In view of the explosion of mathematical theories of knots in the past decade, with consequential applications, this book sets down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device - the knot.

What else needs to be said about knots? Almost 650 pages of incredible knowledge, presented in a truzly unique manner. This is not a book of knots, it is the BOOK OF KNOTS. Was muss noch über Knoten gesagt werden? Fast 650 Seiten unglaubliches Wissen, präsentiert in einer wahrhaft einzigartigen Weise. Dies ist kein Buch über Knoten, es ist das BUCH DER KNOTEN.

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

Colin Adams, well-known for his advanced research in topology and knot theory, is the author of this exciting new book that brings his findings and his passion for the subject to a more general audience. This beautifully illustrated comic book is appropriate for many mathematics courses at the undergraduate level such as liberal arts math, and topology. Additionally, the book could easily challenge high school students in math clubs or honors math courses and is perfect for the lay math enthusiast. Each copy of Why Knot? is packaged with a plastic manipulative called the Tangle R. Adams uses the Tangle because "you can open it up, tie it in a knot and then close it up again." The Tangle is the ultimate tool for knot theory because knots are defined in mathematics as being closed on a loop. Readers use the Tangle to complete the experiments throughout the brief volume. Adams also presents a illustrative and engaging history of knot theory from its early role in chemistry to modern applications such as DNA research, dynamical systems, and fluid mechanics. Real math, unreal fun!

Inka khipus--spun and plied cords that record information through intricate patterns of knots and colors--constitute the only available primary sources on the Inka empire not mediated by the hands, minds, and motives of the conquering Europeans. As such, they offer direct insight into the worldview of the Inka--a view that differs from European thought as much as khipus differ from alphabetic writing, which the Inka did not possess. Scholars have spent decades attempting to decipher the Inka khipus, and Gary Urton has become the world's leading authority on these artifacts. In Inka History in Knots, Urton marshals a lifetime of study to offer a grand overview of the types of quantative information recorded in khipus and to show how these records can be used as primary sources for an Inka history of the empire that focuses on statistics, demography, and the "longue durée" social processes that characterize a civilization continuously adapting to and exploiting its environment. Whether the Inka khipu keepers were registering census data, recording tribute, or performing many other administrative tasks, Urton asserts that they were key players in the organization and control of subject populations throughout the empire and that khipu record-keeping vitally contributed to the emergence of political complexity in the Andes. This new view of the importance of khipus promises to fundamentally reorient our understanding of the development of the Inka state and the possibilities for writing its history.

This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.

A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.