Courses
Graduate Course Descriptions

MAT 500 Mathematics Teaching Seminar (1)
In-depth topics related to preparing and presenting lessons, testing and grading, and classroom management, includes videotaping of practice teaching sessions. Does not count as program credit for M.S. in mathematics.

MAT 508 Mathematical Foundations for Inservice Elementary School Teachers (3)
Numeration, place value, intuitive geometry, measurement, arithmetic algorithms. Does not count as program credit for M.S. in mathematics.

MAT 509 Mathematical Foundations for Inservice Middle School Teachers (3)
Intuitive geometry, integers, rational numbers, probability, graphing, metric system, word problems. Does not count as program credit for M.S. in mathematics.

MAT 510 Mathematics for Teachers of Junior High School Mathematics (3)
The real number system and major subsystems, introduction to algebra, informal geometry, consumer mathematics, and introduction to BASIC programming. Open only to elementary and special education majors and does not count as program credit for M.S. in mathematics.

MAT 515 Introduction to Differential Equations II (3)
Systems of linear differential equations, characteristic equations, operator methods, approximating solutions, Laplace transforms. Prerequisite: MAT 285.

MAT 517 Introduction to Partial Differential Equations (3)
Integrability conditions, quasilinear and linear equations, applications to physics, classification of second order equations and canonical forms, separation of variables. Prerequisite: MAT 285.

MAT 518 *Linear Programming (3)
Convex sets, linear inequalities, extreme-point solutions, simplex procedure, applications. Prerequisite: MAT 326.

MAT 519 *Optimization in Mathematical Programming (3)
Selected topics in optimization from linear and nonlinear programming. Prerequisites: MAT 280, and 418 or 518.

MAT 520 Probability and Mathematical Statistics II (3)
Central limit theorem, estimation, hypothesis tests. Prerequisite: MAT 320.

MAT 521 Number Theory (3)
Induction, well ordering, division algorithm, Euclidean algorithm, Fundamental Theorem of Arithmetic, number theoretic functions, congruences. Prerequisite: MAT 326 and 340.

MAT 523 Modern Algebra I (3)
Elementary notions in groups, Fundamental Theorem of Finitely Generated Groups, permutation groups, quotient groups, the isomorphism theorems, applications of transformation groups. Prerequisite: MAT 326 and 340.

MAT 524 Modern Algebra II (3)
Survey of standard algebraic systems: rings, integral domains, fields, modules, polynomial rings, quotient rings, fields of quotients. Prerequisite: MAT 423 or 523.

MAT 526 Linear Algebra II (3)
Determinants; polynomials; complex numbers; single linear transformations; orthogonal, unitary, and symmetric linear transformations. Prerequisite: MAT 326 and 340.

MAT 536 Theory of Functions of a Complex Variable (3)
Complex numbers and functions, limits, continuity, differentiation, analytic functions, branches, contour integration, series. Prerequisite: MAT 280, 326, and 340.

MAT 537 Graph Theory (3)
An introduction to graphs and a sampling of their numerous and diverse applications. Prerequisite: MAT 326 and 340.

MAT 539 Combinatorics (3)
Counting and enumeration techniques, inversion formulas and their applications, and counting schemata relative to permutations of objects. Prerequisites: MAT 169, 326, and 340.

MAT 541 Advanced Calculus I (3)
Point set theory, sequences, continuity, uniform continuity, limits, mean value theorems, L’Hospital’s rule. Prerequisites: MAT 280, 326, and 340.

MAT 542 Advanced Calculus II (3)
Riemann integration, Taylor’s theorem, improper integrals, infinite series, uniform convergence. Prerequisite: MAT 441 or 541.

MAT 560 *Numerical Analysis I (3)
Methods of solving equations and systems of equations, error analysis, difference equations. Prerequisites: MAT 280, 326, and knowledge of a programming language.

MAT 561 *Numerical Analysis II (3)
Interpolating polynomials, numerical differentiation and integration, numerical solutions of differential equations, roundoff error. Prerequisites: MAT 285, and 460 or 560.

*Students will use university computers and appropriate software as a part of course requirements.

MAT 572 Modern Geometry (3)
Heuristic and analytic treatment of a branch of modern geometry, such as projective or differential geometry. Prerequisite: MAT 280, 326, and 340.

MAT 575 General Topology (3)
General topological spaces, bases and subbases, continuity. Prerequisite: MAT 169, 326, and 340.

MAT 581 History of Mathematics (3)
The history of mathematics from antiquity through the 17th century. Does not count as program credit for M.S. in mathematics. Prerequisite: MAT 167.

MAT 588 Mathematics for Inservice Secondary School Teachers I (1-3) Special mathematical topics for in service secondary school mathematics teachers, to include algebra, number theory, graph theory, and combinatorics. Does not count as program credit for M.S. in mathematics. Prerequisites: 24 hours of mathematics, excluding pre-calculus courses, and secondary mathematics teaching experience.

MAT 589 Mathematics for Inservice Secondary School Teachers II (1-3) Special mathematical topics for inservice secondary school mathematics teachers, to include probability theory, analysis, applied mathematics, topology, geometry. Does not count as program credit for M.S. in mathematics. Prerequisites: 24 hours of mathematics, excluding pre-calculus courses, and secondary mathematics teaching experience.

MAT 592 Special Problems I, II (1-3 each)

MAT 601 Differential Geometry I (3)
An introduction to the theory of plane curves, space curves, and surfaces. Prerequisite: Permission of instructor.

MAT 603 Modern Algebra (3)
Simple groups, solvable groups, the Sylow theorems, presentations of groups, category terminology, introductory homological algebra. Prerequisite: MAT 424 or 524.

MAT 605 Ordinary Differential Equations (3)
Topics from the theory of ordinary differential equations. Specific topics to be selected by the instructor. Prerequisite: MAT 285.

MAT 606 Partial Differential Equations (3)
Dirichlet, Neumann, and mixed boundary value problems; classical techniques of solution of partial differential equations and applications. Prerequisite: MAT 285.

MAT 610 Numerical Linear Algebra (3)
Theory and practice of matrix computations, matrix norms, singular value decomposition, linear systems, LU decomposition, QR decomposition, methods for eigenvalue problems. Prerequisite: MAT 326 and a knowledge of eigenvalues and eigenvectors.

MAT 629 Applied Combinatorics and Graph Theory (3) Combinatorial/graphical techniques for complexity analysis recurrence relations, Polya theory, NP complete problems. May also be taken as CSC 629. Prerequisite: CSC 616 or permission of instructor.

MAT 636 Functions of a Complex Variable (3)
Taylor and Laurent series, residue calculus, conformal mapping with applications, integral formulas of the Poisson type, analytic continuation. Prerequisite: MAT 436 or 536.

MAT 641 Functions of a Real Variable I (3)
Foundations of real analysis and introduction to Lebesgue integration. Prerequisite: MAT 442 or 542.

MAT 642 Functions of Real Variable II (3)
Continuation of MAT 641. Prerequisite: MAT 641.

MAT 650 Computer Assisted Mathematics I (3)
Applications of computer algebra software to mathematical modeling. Modeling projects and experiments employing both numeric and symbolic computation using software such as DERIVE, Maple, and Mathematica. The laboratory setting and project format will permit investigations of a deeper nature than would be possible due to time constraints in a typical 3-hour lecture course. May be repeated for a maximum of 6 hours credit. Prerequisite: Permission of instructor.

MAT 651 Computer Assisted Mathematics II (3)
Application of computer algebra software to data analysis, partial differential equations, statistics, non-linear regression, and linear algebra. May be repeated for a maximum of 6 hours of credit. Prerequisite: Permission of instructor.

MAT 657 Dimensions of Learning in Mathematics I (3)
Broad introduction to the concepts, contexts, and practices of teaching, as well as specific instruction in secondary mathematics methods. This course includes a clinical supervision component. Prerequisites: Admission to the Master of Arts in Teaching degree program.

MAT 658 Dimensions of Learning in Mathematics Education II (3) Continuation of MAT 657. Prerequisite: MAT 657.

MAT 681 Topics in Algebra I, II, III (3)
May be repeated for a maximum of 9 hours credit. Prerequisites: MAT 423 or 523, and permission of instructor.

MAT 682 Topics in Analysis I, II, III (3)
May be repeated for a maximum of 9 hours credit. Prerequisite: Permission of instructor.

MAT 683 Topics in Topology and Geometry I, II, III (3)
May be repeated for a maximum of 9 hours credit. Prerequisite: Permission of instructor.

MAT 684 Topics in Applied Mathematics I, II, III (3)
May be repeated for a maximum of 9 hours credit. Prerequisite: Permission of instructor.

MAT 685 Topics in Computational Mathematics I, II, III (3)
May be repeated for a maximum of 9 hours credit. Prerequisite: Permission of instructor.

MAT 689 Mathematics Seminar I, II (3)
Six hours of seminar are required for the M.S. degree in mathematics. Prerequisite: Permission of instructor.

MAT 691 Research in Mathematics (1-16)
Does not count as program credit for M.S. in mathematics.

MAT 697 Independent Study and Research (Hours arranged)
Not to be counted as credit towards a degree. Students may enroll in this course to meet the continuous enrollment requirement.

MAT 698 Thesis (1-6)
May be repeated for a maximum of 6 hours credit.

MAT 720 Mathematics for Scientific Computing I (3)
Prerequisite: Permission of instructor. Numerical methods for the solution of matrix equations and for eigenvector/value finding techniques, including criteria for selection among available algorithms, are covered.

MAT 721 Mathematics for Scientific Computing II (3)
Prerequisite: MAT 720 or permission of instructor. Techniques for interpolation and differentiation; numerical techniques for the solution of ODEs and PDEs, including Runge-Kutta, Adams/Bashforth, spectral, and shooting methods.

MAT 771 Functional Analysis for Computional Science (3)
Prerequisites: MAT 442 or 552, and MAT 641. An introduction to functional analysis.

MAT 772 Numerical Analysis for Computional Science (3)
Prerequisites: MAT 610 and 771. A comprehensive introduction to computational mathematics.

MAT 773 Signal Analysis for Computional Science (3)
Prerequisites: MAT 771. The mathematical analysis of time series and signals.

Mathematics Refresher and Enrichment Program (M-REP)

MAT 584 Calculus Review I (1-3)
A review of topics from single-variable calculus to include limits, continuity, derivatives, and integration, with applications relevant to the high school curriculum. Prerequisite: Permission of instructor.

MAT 585 Calculus Review II (1-3)
A review of topics from single-variable calculus to include methods of integration, L’Hopital’s rule, improper integrals, infinite series and vectors, with applications relevant to the high school curriculum. Prerequisite: MAT 584 or permission of instructor.

MAT 586 Geometry Review for High School Teachers (1-3)
May be repeated for a maximum of 6 hours credit. Topics from Euclidean geometry, transformational geometry, plane analytic geometry, and topology.

MAT 587 Problem Solving in School Mathematics (1-3)
May be repeated for a maximum of 6 hours credit. Includes strategies for solving both standard and nonstandard mathematical problems. Prerequisite: MAT 585 or permission of instructor.

None of the courses MAT 584 - 587 will count toward any degree in mathematics.