Knot Theory (Mathematical Association of America Textbooks) [Hardcover]

Charles Livingston (Author)

Book Description

ISBN-10: 0883850273 | ISBN-13: 978-0883850275 | Publication Date: September 5, 1996

Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented. The interplay between topology and algebra, known as algebraic topology, arises early in the book, when tools from linear algebra and from basic group theory are introduced to study the properties of knots, including one of mathematics' most beautiful topics, symmetry. The book closes with a discussion of high-dimensional knot theory and a presentation of some of the recent advances in the subject - the Conway, Jones and Kauffman polynomials. A supplementary section presents the fundamental group, which is a centerpiece of algebraic topology.

Editorial Reviews

Review

'The author's book would be a good text for an undergraduate course in knot theory ... The topics in the book are nicely tied together ... The topics and the exercises together can provide an opportunity for many undergraduates to get a real taste of what present day mathematics is like.' Mathematical Reviews

'Get knotted ... ' Scouting for Boys

Book Description

Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience of mathematical readers, from undergraduates to professionals. The author introduces tools from linear algebra and basic group theory and uses these to study the properties of knots, high-dimensional knot theory and the Conway, Jones and Kauffman polynomials.

Product Details

• Hardcover: 258 pages
• Publisher: The Mathematical Association of America (September 5, 1996)
• Language: English
• ISBN-10: 0883850273
• ISBN-13: 978-0883850275
• Product Dimensions: 7.2 x 5 x 1.1 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #675,860 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

4.0 out of 5 stars Good for an introduction, November 13, 2000

By 

Ollie Nanyes (Peoria, IL USA) - See all my reviews
(REAL NAME)   

This review is from: Knot Theory (Mathematical Association of America Textbooks) (Hardcover)

This book is an excellent introduction to knot theory for the serious, motivated undergraduate students, beginning graduate students,mathematicains in other disciplines, or mathematically oriented scientists who want to learn some knot theory.

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.

3 of 3 people found the following review helpful:

4.0 out of 5 stars Fun, yet brief at times, August 9, 2006

By 

K. M. di Passero "Aloixa" (Los Angeles, CA United States) - See all my reviews
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This review is from: Knot Theory (Mathematical Association of America Textbooks) (Hardcover)

I really do enjoy this book - but picked it up as a means of teaching myself Knot Theory... as was the case with many of my text books in college, brevity (for the sake of publishing costs) makes some concepts more of a challenge to grasp. Overall, the illustrations are great, and if you do the exercizes, the material tends to flow more easliy. It seemed to me the book worked backwards a bit - first covering a subject, than introducing it comprehensively later on - not what I'm used to.
Keep in mind, I'm not a Mathematician, merely a graduate student of mathematics, who is interested in learning about this subject on my own.

1 of 1 people found the following review helpful:

4.0 out of 5 stars Excellent!, January 10, 2002

By A Customer

This review is from: Knot Theory (Mathematical Association of America Textbooks) (Hardcover)

Livingston does a good job on basic knot theory in this text. While Adams seems to jump around a bit in his book, Livingston keeps a nice flow to his work. The proofs require another text and a good background in algebra to understand, but the problems are wonderful for a deeper understanding of the material.