Georgia Institute of Technology College of Sciences

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.

Elementary combinatorial techniques used in discrete problem solving: counting methods, solving linear recurrences, graph and network models, related algorithms, and combinatorial designs.

Theory of linear operators on Hilbert space; spectral theory of bounded and unbounded operators; applications

An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. (2nd of two courses in sequence)