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Why Knot?: An Introduction to the Mathematical Theory of Knots with Tangle

ISBN: 978-0-470-45212-7
62 pages
December 2008, ©2009
Why Knot?: An Introduction to the Mathematical Theory of Knots with Tangle (0470452129) cover image


Those with an interest in knots, both young and old, will enjoy reading Why Knot? An Introduction to the Mathematical Theory of Knots.  Colin Adams, well-known for his advanced research in topology and knot theory, is the author of this new book that brings his findings and his passion for the subject to a more general audience.  Adams also presents a history of knot theory from its early role in chemistry to modern applications such as DNA research, dynamical systems, and fluid mechanics. Real math, unreal fun!

Each copy of Why Knot? is packaged with a plastic manipulative called the Tangle®. Adams uses the Tangle because “you can open it up, tie it in a knot and then close it up again.” The Tangle is the ultimate tool for knot theory because knots are defined in mathematics as being closed on a loop. Readers use the Tangle to complete the experiments throughout the brief volume.

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Table of Contents

Preface iv

Section 1 Introduction 1

Section 2 Mathematical Knots: What Are They? 6

A The Basic Idea 6

B Composition 11

C Crossing Number 16

D Reidemeister Moves 19

E Links 23

F Unknotting Number 31

G How Many Knots Are There? 35

H Denoting Pictures of Knots 40

Section 3 Knots: What Good Are They? 44

A History of Knots 44

B Knotted DNA 45

C Knotted Molecules 47

D Random Knotting 50

Section 4 The Future 52

Appendix 1 Extra Fun 54

Appendix 2 Prime Knots Through 8 Crossings 56

Appendix 3 Prime Links Through 7 Crossings 58

Further Reading 59

Answers to Some Experiments 60

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The Wiley Advantage

  • Humorous tone and friendly format make this book accessible and enjoyable
  • Wide appeal: for higher education undergraduate, gifted high school students, or anyone with an interest in mathematics
  • Modern applications including DNA research, dynamical systems, and fluid mechanics
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