Differential Geometry and Topology of Curves and Surfaces (Math 497C)
Spring 2004, Penn State
|M W F 1:25-2:15 Pond 122
||Th 1:25-2:15 Pond 122
- Professor Mohammad Ghomi
- Robert Yuncken
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.