A second course in ordinary differential equations, from the dynamical systems point of view. Topics include: existence and uniqueness theorems; linear systems; qualitative study of equilibria and attractors; bifurcation theory; introduction to chaotic systems. Further topics as chosen by the instructor. Applications drawn from physics, biology, and engineering. Prerequisites: MATH 3351 or APMA 3080 and MATH 3310 or MATH 4310.

Topics include the fundamental group, covering spaces, covering transformations, the universal covering spaces, graphs and subgroups of free groups, and the fundamental groups of surfaces. Additional topics will be from homology, including chain complexes, simplicial and singular homology, exact sequences and excision, cellular homology, and classical applications. Prerequisite: MATH 5352, 5770, or equivalent.

Introduces measure and integration theory. Prerequisite: MATH 5310 or equivalent.

Topics include smooth manifolds and functions, tangent bundles and vector fields, embeddings, immersions, transversality, regular values, critical points, degree of maps, differential forms, de Rham cohomology, and connections. Prerequisite: MATH 5310, 5770, or equivalent.

Development of mathematical models and their solutions, including linear programming, the simplex algorithm, dual programming, parametric programming, integer programming, transportation models, assignment models, and network analysis. Prerequisites: MATH 1320, 3351 and a proof-based course (3000, 3310 or 3354).

Studies the fundamental theorems of analytic function theory.

Covers the material from Math 2310 (multivariable calculus) plus topics from complex numbers, set theory, and linear algebra. Prepares students for taking advanced mathematics classes at an early stage. Credit is not given for both Math 2310 and Math 2315.

This course is a continuation of MATH 2315. Covers topics from linear algebra/differential equations/real analysis. Success in this course and MATH 2315 (grades of B- or higher) exempts the student from the math major requirement of taking MATH 3351 and MATH 3250. Students are encouraged to take more advanced courses in these areas. Prerequisite: MATH 2315.

Includes Taylor's theorem, solution of nonlinear equations, interpolation and approximation by polynomials, numerical quadrature. May also cover numerical solutions of ordinary differential equations, Fourier series, or least-square approximation. Prerequisite: MATH 3250 and computer proficiency.

Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.