sp19

Spring 2019

Archived: 

Iterative Methods for Systems of Equations

Iterative methods for linear and nonlinear systems of equations including Jacobi, G-S, SOR, CG, multigrid, fixed point methods, Newton quasi-Newton, updating, gradient methods. Crosslisted with CSE 6644.

Numerical Methods in Finance

This course contains the basic numerical and simulation techniques for the pricing of derivative securities.

Industrial Mathematics II

Applications of mathematical techniques from MATH 6514 to solve real-world problems. Group projects to solve industrial problems in topics chosen by the instructor. (2nd of two courses)

Differential Geometry I

Core topics in differential and Riemannian geometry including Lie groups, curvature, relations with topology.

Partial Differential Equations II

This course covers the general mathematical theory of linear stationary and evolution problems plus selected topics chosen on the instructor's interests.

Real Analysis II

Topics include L^p, Banach and Hilbert spaces, basic functional analysis.

Real Analysis I

Measure and integration theory

Complex Analysis

Complex integration, including Goursat's theorem; classification of singularities, the argument principle, the maximum principle; Riemann Mapping theorem; analytic continuation and Riemann surfaces; range of an analytic function, including Picard's theorem.

Ordinary Differential Equations II

This sequence develops the qualitative theory for systems of differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, and normal forms. (2nd of two courses)

Multivariate Statistical Analysis

Multivariate normal distribution theory, correlation and dependence analysis, regression and prediction, dimension-reduction methods, sampling distributions and related inference problems, selected applications in classification theory, multivariate process control, and pattern recognition.

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