Math 307, Topology
Not offered in 2005-2006
Alternates with Math 309

 Topology deals with the properties of an object that no amount of bending, twisting, stretching, or shrinking can change (unlike geometry, which deals with the rigid properties of objects, such as length and angles). Take a piece of string, tie a knot in it, and glue the ends together. The result is a knot. Knot theory is a branch of topology that deals with knots and links in three-dimensional space.

• Given a knot, how do you decide if it can be untangled?
• Given two knots, how do you decide if one can be made to look like the other, using only bending, twisting, stretching, or shrinking?

The study of knots is over 100 years old, and some of the most exciting results have occurred in the last ten years. Knot theory has evolved from an area in "pure" mathematics to include applications in molecular biology, chemistry, fluid dynamics, and quantum mechanics. This course is an introduction to the theory of knots. Among other topics, we will cover methods of knot tabulation, surfaces applied to knots, polynomials associated to knots, and applications of knot theory. In addition to learning the theory, we will look at open problems in the field.

Math 307 counts toward the mathematics major/minor as a 300-level elective. Majors could fulfill the major presentation requirment in this course in 2004-05.

Prerequisite: 302.
Distribution: Mathematical Modeling
Not offered in 2005-06.

• Megan Kerr mkerr@wellesley.edu
• Department of Mathematics
• Date Created: October 26, 1994
• Last Modified: June 28, 2005
• Expires: June 30, 2006