Knot Book: An Elementary Introduction to the Mathematical Theory of Knots

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Over a century old, knot theory is today one of the most active areas of modern mathematics. The study of knots has led to important applications in DNA research and the synthesis of new molecules. And it is having a significant impact on statistical mechanics and quantum field theory. Many of the problems discussed in knot theory, including those treated here, can be understood with only a background of high school algebra and can be solved by the curious amateur. All you need to begin is a piece of string, a ...
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Overview

Over a century old, knot theory is today one of the most active areas of modern mathematics. The study of knots has led to important applications in DNA research and the synthesis of new molecules. And it is having a significant impact on statistical mechanics and quantum field theory. Many of the problems discussed in knot theory, including those treated here, can be understood with only a background of high school algebra and can be solved by the curious amateur. All you need to begin is a piece of string, a little math, a little imagination, and Colin Adams's The Knot Book - the first book to make cutting-edge research in knot theory accessible to a nonspecialist audience. What are the different properties and classifications of knots? How do you determine whether a knot is actually knotted or can be untangled? What is the appropriate measure of the complexity of a knot? What does knot theory research offer to other sciences? In The Knot Book Colin Adams describes and illustrates the work being done to answer these questions. Starting with the simplest knot the trivial knot or unknot, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians now can solve, as well as those that remain open. He also looks at how knot theory is providing important insights in biology, chemistry, physics, and other fields. Included are hundreds of illustrations of knots including a table at the end of the book displaying nearly 200 different knots as well as worked examples, exercises open problems - even a few knot jokes and pastimes. Colin Adams explains knot theory with an enthusiasm and an informal style that makes this seemingly mysterious subject easy to approach. With The Knot Book and a mathematical background that includes no more than a familiarity with polynomials, you will be able to understand and work with some of the discipline's most modern and provocative ideas.
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Editorial Reviews

Booknews
For the nonspecialist seeking the advanced merit badge, addresses such questions as the properties and types of knots, distinguishing between a true knot and a mere tangle, and measuring a knot's complexity. The emerging branch of mathematics dealing with knots is finding applications in DNA research and synthesizing new molecules, and is providing some interesting puzzles for statistical mechanics and quantum field theory. Does not cover knotholes. Illustrates nearly 200 knots. Annotation c. Book News, Inc., Portland, OR booknews.com
From the Publisher
"Adams is an expert in knot theory, and this shows in the clarity and accuracy of his writing, and in the rich store of examples and problems . . . We are going to see much more of knot theory and its applications, and this book is an excellent place to start." —Nature
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Product Details

  • ISBN-13: 9780716723936
  • Publisher: Freeman, W. H. & Company
  • Publication date: 3/28/1994
  • Pages: 302
  • Product dimensions: 6.40 (w) x 9.53 (h) x 1.06 (d)

Meet the Author

Colin Adams is Professor of Mathematics at Williams College. He is one of the world’s leading researchers of knot theory and has published widely on this and other mathematical topics. He is the co-author of How to Ace Calculus and winner of the Mathematical Association of America Distinguished Teaching Award for 1998.

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Table of Contents

Preface
Ch. 1 Introduction 1
Ch. 2 Tabulating Knots 31
Ch. 3 Invariants of Knots 57
Ch. 4 Surfaces and Knots 71
Ch. 5 Types of Knots 107
Ch. 6 Polynomials 147
Ch. 7 Biology, Chemistry, and Physics 181
Ch. 8 Knots, Links, and Graphs 215
Ch. 9 Topology 243
Ch. 10 Higher Dimensional Knotting 265
Knot Jokes and Pastimes 276
Appendix: Table of Knots, Links, and Knot and Link Invariants 279
Suggested Readings and References 291
Index 303
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