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Knots and Links download epub

by Peter R. Cromwell


Epub Book: 1407 kb. | Fb2 Book: 1971 kb.

Peter Cromwell has written a textbook designed for use at advanced undergraduate or beginning graduate level courses. This is a great book on knot theory which can be read and utilized by all levels of mathematicians.

Peter Cromwell has written a textbook designed for use at advanced undergraduate or beginning graduate level courses.

Cromwell, Peter R. 2008. The distribution of knot types in Celtic interlaced ornament. Journal of Mathematics and the Arts, Vol. 2, Issue.

Peter Cromwell has written a textbook on knot theory designed for use in advanced undergraduate or beginning graduate-level courses. The exposition is detailed and careful yet engaging and full of motivation.

Peter R. Cromwell, Cromwell Peter R. Cambridge University Press, Oct 14, 2004 - Mathematics - 328 pages

Peter R. Cambridge University Press, Oct 14, 2004 - Mathematics - 328 pages.

Finding books BookSee BookSee - Download books for free. 2 Mb. The Story of Civilization: Part VIII, The Age of Louis XIV: A History of European Civilization in the Period of Pascal, Moliere, Cromwell, Milton, Peter the Great, Newton, and Spinzoa: 1648-1715. Will Durant, Ariel Durant. Category: Geometry and topology. Category: Algebraic and differential topology.

It can be used for upper-division courses, and assumes only knowledge of basic algebra and elementary topology.

This paper examines the fundamental properties of thi. More). 17. View via Publisher.

Topology and its Applications

Topology and its Applications. This paper examines the fundamental properties of this arc-presentation.

The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. Cromwell, Peter R. (2004). Cambridge University Press, Cambridge

The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. W. H. Freeman & Company. Armstrong, M. A. (1983) Cromwell, Peter R. Cambridge University Press, Cambridge.

Cambridge university press. Knot theory is a perfect introduction to this and makes a good second course in topology. Published by the press syndicate of the university of cambridge.

Knot theory is the study of embeddings of circles in space. Peter Cromwell has written a textbook on knot theory designed for use in advanced undergraduate or beginning graduate-level courses. The exposition is detailed and careful yet engaging and full of motivation. Numerous examples and exercises serve to help students through the material, while an instructor's manual is available online.

Comments: (3)

Togar
This is a great book on knot theory which can be read and utilized by all levels of mathematicians. Amazing.
Stick
Clear, extraordinarily accurate and well stocked with examples. An excellent textbook for beginners. Too bad it was written before the recent breakthroughs in the field.
Doktilar
The topics covered in this book are terrific. The presentation is disappointing.

Some pluses: In theory the book is accessible to advanced undergraduates without a prerequisite course in topology. Necessary results from that field are presented as "facts" in Chapter 2. (Nonetheless, a course in graph theory is a stated prerequisite, and is often relied on in the text.) The bibliography is quite extensive. A publisher's blurb somewhere trumpets the "hundreds" of diagrams in the book -- but more than a third of these appear in appendices and catalogues of knots. The discussion of arc presentations of braids in Ch. 10, a subject on which PC (the author) has published extensively, is quite interesting.

The main disappointment is that there aren't nearly enough diagrams in the main text, making many arguments hard to follow. PC relies instead on terse, formal mathematical descriptions as much as possible. Chapter 2's long recital of definitions and theorems from topology -- which, by hypothesis, are subjects in which his expected reader lacks background -- is a relative desert of diagrams. Chapter 3's description of companion and satellite knots is accompanied by an unlabeled diagram that leaves one confused as to which knot is which. The description of Seifert surfaces in Chapter 6 is so abstract I found it impossible to visualize even on repeated readings, before I consulted another text. And even if a diagram were too much to ask, would it really have stressed PC to include a sentence saying that a "meridian" wraps round the torus the short way and a "longitude" the long way, instead of leaving these non-intuitive defnitions implicit in equations (@10)? PC also often refers to diagrams in earlier chapters, thus chopping up your concentration by making you flip pages.

By contrast, compare any book by Kauffman (or even his original papers). They're very generous with diagrams, even incorporating them into lines of a proof. The original 1998 paper by Bar-Natan, Fulman & Kauffman, written for pros, is a much clearer exposition of the important concept of "surgery equivalence" than is PC's description for beginners (Chapter 6 @114-118). Even though most of PC's diagrams are based on the paper's, he uses only a few of them and has stripped them of helpful labels. (The paper is available for free online as I write this.)

Another sharp contrast is Colin Adams's "The Knot Book", published by Freeman. Although written more like a popularization than a math textbook, it has significant overlap with the book under review, even including some of the material on braids in PC's chapter 10. It made it relatively easy to grasp satellites/companions, the Seifert algortithm and many other topics, including the Kauffman bracket polynomial, another instance where PC is confusing despite his use of diagrams. I srongly recommend it as an adjunct read.

In addition to 1 point off for the obscure style, I automatically deducted 1 star because the book lacks solutions or even hints to exercises. The proofs of many significant theorems are left as exercises, so this is no small thing. (PC's own website disclaims that solutions will be available anytime soon, if ever.) Also, many of the exercises say "show" and others say "prove", but the distinction, if any, is not clear in context; often you're asked to "show" certain things are true "for any knot", e.g. @Ex.3.10.5.

To give credit where credit is due, PC very swiftly and graciously replied to an email inquiry from me about a point that I'd misunderstood. I very much appreciate that, and it says good things about the author. But it's not a workable solution for everyone, or even for all the stuff that confused me. I hope that PC will be a bit more indulgent to beginners in a future edition of this book.

Finally, some wags of the finger to the publisher: (1) The blurb mentions applications of knot theory to chemistry, biology, etc., but such stuff occupies less than 1.5 pages out of 280+ of text (a biology example that is mentioned briefly, followed by cites to some papers (@212-213).) (2) When I bought this book in 2005, the cover price was $40; as of this review it's gone up 40+%, if we ignore Amazon's discount. It's a handsome book, printed on expensive coated stock, a kind Cambridge also uses for textbooks with lots of color. But all the illustrations are black-and-white line drawings -- no need for such fancy paper at all. Had the publisher made a more sensible production choice, maybe the price for the paperback could have stayed at a more reasonable and student-friendly level.
Knots and Links download epub
Mathematics
Author: Peter R. Cromwell
ISBN: 0521839475
Category: Science & Math
Subcategory: Mathematics
Language: English
Publisher: Cambridge University Press (November 22, 2004)
Pages: 346 pages