Oklahoma State University

577

MATH 5283 Complex Analysis I Prerequisites: MATH 4153 or MATH 5053. Description: Basic topology of the plane, functions of a complex variable, analytic functions, transformations, infinite series, integration and conformal mapping. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5293 Complex Analysis II Prerequisites: MATH 5283. Description: Riemann Mapping Theorem, meromorphic functions, analytic continuation, Dirichlet problem, and entire functions. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5303 General Topology Prerequisites: MATH 4143 or MATH 5043 or consent of instructor. Description: Basic properties of topological spaces and continuous functions, including connectedness, compactness, and separation and countability axioms. Metric, product, and quotient spaces, Urysohn lemma, and Tietze extension theorem. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture

MATH 5473 Financial Calculus Prerequisites: MATH 4143 or MATH 5043, STAT 4203 or consent of instructor. Description: Introduction to derivative pricing and market derivatives. Introduction to the Ito-Doeblin calculus and martingales; the martingale properties of Brownian motion, the Black-Scholes-Merton theory as a simple, special case of martingale pricing, market models of modern fixed income pricing. Insurance, hedging, and options. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5543 Numerical Analysis for Differential Equations Prerequisites: MATH 4233, MATH 4513 or CS 4513. Description: Advanced machine computing, algorithms, analysis of truncation and rounding errors, convergence and stability applied to discrete variables, finite elements, and spectral methods in ordinary and partial differential equations. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5553 Numerical Analysis for Linear Algebra Prerequisites: MATH 3013, and MATH 4513 or CS 4513. Description: Advanced machine computing, algorithms, analysis of rounding errors, condition, convergence, and stability applied to direct and iterative solution of linear systems of equations, linear least squares problems, and algebraic eigenvalue problems, including LU and QR factorization, conjugate gradients, QR algorithm, and Lanczos method. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5563 Finite Element Methods for Partial Differential Equations Prerequisites: MATH 4023; MATH 4263; and MATH 4513 or CS 4513 or equivalent. MATH 4143 or MATH 5043 preferred. Description: Theory and practice of finite element methods, including elliptic boundary value problems, weak formulations, the Ritz-Galerkin method, conforming and non-conforming finite elements, error estimates, and numerical experiments. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics MATH 5580 Case Studies in Applied Mathematics Prerequisites: MATH 2233, MATH 4013, and knowledge of computer programming. Description: Selected mathematical problems from industry. Independent problem-solving, oral presentation of solutions, and technical report writing. Seminar-style format. Offered for variable credit, 1-3 credit hours, maximum of 6 credit hours. Credit hours: 1-3 Contact hours: Other: 1 Levels: Graduate

Department/School: Mathematics MATH 5313 Geometric Topology Prerequisites: MATH 4613 or MATH 5003, MATH 5303.

Description: Manifolds, complexes, the fundamental group, covering spaces, combinatorial group theory, the Seifert-Van Kampen theorem, and

related topics. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture

Department/School: Mathematics MATH 5413 Differential Geometry Prerequisites: MATH 4013 or MATH 4143 or MATH 5043.

Description: Differential manifolds, vector fields, differential forms, connections, Riemannian metrics, geodesics, completeness, curvature, and related topics. Credit hours: 3 Contact hours: Lecture: 3 Levels: Graduate Schedule types: Lecture Department/School: Mathematics

Schedule types: Independent Study Department/School: Mathematics