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1. An Introduction to Knot Theory (Graduate Texts in Mathematics) by W.B.Raymond Lickorish | |
Hardcover: 220
Pages
(1997-10-03)
list price: US$79.95 -- used & new: US$53.90 (price subject to change: see help) Asin: 038798254X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Thorough and intriguing |
2. Knot Theory by Vassily Manturov | |
Hardcover: 416
Pages
(2004-02-24)
list price: US$109.95 -- used & new: US$87.96 (price subject to change: see help) Asin: 0415310016 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Best of Knots |
3. Why Knot?: An Introduction to the Mathematical Theory of Knots by Colin Adams | |
Paperback: 62
Pages
(2004-03-29)
list price: US$29.95 Isbn: 1931914222 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
A complete introduction to an area of math that is neglected. That is unfortunate, as it is easily demonstrated |
4. Knot Theory (Mathematical Association of America Textbooks) by Charles Livingston | |
Hardcover: 258
Pages
(1996-09-05)
list price: US$49.95 -- used & new: US$43.95 (price subject to change: see help) Asin: 0883850273 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (5)
As good as it gets in introducing knot theory
Fun, yet brief at times
Excellent!
Good for an introduction Prequisites are a bare minimum:some linear algebra and a course in modern algebra should suffice, though a first geometrically oriented topology course (e. g., a course out of Armstrong, or Guillemin/Pollack) would be helpful. Many different aspects of knot theory are touched on, including some of the polynomial invariants, knot groups, Alexander polynomial and related abelian invariants, as well as some of the more geometric invariants. This book would serve as a nice complement to C. Adams "Knot Book" in that Livingston covers fewer topics, but goes into more mathematical detail. Livingston also includes many excellent exercises. Were an undergraduate to request that I do a reading course in knot theory with him/her, this would be one of the two books I'd use (Adam's book would be the other). This book is intentionally written at a more elementary level than, say Kaufmann (On Knots), Rolfsen (Knots and Links), Lickorish (Introduction to Knot Theory) or Burde-Zieshcang (Knots), and would be a good "stepping stone" to these classics.
A very thorough volume for the serious student |
5. Introduction to Knot Theory (Dover Books on Mathematics) by Richard H. Crowell, Ralph H. Fox | |
Paperback: 192
Pages
(2008-09-27)
list price: US$14.95 -- used & new: US$7.30 (price subject to change: see help) Asin: 0486468941 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, it offers an accessible treatment that requires no previous knowledge of algebraic topology. 1963 edition. |
6. Knots: Mathematics with a Twist by Alexei Sossinsky | |
Paperback: 160
Pages
(2004-04-15)
list price: US$19.00 -- used & new: US$10.01 (price subject to change: see help) Asin: 0674013816 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Ornaments and icons, symbols of complexity or evil, aesthetically appealing and endlessly useful in everyday ways, knots are also the object of mathematical theory, used to unravel ideas about the topological nature of space. In recent years knot theory has been brought to bear on the study of equations describing weather systems, mathematical models used in physics, and even, with the realization that DNA sometimes is knotted, molecular biology. This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject. A guide to the basic ideas and applications of knot theory, Knots takes us from Lord Kelvin's early--and mistaken--idea of using the knot to model the atom, almost a century and a half ago, to the central problem confronting knot theorists today: distinguishing among various knots, classifying them, and finding a straightforward and general way of determining whether two knots--treated as mathematical objects--are equal. Communicating the excitement of recent ferment in the field, as well as the joys and frustrations of his own work, Alexei Sossinsky reveals how analogy, speculation, coincidence, mistakes, hard work, aesthetics, and intuition figure far more than plain logic or magical inspiration in the process of discovery. His spirited, timely, and lavishly illustrated work shows us the pleasure of mathematics for its own sake as well as the surprising usefulness of its connections to real-world problems in the sciences. It will instruct and delight the expert, the amateur, and the curious alike. (20030201)Customer Reviews (7)
Basic introduction to knot theory within the grasp of the second-year undergraduate
Ultimately: unsatisfying
A Fun Book
Read the Adams book instead Another error is made when giving an example of calculating the Conway polynomial for a link with two separate circles (page 68): the right-hand side of the equation should have no term in x.Figure 2.15 (algebraic representation of a braid) also has an error: the upper-right-hand braid elementary braid is b2, not b1.(The text below the diagram is correct, but the diagram itself has it wrong.) For a beginner who is learning the subject, the necessity of sorting out the author's errors is unacceptable.A book with so many errors should have an errata (list of corrections) on the web, but I searched and found none. I though the braid chapter was well-written.I have not studied braids before and it made the situation pretty clear. On the plus side, the drawings are excellent, the best I have seen in any knot book.For example, figure 3.3 (page 40) has a nice diagram clearly showing various "problems" that might happen momentarily during Reidemeister moves.In this case, a picture is worth a thousand words. I did not enjoy the author's mini-digressions into non-mathematical applications of knots.They went on too long and didn't relate well to the mathematics in the book. Finally, this author seems to have a bit of an attitude.He makes it sound like he almost beat Kaufmann to discovering Kaufmann's bracket.Then he goes on to point out that the Celtic people discovered a form of it centuries ago (beating Kaufmann).Sounds like sour grapes to me.He makes frequent comments such as "the attentive reader will notice," which I found annoying after a while.Readers do not like to be insulted. After a full day with this book, I am tossing it into the trash.The Knot Book by Colin Adams is solid on the math and a better overall introduction to the math side.
It is not that bad, but full of mistakes On the other hand, I thought explanations were pretty good. So I would certainly not recommend it as a starter, but if you know enough of knot theory, the mistakes should keep you entertained... ... Read more |
7. The Knot Book by Colin Adams | |
Paperback: 307
Pages
(2004-08-11)
list price: US$30.00 -- used & new: US$27.00 (price subject to change: see help) Asin: 0821836781 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description A knot seems a simple, everyday thing, at least to anyone who wears lacedshoes 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 cantake one of 1,388,705 permutations, and more are possible. All this thrillsmathematics professor Colin Adams, whose primer offers an engaging if challenging introduction to the mysterious, often unproven, but, hesuggests, ultimately knowable nature of knots of all kinds--whethernontrivial, satellite, torus, cable, or hyperbolic. As perhaps befits itssubject, Adams's prose is sometimes, well, tangled ("a knot is amphicheiralif it can be deformed through space to the knot obtained by changing everycrossing in the projection of the knot to the opposite crossing"), but hisbook is great fun for puzzle and magic buffs, and a useful reference forstudents of knot theory and other aspects of higher mathematics.--Gregory McNamee Customer Reviews (11)
..almost great
bonne introduction
Good Introduction to Knots
Written for a non-mathematician but certainly enjoyable by mathematicians!
Pretty good introduction |
8. On Knots. (AM-115) by Louis H. Kauffman | |
Paperback: 498
Pages
(1987-10-01)
list price: US$85.00 -- used & new: US$49.21 (price subject to change: see help) Asin: 0691084351 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Customer Reviews (2)
A good reference/second book on knot theory The strength of this book is the "hands on" explinations given about many of the standard topics on knot theory (Alexander polynomial, Skein invariants, covering spaces, etc.) and I feel that the author does a great job on relating many of the combinatorial invariants to the topology of the knot complement.Many informative illustrations and examples are provided. This is one of the first references I look to when I need a refresher on a topic, or if I encounter something in classical knot theory that I am unfamiliar with. Also, this book is just plain fun to read! Of course, this book is from the mid 80's and therefore does not cover some of the more modern material. Frankly, I've found that anything written by professor Kauffman to be well written and worth reading.
Good intro to knot theory, with a lot of technical detail |
9. Subfactors and Knots (Cbms Regional Conference Series in Mathematics) by Vaughan F. R. Jones | |
Paperback: 113
Pages
(1991-11-15)
list price: US$22.00 -- used & new: US$21.68 (price subject to change: see help) Asin: 0821807293 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
introduction to knot theory -subfactor theory: It gives the possible values of the index, nevertheless it is too sketchy and one solely interested in this subject should read his inventiones papers. -knottheory: this is the best part of the books which explain withoutprerequisites and with great clarity the way to compute knotinvariants. -a pot pourri about 'knot and statistical mechanics'generalization. This part is the worst since the book is now quite old andthe idea are not clear. This book as the virtues of lectures (clarity,geometric ideas) and it's defaults (few computations, lack of rigor) ... Read more |
10. Formal Knot Theory (Dover Books on Mathematics) by Louis H. Kauffman | |
Paperback: 272
Pages
(2006-07-07)
list price: US$14.95 -- used & new: US$7.00 (price subject to change: see help) Asin: 048645052X Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in combinatorics. 1983 edition. Includes 51 illustrations. Customer Reviews (2)
text low quality
Brisk and intuitive way to dive into knot theory |
11. Knots and Links by Peter R. Cromwell | |
Paperback: 346
Pages
(2004-11-15)
list price: US$63.00 -- used & new: US$25.98 (price subject to change: see help) Asin: 0521548314 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
Not exactly friendly for beginners (closer to 3 stars, actually) |
12. Knots and Surfaces: A Guide to Discovering Mathematics (Mathematical World, Vol. 6) by David W. Farmer, Theodore B. Stanford | |
Paperback: 101
Pages
(1995-11-28)
list price: US$22.00 -- used & new: US$21.41 (price subject to change: see help) Asin: 0821804510 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Suitable for a one-semester course at the beginning undergraduate level, there are no prerequisites for understanding the text. Any college student interested in discovering the beauty of mathematics will enjoy a course taught from this book. The book has also been used successfully with nonscience students who want to fulfill a science requirement. Customer Reviews (2)
EXCELLENT INTRODUCTION TO UNUSUAL MATHEMATICAL TOPICS
Intellectual Treat |
13. Applications of Knot Theory (Proceedings of Symposia in Applied Mathematics) by Dorothy Buck and Erica Flapan | |
Hardcover: 186
Pages
(2009-05-28)
list price: US$49.00 -- used & new: US$42.75 (price subject to change: see help) Asin: 0821844660 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
14. Knot Theory and Its Applications (Modern Birkhäuser Classics) by Kunio Murasugi | |
Paperback: 342
Pages
(2007-10-03)
list price: US$44.95 -- used & new: US$34.99 (price subject to change: see help) Asin: 081764718X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as to problems in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of researchers, beginning graduate students, and senior undergraduate students in these fields. The book contains most of the fundamental classical facts about the theory, such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials; also included are key newer developments and special topics such as chord diagrams and covering spaces. The work introduces the fascinating study of knots and provides insight into applications to such studies as DNA research and graph theory. In addition, each chapter includes a supplement that consists of interesting historical as well as mathematical comments. The author clearly outlines what is known and what is not known about knots. He has been careful to avoid advanced mathematical terminology or intricate techniques in algebraic topology or group theory. There are numerous diagrams and exercises relating the material. The study of Jones polynomials and the Vassiliev invariants are closely examined. "The book ...develops knot theory from an intuitive geometric-combinatorial point of view, avoiding completely more advanced concepts and techniques from algebraic topology...Thus the emphasis is on a lucid and intuitive exposition accessible to a broader audience... The book, written in a stimulating and original style, will serve as a first approach to this interesting field for readers with various backgrounds in mathematics, physics, etc. It is the first text developing recent topics as the Jones polynomial and Vassiliev invariants on a level accessible also for non-specialists in the field." -Zentralblatt Math |
15. Knot Theory by Kurt Reidemeister | |
Paperback: 143
Pages
(1983-09)
list price: US$20.00 -- used & new: US$20.00 (price subject to change: see help) Asin: 0914351001 Canada | United Kingdom | Germany | France | Japan | |
16. Knots and Links (AMS Chelsea Publishing) by Dale Rolfsen | |
Hardcover: 439
Pages
(2003-12)
list price: US$58.00 -- used & new: US$45.98 (price subject to change: see help) Asin: 0821834363 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Besides providing a guide to understanding knot theory, the book offers "practical" training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements. It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. |
17. Gauge Fields, Knots, and Gravity (Series on Knots and Everything) by John C. Baez, Javier P. Muniain | |
Paperback: 480
Pages
(1994-09)
list price: US$52.00 -- used & new: US$46.38 (price subject to change: see help) Asin: 9810220340 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (6)
Fantastic Text
My favourite text of all time (so far)
An excellent book !
Perfect
Worth its weight in gold! |
18. Why Knot: An Introduction to the Mathematical Theory of Knots with Tangle (Key Curriculum Press) by Colin Adams | |
Paperback: 62
Pages
(2008-06-16)
-- used & new: US$43.75 (price subject to change: see help) Asin: 0470413492 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Each copy of Why Knot? is packaged with a plastic manipulative called the Tangle®. Adams uses the Tangle because “you can open it up, tie it in a knot and then close it up again.” The Tangle is the ultimate tool for knot theory because knots are defined in mathematics as being closed on a loop. Readers use the Tangle to complete the experiments throughout the brief volume. |
19. Handbook of Knot Theory | |
Hardcover: 502
Pages
(2005-10-10)
list price: US$181.00 -- used & new: US$131.10 (price subject to change: see help) Asin: 044451452X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
20. Physical and Numerical Models in Knot Theory: Including Applications to The Life Sciences by et al Jorge A. Calvo (Editor) | |
Hardcover: 628
Pages
(2005-09)
list price: US$193.00 -- used & new: US$176.89 (price subject to change: see help) Asin: 9812561870 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
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