Course 417-502, Fall 2006

The first day handout is available for download.

Please refer to my personal homepage for contact information.

Homework assignments

1. due 09/08/06
2. due 09/15/06 (extended to 09/18)
3. due 09/22/06
4. due 10/02/06
5. due 10/09/06
6. due 10/16/06
7. due 10/30/06
8. due 11/06/06
9. due 11/13/06
10. due 11/20/06
11. due 12/01/06

Challenges

1. Show that Banach's Fixed-Point Theorem (Parts I and II) actually holds on closed sets, even if unbounded. You cannot use the a priori existence of p in this case, since Brouwer's Fixed-Point Theorem does not hold.
2. Show that all norms are equivalent on Rⁿ. Proceed in two steps: first, show that any norm is a continuous function with respect to the maximum norm. Second, consider this norm on the unit sphere (the sphere for the maximum norm) and apply what you know about continuous functions.