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COURSE DESCRIPTIONS MATHEMATICS (MAT)

5003 Modern Mathematics for Teachers
(3-0)3 hours credit. A practical orientation concerned with the classroom uses of mathematics for teachers of K-12. Cannot be applied toward the Master of Science degree in Mathematics.

5013 Computers for Mathematics Teachers
(3-0)3 hours credit. A course for mathematics teachers on integrating the computer into the mathematics curriculum, with an algorithmic-oriented introduction to computer programming in BASIC or Pascal and the extensive use of mathematical software packages such as Derive. This course cannot be applied to the Master of Science degree in Mathematics with a concentration in Mathematics or the Master of Science degree in Statistics. (Same as CS 5063. Credit cannot be earned for both MAT 5013 and CS 5063.)



5023 Problem-Solving Seminar
(3-0)3 hours credit. Students will have the opportunity to engage in extensive experience and practice in solving mathematical problems.

5033 Foundations and Fundamental Concepts of Mathematics
(3-0)3 hours credit. Topics include the study of mathematics in antiquity as an empirical science, the shift from inductive reasoning to axiomatic structures, the development of geometry in the plane and 3-space, the discovery of analysis, the emergence of axiomatic systems, and the focus on algebraic structures. This course cannot be applied to the Master of Science degree in Mathematics with a concentration in Mathematics or the Master of Science degree in Statistics.

5043 Euclidean and Non-Euclidean Geometry
(3-0)3 hours credit. Topics will be selected from advanced Euclidean and non-Euclidean geometry, solid analytic geometry, and differential geometry. This course cannot be applied to the Master of Science degree in Mathematics with a concentration in Mathematics or the Master of Science degree in Statistics.

5103 Introduction to Mathematical Analysis
(3-0)3 hours credit. Prerequisite: MAT 4213 or consent of instructor. Axiomatic construction of the reals, metric spaces, continuous functions, differentiation and integration, partial derivatives, and multiple integration. This course cannot be applied to the Master of Science degree in Mathematics with a concentration in Mathematics or the Master of Science degree in Statistics. For the Mathematics Education concentration, this course can substitute for MAT 5203.

5173 Algebra I
(3-0)3 hours credit. Prerequisite: MAT 4233 or consent of instructor. The opportunity for development of basic theory of algebraic structures. Areas of study include finite groups, isomorphism, direct sums, polynomial rings, algebraic numbers, number fields, unique factorization domain, prime ideals, and Galois groups.

5203 Theory of Functions of a Real Variable I
(3-0)3 hours credit. Prerequisite: MAT 4213 or consent of instructor. Measure and integration theory.

5213 Theory of Functions of a Real Variable II
(3-0)3 hours credit. Prerequisite: MAT 5203. Further development of measure and integration theory, metric space topology, and elementary Banach space theory.

5223 Theory of Functions of a Complex Variable I
(3-0)3 hours credit. Prerequisite: MAT 3213 or MAT 4213. Complex integration, Cauchy’s theorem, calculus of residues, and power series.

5233 Theory of Functions of a Complex Variable II
(3-0)3 hours credit. Prerequisite: MAT 5223. Infinite products, entire functions, Picard’s theorem, Riemann mapping theorem, and functions of several complex variables.

5243 General Topology I
(3-0)3 hours credit. Prerequisite: MAT 4273 or consent of instructor. Topological spaces, metric spaces, continua, and plane topology.

5253 General Topology II
(3-0)3 hours credit. Prerequisite: MAT 5243. Areas of study include introductory algebraic topology and introduction to topology of manifolds.

5283 Linear Algebra and Matrix Theory
(3-0)3 hours credit. Prerequisite: MAT 2233 or an equivalent. A study of linear algebraic structures and algebraic properties of matrices.

5293 Numerical Linear Algebra
(3-0)3 hours credit. Prerequisite: MAT 2233 or an equivalent. Direct and iterative methods for solving general linear systems, the algebraic eigenvalue problem, least squares problems, and solutions of sparse systems arising from partial differential equations. (Same as CS 5293. Credit cannot be earned for both MAT 5293 and CS 5293.)

5313 Algebra II
(3-0)3 hours credit. Prerequisite: MAT 5173. Areas of study include: groups, rings, fields, Galois theory, ideal theory, and representations of groups, module theory, and homological algebra.

5403 Functional Analysis I
(3-0)3 hours credit. Prerequisites: MAT 2233, MAT 4273, and MAT 5203, or their equivalents. Topological vector spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces, dual spaces, Hahn-Banach theorem, and bounded linear operators.

5413 Functional Analysis II
(3-0)3 hours credit. Prerequisite: MAT 5403. Riesz representation theorem, spectral theory, Banach algebras, and C*-algebras.

5553 Harmonic Analysis
(3-0)3 hours credit. Prerequisites: Either MAT 3223 and MAT 4223, or consent of instructor. Theory of the Fourier, Laplace, and Hilbert transforms. Elements of the distribution theory. Harmonic functions. Function spaces: Lp-spaces, Hardy spaces, Sobolev spaces.

5603 Numerical Analysis
(3-0)3 hours credit. Prerequisite: MAT 3633 or consent of instructor. Emphasis on the mathematical analysis of numerical methods. Areas of study include solution of nonlinear equations and function optimization, approximation theory and numerical quadrature. (Same as CS 5603. Credit cannot be earned for both MAT 5603 and CS 5603.)

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5613 Numerical Solutions of Differential Equations
(3-0)3 hours credit. Prerequisite: MAT 5603 or an equivalent. Emphasis on the mathematical analysis of numerical methods. Areas of study include the analysis of single and multistep methods of ordinary differential equations. Analysis of finite difference and finite element methods for partial differential equations.

5653 Differential Equations I
(3-0)3 hours credit. Prerequisites: MAT 3613 and MAT 4213, or consent of instructor. Solution of initial-value problems, linear systems with constant coefficients, exponentials of operators, canonical forms and generic properties of operators, and contractions.

5663 Differential Equations II
(3-0)3 hours credit. Prerequisite: MAT 5653. Dynamic systems, the fundamental existence and uniqueness theorem, stability, the Poincare-Bendixson theorem, introduction to perturbation, and bifurcation theory.

5673 Partial Differential Equations I
(3-0)3 hours credit. Prerequisite: MAT 3623, MAT 5663, or consent of instructor. Classical theory of initial value and boundary value problems for partial differential equations.

5683 Partial Differential Equations II
(3-0)3 hours credit. Prerequisite: MAT 5673. Modern topics in partial differential equations.

5833 Perturbation Theory in Applied Mathematics
(3-0)3 hours credit. Prerequisite: MAT 3613, MAT 5653, or consent of instructor. Perturbation theory, asymptotic analysis, and boundary layer expansions.

5973 Directed Research
3 hours credit. Prerequisites: Graduate standing and permission in writing (form available) of the instructor and the student’s Graduate Advisor of Record. The directed research course may involve either a laboratory or a theoretical problem. May be repeated for credit, but not more than 6 hours, regardless of discipline, will apply to the Master’s degree.

6603 Optimization Techniques in Operations Research
(3-0)3 hours credit. Prerequisite: MAT 2213, MAT 2233, or consent of instructor. Analysis and application of optimization techniques in operations research. Emphasis on linear programming, nonlinear programming, and integer programming.

6901 Teaching Seminar
(1-0) 1 hour credit. Prerequisite: Designation as a teaching assistant in the Department of Mathematics. Designed to improve the instructional effectiveness of graduate students’ teaching at the college level. Topics include boardwork, clear speech, teacher-student interaction, professional responsibilities, course content and pace, grading policy, test writing, sensitivity to student needs, information and technical support and guest lectures on special topics. The grade report for the course is either “CR” (satisfactory performance) or “NC” (unsatisfactory performance). This course cannot be applied as credit toward a Master of Science degree in Mathematics.

6953 Independent Study
3 hours credit. Prerequisites: Graduate standing and permission in writing (form available) of the instructor and the student’s Graduate Advisor of Record. Independent reading, research, discussion, and/or writing under the direction of a faculty member. For students needing specialized work not normally or not often available as part of the regular course offerings. May be repeated for credit, but not more than 6 hours, regardless of discipline, will apply to the Master’s degree.

6961 Comprehensive Examination
1 hour credit. Prerequisite: Approval of the appropriate graduate program committee to take the Comprehensive Examination. Independent study course for the purpose of taking the Comprehensive Examination. May be repeated as many times as approved by the Graduate Program Committee. Enrollment is required each term in which the Comprehensive Examination is taken if no other courses are being taken that term. The grade report for the course is either “CR” (satisfactory performance on the Comprehensive Examination) or “NC” (unsatisfactory performance on the Comprehensive Examination).

6963 Topics in Mathematics Education
(3-0)3 hours credit. Prerequisite: Consent of instructor. An organized course offering the opportunity for specialized study not normally or not often available as part of the regular course offerings. This course may be repeated for credit when topics vary. This course cannot be applied toward any Master’s degree in the Department of Mathematics.

6973 Special Problems
(3-0)3 hours credit. Prerequisite: Consent of instructor. An organized course offering the opportunity for specialized study not normally or not often available as part of the regular course offerings. Special Problems courses may be repeated for credit when topics vary, but not more than 6 hours, regardless of discipline, will apply to the Master’s degree.

6983 Master’s Thesis
3 hours credit. Prerequisite: Permission of the Graduate Advisor of Record and thesis director. Thesis research and preparation. May be repeated for credit, but not more than 6 hours will apply to the Master’s degree. Credit will be awarded upon completion of the thesis. Enrollment is required each term in which the thesis is in progress.

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