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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 study of the linear programming problem, including the simplex method, duality, and sensitivity analysis with applications to matrix games, integer programming and networks.
Introduction to algebraic methods in topology. Includes homotopy, the fundamental group, covering spaces, simplicial complexes. Applications to fixed point theory and group theory.
Topics from complex function theory, including contour integration and conformal mapping
Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n
Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series
The measurement and quantification of information. These ideas are applied to the probabilistic analysis of the transmission of information over a channel along which random distortion of the message occurs.
Hypothesis testing, likelihood ratio tests, nonparametric tests, bivariate and multivariate normal distributions
Renewal theory, Poisson processes and continuous time Markov processes, including an introduction to Brownian motion and martingales
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