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Title: Knot Theory by Charles Livingston ISBN: 0-88385-027-3 Publisher: The Mathematical Association of America Pub. Date: 05 September, 1996 Format: Hardcover Volumes: 1 List Price(USD): $41.95 |
Average Customer Rating: 4 (3 reviews)
Rating: 4
Summary: Excellent!
Comment: 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.
Rating: 4
Summary: Good for an introduction
Comment: 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.
Rating: 4
Summary: A very thorough volume for the serious student
Comment: Livingston's book is very concise and dense. It contains a lot of information, but is not the kind of book you could sit down and read through from cover to cover. It is excellent as a reference, a sort-of knot theory encyclopedia.
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Title: The Knot Book : An Elementary Introduction to the Mathematical Theory of Knots by Colin C. Adams ISBN: 0805073809 Publisher: Owl Books Pub. Date: 06 December, 2000 List Price(USD): $17.00 |
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Title: Geometry, Relativity and the Fourth Dimension by Rudolf Rucker ISBN: 0486234002 Publisher: Dover Pubns Pub. Date: 01 June, 1977 List Price(USD): $7.95 |
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Title: A Friendly Introduction to Graph Theory by Fred Buckley, Marty Lewinter ISBN: 0130669490 Publisher: Prentice Hall Pub. Date: 14 November, 2002 List Price(USD): $92.00 |
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Title: Curvature and Homology : Enlarged Edition by Samuel I. Goldberg ISBN: 048640207X Publisher: Dover Pubns Pub. Date: 07 July, 1998 List Price(USD): $22.95 |
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Title: Mathematical Physics by Robert Geroch ISBN: 0226288625 Publisher: University of Chicago Press Pub. Date: October, 1985 List Price(USD): $26.00 |
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