## The Knot Book: An Elementary Introduction to the Mathematical Theory of KnotsKnots 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 from our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research. The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in The Knot Book. |

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### Other editions - View all

The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots Colin Conrad Adams No preview available - 1994 |

The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots Colin C. Adams No preview available - 2000 |

### Common terms and phrases

&xercise Alexander polynomial alternating knot alternating links amphicheiral B-split boundary component bracket polynomial braid index called circle closed braid color composite knot compute conjecture corresponding crossing changes crossing number curve deformed denote disk edges embedding equation equivalent Euler characteristic fact fewer crossings figure-eight knot four-space glue gluing HOMFLY polynomial hyperbolic knots integers intersection invariant isotopy Jones polynomial knot or link knot projection knot theory knots and links least number link projection linking number loop meridian minimal genus Möbius band molecule nontrivial knot notation number of crossings obtain oriented link pair planar graph prime knots projection plane prove q)-torus knot rational tangle reduced alternating projection Reidemeister moves result satellite knot Seifert surface Seifert's algorithm sequence Show signed planar graph solid torus space sphere splittable strands string three-manifold three-space tion topology torus knot trefoil knot triangles tricolorable trivial knot trivial link twist unknotting number Unsolved Question vertex vertices