The Knot Book 1st edition by Colin Adams- Ebook PDF Instant Download/Delivery: 1470424909 , 9781470424909
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ISBN 10: 1470424909
ISBN 13: 9781470424909
Author: Colin Adams
Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. The Knot Book is an introduction to this rich theory, starting from our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research. The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in The Knot Book.
The Knot Book 1st Table of contents:
Chapter 1 Introduction
1.1 Introduction
1.2 Composition of Knots
1.3 Reidemeister Moves
1.4 Links
1.5 Tricolorability
1.6 Knots and Sticks
Chapter 2 Tabulating Knots
2.1 History of Knot Tabulation
2.2 The Dowker Notation for Knots
2.3 Conway’s Notation
2.4 Knots and Planar Graphs
Chapter 3 Invariants of Knots
3.1 Unknotting Number
3.2 Bridge Number
3.3 Crossing Number
Chapter 4 Surfaces and Knots
4.1 Surfaces without Boundary
4.2 Surfaces with Boundary
4.3 Genus and Seifert Surfaces
Chapter 5 Types of Knots
5.1 Torus Knots
5.2 Satellite Knots
5.3 Hyperbolic Knots
5.4 Braids
5.5 Almost Alternating Knots
Chapter 6 Polynomials
6.1 The Bracket Polynomial and the Jones Polynomial
6.2 Polynomials of Alternating Knots
6.3 The Alexander and HOMFLY Polynomials
6.4 Amphicheirality
Chapter 7 Biology, Chemistry and Physics
7.1 DNA
7.2 Synthesis of Knotted Molecules
7.3 Chirality of Molecules
7.4 Statistical Mechanics and Knots
Chapter 8 Knots, Links, and Graphs
8.1 Links in Graphs
8.2 Knots in Graphs
8.3 Polynomials of Graphs
Chapter 9 Topology
9.1 Knot Complements and Three-Manifolds
9.2 The Three-Sphere and Lens Spaces
9.3 The Poincaré Conjecture, Dehn Surgery, and the Gordon–Luecke Theorem
Chapter 10 Higher Dimensional Knotting
10.1 Picturing Four Dimensions
10.2 Knotted Spheres in Four Dimensions
10.3 Knotted Three-Spheres in Five-Space
Knot Jokes and Pastimes
Appendix: Table of Knots, Links, and Knot and Link Invariants
Suggested Readings and References
Index
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