grade of “B” or better is required. 