Georgia Institute of Technology College of Sciences

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

Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices.

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

Continuation of Abstract Algebra I, with emphasis on Galois theory, modules, polynomial fields, and the theory of linear associative algebra.

Combinatorial problem-solving techniques including the use of generating functions, recurrence relations, Polya theory, combinatorial designs, Ramsey theory, matroids, and asymptotic analysis.

This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.