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MATH 444

Introduction to Knot Theory

Catalog2026-2027
Credits3 units
LevelUpper Division
Standard

Overview

Description

Knot Theory is the study of knots and links in 3-space. It is a fundamental part of low-dimensional topology, but knots have found applications in biology, chemistry, physics and beyond. The classification of knots is the theory’s main goal, a hard and unsolved problem, chiefly studied by means of knot invariants. This class is an introduction to knot theory, and will present many examples of knots, and study a host of knot invariants: The Alexander and Jones polynomials, knot genera, etc.

Requirements

Prerequisites

MATH 330

Corequisites

MATH 331
Original catalog text

Prerequisites

Prerequisite(s): MATH 330.

Corequisites

Corequisite(s): MATH 331

Units

Lecture3

Catalog Details

Offering

Offered: Every Fall - Odd Years

Terms

fall

Attributes

Standard

Learning Outcomes

  • calculate the Alexander-Conway, Jones and HOMFLYPT polynomial of a knot/link using skein relations.
  • describe and classify the certain families of knots, such as torus knots and twist knots.
  • use a Seifert surface of a knot/link to compute its signature, determinant and linking form.