Georgia Institute of Technology College of Sciences

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

Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series

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

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

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

The fundamentals of graph theory: trees, connectivity, Euler torus, Hamilton cycles, matchings, colorings and Ramsey theory.

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

MATH 3215, MATH 3235, MATH 3670, and MATH 3740 are mutually exclusive; students may not hold credit for more than one of these courses.