A Gentle Introduction To Knots Links And Braids
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A Gentle Introduction To Knots Links And Braids
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Author : Ruben Aldrovandi
language : en
Publisher: World Scientific
Release Date : 2021-10-14
A Gentle Introduction To Knots Links And Braids written by Ruben Aldrovandi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-14 with Science categories.
The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
A Gentle Introduction To Knots Links And Braids
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Author : Ruben Aldrovandi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2021-10-14
A Gentle Introduction To Knots Links And Braids written by Ruben Aldrovandi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-14 with Science categories.
The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles - the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems - are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory. This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Computers categories.
An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Formal Knot Theory
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Author : Louis H. Kauffman
language : en
Publisher: Courier Corporation
Release Date : 2006-01-01
Formal Knot Theory written by Louis H. Kauffman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Mathematics categories.
This exploration of combinatorics and knot theory is geared toward advanced undergraduates and graduate students. The author, Louis H. Kauffman, is a professor in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. Kauffman draws upon his work as a topologist to illustrate the relationships between knot theory and statistical mechanics, quantum theory, and algebra, as well as the role of knot theory in combinatorics. Featured topics include state, trails, and the clock theorem; state polynomials and the duality conjecture; knots and links; axiomatic link calculations; spanning surfaces; the genus of alternative links; and ribbon knots and the Arf invariant. Key concepts are related in easy-to-remember terms, and numerous helpful diagrams appear throughout the text. The author has provided a new supplement, entitled "Remarks on Formal Knot Theory," as well as his article, "New Invariants in the Theory of Knots," first published in The American Mathematical Monthly, March 1988.
Knots Groups And 3 Manifolds Am 84 Volume 84
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Author : Lee Paul Neuwirth
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Knots Groups And 3 Manifolds Am 84 Volume 84 written by Lee Paul Neuwirth and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends. In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin. Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.
Knot Theory And Its Applications
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Author : Kunio Murasugi
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-29
Knot Theory And Its Applications written by Kunio Murasugi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-29 with Mathematics categories.
This 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.
Encyclopedia Of Knot Theory
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Author : Colin Adams
language : en
Publisher: CRC Press
Release Date : 2021-02-10
Encyclopedia Of Knot Theory written by Colin Adams and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Education categories.
"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory
Inside Out Back Again
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Author : Thanhhà Lai
language : en
Publisher: Random House
Release Date : 2023-06-15
Inside Out Back Again written by Thanhhà Lai and has been published by Random House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-15 with Juvenile Fiction categories.
Ten-year-old Hà has only ever known Saigon: the thrills of its markets, the joy of its traditions, and the warmth of her family and friends close by. But when the Vietnam War reaches the gates of her home, Hà and her family are forced to flee. The journey onboard a refugee ship bound for America is hard - but nothing can prepare Hà for the strangeness of the country that greets them on the other side. The language is impossible, the food is strange - and not all the locals are friendly. But amongst her struggles, Hà finds joy, friendship - and most of all, the power of hope, love and family.
An Introduction To Knot Theory
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Author : W.B.Raymond Lickorish
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To Knot Theory written by W.B.Raymond Lickorish and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Curly Like Me
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Author : Teri LaFlesh
language : en
Publisher: Turner Publishing Company
Release Date : 2010-04-15
Curly Like Me written by Teri LaFlesh and has been published by Turner Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-15 with Health & Fitness categories.
The simple secrets to growing your curls healthy and long. Tightly curly hair isn't like any other type of hair, and it needs totally different care to make it happy. Do you spend countless hours—and untold dollars—on weaves, perms, salon visits, and products that promise to change, heal, or make your hair more manageable, only to end up even more frustrated? Do you wrestle daily with hair you can't get a brush through? Do you struggle to keep from hurting your child when you comb through her tight curls? Would you like to grow your tightly curly hair long and healthy? If you answered yes to any of these questions, this book was written for you. It gives you the information and techniques you need to celebrate—not fight against—your very curly hair. You will learn how not only to care for your curls, but to cherish them, all the while saving time, effort, and money. Curly Like Me is the off-the-grid, do-it-yourself owner's manual for tightly curly hair: Learn how to wear your own curls in their natural curl patterns Over 250 photographs and illustrations Includes the best products, tools, ingredients, curl-enhancing hairstyle ideas, tips for growing out your perm, and more Shows you pain-free techniques on how to comb and style your curls or your child's curls Over thirty easy, curl-enhancing hairstyle ideas, tips for growing out your perm, and more Helps you save money by avoiding costly treatments, products, marketing misinformation, and frequent salon visits so you can enjoy your own curls without pain, chemicals, or the use of weaves or extensions The story (with lots of photos) of Teri's journey from hair broken by relaxers, texturizers, improper care, trying to force it to conform, and fighting her weave addiction to finally understanding her own curls. End your struggles with misunderstood, damaged hair and begin your journey to thriving natural curls.