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The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
 
Colin C. Adams Williams College, Williamstown, MA
Front Cover for The Knot Book
Available Formats:
Softcover ISBN: 978-0-8218-3678-1
Product Code: KNOT
List Price: $37.00
MAA Member Price: $33.30
AMS Member Price: $29.60
Electronic ISBN: 978-1-4704-2490-9
Product Code: KNOT.E
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $27.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $55.50
MAA Member Price: $49.95
AMS Member Price: $44.40
Front Cover for The Knot Book
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  • Front Cover for The Knot Book
  • Back Cover for The Knot Book
The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
Colin C. Adams Williams College, Williamstown, MA
Available Formats:
Softcover ISBN:  978-0-8218-3678-1
Product Code:  KNOT
List Price: $37.00
MAA Member Price: $33.30
AMS Member Price: $29.60
Electronic ISBN:  978-1-4704-2490-9
Product Code:  KNOT.E
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $27.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $55.50
MAA Member Price: $49.95
AMS Member Price: $44.40
  • Book Details
     
     
    2004; 307 pp
    MSC: Primary 57;

    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 with 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.

    Colin Adams received the Mathematical Association of America (MAA) Award for Distinguished Teaching and has been an MAA Polya Lecturer and a Sigma Xi Distinguished Lecturer.

    Other key books of interest available from the AMS are Knots and Links and The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes.

    Readership

    Undergraduates, graduate students, and research mathematicians interested in topology and knot theory.

  • Table of Contents
     
     
    • Front Cover
    • Contents
    • Preface
    • 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
    • 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 Poincare 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
    • Jokes
    • Pastimes
    • Appendix
    • Table of Knots, Links, and Knot and Link Invariants
    • Suggested Readings and References
    • Index
    • Corrections to the 2004 AMS Printing
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     
    • From reviews of the first edition:

      Amazingly understandable … After reading it twice, I still pick it up and scan it … this book belongs in every mathematical library.

      Charles Ashbacher, Book Reviews Editor, Journal of Recreational Mathematics
    • Throughout the book there are lots of exercises of various degrees of difficulty. Many 'unsolved questions' provide opportunity for further research. I liked reading this book. ... well written, enjoyable to read, and very accessible.

      Zentralblatt MATH
    • I thought the book was very well suited for an undergraduate knot theory/ topology course. The exposition was very clear.

      Jennifer Taback, Bowdoin College
  • Request Exam/Desk Copy
  • Request Review Copy
  • Get Permissions
2004; 307 pp
MSC: Primary 57;

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 with 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.

Colin Adams received the Mathematical Association of America (MAA) Award for Distinguished Teaching and has been an MAA Polya Lecturer and a Sigma Xi Distinguished Lecturer.

Other key books of interest available from the AMS are Knots and Links and The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes.

Readership

Undergraduates, graduate students, and research mathematicians interested in topology and knot theory.

  • Front Cover
  • Contents
  • Preface
  • 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
  • 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 Poincare 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
  • Jokes
  • Pastimes
  • Appendix
  • Table of Knots, Links, and Knot and Link Invariants
  • Suggested Readings and References
  • Index
  • Corrections to the 2004 AMS Printing
  • Back Cover
  • From reviews of the first edition:

    Amazingly understandable … After reading it twice, I still pick it up and scan it … this book belongs in every mathematical library.

    Charles Ashbacher, Book Reviews Editor, Journal of Recreational Mathematics
  • Throughout the book there are lots of exercises of various degrees of difficulty. Many 'unsolved questions' provide opportunity for further research. I liked reading this book. ... well written, enjoyable to read, and very accessible.

    Zentralblatt MATH
  • I thought the book was very well suited for an undergraduate knot theory/ topology course. The exposition was very clear.

    Jennifer Taback, Bowdoin College
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