Co-sponsored by Chautauqua Programs

For the faculty members whose main focus is teaching undergraduate students, PCMI offers the opportunity to renew excitement about mathematics, talk with peers about new teaching approaches, address some challenging research questions, and interact with the broader mathematical community. Each year the theme of the UFP bridges the research and education themes of the Summer Session.

Knot Theory

Colin Adams, Williams College

In this UFP program, participants will learn how to teach an undergraduate course in knot theory, how to do research in knot theory and how to direct student research in knot theory. We will also see knot theory in the broader context of low dimensional topology, allowing for interaction with the other PCMI participants.

Knot theory is a great topic for exciting students about mathematics. It is visual and hands on.  Students can begin working on problems the first day with their shoelaces. Knot theory is also an incredibly active field. There is a tremendous amount of work going on currently, and one can easily state open problems. It also has important applications to chemistry, biochemistry and physics.

This workshop is aimed at undergraduate teachers who are interested in knowing more about knot theory and the broader context of low dimensional topology. The goals of the workshop are as follows:

1. Participants will be able to teach an undergraduate course in knot theory.

2. Participants will be able to do research in knot theory.

3. Participants will be able to direct student research in knot theory.

4. Participants will be able to add knot theory topics to other courses they teach.

5. Participants will be able to give expository talks about this fascinating field.

Each day will consist of two sessions. The first hour will be devoted to learning about specific topics in knot theory and low dimensional topology. These will include various types of knots, knot tabulation, various invariants associated to knots, questions related to stick knots and constructing knots at the molecular level and knot complements and the surfaces they contain.

The second hour will be when we conjecture wildly, throw around ideas, and do original research. We will also use this slot to talk about issues related to teaching this  and other material, including topics such as math as performance art, and humor in mathematics.

The Coordinator of PCMI's Undergraduate Faculty Program isDaniel Goroff, Dean of Faculty at Harvey Mudd College, and Co-coordinator is William Barker, Bowdoin College.