Ebook: The knot book : an elementary introduction to the mathematical theory of knots

"Over a century old, knot theory is today one of the most active areas of modern mathematics. The study of knots has led to important applications in DNA research and the synthesis of new molecules. And it is having a significant impact on statistical mechanics and quantum field theory." "Many of the problems discussed in knot theory, including those treated here, can be understood with only a background of high school algebra and can be solved by the curious amateur. All you need to begin is a piece of string, a little math, a little imagination, and Colin Adams's The Knot Book - the first book to make cutting-edge research in knot theory accessible to a nonspecialist audience." "What are the different properties and classifications of knots? How do you determine whether a knot is actually knotted or can be untangled? What is the appropriate measure of the complexity of a knot? What does knot theory research offer to other sciences? In The Knot Book Colin Adams describes and illustrates the work being done to answer these questions. Starting with the simplest knot (the trivial knot or unknot), Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians now can solve, as well as those that remain open. He also looks at how knot theory is providing important insights in biology, chemistry, physics, and other fields. Included are hundreds of illustrations of knots (including a table at the end of the book displaying nearly 200 different knots) as well as worked examples, exercises open problems - even a few knot jokes and pastimes." "Colin Adams explains knot theory with an enthusiasm and an informal style that makes this seemingly mysterious subject easy to approach. With The Knot Book and a mathematical background that includes no more than a familiarity with polynomials, you will be able to understand and work with some of the discipline's most modern and provocative ideas."--BOOK JACKET.  Read more... Introduction -- Tabulating knots -- Invariants of knots -- Surfaces and knots -- Types of knots -- Polynomials -- Biology, chemistry, and physics -- Knots, links, and graphs -- Topology -- Higher dimensional knotting -- Knot jokes and pastimes -- Appendix: Table of knots, links, and knot and link invariants