400

Independent study of a selected list of readings approved by a faculty advisor. Permission of department required.

Studies from selected areas of mathematics. Written reports and formal presentations will be required. Senior standing or permission of instructor required.

Students are partitioned into small groups and given problems from the Mathematical Contest in Modeling, or similar material, to work on together. Written reports and formal presentations will be required. Departmental approval required.

Selected readings, discussions, and reports on topics in mathematics. Permission of department required.

Vector calculus; Jacobian matrices and their determinants; differentiation and integration of differential forms and applications to physics; generalizations of the fundamental theorem of calculus, including Green's theorem, the divergence theorem, Gauss's theorem, and Stokes' theorem; potential theory.

Topics vary, depending on the instructor, but may include measure and integration, basic functional analysis, complex analysis, residue theory, and special functions.

Introduction to graph theory. Topics chosen from: connectivity, trees, eulerian and hamiltonian graphs, matchings, factorizations, and colorings. Applications chosen from: the shortest path problem, communication networks, the traveling salesman problem, the optimal assignment problem, and scheduling algorithms.

The capstone course in the Honors Program in Mathematics. Each student will conduct research under the mentorship of a faculty member, culminating in a written thesis and an oral presentation. This course is by invitation only.