Georgia Institute of Technology College of Sciences

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

Topics from complex function theory, including contour integration and conformal mapping

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.

Sampling distributions, Normal, t, chi-square and F distributions. Moment generating function methods, Bayesian estimation and introduction to hypothesis testing

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.

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