Fall Quarter 2001

Tuesdays and Thursdays, 3:10 - 4:30

Text: "What is Mathematics?" by R. Courant and H. Robbins, $13.96 at the following place: Amazon.com

Office Hours: Whenever you find me in my office.

Course Description: Every educator has to understand what "understanding" means. Whenever we try to help a student who is struggling to understand a mathematical concept, as we know very well, teaching and lecturing never works. To become a better teacher, we have to know what's going on in the student's brain so that we can help the process of understanding take place.

I think the best way to know what understanding is is to go through and experience the important transition from not understanding to understanding yourself. You can then analyze what happened to you when the transition takes place in your own brain.

For this purpose, I will use "discrete group actions on the 2- dimensional hyperbolic space" as our subject. Of course you don't understand what it means now. But you will, I hope, at the end of the quarter.

If you look at the text I chose, you will never find anything related to the subject I mentioned above. You are puzzled. And yes, the journey to understanding the understanding starts now!

Prerequisite: Knowledge from the undergraduate mathematics courses such as MAT 108, 127AB, and 149AB or 150AB, (or their equivalent) is desirable, but not required for the understanding of the material to be covered.

Topics discussed: Geometric construction, cell-decomposition of Riemann surfaces, mechanical linkage, map coloring, and discrete groups.

Course grade: Every student taking the course for credit will be required to give a 30 minutes presentation at the end of the quarter. The course grade will be based on your performance of the presentation and the attendance of the course/laboratory.