sp16

Spring 2016

Archived: 

Applied Stochastic Dynamics

Special topics on Applied Stochastic Dynamics offered in Spring 2016 by Molei Tao.

Algebraic Topology I

The fundamental group, covering spaces, core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality.

Stochastic Processes II

Continuous time Markov chains. Uniformization, transient and limiting behavior. Brownian motion and martingales. Optional sampling and convergence. Modeling of inventories, finance, flows in manufacturing and computer networks. (Also listed as ISyE 6762)

Math Methods of Applied Sciences II

Review of vector calculus and and its application to partial differential equations.

Numerical Methods for Ordinary Differential Equations

Analysis and implementation of numerical methods for initial and two point boundary value problems for ordinary differential equations.

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.

Advanced Numerical Methods for Partial Differential Equations

Analysis and implementation of numerical methods for nonlinear partial differential equations including elliptic, hyperbolic, and/or parabolic problems.

Numerical Methods in Finance

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

Differential Geometry I

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

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