## Stephen Bean

### 2003-04 Courses

#### MAT 110: On the Shoulders of Giants: Great Mathematical Ideas

In 2003-04, the Math Dept. will begin offering Math 110, a new option for completing the Mathematics requirement at Cornell. The content of this course will vary depending on the instructor. Since I am going to be the first instructor for the course in Block 9 of 2004, I thought I'd better try to tell you a little bit about what I am planning.

We will be working from an American Mathematical Society monograph text entitled "Knots and Surfaces: A Guide to Discovering Mathematics" , by David Farmer and Theodore Standford. As the title suggests, the object is to have students study examples and make and prove conjectures about general patterns. The subject matter is highly visual in nature, so might not appeal to some students. It begins with the study of networks and graphs. These are just patterns of links between points (a.k.a. vertices or nodes). They look a little like a failed attempt at "connect the dots".

If you would like a sample of the kind of "graphs" we might be looking at, here's a sample of the kind of problem we would be tackling in the first week of class.

From there, the course will move on to show how we can use the results we discover from graphs to distinguish between different surfaces like a sphere or a doughnut. If you're thinking that you have no trouble doing that, you're right, because you can see the surface from the outside. But try imagining that you are living on the surface itself. You're not allowed to fly above it or burrow into it. After all, aren't we all 3-D creatures who wonder about the geometric properties of our universe? (Well, we're all 3-D creatures anyway). We can't experience anything like a viewpoint from "above" or "under" that universe. We must answer those questions from within it.

It's somewhat doubtful, given the time frame of the block plan, that the Math 110 course will actually get to the Chapter in the text on knots themselves. But we can always try.

 Contact Information Mailing Address Stephen Bean Box 2227 Cornell College 810 Commons Circle Mt. Vernon, IA  52314 Phone (319) 895-4127 E-Mail sbean@cornellcollege.edu Fax (319) 895-4478