MATH 321
Knot Theory Spring 2024
Division III Quantitative/Formal Reasoning

Take a piece of string, tie a knot in it, and glue the ends together. The result is a knotted circle, known as a knot. For the last 100 years, mathematicians have studied knots, asking such questions as, “Given a nasty tangled knot, how do you tell if it can be untangled without cutting it open?” Some of the most interesting advances in knot theory have occurred in the last ten years.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 relationships between knot theory and chemistry and physics. In addition to learning the theory, we will look at open problems in the field.