Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors). ETSU does not have a formal graduate class on knot theory, but these notes may be used in an Independent Study (MATH 5900).

Notes are available for a less rigorous class in knot theory. See my online page for Introduction to Knot Theory Class Notes based on Charles Livingston's Knot Theory, The Carus Mathematical Monographs, Volume 24 (MAA, 1993).

Part I. A Short Course of Knots and Physics

1. Physical Knots
2. Diagrams and Moves
3. States and the Bracket Polynomial
4. Alternating Links and Checkerboard Surfaces
5. The Jones Polynomial and its Generalizations
6. An Oriented State Model for V_K(t)
7. Braids and the Jones Polynomial
8. Abstract Tensors and the Yang-Baxter Equation
9. Formal Feynman Diagrams, Bracket as aVacuum-Vacuum Expectation and the Quantum Group SL(2)q
10. The Form of the Universal R-matrix
11. Yang-Baxter Models for Specializations of the Homfly Polynomial
12. The Alexander Polynomial
13. Knot-Crystals - Classical Knot Theory in a Modern Guise
14. The Kauffman Polynomial
15. Oriented Models and Piecewise Linear Models
16. Three Manifold Invariants from the Jones Polynomial
17. Integral Heuristics and Witten's Invariants
18. Appendix - Solutions ot hte Yang-Baxter Equation

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