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.

Differential and integral calculus in Euclidean spaces. Implicit and inverse function theorems, differential forms and Stokes' theorem. Prerequisites: multivariable calculus, basic real analysis, linear algebra and one of the following: MATH 4310, MATH 4651, MATH 4770, MATH 3315, or instructor permission.

Review of topics from Math 3351: vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth and generality. The course continues with more advanced topics including Jordan canonical forms and introduction to bilinear forms. Prerequisites: a proof-based course and familiarity with computational aspects of elementary linear algebra. Math 3354 is strongly recommended

Structural properties of basic algebraic systems such as groups, rings, and fields. A special emphasis is made on polynomials in one and several variables, including irreducible polynomials, unique factorization, and symmetric polynomials. Time permitting such topics as group representations or algebras over a field may be included. Prerequisites: MATH 3351 or 4651 and MATH 3354 or permission of the instructor.

This course will introduce students to the techniques and methods of mathematical research. Students will independently work with mathematical literature on a topic assigned by the instructor and present their findings in various formats (presentation, paper etc.).

This is the second semester of a two semester sequence for the purpose of the completion of a Distinguished Major Thesis. A faculty member guides the student through all phases of the process which culminates in an open presentation of the thesis to an audience including a faculty evaluation committee. Prerequisite: MATH 4900.

Reading and study programs in areas of interest to individual students. For third- and fourth-years interested in topics not covered in regular courses. Students must obtain a faculty advisor to approve and direct the program.

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).

Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. Prerequisite: MATH 2310, 3351, or instructor permission.

A rigorous program of supervised study designed to expose the student to a particular area of mathematics. Prerequisite: Instructor permission and graduate standing.