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Author: Michael Ungs
Publisher: Lulu.com
Published: 2009-11-06
Total Pages: 635
ISBN-13: 0557115507
DOWNLOAD EBOOKA detailed mathematical derivation of space curves is presented that links the diverse fields of superfluids, quantum mechanics, and hydrodynamics by a common foundation. The basic mathematical building block is called the theory of quantum torus knots (QTK).
Author: Michael Ungs
Publisher: Lulu.com
Published: 2010-08-16
Total Pages: 616
ISBN-13: 0557605016
DOWNLOAD EBOOKAppendicies A to I that are referenced by Volumes I and II in the theory of quantum torus knots (QTK). A detailed mathematical derivation of space curves is provided that links the diverse fields of superfluids, quantum mechanics, and hydrodynamics.
Author: Michael Ungs
Publisher: Lulu.com
Published: 2010-06-23
Total Pages: 726
ISBN-13: 0557459885
DOWNLOAD EBOOKA detailed mathematical derivation of space curves is presented that links the diverse fields of superfluids, quantum mechanics, Navier-Stokes hydrodynamics, and Maxwell electromagnetism by a common foundation. The basic mathematical building block is called the theory of quantum torus knots (QTK).
Author: Dale Rolfsen
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 458
ISBN-13: 0821834363
DOWNLOAD EBOOKRolfsen'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: Colin Conrad Adams
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 330
ISBN-13: 0821836781
DOWNLOAD EBOOKKnots 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.
Author:
Publisher:
Published: 2020-05-06
Total Pages: 698
ISBN-13: 9780578684680
DOWNLOAD EBOOKAuthor: Kunio Murasugi
Publisher: Springer Science & Business Media
Published: 2009-12-29
Total Pages: 348
ISBN-13: 0817647198
DOWNLOAD EBOOKThis book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
Author: W.B.Raymond Lickorish
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 213
ISBN-13: 146120691X
DOWNLOAD EBOOKA 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.
Author: Dirk Kreimer
Publisher: Cambridge University Press
Published: 2000-07-20
Total Pages: 276
ISBN-13: 9780521587617
DOWNLOAD EBOOKThis volume explains how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. The author emphasizes how new discoveries in mathematics have inspired conventional calculational methods for perturbative quantum field theory to become more elegant and potentially more powerful methods. The material illustrates what may possibly be the most productive interface between mathematics and physics. As a result, it will be of interest to graduate students and researchers in theoretical and particle physics as well as mathematics.
Author: Jiannis K. Pachos
Publisher: Cambridge University Press
Published: 2012-04-12
Total Pages: 220
ISBN-13: 1139936689
DOWNLOAD EBOOKCombining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.
