Handbook

The major theme of this Level 3 pure mathematics course is the study of properties of curves and surfaces that are preserved under changes: differentiable changes in differential geometry and continuous changes in topology. Differential geometry is here treated as a continuation of vector calculus studied in earlier courses.

The course begins 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, before progressing to surfaces and how they bend both internally and externally and look at minimal surfaces and geodesics. The course also explores why a map of the earth must be distorted in our study of Gauss’ “Remarkable Theorem” and then study the Gauss-Bonnet Theorem. In the last section, Euler characteristic and the platonic solids, Mobius bands and other surfaces and the study of the elementary combinatorial topology of surfaces is covered. The course culminates in the complete classification of topological surfaces.

Note: Offered in even numbered years only.