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The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (amsns AMS non-series title)
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The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (amsns AMS non-series title)

4.08 of 5 stars 4.08  ·  rating details  ·  50 ratings  ·  4 reviews
Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. "The Knot Book" is an introduction to this rich theory, starting with our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current re ...more
Paperback, 307 pages
Published September 9th 2004 by American Mathematical Society (first published March 1994)
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The book provides a general overview that is fairly accessible to a lay person like myself. I had some difficulty with explanations of rational knots. The accompanying illustration seemed different from the text explanation. The explanation of hyperbolic knots requires much more mathematical knowledge than I currently have. Fortunately, the annotated bibliography is very thorough, so I'll try a couple of those books.

I had to return this book to the library before I could finish it. I expect to r
Philip Rideout
This book is a rarity because it sits exactly at the right level of math for me: it's advanced enough to feel like a real mathematics book with theories and equations and whatnot, but it's still much more engaging than a college textbook. I admit that I just never "got" some of the more advanced stuff like hyperbolic knots, but Jones Polynomials etc are fairly easy to understand and fascinating.
Covers a large number of topics (e.g. analysis, algebra, topology) without assuming much background. Provides lots of interesting things to think about, and will often gloss over the technical details, which I think makes this book work very well actually.

My favorite parts were probably supercoiling, knot and graph polynomials, and the discussions of three-manifolds.
The most readable math text about what I find to be the most interesting field in math.
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