Georgia Institute of Technology College of Sciences

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

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

This course includes topics on professional development and responsible conduct of research. The course satisfies the GT RCR Academic Policy for Doctoral Students to complete in-person RCR training.

Spectral theory of bounded and unbounded operators, major theorems of functional analysis, additional topics.

Fourier analysis on the torus and Euclidean space.

Lebesgue measure and integration, differentiation, abstract measure theory.

This course is equivalent to MATH 6579. Students should not be able to obtain credit for both MATH 6579 and MATH 6337.