Customer Reviews

Knots and Surfaces

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This unique and vibrant book is an introductory book on knot theory that somehow sneaks in a lot more rigorous mathematics than you would expect. Without seeming overly difficult, it somehow manages to include a concise introduction to the basics of knot theory, basic topology, and even a little bit of graph theory, algebraic topology and the necessary algebra.

While assuming little background, this book covers an extraordinarily diverse range of material, and ties it all together. The book is written so that a third-year undergraduate could understand it, but it's interesting enough that a graduate student will still find it fascinating.

What I love most about this book is the choice and ordering of topics--the authors dive right into the material, going to some depth in exploring polynomial invariants before they even touch any "abstract nonsense" so to speak; the machinery is developed throughout the book, as it is needed, and as a result seems natural and fully motivated.

I think this book is excellent for self-study; it would also make a great textbook for a course, although to some extent the material in the course would be dictated by what the book covers. I also think that someone teaching a topology or graph theory courses should keep this book in mind and recommend it to any students inquiring about connections to knot theory.