Handbook

This major theme of this course is the study of properties of curves and surfaces that are preserved under changes: differentiable changes in differential geometry and continuous changes intopology. The differential geometry is treated as a continuation of vector calculus studied in earlier courses.

We begin with the study of curves in the plane and analyse what it means to be curved rather than straight, and then cover curves in space and how they curve and twist. We progresses to surfaces and how they bend both internally and externally and look at minimal surfaces and geodesics. We show why a map of the earth must be distorted in our study of Gauss' "Remarkable Theorem" and then cover the Gauss-Bonnet Theorem. In the last section, we cover the Euler characteristic and the platonic solids, Mobius bands and other surfaces and study the elementary combinatorial topology of surfaces. The course culminates in the complete classification of topological surfaces..

Note: Offered in even numbered years only.