Mathematics Courses (MTH)

Note: Multivariable calculus and a course in proof techniques or its equivalent or permission of the mathematics adviser 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.
MTH 5520
Graph Theory (3)
  The elements of graph theory including: trees; bipartite, chordal and planar graphs; graph coloring; graph traversals; and flows 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.
MTH 5524
Real Analysis I (3)
  A study of the real number system, completeness, limits, continuity, sequences, differentiation, and the Riemann integral.
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. 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.
MTH 5536
Number Theory (3)
  This course covers divisibility, congruences, prime numbers, Fermat’s theorem, Diophantine equations, number theoretic functions, quadratic reciprocity.
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. 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. Prerequisite: MTH 4441 or MTH 5541.
MTH 5551
Mathematical Statistics I (3)
  A study of probability theory, sample spaces, random variables, mutual exclusion, independence, conditional probability, permutations and combinations, common discrete and continuous distributions, expected value, mean, variance, multivariate distributions, covariance, Central Limit Theorem.
MTH 5552
Mathematical Statistics II (3)
  A study of the fundamentals of the theory of statistics, the Central Limit Theorem, point estimation, sufficiency, consistency, hypothesis testing, sampling distributions, confidence intervals, linear regression models, interpretation of experimental results, Bayesian Estimation. Prerequisite: MTH 4451 or MTH 5551.
MTH 5560
Topology (3)
  An introduction to metric and topological spaces and associated topics, separation axioms, compactness, and connectedness.
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 covers trees, network models and Petrinets, Boolean algebra and combinatorial circuits, automata, grammars, and languages. 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)
  A study of generating functions, Inclusion-Exclusion, Burnside’s Theorem and Polya’s Enumeration Formula.
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 approved 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 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.
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