Intensive study and activity in a topic related to mathematics, its applications, or the teaching of mathematics. May be repeated. Grading is S/U. Prereq.: Consent of graduate coordinator. 1–6 s.h. (syllabus)
Intensive preparation for teaching lower-level mathematics courses, featuring formal instruction and orientation on teaching issues, evaluated presentations, mentored classroom instruction, and weekly teaching seminars. Topics include course design, policies, syllabi, grading; classroom teaching problems; orientation in Mathematics Assistance Center, specific lower-level mathematics courses, online tutorial services. Required of and limited to graduate assistants in the Department of Mathematics and Statistics. To be taken each semester student is a graduate assistant. Grading is S/U. Does not count toward credit in the program. 1 s.h. (syllabus)
Theory and solution techniques used in engineering applications. Topics include brief review of ordinary differential equations and linear algebra; vector calculus, integral theorems, complex analysis, series, residue theory, potential theory, special functions, integral transforms, partial differential equations and applications in mathematical modeling. Prereq.: MATH 3705. 3 s.h. (syllabus)
Theory and solution techniques used in engineering applications. Topics include brief review of ordinary differential equations and linear algebra; vector calculus, integral theorems, complex analysis, series, residue theory, potential theory, special functions, integral transforms, partial differential equations and applications in mathematical modeling. Prereq.: MATH 6910. 3 s.h. (syllabus)
Order-theoretic foundations of mathematics: ordered structures; topologies; powerset operators of a function; applications to continuity, compactness, algebra, and analysis. Prereq.: Math 3721 and 3751; or consent of graduate coordinator. 3 s.h. (syllabus)
A continuation of MATH 5821 with special emphasis on groups acting on sets, Sylow’s Theorem and its applications, ring homomorphisms, ideals, and polynomial rings. Credit will not be given for MATH 4822 and 6922. Prereq.: MATH 3721 or 5821. 3 s.h. (syllabus)
This course introduces the major results in field theory necessary to study Galois Theory. These results include splitting fields, algebraic extensions, and finite fields. Prereq.: MATH 4822 or 6922. 3 s.h. (syllabus)
This course introduces Galois Theory with special emphasis upon the Galois group, the Fundamental Theorem of Galois Theory, and radical extensions. Prereq.: MATH 4823 or 6923. 3 s.h. (syllabus)
Eigenvalue-eigenvector analysis, boundary value problems, and approximation methods for partial differential equations, and additional topics. Prereq.: Math 3720, 3760, knowledge of high-level programming language, and either Math 5852 or 5861; or consent of graduate coordinator. 3 s.h. (syllabus)
Advanced study of number theory: theory and distribution of primes, computational number theory, and additive number theory. Prereq.: Math 5828. 3 s.h. (syllabus)
Classical differential geometry of curves and surfaces, differentiable manifolds with tensors. Prereq.: Math 5852. 3 s.h. (syllabus)
General theory of incidence structures and modern geometric theories. Prereq.: Math 3721 and either 4830 or 5835. 3 s.h. (syllabus)
Advanced study of graph theory, graph algorithms, and applications of graph theory. Topics may include Ramsey theory, extremal graph theory, flows and networks, planarity, graph colorings, and combinatorial optimization. Prereq.: Math 5835. 3 s.h. (syllabus)
Advanced study of combinatorial models. Topics may include extremal set theory, matroids, inversion formulae, counting techniques, generating functions, difference sets, combinatorial designs, and incidence structures. Prereq.: Math 5835 and 3721. 3 s.h. (syllabus)
Identical with Stat 6940. 3 s.h. (syllabus)
Topics may include integer programming, advanced linear programming, nonlinear programming, dynamic programming, queuing theory, Markov analysis, game theory, and forecasting models. Prereq.: Stat 3743 and Math 5845. 3 s.h. (syllabus)
Identical with Stat 6943. 3 s.h. (syllabus)
Identical with Stat 6944. 3 s.h. (syllabus)
Identical with Stat 6945. 3.s.h. (syllabus)
Identical with Stat 6948. 3 s.h. (syllabus)
Proofs of existence and uniqueness of solutions of non-autonomous, nonlinear equations. Additional topics may include advanced linear systems, partial differential equations, and integral equations. Prereq.: Math 5852 and either 3705 or 5855.; or consent of graduate coordinator. 3 s.h. (syllabus)
Introduction to partial differential equations (PDE) including solution techniques and applications. Classifications of the basic types of PDE’s (hyperbolic, parabolic and elliptic) and dependence on boundary and initial conditions. Topics include Fourier series, integral transforms (Fourier, Laplace), and applications in vibrations, electricity, heat transfer, fluids or other selected topics. Prereq.: MATH 3705 and MATH 3720. 3 s.h. (syllabus)
Lebesgue integration and measure on the real line. General measure theory and functional analysis, including the Radon-Nikodym theorem, the Fubini theorem, the Hahn-Banach theorem, the closed graph and open mapping theorems, and weak topology. Prereq.: Math 5852 and either 4880 or 6915 for 6965, 6965 for 6966; or consent of graduate coordinator. 3 + 3 s.h. (6965 Syllabus) (6966 Syllabus)
Analytic and meromorphic functions of a complex variable, contour integration, the Cauchy-Goursat Theorem, Taylor and Laurent series, residues and poles, conformal mapping. Prereq.: Math 3751 or consent of graduate coordinator. Credit will not be given for both Math 4875 and 6975. 3 s.h. (syllabus)
The Cauchy theorem, the Weierstraß, Mittag-Lefler, Picard, and Riemann theorems, Riemann surfaces, harmonic functions. Prereq.: Math 4875 or 6975; or consent of graduate coordinator. 3 s.h. (syllabus)
Basic concepts of topological spaces and mappings between them, including compactness, connectedness, and continuity. Prereq.: Math 3721 and 3751; or consent of graduate coordinator. Credit will not be given for both Math 4880 and 6980. 3 s.h. (syllabus)
Separation, metrization, compactification. Additional topics may be selected from point-set topology, fuzzy topology, algebraic topology, combinatorial topology, topological algebra. Prereq.: Math 4880 or 6980; or consent of graduate coordinator. 3 s.h. (syllabus)
Topics may include elements of recursive function theory, Gödel's incompleteness theorem, decision problems for theories, order-theoretic models. Prereq.: One of Math 2683 or 6915, and one of Math 5884 or 6984; or consent of graduate coordinator. 3 s.h. (syllabus)
Study under the supervision of a staff member. Prereq.: consent of graduate coordinator. May be repeated. 3 s.h.
Specialized topics selected by the staff. Prereq.: consent of graduate coordinator and department chair. 3 s.h. (6995 Syllabus) (syllabus 6995D) (syllabus 6995E) (6995F Syllabus) (6995G Syllabus) (6995I Syllabus) (syllabus 6995K) (6995M Syllabus) (6995V Syllabus)
Individual research project culminating in a written report or paper, though not as broad in scope as a thesis. May be repeated once if the second project is in a different area of mathematics. 1–3 s.h.
A student may register for 6 s.h. in one semester or for 3 s.h. in each of two semesters. 3–6 s.h.