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
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.