Projects

Some basic notions in complex analysis. Topics include analytic functions, complex integration, infinite series, contour integration, and conformal mappings.

Fundamentals of linear algebra and matrix theory are covered. Topics include vectors in Euclidean spaces, solving systems of linear equations, matrix algebra, inverses, determinants, eigenvalues, and eigenvectors. Also vector spaces and the basic notions of span, subspace, linear independence, basis, dimension, linear transformation, kernel and range are considered.

Introduction to analytic and numerical methods for solving differential equations. Topics include numerical methods and qualitative behavior of first order equations, analytic techniques for separable and linear equations, applications to population models and motion problems; techniques for solving higher order linear differential equations with constant coefficients (including undetermined coefficients, reduction of order, and variation of parameters), applications to physical models; the Laplace transform (including intial value problems with discontinuous forcing functions).

An introduction to mathematical logic and proof within the context of discrete structures. Topics include basic mathematical logic, elementary number theory, basic set theory, functions, and relations.