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Introduction to numerical algorithms for some basic problems in computational mathematics. Discussion of both implementation issues and error analysis. Crosslisted with CX 4640 (formerly CS 4642).
Fourier series, Fourier integrals, boundary value problems for partial differential equations, eigenvalue problems
A broad introduction to the local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations.
The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem
Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces
Method of characteristics for first and second order partial differential equations, conservation laws and shocks, classification of second order systems and applications.
Topics from complex function theory, including contour integration and conformal mapping
Sampling distributions, Normal, t, chi-square and F distributions. Moment generating function methods, Bayesian estimation and introduction to hypothesis testing
Simple random walk and the theory of discrete time Markov chains
This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.
Georgia Institute of TechnologyNorth Avenue, Atlanta, GA 30332Phone: 404-894-2000