The Knot Book by Colin Adams (PDF)

Description

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”.

User’s Reviews

Editorial Reviews: Review “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 About 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a very thorough and almost always easy to follow presentation of knot theory with lots of applications to think about. I think occasionally, Adams is a little blase in his writing, but all-in-all, a great book![edit] Having gotten much further along in the book, I will mention that as a person who is mostly blind, I did not find all of the diagrams visually accessible. In particular, the author tries to be “realistic” with some of the closed braid representations, drawing the crossings very close together. This made it more difficult than necessary to work some of the exercises based on these diagrams.

⭐Knots have been used for thousands of years in a nautical sense and even longer in textiles, toys and games, clothing/sewing, hair styling, jewelry, and weaponry. One of my favorites was playing cat’s cradle with my parents and my friends growing up, we had fun seeing what knots we could make. This book does a poor job of giving credit to where the mathematics is being pulled from. Though, the field is comparatively young in mathematics so maybe one day credit will be given where it is due. A good book for thinking of knots in abstraction and introducing how some use knots in mathematics. I appreciate that the author at least addressed that knots are not of mathematical origins, he is far ahead of many in the field who try to erase the cultural significance of knots or try to rewrite them in terms of their own mathematics.

⭐Knots inherently need to be visualized to be understood and this book comes with so many gorgeous visualizations. It made me confident that Knot Theory could be an excellent way to teach abstract algebra to kids and introduce them to deep ideas like symmetry.Even if you don’t have an immediate use case for knots, the book also fares well as a coffee book since you can always open up a random page, look at a pretty knot, and contemplate their beauty for a few moments before you move on with the rest of your day.

⭐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!

⭐I purchased this book as the textbook for a senior-level mathematics course in my undergrad. However, this book does not “read like a textbook.” This book has been one of the easiest reads in a mathematics-heavy book I have ever had the pleasure of laying my eyes on. The pictures are clear, the words are concise, the ideas are organized logically and in proper order such that ideas are clearly described and explained in a manner that you don’t have to be a mathematics major to understand what is being talked about.While I purchased this book as a necessity for my coursework, if you have any kind of interest in mathematics (or just logic/puzzle games) the book is extremely interesting and you will learn A LOT.Highly recommended. Very well-done book, especially for a topic as “obscure” as knot theory.

⭐Readers of the 1994 first edition of this book (published by W. H. Freeman and Company), or its “Second printing” also dated 1994, should check page 119 to see if, in their copy, hyperbolic knots were discovered in 1974 or 1977. The author makes no mention of this and other corrections.

⭐This book is written very well. I use this book in conjunction with more formal Knot Theory books. The writing is simpler and easier to understand than the more technical books. It has been very useful in helping me understand simple concepts needed to do my research.

⭐This a really great book. It has everything needed for doing a Course in Knot Theory just by your own. It contains all level exercises from the bare beginner to the open questions in the field. If you love Math, I pretty sure you’ll enjoy this book pretty much.

⭐I bought this book following on from an undergraduate topology course in which I enjoyed the geometric topology, and knot theory seemed a reasonable next step. It really is a basic introduction to the topic – I now have a good idea about the various ways to describe knots and determine if 2 knots are the same, and I know the difference between knots, links and braids.It is fairly well written, but at times seems a bit disconnected. It certainly gave me what I wanted on the subject without either being too basic or too technical.The title of my review? The cover of the book, if you miss out the subtitle, looks just like the sort of thing you might buy for a budding ship’s captain so he can rig his sails properly. It isn’t.

⭐ideal follow on to Sossinsky’s Knotsexpands on this primerclear and helpful diagramsrecommended

⭐Quick delievery. Recieved what was expected.

⭐This elementary introduction of knot theory is widely referenced in the academic literature. The author works hard to make basic ideas behind knot theory accessible. Knot theory has developed extensively since this text was first pubished are many important devlopments are not addressed. However, as was no doubt intended, it remains a very helpful guide to fundamental aspects of knot theory. The exercises are well worth exploring. A useful text still.

⭐Un libro muy ameno, de lectura cómoda y con el que se aprende mucho sobre teoría de nudos.

⭐

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