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## Graduate Math Courses

**505. Seminar in Mathematics**. 1 to 3 credits.

**512. Modern Analysis I**. 3 credits. Prerequisite: Math 432. Algebras and sigma algebras, Borel sets, measures, measurable sets and Lebesgue measure, non-measurable sets, measurable functions, the definition and basic properties of the Lebesgue integral, Fatou's lemma, the monotone convergence theorem, and Lebesgue's dominated convergence theorem.

**513. Modern Analysis II**. 3 credits. Prerequisite: Math 512. Product measures, Fubini's theorem, the Radon Nikodym theorem, inequalities of Holder and Minkowski, definitions and basic properties of normed spaces and Banach spaces, some classical Banach spaces such as Lp and lp, bounded linear operators, and dual spaces.

**515, 516. Applied Mathematics**. 3 credits each. Prerequisite: Math 266 or consent of instructor. The content of the course varies but includes current topics in applied mathematics such as: (1) ordinary or partial differential equations, (2) approximation theory and perturbation techniques, (3) modeling and computer simulation, (4) special functions, (5) numerical analysis, (6) variational methods, (7) transforms, (8) integral equations.

**518, 519. Algebra I, II**. 3 credits each. Prerequisite: Math 441 and 442. Group theory, rings and fields, vector spaces, Galois theory and finite fields.

**520, 521. Topology I, II**. 3 credits each. Prerequisite: Math 431. Point set topology, including metric spaces and such topics as homeomorphisms, separation axioms, compactness, connectedness, general convergence, compactification and metrizability.

**541. Linear Statistical Models**. 3 credits. Prerequisite: Math 422 or consent of instructor. Distributions of quadratic forms, general linear hypotheses of full rank, least squares, Gauss-Markoff theorem, estimability, parametric transformations, Cochran's theorem, projection operators and conditional inverses in generalized least squares, applications to ANOVA and experimental design models.

**542. Advanced Topics in Statistics and Probability**. 3 credits. Prerequisite: Math422 or consent of instructor. The content of the course varies but may include (but is not restricted to) current topics in statistics and probability such as (1) time series, (2) sampling, (3) nonparametric statistics, (4) experimental design, (5) probability theory, (6) statistical theory, (7) multivariate statistical analysis.

**403. Theory of Probability**. 3 credits.

**405. Selected Topics in Mathematics**. 1 to 3 credits.

**408. Combinatorics**. 3 credits.

**409. Geometry**. 3 credits.

**412. Differential Equations**. 3 credits.

**415. Topics in Applied Mathematics**. 1 to 3 credits.

**416. Topics in Statistics**. 1 to 3 credits.

**421, 422. Statistical Theory**. 6 credits.

**431, 432. Advanced Calculus**. 6 credits.

**435. Theory of Numbers**. 3 credits.

**441. Abstract Algebra**. 3 credits.

**442. Linear Algebra**. 3 credits.

**450. Elements of Topology**. 3 credits.

**460. Mathematical Modeling**. 3 credits.

**461, 462. Numerical Analysis**. 6 credits.

**465. Operations Research**. 3 credits.

**471. Introduction to Complex Variables**. 3 credits.

**494, 495. Reading Course in Mathematics**. Credit not to exceed 1 hour a semester and total credit not to exceed 3 hours.