Editorial Reviews:
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 has had a significant impact on statistical mechanics and quantum field theory.
Colin Adams?s The Knot Book is the first book to make cutting-edge research in knot theory accessible to a non-specialist audience. Starting with the simplest knots, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians can now solve, as well as those that remain open. He also explores how knot theory is providing important insights in biology, chemistry, physics, and other fields. The new paperback edition has been updated to include the latest research results, and includes hundreds of illustrations of knots, as well as worked examples, exercises and problems.
With a simple piece of string, an elementary mathematical background, and The Knot Book, anyone can start learning about some of the most advanced ideas in contemporary mathematics.
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
Customer Reviews:
Displaying 1 to 5 of 10 total reviews (Page 1 of 3):
 bonne introduction
Ce livre est une bonne introduction à la théorie des naeuds: panorama impressionnant, il donne envie d'en savoir d'avantage. Je lui enlève une étoile car un certain nombre de dessin sont incompréhensibles.  Good Introduction to Knots
In terms of content, I would rate this book 4-5 stars. However, I rated it three stars because it had a flaw in terms of readibility. If you are willing to devote a lot of time to the subject, and are willing to take the time to work through all of the exercises, then this is the book for you. However, if you are just looking for some light reading on an unusual subject, there is a problem with the book. In many cases, if you don't complete the exercises, your ability to understand what follows in the chapter will be impaired. I bought the book to read on the train, and did not really have the facilities to work through all of the exercises. For me, the book would be greatly improved if solutions to some of the exercises (at least in sketch form) were included as an appendix.
In addition to being a good introduction to knots, the book also covers many othet topics in topology as well. At the end of the book, the author tries to show that there are practical applications to knot theory, but for the most part he appeared to be stretching. It seems that knot theory is pretty close to being "pure" mathematics. One thing that he did miss, however, was the application of knot theory to tying neckties. That would have been really practical!  Written for a non-mathematician but certainly enjoyable by mathematicians!
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. Pretty good introduction
One can make nothing wrong buying this book. It gives an easy introduction, and most parts are well explained. Don't expect to become an expert in knot theory after reading it but at least you are then familiar with the basics. Great introduction to knot theory
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. More Customer Reviews:
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