Math 497 will study the geometry and topology of surfaces such as spheres, tori, Klein bottles, cylinders and Mobius strips along with their three dimensional analogs. The text (The Shape of Space by J Weeks) takes as its point of departure a short children's book (Flatland: A Romance of Many Dimensions by E Abbott 1952) which is an attempt to visualize four dimensional space. The text and the course will emphasize visualization of the properties of these objects through many figures as well as games such as asteroids and variations on tic-tac-toe and attempts to picture implications of the topology of our universe. The topics covered will include flat, spherical and hyperbolic geometries and some associated topology such as orientability and the Gauss-Bonnet formula. Students will be encouraged to look at some topic in more detail on their own for a final project.
This course will only require high school mathematics.
For more information send e-mail to < babson@math.washington.edu>.