Mathematics
 

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.

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.

6920. Advanced Abstract Algebra. Study of algebraic structures, substructures, morphisms, and quotient structures, with additional topics from group theory, field extensions, and/or Galois Theory. Prereq.: Math 5822 and 5825; or consent of graduate coordinator. 3 s.h.

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.

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.

6930. Differential Geometry. Classical differential geometry of curves and surfaces, differentiable manifolds with tensors. Prereq.: Math 5852. 3 s.h.

6933. Geometry. General theory of incidence structures and modern geometric theories. Prereq.: Math. 3721 and either 4830 or 5835. 3 s.h.

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.

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.

6940. Advanced Data Analysis. Identical with Stat 6940. 3 s.h.

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.

6943. Mathematical Statistics I. Identical with Stat 6943. 3 s.h.

6944. Mathematical Statistics II. Identical with Stat 6944. 3 s.h.

6945. Stochastic Processes. Identical with Stat 6945. 3 s.h

6948. Linear Models. Identical with Stat 6948. 3 s.h.

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.

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 5880 or 6915 for 6965, 6965 for 6966; or consent of graduate coordinator. 3+3 s.h.

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 5875 and 6975. 3 s.h.

6976. Complex Anaylsis II. The Cauchy theorem, the Weierstraß, Mittag-Lefler, Picard, and Riemann theorems, Riemann surfaces, harmonic functions. Prereq.: Math 5875 or 6975; or consent of graduate coordinator. 3 s.h.

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 5880 and 6980. 3 s.h.

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 5880 or 6980; or consent of graduate coordinator. 3 s.h.

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.

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.

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.

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.

* additional fee required

Statistics
 

6940.* Advanced Data Analysis. An overview of techniques in data analysis. Includes strong emphasis on visual interpretation of data. Topics include one or more samples, proportions, odds, regression, and multiple comparisons. Prereq.: Math/Stat 5844; or consent of graduate coordinator. 3 s.h.

6943. Mathematical Statistics I. Random variables, their distributions and densities. Families and exponential families of distribution. Independence, joint distributions, conditional probability and expectation. Convergence and limit theorems. Prereq.: Math. 3751; or consent of graduate coordinator. Credit will not be given for both 5843 and 6943. 3 s.h.

6944. Mathematical Statistics II. A study of theories and properties of statistical hypotheses testing and estimation, including maximum likelihood method, likelihood ratio tests, sufficiency, and related topics. Prereq.: Math/Stat 5843 or 6943; or consent of graduate coordinator. Credit will not be given for both 5844 and 6944. 3 s.h.

6945. Stochastic Processes. An advanced study of stochastic processes. Topics include: Markov chains, Poisson processes, nonhomogeneous Poisson processes, renewal theory, conditional probability and expectation. Prereq.: Math/Stat 5843 or 6943; or consent of graduate coordinator. 3 s.h.

6946. Sampling Methods. Methods for survey design and analysis. Topics include basic theory of surveys, descriptions of data, sampling distributions, design of survey, sources of error, questionnaire design, and sampling techniques. Prereq.: Stat 5817; or consent of graduate coordinator. 3 s.h.

6948.* Linear Methods. A study of linear statistical methods of the relationship between analysis of variance and regression and the assumptions underlying the analysis of variance. Prereq.: Math 3720 and Math/Stat 5844 or 6944; or consent of graduate coordinator. 3 s.h.

6949.* Design and Analysis of Experiments. Fundamental principles of design and analysis of experiments. Topics include blocking, multi-factor testing, multiple comparisons, repeated measures, crossing and nesting designs. Prereq.: Math/Stat 5844 or 6944; or consent of graduate coordinator. 3 s.h.

* additional fee required