Download or read book A Gentle Introduction To Knots Links And Braids written by Ruben Aldrovandi and published by World Scientific. This book was released on 2021-10-14 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Gentle Introduction to Knots Links and Braids written by Ruben Aldrovandi and published by World Scientific Publishing Company. This book was released on 2021-10-14 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Braiding written by Albertus Georg Schaake and published by . This book was released on 1990 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Formal Knot Theory written by Louis H. Kauffman and published by Courier Corporation. This book was released on 2006-01-01 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Knots Groups and 3 Manifolds AM 84 Volume 84 written by Lee Paul Neuwirth and published by Princeton University Press. This book was released on 2016-03-02 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Encyclopedia of Knot Theory written by Colin Adams and published by CRC Press. This book was released on 2021-02-10 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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
Download or read book Knot Theory and Its Applications written by Kunio Murasugi and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Inside Out Back Again written by Thanhha Lai and published by Univ. of Queensland Press. This book was released on 2013-03-01 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moving to America turns H&à's life inside out. For all the 10 years of her life, H&à has only known Saigon: the thrills of its markets, the joy of its traditions, the warmth of her friends close by, and the beauty of her very own papaya tree. But now the Vietnam War has reached her home. H&à and her family are forced to flee as Saigon falls, and they board a ship headed toward hope. In America, H&à discovers the foreign world of Alabama: the coldness of its strangers, the dullness of its food, the strange shape of its landscape, and the strength of her very own family. This is the moving story of one girl's year of change, dreams, grief, and healing as she journeys from one country to another, one life to the next.
Download or read book Curly Like Me written by Teri LaFlesh and published by Turner Publishing Company. This book was released on 2010-04-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Knot Theory written by W.B.Raymond Lickorish and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Knots and Surfaces written by David W. Farmer and published by American Mathematical Soc.. This book was released on 1996 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: In most mathematics textbooks, the most exciting part of mathematics --- the process of invention and discovery --- is completely hidden from the reader. The aim of Knots and Surfaces is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you.
Download or read book Introduction to Quantum Computing written by Ray LaPierre and published by Springer Nature. This book was released on 2021-09-27 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantum key distribution, and some of the famous quantum algorithms. As well as covering quantum gates in depth, it also describes promising platforms for their physical implementation, along with error correction, and topological quantum computing. With quantum computing expanding rapidly in the private sector, understanding quantum computing has never been so important for graduates entering the workplace or PhD programs. Assuming minimal background knowledge, this book is highly accessible, with rigorous step-by-step explanations of the principles behind quantum computation, further reading, and end-of-chapter exercises, ensuring that undergraduate students in physics and engineering emerge well prepared for the future.
Download or read book I Know Why the Caged Bird Sings written by Maya Angelou and published by Random House. This book was released on 2010-07-21 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a book as joyous and painful, as mysterious and memorable, as childhood itself. I Know Why the Caged Bird Sings captures the longing of lonely children, the brute insult of bigotry, and the wonder of words that can make the world right. Maya Angelou’s debut memoir is a modern American classic beloved worldwide. Sent by their mother to live with their devout, self-sufficient grandmother in a small Southern town, Maya and her brother, Bailey, endure the ache of abandonment and the prejudice of the local “powhitetrash.” At eight years old and back at her mother’s side in St. Louis, Maya is attacked by a man many times her age—and has to live with the consequences for a lifetime. Years later, in San Francisco, Maya learns that love for herself, the kindness of others, her own strong spirit, and the ideas of great authors (“I met and fell in love with William Shakespeare”) will allow her to be free instead of imprisoned. Poetic and powerful, I Know Why the Caged Bird Sings will touch hearts and change minds for as long as people read. “I Know Why the Caged Bird Sings liberates the reader into life simply because Maya Angelou confronts her own life with such a moving wonder, such a luminous dignity.”—James Baldwin From the Paperback edition.
Download or read book TRADOC Pamphlet TP 600 4 The Soldier s Blue Book written by United States Government Us Army and published by . This book was released on 2019-12-14 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manual, TRADOC Pamphlet TP 600-4 The Soldier's Blue Book: The Guide for Initial Entry Soldiers August 2019, is the guide for all Initial Entry Training (IET) Soldiers who join our Army Profession. It provides an introduction to being a Soldier and Trusted Army Professional, certified in character, competence, and commitment to the Army. The pamphlet introduces Solders to the Army Ethic, Values, Culture of Trust, History, Organizations, and Training. It provides information on pay, leave, Thrift Saving Plans (TSPs), and organizations that will be available to assist you and your Families. The Soldier's Blue Book is mandated reading and will be maintained and available during BCT/OSUT and AIT.This pamphlet applies to all active Army, U.S. Army Reserve, and the Army National Guard enlisted IET conducted at service schools, Army Training Centers, and other training activities under the control of Headquarters, TRADOC.
Download or read book In the Time of the Butterflies written by Julia Alvarez and published by Algonquin Books. This book was released on 2010-01-12 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating its 30th anniversary in 2024, internationally bestselling author and literary icon Julia Alvarez's In the Time of the Butterflies is "beautiful, heartbreaking and alive ... a lyrical work of historical fiction based on the story of the Mirabal sisters, revolutionary heroes who had opposed and fought against Trujillo." (Concepción de León, New York Times) Alvarez’s new novel, The Cemetery of Untold Stories, is coming April 2, 2024. Pre-order now! It is November 25, 1960, and three beautiful sisters have been found near their wrecked Jeep at the bottom of a 150-foot cliff on the north coast of the Dominican Republic. The official state newspaper reports their deaths as accidental. It does not mention that a fourth sister lives. Nor does it explain that the sisters were among the leading opponents of Gen. Rafael Leónidas Trujillo’s dictatorship. It doesn’t have to. Everybody knows of Las Mariposas—the Butterflies. In this extraordinary novel, the voices of all four sisters--Minerva, Patria, María Teresa, and the survivor, Dedé--speak across the decades to tell their own stories, from secret crushes to gunrunning, and to describe the everyday horrors of life under Trujillo’s rule. Through the art and magic of Julia Alvarez’s imagination, the martyred Butterflies live again in this novel of courage and love, and the human costs of political oppression. "Alvarez helped blaze the trail for Latina authors to break into the literary mainstream, with novels like In the Time of the Butterflies and How the García Girls Lost Their Accents winning praise from critics and gracing best-seller lists across the Americas."—Francisco Cantú, The New York Times Book Review "This Julia Alvarez classic is a must-read for anyone of Latinx descent." —Popsugar.com "A gorgeous and sensitive novel . . . A compelling story of courage, patriotism and familial devotion." —People "Shimmering . . . Valuable and necessary." —Los Angeles Times "A magnificent treasure for all cultures and all time.” —St. Petersburg Times "Alvarez does a remarkable job illustrating the ruinous effect the 30-year dictatorship had on the Dominican Republic and the very real human cost it entailed."—Cosmopolitan.com
Download or read book On Knots written by Louis H. Kauffman and published by Princeton University Press. This book was released on 1987 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.
