Classical introduction to probability theory including expectation, notions of convergence, laws of large numbers, independence, large deviations, conditional expectation, martingales, and Markov chains.

Reading or research in topics of current interest.

Independent research conducted under the guidance of a faculty member.

The Laplace transform and applications, Fourier series, boundary value problems for partial differential equations.

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

An introduction to linear alegbra including eigenvalues and eigenvectors, applications to linear systems, least squares. Credit not awarded for both MATH 1553 and MATH 1522, MATH 1502, MATH 1504, MATH 1512, MATH 1554 or MATH 1564.