Author: A. B. Sossinsky
Publisher: Harvard University Press
Release Date: 2002
This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject, and a guide to the basic ideas and applications of knot theory. 63 illustrations.
Author: Markus Banagl
Publisher: Springer Science & Business Media
Release Date: 2010-11-25
The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.
Author: S Suzuki
Publisher: World Scientific
Release Date: 1997-07-04
This volume consists of ten lectures given at an international workshop/conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The workshop was attended by nearly 170 mathematicians from Japan and 14 other countries, most of whom were specialists in knot theory. The lectures can serve as an introduction to the field for advanced undergraduates, graduates and also researchers working in areas such as theoretical physics. Contents:Tunnel Number and Connected Sum of Knots (K Morimoto)Topological Imitations (A Kawauchi)Surfaces in 4-Space: A View of Normal Forms and Braidings (S Kamada)Knot Types of Satellite Knots and Twisted Knots (K Motegi)Random Knots and Links and Applications to Polymer Physics (T Deguchi & K Tsurusaki)Knots and Diagrams (L H Kauffman)On Spatial Graphs (K Taniyama)Energy and Length of Knots (G Buck & J Simon)Chern-Simons Perturbative Invariants (T Kohno)Combinatorial Methods in Dehn Surgery (C M Gordon) Readership: Mathematicians and mathematical physicists. keywords:Lectures;Knots;Conference;Proceedings;Tokyo (Japan)
Author: Mario Livio
Publisher: Simon and Schuster
Release Date: 2011-02-22
Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
Release Date: 2004
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 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.
Author: Philippe Petit
Release Date: 2013-04-09
Genre: Crafts & Hobbies
“Mr. Petit is the perfect teacher” in this fascinating, educational volume on knot-tying—an art and science that has held civilization together (The Wall Street Journal). Philippe Petit is known for his astounding feat of daring when, on August 7, 1974, he stepped out on a wire illegally rigged between the World Trade Center’s twin towers in New York City. But beyond his balance, courage, and showmanship, there was one thing Petit had to be absolutely certain of—his knots. Without the confidence that his knots would hold, he never would have left the ground. In fact, while most of us don’t think about them beyond tying our shoelaces, the humble knot is crucial in countless contexts, from sailing to sports to industrial safety to art, agriculture, and more. In this truly unique book, Petit offers a guide to tying over sixty of his essential knots, with practical sketches illustrating his methods and clear tying instructions. Filled with photos in which special knots were used during spectacular high-wire walks, quirky knot trivia, personal anecdotes, helpful tips, magic tricks, and special tying challenges, Why Knot? will entertain and educate readers of all ages. “In reading Philippe’s book we are cogently reminded that without the ability to secure a rope, or tether a goat, or make fast the sheets of a galley, much of the civilization that we take for granted would disappear as easily as a slipknot in the hands of a Vegas conjuror.” —Sting, musician and activist “His descriptions are clear, he deploys humor frequently and he makes his points with anecdotes that are colorful and memorable. Explaining the purpose and creation of knots and thanks to those flawless drawings Mr. Petit earns perfect marks.” —The Wall Street Journal
Author: Jørgen E. Andersen
Publisher: American Mathematical Soc.
Release Date: 2011
In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.
This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics
Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book"".
Author: Louis H. Kauffman
Publisher: World Scientific
Release Date: 1995
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.
Author: Matthew He
Publisher: John Wiley & Sons
Release Date: 2011-03-16
Mathematics of Bioinformatics: Theory, Methods, andApplications provides a comprehensive format forconnecting and integrating information derived from mathematicalmethods and applying it to the understanding of biologicalsequences, structures, and networks. Each chapter is divided into anumber of sections based on the bioinformatics topics and relatedmathematical theory and methods. Each topic of the section iscomprised of the following three parts: an introduction to thebiological problems in bioinformatics; a presentationof relevant topics of mathematical theory and methods to thebioinformatics problems introduced in the first part; anintegrative overview that draws the connections and interfacesbetween bioinformatics problems/issues and mathematicaltheory/methods/applications.