Spring 07 Schedules

[MelchyBeau]

MATH 520 Algebra (3) Review and continuation of the study of algebra begun in MATH 470. Covers some of the following: the theory of finite group theory including the Sylow Theorems, polynomial ring, unique factorization, number fields, and finite fields. The latter half of the course will cover field extensions of Galois theory, including the classic theorems on the unsolvability of the general quintic and the impossibility of certain ruler and compass constructions, such as trisecting an angle.

MATH 552 Introduction to Differential Topology and Geometry (3) Introduction to curves, surfaces, and possibly higher dimensional manifolds from the point of view of differential topology and/or differential geometry. Includes some of the following: curves (e.g., Frenet-Serret theorem and its consequences, isoparametric inequality, four-vertex theorem, line integrals, Fenchel's theorem), the topological classification of surfaces, vector fields, curvature on surfaces (leading up to some of the following: geodesics, minimal surfaces, Gauss's Theorema Egregium, and the Gauss-Bonnet theorem), introduction to higher dimensional manifolds, differential forms and integration

and a Seminar Class on Digraphs