Introduction to Differential Topology and Geometry

Catalog description

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, isoperimetric inequality, four-vertex theorem, line integrals, Fenchel’s Theorem); the topological classification of surfaces, vector fields, and curvature on surfaces (leading up to some of the following: geodesics, minimal surfaces, Gauss’s theorema egregium, and the Gauss-Bonnet Theorem); and introduction to higher dimensional manifolds, differential forms, and integration (possibly including Stokes’ Theorem and global invariants such as the Euler characteristic and de Rham cohomology). Enrollment Requirement(s): MATH 260 . Prerequisite(s): for undergraduates and Enrollment Requirement for graduate students: MATH 430 , and either MATH 364 or MATH 374 , all with a grade of C (2.0) or better.