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Open Algebra and Knots
The theory of knots has been well studied since the early 20th century, and has many connections to geometry and topology, and applications to physics, biology, and beyond. We’ll investigate perhaps its most fundamental connection: to algebra. In what ways are knots algebraic objects? How can we use algebraic structures and reasoning to classify knots? And how can this help us to think algebraically beyond the classroom?
- Author
- Matthew Salomone
- Publisher
- Bridgewater State University
- Source
- LibreTexts
- License
- GNU FDL
- Language
- EN
- Category
- Basic Sciences
Contents· 18 sections
- 01: Rational Tangles
- 1.01: Tangle Basics
- 1.02: Tangle Arithmetic
- 02: Knots and Numbers
- 2.01: Notations for Knots
- 2.02: Numerical Knot Invariants
- 2.03: Colorings of Knots
- 2.04: Colorings of Tangles
- 03: Knots and Algebra
- 3.01: Algebraic Structures
- 3.02: Colorings and Quandles
- 3.03: Knot Groups
- 3.04: Invariant Polynomials
- 3.05: Portfolio Problems
- 04: Workshop Project
- 4.01: Project Overview
- 05: Knot Your Average Algebra
- 5.01: Seminar Videos