The Differential Geometry of Curves and Surfaces Math 32a 

Course Prospectus

The Breather Pseudospherical
Surface

Math 32a will cover the classical theory of curves in the Euclidean plane and of curves and surfaces in a Euclidean space of three dimensions. However our approach will definitely not be the classical one. Although we will cover the same theoretical ground as found in standard courses and textbooks, in addition to stating and proving theorems in the usual manner, we will also develop an algorithmic approach to the theory. In fact the socalled "Main Theorems" of the subject are in essence completely constructive prescriptions for recreating curves and surfaces from certaun "invariant" curvature data, and the students will be asked to implement these prescriptions as computer algorithms. Richard Palais
