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

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