## Mathematics 197S, Fall 2007

### Introduction to Knot Theory (Seminar
in Topology)

Instructor: Lenny Ng

E-mail: ng AT math.duke.edu

Office: Physics 231

Office phone: 919-660-6972

Office hours: Tuesdays 3-4 pm, Wednesdays 11:30 am - 12:30 pm

Textbook: *The Knot Book: An Elementary Introduction to the Mathematical
Theory of Knots*, by Colin C. Adams

Course meeting time and place: TuTh 11:40am - 12:55pm, Physics 119

Handouts:

**Please go to Blackboard for assignments and other handouts.**

Here's
the course synopsis (mainly repeating the information in the syllabus):

**Prerequisites:** Some familiarity with basic topology (e.g.,
fundamental groups) and algebra (group theory) helpful but not absolutely
necessary. The level of the course may depend on the background of the
students.

**Synopsis of course content:** The mathematical theory of knots --
closed loops in space that can be deformed but not broken -- is a central
part of modern-day geometry, and touches beautifully on such disparate
subjects as topology, combinatorics, and algebra.

This course is an introduction to knot theory, with an emphasis on
combinatorial and geometric aspects. We will explore methods to draw and
relate knots; knot invariants such as colorability, the Alexander
polynomial, and the Jones polynomial; special types of knots such as torus
knots and alternating knots; relations with the theory of braids;
connections with biology, chemistry, and physics; and the significance of
knots in geometry and topology. Prerequisites will hopefully be kept to a
minimum.

**Assignments:** periodic homework sets; no exams; each student will
do a project, writing a short paper and making an in-class presentation
explaining their project to the class.