# Mathematics Courses (MTH)

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.

## MTH 5512 - Discrete Mathematics (3)

Topics include counting techniques such as Pigeon-hole Principle, permutations, combinations, binomial coefficients, inclusion-exclusion, and relations and graphs. This course contains additional graduate-level content equivalent to a one-hour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course.

## MTH 5520 - 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 graduate-level content equivalent to a one-hour 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.

## MTH 5522 - 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 graduate-level content equivalent to a one-hour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course.

## MTH 5524 - Real Analysis I (3)

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

## MTH 5525 - 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 graduate-level content equivalent to a one-hour 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.

## MTH 5526 - 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 graduate-level content equivalent to a one-hour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course.

## MTH 5536 - Number Theory (3)

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

## MTH 5541 - 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 graduate-level content equivalent to a one-hour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the course. Prerequisite: MTH 3331.

## MTH 5542 - 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 graduate-level content equivalent to a one-hour 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.

## MTH 5560 - Topology (3)

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

## MTH 6600 - 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.

## MTH 6601 - 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.

## MTH 6610 - 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.

## MTH 6612 - Advanced Discrete Mathematics (3)

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

## MTH 6615 - 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.

## MTH 6616 - 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.

## MTH 6620 - 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.

## MTH 6621 - 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.

## MTH 6624 - 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.

## MTH 6625, 6626, 6627 - 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.

## MTH 6630 - 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.

## MTH 6632 - Non-Euclidean Geometry (3)

A study of non-Euclidean geometries with emphasis given to their logical development.

## MTH 6633 - 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.

## MTH 6640 - 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.

## MTH 6650 - 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.

## MTH 6691 - 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.

## MTH 6692 - Research and Thesis (1-6)

Under the guidance of the student’s adviser and the chair of the department, the student may pursue original research or project in a particular area of mathematics. The completion of a thesis is required. The results and conclusions must be successfully defended before the student’s graduate committee. Grading System is a Pass/Fail. Prerequisites: 3.0 GPA and permission of the Chair of the Mathematics and Statistics department.

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