Customer Reviews

Knot Theory (Mathematical Association of America Textbooks)

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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.

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.

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.

As a survey of the basics of knot theory, this book is as good as it gets. The opening chapter is a history of knot theory, which is followed by a chapter on the mathematical definition of knots. The remainder of the book is a series of descriptions of knots, how they are represented, classified and the mathematical machinery used to transform them.
Very little in the way of deep mathematical knowledge is needed to understand the presentation, one of the most important requirements is the ability to think in spatial terms. Exercises are given at the end of each section although no solutions are provided.
Many areas of mathematics began as an abstract theory and after some time, applications are found. Knot theory is an element of this set; one of the applications is that it can be used to describe how proteins fold. A protein is a long chain of connected amino acids, but its' ability to be biochemically active is based on the structure that it folds into after construction. This book is a lively understandable introduction to this fascinating field; it is suitable for self-study or a special topics class in the area of knots.

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.