COURSES / PROGRAMS
Mathematics

MATH 301/302 Graduate Tutorial Courses 13 cr. Prerequisite: graduate standing or consent of instructor.

MATH 303 Measure and Integration 3.0; 3 cr. A first course in measure theory, including general properties of measures, construction of Lebesgue measure in Rn, Lebesgue integration and convergence theorems, Lpspaces, HardyLittlewood maximal function, Fubini's theorem, and convolutions. Prerequisite: MATH 223 or graduate standing. Annually.

MATH 304 Complex Analysis 3.0; 3 cr. A second course in complex analysis, covering the homotopy version of Cauchy's theorem, the open mapping theorem, maximum principle, Schwarz's lemma, harmonic functions, normal families, Riemann mapping theorem, Riemannian metrics, method of negative curvature, Picard's theorem, analytic continuation, monodromy, and modular function. Prerequisite: MATH 227 or graduate standing. Annually.

MATH 305 Functional Analysis 3.0; 3 cr. Vector spaces, Hamel basis, HahnBanach theorem, Banach spaces, continuous linear operators and functionals, Hilbert spaces, and weak topologies. Prerequisite: MATH 223 or graduate standing. Annually.

MATH 306 Calculus on Manifolds 3.0; 3 cr. Prerequisite: MATH 223. Offered Occasionally

MATH 307 Topics in Analysis 3.0; 3 cr.

MATH 314 Algebraic Topology I 3.0; 3 cr. Closed surfaces, categories and functors, homotopy, the fundamental group functor, and covering spaces. Prerequisites: MATH 214 and MATH 241 or graduate standing. Annually.

MATH 315 Algebraic Topology II 3.0; 3 cr. Singular homology with applications to Euclidean spaces and an introduction to cohomology theory. Prerequisite: MATH 314. Offered Occasionally

MATH 316 Topics in Topology 3.0; 3 cr.

MATH 341 Modules and Rings 3.0; 3 cr. Fundamental concepts of modules and rings, projective and injective modules, modules over a PID, Artinian and Noetherian modules and rings, modules with composition series, semisimplicity, and tensor products. Prerequisite: MATH 241 or graduate standing. Annually.

MATH 342 Modules and Rings II 3.0; 3 cr. A course covering more advanced topics in modules and rings. Prerequisite: MATH 341. Annually.

MATH 343 Field Theory 3.0; 3 cr. Prerequisite: MATH 242.

MATH 344 Commutative Algebra 3.0; 3 cr. Prerequisites: MATH 242 and MATH 341.

MATH 345 Topics in Algebra 3.0; 3 cr.

MATH 350 Discrete Models for Differential Equations 3.1; 3 cr. A detailed study of methods and tools used in deriving discrete algebraic systems of equations for ordinary and partial differential equations: finite difference and finite element discretization procedures; generation and decomposition of sparse matrices, finiteprecision arithmetic, illconditioning and preconditioning, scalar, vector, and parallelized versions of the algorithms. The course includes tutorial immersion sessions in which students become acquainted with stateoftheart scientific software tools on standard computational platforms. Prerequisite: Linear Algebra and the equivalent of Math of MATH/CMPS 251 (which can be taken concurrently) or consent of instructor. Same as CMPS 350. Annually.

MATH 351 Optimization and NonLinear Problems 3.1; 3 cr. A study of practical methods for formulating and solving numerical optimization problems that arise in science, engineering, and business applications. Newtonâ€™s method for nonlinear equations and unconstrained optimization. Simplex and interiorpoint methods for linear programming. Equality and inequalityconstrained optimization. Sequential Quadratic Programming. Emphasis is on algorithmic description and analysis. The course includes an implementation component where students develop software and use stateoftheart numerical libraries. Prerequisite: MATH/CMPS 350 or consent of instructor. Same as CMPS 351. Annually.

MATH 358 Introduction to Symbolic Computing 3.0; 3 cr. Introductory topics in computer algebra and algorithmic number theory that includes fast multiplication of polynomials and integers, fast Fourier transforms, primality testing and integers factorization. Applications to cryptography and pseudorandom number generation. Linear algebra and polynomial factorization over finite fields. Applications to errorcorrecting codes. Introduction to Grobner bases. Prerequisite: Good background in programming, linear algebra, discrete mathematics or consent of instructor. Same as CMPS 358. Annually.
 MATH 360 Special Topics in Computational Science 3.0; 3 cr.
A course on selected topics in computational science that changes according to the interests of visiting faculty, instructors, and students. Selected topics cover stateoftheart tools and applications in computational science. Prerequisite: Consent of instructor. Same as CMPS 360. Annually.
 MATH 395A/395B Comprehensive Exam 0 cr.
Prerequisite: Consent of adviser
 MATH 399 MA or MS Thesis 6 cr.
