
Department of Mathematics Graduate CoursesMAP 5345 Partial Differential Equations (3) Prereq: MAC 2313. Major topics: solutions of firstorder, quasilinear partial differential equations, classification and reduction of normal form of linear secondorder equations, separation of variables, SturmLouisville problems, Fourier series, Fourier integral, Fourier transforms, applications to initial value and initial boundary value problems. MAS 5145 Linear Algebra (3) Prereq: MAS 3105. Major topics: review of linear algebra, applications of matrices, practical methods of matrix computation, computations using Guassian elimination, Fredholm alternative, choice of pivots, modified systems, unitary transformations and applications, eigenspaces, Schur, QR, and singular value decomposition, similarity transformations, defective matrices, Jordan form, iterative solutions, norms of matrices, quadratic forms and variational principles. MAS 5204 Number Theory (3) Prereq: MAC 2313. Major topics: mathematical induction, linear Diophantine equations and congruences, Chinese remainder theorem, EulerFermat theorems, quadratic reciprocity law. MAS 5311 Algebraic Structures (3) Prereq: MAS 4301. Major topics: groups, direct products, linear algebras, rings, fields extensions of rings and fields, Galois theory. MAS 5317 Structures of the Real Number System (3) Prereq: MAC 2313. Major topics: concepts in set theory, relations and their properties, evaluation of numeration systems, integers, rational and irrational numbers, the field of real numbers, introduction to the theory of matrices. MAS 5328 Group Theory in the Physical Sciences (3). MAT 5907 Directed Individual Study (16) Prereq: Consent of Mathematics Chairperson. Independent study or research under supervision of faculty member in various topics. MAT 5932 Topics in Mathematics (3) Course centers around current interest or of special interest to students or instructors. Topics or focus vary. MAT 5939 Seminar in Mathematics (3) Course centers around current interest or of special interest to students or instructors. Topics or focus vary. MHF 5206 Structures and Concepts of Arithmetic (3) Prereq: MAC 2313. Major topics: ZermeloFrankel axioms for set theory, finite and infinite sets, ordinal numbers, cardinal numbers, the Axiom of Choice and some of its equivalents. MTG 5220 Logic and Geometry (3) Prereq: MAC 2313. Major topics: foundations of mathematical logic and geometry, sentential logic, survey of fundamental concepts of nonmetric geometry, metric geometry in development of geometry as a mathematical system. STA 5155 Statistical Inference (3) Prereq: STA 3034. Major topics: nature and importance of statistics, descriptive statistics, probability theory and sampling distribution, experimental designs and data analysis, introduction to matrix algebra, regression analysis, introduction to times series analysis.

