WISE 187 Spring 2002

Module I
Curves and Surfaces


January 29 - February 14
We are going to explore the world of curves and surfaces. By concrete constructions, the students will discover fundamental characteristics such as orientability, genus, boundary components. We will see how two surfaces with "enough" common characteristics can be deformed one into the other.

A word in a certain alphabet will tell us how to glue the edges of a paper polygon to make a surface. Moreover, this word will provide us with a great deal of information about how two curves (or strings) intersect on this surface.

During the course, we will get familiar with a C++ program that computes this information about the intersection of curves on a surface. Students with computer science background can take on the challenge of designing new programs of this kind.

We will see how all these concepts are used in some of the recent discoveries in mathematics.