Graduate MATH Courses

- 4823 - Abstract Algebra III (syllabus)
- 4822 - Abstract Algebra II (syllabus)
- 4832 - Euclidean Transformations (syllabus)
- 4855 - Ordinary Differential Equations (syllabus)
- 4857 - Partial Differential Equations (syllabus)
- 4875 - Complex Variables (syllabus)
- 4880 - Topology (syllabus)
- 5821 - Topics in Abstract Algebra (syllabus)
- 5825 - Advanced Linear Algebra (syllabus)
- 5828 - Number Theory (syllabus)
- 5835 - Combinatorics and Graph Theory (syllabus)
- 5843 - Theory of Probability (syllabus)
- 5844 - Theory of Statistics (syllabus)
- 5845 - Operations Research (syllabus)
- 5851 - Topics in Analysis (syllabus)
- 5852 - Real Analysis II (syllabus)
- 5860 - Topics in Numerical Analysis (syllabus)
- 5861 - Numerical Analysis II (syllabus)
- 5884 - Mathematical Logic (syllabus)
- 5895 -Selected Topics in Mathematics (5895M syllabus) (5895N syllabus) (5895O Syllabus) (5895P Syllabus) (5895W Syllabus) (5895X Syllabus)

- 6900 - Mathematics Workshop

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)

- 6905 - Teaching Practicum

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)

- 6910/6911 Advanced Engineering Mathematics 1 & 2

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. 3 + 3 s.h. (6910 syllabus) (6911 syllabus)

- 6915 - Mathematical Foundations

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)

- 6922 - Advanced Topics in Group and Ring Theory

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)

- 6923 - Advanced Topics in Field Theory

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)

- 6924 - Galois Theory

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)

- 6925 - Advanced Numerical Analysis

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)

- 6928 - Advanced Number Theory

Advanced study of number theory: theory and distribution of primes, computational number theory, and additive number theory. Prereq.: Math 5828. 3 s.h. (syllabus)

- 6930 - Differential Geometry

Classical differential geometry of curves and surfaces, differentiable manifolds with tensors. Prereq.: Math 5852. 3 s.h. (syllabus)

- 6933 – Geometry

General theory of incidence structures and modern geometric theories. Prereq.: Math 3721 and either 4830 or 5835. 3 s.h. (syllabus)

- 6937 - Graph Theory

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)

- 6938 - Combinatorics

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)

- 6940 - Advanced Data Analysis

Identical with Stat 6940. 3 s.h. (syllabus)

- 6942 - Advanced Operations Research

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)

- 6943 - Mathematical Statistics I

Identical with Stat 6943. 3 s.h. (syllabus)

- 6944 - Mathematical Statistics II

Identical with Stat 6944. 3 s.h. (syllabus)

- 6945 - Stochastic Processes

Identical with Stat 6945. 3.s.h. (syllabus)

- 6948 - Linear Models

Identical with Stat 6948. 3 s.h. (syllabus)

- 6955 - Advanced Differential Equations

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)

- 6957- Partial Differential Equations

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)

- 6965, 6966 - Abstract Analysis I, II

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)

- 6975 - Complex Analysis I

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)

- 6976 - Complex Analysis II

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)

- 6980 - Topology I

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)

- 6981 - Topology II

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)

- 6984 - Mathematical Logic I

Syntax and semantics of propositional and first-order calculi with applications. Prereq.: Phil 3719 or Math 3721 or Math 3751; or consent of graduate coordinator. Credit will not be given for both Math 5884 and 6984. 3 s.h. (syllabus)

- 6985 - Mathematical Logic II

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)

- 6990 - Independent Study

Study under the supervision of a staff member. Prereq.: consent of graduate coordinator. May be repeated. 3 s.h.

- 6995 - Special Topics

Specialized topics selected by the staff. Prereq.: consent of graduate coordinator and department chair. 3 s.h. (6995 Syllabus) (syllabus 6995E) (6995F Syllabus) (6995G Syllabus) (6995I Syllabus) (syllabus 6995K) (6995M Syllabus) (6995V Syllabus)

- 6996 - Mathematical Project

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.

- 6999 – Thesis

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.