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Open Algebra and Knots

Nguồn ngoài

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?

Tác giả
Matthew Salomone
Nhà xuất bản
Bridgewater State University
Nguồn
LibreTexts
Giấy phép
GNU FDL
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Mục lục· 18 mục
  1. 01: Rational Tangles
  2. 1.01: Tangle Basics
  3. 1.02: Tangle Arithmetic
  4. 02: Knots and Numbers
  5. 2.01: Notations for Knots
  6. 2.02: Numerical Knot Invariants
  7. 2.03: Colorings of Knots
  8. 2.04: Colorings of Tangles
  9. 03: Knots and Algebra
  10. 3.01: Algebraic Structures
  11. 3.02: Colorings and Quandles
  12. 3.03: Knot Groups
  13. 3.04: Invariant Polynomials
  14. 3.05: Portfolio Problems
  15. 04: Workshop Project
  16. 4.01: Project Overview
  17. 05: Knot Your Average Algebra
  18. 5.01: Seminar Videos