Knot Book

14 customer reviews
ISBN-13: 978-0716723936
ISBN-10: 071672393X
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Hardcover, January, 1994
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Editorial Reviews Review

In February 2001, scientists at the Department of Energy's Los Alamos National Laboratory announced that they had recorded a simple knot untying itself. Crafted from a chain of nickel-plated steel balls connected by thin metal rods, the three-crossing knot stretched, wiggled, and bent its way out of its predicament--a neat trick worthy of an inorganic Houdini, but more than that, a critical discovery in how granular and filamentary materials such as strands of DNA and polymers entangle and enfold themselves.

A knot seems a simple, everyday thing, at least to anyone who wears laced shoes or uses a corded telephone. In the mathematical discipline known as topology, however, knots are anything but simple: at 16 crossings of a "closed curve in space that does not intersect itself anywhere," a knot can take one of 1,388,705 permutations, and more are possible. All this thrills mathematics professor Colin Adams, whose primer offers an engaging if challenging introduction to the mysterious, often unproven, but, he suggests, ultimately knowable nature of knots of all kinds--whether nontrivial, satellite, torus, cable, or hyperbolic. As perhaps befits its subject, Adams's prose is sometimes, well, tangled ("a knot is amphicheiral if it can be deformed through space to the knot obtained by changing every crossing in the projection of the knot to the opposite crossing"), but his book is great fun for puzzle and magic buffs, and a useful reference for students of knot theory and other aspects of higher mathematics. --Gregory McNamee --This text refers to an out of print or unavailable edition of this title.


"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 --This text refers to the Paperback edition.

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Product Details

  • Hardcover: 306 pages
  • Publisher: W.H. Freeman & Company (January 1994)
  • Language: English
  • ISBN-10: 071672393X
  • ISBN-13: 978-0716723936
  • Product Dimensions: 9.5 x 6.4 x 1.1 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #1,202,623 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

41 of 42 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on June 26, 2002
Format: Paperback
Knot theory has been a branch of mathematics that has been around for over a century, and now is finding applications in mnay areas, some of these being electrical circuit analysis, genetics, dynamical systems, and cryptography. This book, written for the layman or the beginning student of mathematics, is an excellent overview of what is known (and not known) in knot theory. Because of the pictorial nature of the subject, knot theory is an excellent way to get people interested in mathematics. Knot theory now is an established branch of mathematics, and it involves the use of tools from topology, analysis, and algebra. The problem of distinguishing one knot from another is one of the major questions in knot theory, and its partial resolution has been assisted by concepts from physics, namely statistical mechanics and quantum field theory. The author discusses the knot recognition problem, and other unsolved problems in the book, and he points out that in knot theory the unsolved problems can be approached by someone with very little background in advanced mathematical techniques. The author does an excellent job of introducing these problems and letting the reader experience, in his words, the joy of doing mathematics.
Chapter 1 is an introduction to the basic terminology of knot theory, and the author gives examples of the most popular elementary knots. He points out the historical origins of the theory, one of these being the attempt by Lord Kelvin to explain the origins of the elements, interestingly. The basic operations on knots are defined, such as composition and factoring, and the famous Reidemeister moves. The proof that planar isotopies and Reidemeister moves suffices to map one projection of a knot to another is omitted.
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27 of 29 people found the following review helpful By A Customer on December 22, 1998
Format: Hardcover Verified Purchase
Well-written, a good introduction to a mathematical research topic that requires only high-school level mathematics as background. Includes good applications to biology and chemistry, and written with a friendly, easy-going style.
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22 of 26 people found the following review helpful By Owen C. Marshall on January 18, 2001
Format: Paperback
I checked this book out of the library on the recommendation of a friend who was taking a knot theory class. While I am comfortable with calculus and differential equations, I have not had much experience with topology or group theory so I was hesitant. She assured me that I would understand the concepts presented there and that it would give a good introduction to the subject.
Wow! Was she ever right! First of all, the book is written in a clear and pleasant conversational style. The author does not hesitate to bring in examples or to show diagrams to clarify an idea. Indeed, with a subject such as knot theory, diagrams are essential! His use of exercises is well justified however, I would say that many laypersons are unfamiliar with proof techniques and thus might have some difficulties with several of those. Algebra is used sparingly at best as Adams prefers to let his words and images convey the ideas.
All in all, I would say that this book does a wonderful job of relating a subject which is at the forefront of mathematics, to the mathematically uninitiated. Hopefully, it will stimulate even further interest.
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6 of 6 people found the following review helpful By Alexander C. Zorach on November 15, 2006
Format: Paperback
This book is aimed at making knot theory accessible to people with little mathematical background, and it does so beautifully. However, the material is not watered down--and there is quite a lot of material in this book, as well as a number of open questions (which are quite difficult). The book starts with basics and seems easy, but it gets into challenging concepts rather quickly. Knot theory is one area of abstract mathematics that is particularly accessible to people with little background and this book works off this assumption quite well. Most importantly, this book is fun--it brings out the fun in the subject, and in mathematics in general!

This book would make excellent reading for anyone who likes puzzles, abstract thought, or novel forms of mathematics. It also would be interesting for mathematicians who want an introduction to knot theory. Someone who wants a more mathematical (but still accessible) treatment might want to check out "Knots and Surfaces" by N. D. Gilbert. In some respects it is a natural follow-up to this book. It is slightly more concise and has more rigorous mathematics in it.
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8 of 10 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on March 8, 2003
Format: Hardcover
Having first been exposed to interesting knots while in undergraduate courses in biology and chemistry and occasionally encountering knots in my mathematical life, I have long maintained a passing interest in the field. However, until now, no single event evoked a reaction strong enough to pique a desire to explore. All it took to change that was the reading of this book by Adams.
Surprisingly complete for an introductory text, it is also amazingly understandable. Requiring only knowledge of polynomials and a mind capable of understanding twists, I found it addictive. This is one area where it pays not to think straight. After reading it twice, I still pick it up and scan it in odd moments. Problems are scattered throughout the book, and many can be solved using only a piece of string. Those that are still unsolved are clearly marked, with is good, since the statements are often very simple.
There are many applications and the number is growing all the time. One of the most profound images and statements of discovery was the pictures of the knotting of the rings of Saturn and commentator Carl Sagan saying, "We don't understand that at all. We will have to invent a whole new branch of physics to understand it." The most esoteric recent explanation of the structure of the universe is the theory of superstrings, where all objects are multi-dimensional knots. A fascinating problem in molecular biology of the gene is the process whereby DNA coils when quiescent and uncoils to be copied. One chapter is devoted to applications, although more would have been helpful.
A non-convoluted introduction to the theory of convolutions, this book belongs in every mathematical library.
Published in Journal of Recreational Mathematics, reprinted with permission.
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