2007-09 - Graduate School - The University of Alabama

Graduate Catalog: Section 6.13http://graduate.ua.edu/catalog/16400.htmlMATH 583 Complex Analysis I. Three hours.Prerequisites: MATH 380 and permission of the department.The basic principles of complex variable theory are discussed. Topics include Cauchy-Riemann equations, Cauchy'sintegral formula, Goursat's theorem, the theory of residues, the maximum principle, and Schwarz's lemma.MATH 585 Introduction to Complex Calculus. Three hours.Prerequisite: MATH 227.Some basic notions in complex analysis. Topics include analytic functions, complex integration, infinite series, contourintegration, and conformal mappings.MATH 588 Theory of Differential Equations I. Three hours.Prerequisites: MATH 238 and MATH 380.Topics covered include existence and uniqueness of solutions, Picard theorem, homogenous linear equations, Floquettheory, properties of autonomous systems, Poincare-Bendixson theory, stability, and bifurcations.MATH 589 Theory of Differential Equations II. Three hours.Prerequisite: MATH 588.Typical topics covered include principal Lyapunov stability and instability theorems; invariance theory; perturbation oflinear systems including stable and unstable manifolds; periodic solutions of systems; Hopf bifurcations; and degreetheory.MATH 591 Teaching College-Level Mathematics. Three hours.Prerequisite: Permission of the instructor or the department.Provides a basic foundation for teaching college-level mathematics; to be taken by graduate students beingconsidered to teach undergraduate-level mathematics courses.MATH 592 Introduction to Graduate Mathematics. Three hours.Prerequisite: MATH 237, MATH 257, or permission of the department.Should prepare beginning graduate students for graduate-level mathematics. Dependent on students' backgrounds,analysis and linear algebra topics will be covered. Proofs and examples will form major course components.MATH 598 Research Not Related to Thesis. Three to nine hours.MATH 599 Thesis Research. Three to six hours.MATH 610 Iterative Methods for Linear Systems. Three hours.Prerequisite: MATH 511.Corequisite: MATH 512.Describes some of the best iterative techniques for solving large sparse linear systems.MATH 623 Convex Analysis II. Three hours.Prerequisite: MATH 523 or permission of the department.Second course in convex analysis. Topics include differential theory, constrained extremum problems, and saddlefunctions and minimax theory for convex functions.MATH 625 Optimization by Vector Space Methods. Three hours.Prerequisite: MATH 580 or permission of the department.Involves applications of geometric principles of linear vector space theory to complex infinite-dimensionaloptimization problems. Topics include linear spaces, Hilbert spaces, least-square estimation, dual spaces, linearoperators and adjoints, optimization of functionals, global and local theory of optimization, and interactive methods ofoptimization.MATH 639 Seminar: Topics in Applied Mathematics. One to three hours.MATH 640 Waves in Fluids. Three hours.Prerequisites: MATH 545 (or AEM 500) and MATH 542, or permission of the department.Analysis of various wave motions and development of fundamental ideas of general application to waves in fluids.Sound waves, water waves, and internal waves.MATH 642 Viscous Flows. Three hours.Prerequisites: MATH 545 (or AEM 500) and MATH 541, or permission of the department.Review of equations of fluid motion, tensors, and the Navier-Stokes equation. The role of viscosity in creeping flowsand boundary layers.MATH 644 Hydrodynamic Stability. Three hours.Prerequisite: MATH 545 or AEM 500.Fundamental ideas, methods, results, and applications of hydrodynamic stability. Introduction to some currentresearch topics.MATH 659 Seminar: Probability Models. One to three hours.