Differential Geometry and Topology of Curves and Surfaces (Math 497C)
Spring 2004, Penn State

Lecture Problem Session
M W F 1:25-2:15 Pond 122 Th 1:25-2:15 Pond 122
Professor Mohammad Ghomi
Teaching Assistant
Robert Yuncken

Course Description
This is an introduction to the study of curves and surfaces in Euclidean 3-space which lays the foundations for and orients the students towards further study of differential geometry and topology. We will have an object oriented approach and study specific examples with the aid of computers. The main theme of the class will be the concept of curvature, and its relation to the local and global properties of curves and surfaces. In particular, we will cover the four vertex theorem, Fairy-Milnor theorem, Gauss's Theorema Egregium, and the Gauss-Bonnet theorem.

Real analysis (integrals, derivatives, stokes theorem), and basic topology (compactness).

Differential Geometry of Curves and Surfaces, by Manfredo do Carmo.

Modern Differential Geometry of Curves and Surfaces with Mathematica, by Alfred Gray, second edition.

The grade is based on class participation, homework assignments which are due every Friday, a midterm on Tuesday Oct 12, and a final exam. The final exam will consist of an oral part, and the presentation of an independent research project.