Formal Knot Theory (Dover Books on Mathematics) [Paperback]

Louis H. Kauffman (Author)

Book Description

ISBN-10: 048645052X | ISBN-13: 978-0486450520 | Publication Date: July 7, 2006

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.

Product Details

• Paperback: 272 pages
• Publisher: Dover Publications (July 7, 2006)
• Language: English
• ISBN-10: 048645052X
• ISBN-13: 978-0486450520
• Product Dimensions: 8.6 x 5.4 x 0.6 inches
• Shipping Weight: 8.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,153,403 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

13 of 18 people found the following review helpful:

4.0 out of 5 stars Brisk and intuitive way to dive into knot theory, June 16, 2007

By 

Lee McKusick (El Granada, CA United States) - See all my reviews
(REAL NAME)   

This review is from: Formal Knot Theory (Mathematical Notes, No. 30) (Paperback)

Formal Knot Theory starts out with a planar diagram of a knot. Then the book shows how to label and name the intersections of the planar diagram. By the seventh page, you have an interesting group of terms and theorms. The author shows a method for converting the planar knot diagram into a Jordan curve with no crossing lines.

I am parked at Page 7 where the author introduces a Duality Conjecture. Here is where combinatorics and issues of Topology are introduced. A planar knot diagram has some very specific kinds of symmetry that can be observed using the labeling introduced. The symmetry and alternate ways of labeling a planar knot eventually develop into combinatorics and matrix statements.

The preparation required to work this book with ease is described as "advanced undergraduates and graduates".

I would ammend the "advanced undergraduate" qualification. This book has a reasonable price and very readable expansion of many knot ideas and problems. This is a good step beyond popular writing about math. This book is accessible and direct as distinguished from some other math books that are deliberately abstruse. Enough set and matrix math is modeled that I can follow along and consult other texts for examples and exersizes I need to work the examples.

Formal Knot Theory has the feel and pace of lecture material for a one semester course on Knots. For instance, I can't find in Formal Knot Theory a chapter heading associating knots with the Euler Polyhedron Theorm. But the Theorm is embedded in the ingenious labeling conventions introduced in the first chapter.

0 of 18 people found the following review helpful:

4.0 out of 5 stars text low quality, April 28, 2008

By 

Brian - See all my reviews

This review is from: Formal Knot Theory (Dover Books on Mathematics) (Paperback)

You can tell this is an older book by looking at the font and quality of the printing. It is low quality. I havn't looked into the book too much, so I can't comment on quality of the information, but it seems to be fairly standard in what it talks about. More of an upper lever introductory text. I would suggest looking into Livingston's book or Adams' as these are much more basic. However Livingston doens't include proofs as much and is kindof unclear on the geometrical approach. Still all are good books.