Georgia Institute of Technology College of Sciences

An introduction to proofs in advanced mathematics, intended as a transition to upper division courses including MATH 4107, 4150 and 4317. Fundamentals of mathematical abstraction including sets, logic, equivalence relations, and functions. Thorough development of the basic proof techniques: direct, contrapositive, existence, contradiction, and induction. Introduction to proofs in analysis and algebra.

Simple random walk and the theory of discrete time Markov chains

Method of characteristics for first and second order partial differential equations, conservation laws and shocks, classification of second order systems and applications.

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

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

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.

Fourier series, Fourier integrals, boundary value problems for partial differential equations, eigenvalue problems

A broad introduction to the local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations.

The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem

Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces