Georgia Institute of Technology College of Sciences

This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.

Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.

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

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.