Open Algebra and Knots

by Matthew Salomone

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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?

Description from LibreTexts.

Publisher
Bridgewater State University
Subjects
Mathematics, Abstract and Geometric Algebra
Licence
GNU Free Documentation License, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Rational Tangles
  7. 1.1: Tangle Basics
  8. 1.2: Tangle Arithmetic
  9. 2: Knots and Numbers
  10. 2.1: Notations for Knots
  11. 2.2: Numerical Knot Invariants
  12. 2.3: Colorings of Knots
  13. 2.4: Colorings of Tangles
  14. 3: Knots and Algebra
  15. 3.1: Algebraic Structures
  16. 3.2: Colorings and Quandles
  17. 3.3: Knot Groups
  18. 3.4: Invariant Polynomials
  19. 3.5: Portfolio Problems
  20. 4: Workshop Project
  21. 4.1: Project Overview
  22. 5: Knot Your Average Algebra
  23. 5.1: Seminar Videos
  24. Back Matter
  25. Index
  26. GNU Free Documentation License
  27. Student Blogs
  28. Detailed Licensing