Knots Molecules And The Universe

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Knots, Molecules, and the Universe

Erica Flapan
Knots Molecules and the Universe Book PDF

Author : Erica Flapan
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 54,8 Mb
Release : 2015-12-22
Category : Algebraic topology
ISBN : 9781470425357

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Knots, Molecules, and the Universe by Erica Flapan Pdf

This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook. The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material. The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.

Encyclopedia of Knot Theory

Colin Adams
Encyclopedia of Knot Theory Book PDF

Author : Colin Adams
Publisher : Chapman & Hall/CRC
Page : 941 pages
File Size : 46,9 Mb
Release : 2021
Category : Mathematics
ISBN : 1138298212

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Encyclopedia of Knot Theory by Colin Adams Pdf

"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 which is useful and accessible to undergraduates, post-graduates, 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 to by top researchers in the field of Knot Theory"--

Knots and Applications

Louis H. Kauffman
Knots and Applications Book PDF

Author : Louis H. Kauffman
Publisher : World Scientific
Page : 502 pages
File Size : 49,9 Mb
Release : 1995
Category : Science
ISBN : 9810220049

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Knots and Applications by Louis H. Kauffman Pdf

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.

Encyclopedia of Knot Theory

Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Encyclopedia of Knot Theory Book PDF

Author : Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Publisher : CRC Press
Page : 954 pages
File Size : 42,8 Mb
Release : 2021-02-10
Category : Education
ISBN : 9781000222388

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Encyclopedia of Knot Theory by Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson Pdf

"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

The Knot Book

Colin Conrad Adams
The Knot Book Book PDF

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 42,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836781

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The Knot Book by Colin Conrad Adams Pdf

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.

Applications of Knot Theory

American Mathematical Society. Short course
Applications of Knot Theory Book PDF

Author : American Mathematical Society. Short course
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 40,9 Mb
Release : 2024-06-16
Category : Mathematics
ISBN : 9780821867716

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Applications of Knot Theory by American Mathematical Society. Short course Pdf

The first three chapters of this book introduce the reader to knot theory, topological chirality and molecular symmetry, and DNA topology. The second half of the book is focused on three particular applications of knot theory.

Knots and Physics

Louis H Kauffman
Knots and Physics Book PDF

Author : Louis H Kauffman
Publisher : World Scientific
Page : 740 pages
File Size : 43,8 Mb
Release : 1994-01-15
Category : Science
ISBN : 9789814502375

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Knots and Physics by Louis H Kauffman Pdf

In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included. This book is an introduction to knot and link invariants as generalized amplitudes (vacuum–vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems. Contents:Physical KnotsStates and the Bracket PolynomialThe Jones Polynomial and Its GeneralizationsBraids and the Jones PolynomialFormal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)qYang-Baxter Models for Specializations of the Homfly PolynomialThe Alexander PolynomialKnot-Crystals — Classical Knot Theory in Modern GuiseThe Kauffman PolynomialThree Manifold Invariants from the Jones PolynomialIntegral Heuristics and Witten' s InvariantsThe Chromatic PolynomialThe Potts Model and the Dichromatic PolynomialThe Penrose Theory of Spin NetworksKnots and Strings — Knotted StringsDNA and Quantum Field TheoryKnots in Dynamical Systems — The Lorenz Attractorand other papers Readership: Physicists, mathematical physicists and mathematicians. keywords: Reviews of the First Edition: “It is an attractive book for physicists with profuse and often entertaining illustrations … proofs … seldom heavy and nearly always well explained with pictures… succeeds in infusing his own excitement and enthusiasm for these discoveries and their potential implications.” Physics Today “… here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind.” Mathematical Reviews

Topology of Polymers

Koya Shimokawa,Kai Ishihara,Yasuyuki Tezuka
Topology of Polymers Book PDF

Author : Koya Shimokawa,Kai Ishihara,Yasuyuki Tezuka
Publisher : Springer Nature
Page : 81 pages
File Size : 42,6 Mb
Release : 2019-12-06
Category : Mathematics
ISBN : 9784431568889

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Topology of Polymers by Koya Shimokawa,Kai Ishihara,Yasuyuki Tezuka Pdf

Plastics, films, and synthetic fibers are among typical examples of polymer materials fabricated industrially in massive quantities as the basis of modern social life. By comparison, polymers from biological resources, including proteins, DNAs, and cotton fibers, are essential in various processes in living systems. Such polymers are molecular substances, constituted by the linking of hundreds to tens of thousands of small chemical unit (monomer) components. Thus, the form of polymer molecules is frequently expressed by line geometries, and their linear and non-linear forms are believed to constitute the fundamental basis for their properties and functions. In the field of polymer chemistry and polymer materials science, the choice of macromolecules has continuously been extended from linear or randomly branched forms toward a variety of precisely controlled topologies by the introduction of intriguing synthetic techniques. Moreover, during the first decade of this century, a number of impressive breakthroughs have been achieved to produce an important class of polymers having a variety of cyclic and multicyclic topologies. These developments now offer unique opportunities in polymer materials design to create unique properties and functions based on the form, i.e., topology, of polymer molecules. The introduction and application of topological geometry (soft geometry) to polymer molecules is a crucial requirement to account for the basic geometrical properties of polymer chains uniquely flexible in nature, in contrast to small chemical compounds conceived upon Euclidian geometry (hard geometry) principles. Topological geometry and graph theory are introduced for the systematic classification and notation of the non-linear constructions of polymer molecules, including not only branched but also single cyclic and multicyclic polymer topologies. On that basis, the geometrical–topological relationship between different polymers having distinctive constructions is discussed. A unique conception of topological isomerism is thus formed, which contrasts with that of conventional constitutional and stereoisomerism occurring in small chemical compounds. Through the close collaboration of topology experts Shimokawa and Ishihara and the polymer chemist Tezuka, this monograph covers the fundamentals and selected current topics of topology applied in polymers and topological polymer chemistry. In particular, the aim is to provide novel insights jointly revealed through a unique interaction between mathematics (topology) and polymer materials science.

Lumen Naturae

Matilde Marcolli
Lumen Naturae Book PDF

Author : Matilde Marcolli
Publisher : MIT Press
Page : 390 pages
File Size : 42,9 Mb
Release : 2020-05-26
Category : Mathematics
ISBN : 9780262358323

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Lumen Naturae by Matilde Marcolli Pdf

Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.

Topological Polymer Chemistry

Yasuyuki Tezuka,Tetsuo Deguchi
Topological Polymer Chemistry Book PDF

Author : Yasuyuki Tezuka,Tetsuo Deguchi
Publisher : Springer Nature
Page : 430 pages
File Size : 49,9 Mb
Release : 2022-02-25
Category : Science
ISBN : 9789811668074

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Topological Polymer Chemistry by Yasuyuki Tezuka,Tetsuo Deguchi Pdf

This book provides a comprehensive description of topological polymers, an emerging research area in polymer science and polymer materials engineering. The precision polymer topology designing is critical to realizing the unique polymer properties and functions leading to their eventual applications. The prominent contributors are led by Principal Editor Yasuyuki Tezuka and Co-Editor Tetsuo Deguchi. Important ongoing achievements and anticipated breakthroughs in topological polymers are presented with an emphasis on the spectacular diversification of polymer constructions. The book serves readers collectively to acquire comprehensive insights over exciting innovations ongoing in topological polymer chemistry, encompassing topological geometry analysis, classification, physical characterization by simulation and the eventual chemical syntheses, with the supplementary focus on the polymer folding, invoked with the ongoing breakthrough of the precision AI prediction of protein folding. The current revolutionary developments in synthetic approaches specifically for single cyclic (ring) polymers and the topology-directed properties/functions uncovered thereby are outlined as a showcase example. This book is especially beneficial to academic personnel in universities and to researchers working in relevant institutions and companies. Although the level of the book is advanced, it can serve as a good reference book for graduate students and postdocs as a source of valuable knowledge of cutting-edge topics and progress in polymer chemistry.

Humanity in a Creative Universe

Stuart A. Kauffman
Humanity in a Creative Universe Book PDF

Author : Stuart A. Kauffman
Publisher : Oxford University Press
Page : 313 pages
File Size : 50,8 Mb
Release : 2016
Category : Science
ISBN : 9780199390458

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Humanity in a Creative Universe by Stuart A. Kauffman Pdf

Much of Stuart Kauffman's work in the philosophy of evolutionary biology has centered on the question of what he calls "prestatability" in evolution: that is, whether or not science can precisely predict the future development of biological features in organisms, using a singular "FinalTheory" of evolution. In this book, Kauffman argues that the development of life on earth is not prestatable, because no theory could ever fully account for the limitless variability of evolution. He believes that the biological universe's primary trait is that it is creative, and that acknowledgingthis creativity will lead to a radically different way in which humans view themselves and all other living beings. It is an argument against Reductive Materialism.Kauffman also asserts that man's Modern preoccupation to explain all things with scientific law has deadened our creative natures. In his words, he aims for the book to be "one that revises our scientific world view of the universe as entirely entailed by law." Instead, he advocates an approach toscience that accounts for "unprestatable" creativity, thus allowing humans to fully realize their creative selves. The book will build off the ideas developed in his last two works, Reinventing the Sacred and Investigations. Incorporating philosophers like Kant and Descartes, as well as the scienceof Newton and Darwin, Humanity in a Creative Universe is Stuart Kauffman's argument for a creative and unpredictable view of modern science.

Knots and Physics

Louis H. Kauffman
Knots and Physics Book PDF

Author : Louis H. Kauffman
Publisher : World Scientific
Page : 794 pages
File Size : 50,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9812384839

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Knots and Physics by Louis H. Kauffman Pdf

This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.

Our Place in the Universe - II

Sun Kwok
Our Place in the Universe II Book PDF

Author : Sun Kwok
Publisher : Springer Nature
Page : 346 pages
File Size : 51,6 Mb
Release : 2021-10-21
Category : Science
ISBN : 9783030802608

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Our Place in the Universe - II by Sun Kwok Pdf

Starting from Newton’s times this follow-up to the author’s Springer book “Our Place in the Universe - Understanding Fundamental Astronomy from Ancient Discoveries” addresses the question of “our place in the Universe” from astronomical, physical, chemical, biological, philosophical and social perspectives. Using the history of astronomy to illustrate the process of discovery, the emphasis is on the description of the process of how we learned and on the exploration of the impacts of discoveries rather than on the presentation of facts. Thus readers are informed of the influence of science on a broad scale. Unlike the traditional way of teaching science, in this book, the author begins by describing the observations and then discusses various attempts to find answers (including unsuccessful ones). The goal is to help students develop a better appreciation of the scientific process and learn from this process to tackle real-life problems.

The Mathematical Legacy of Richard P. Stanley

Patricia Hersh,Thomas Lam,Pavlo Pylyavskyy,Victor Reiner
The Mathematical Legacy of Richard P Stanley Book PDF

Author : Patricia Hersh,Thomas Lam,Pavlo Pylyavskyy,Victor Reiner
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 47,9 Mb
Release : 2016-12-08
Category : Combinatorial analysis
ISBN : 9781470427245

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The Mathematical Legacy of Richard P. Stanley by Patricia Hersh,Thomas Lam,Pavlo Pylyavskyy,Victor Reiner Pdf

Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.

The Best Writing on Mathematics 2017

Mircea Pitici
The Best Writing on Mathematics 2017 Book PDF

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 242 pages
File Size : 43,9 Mb
Release : 2017-11-14
Category : Mathematics
ISBN : 9780691178639

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The Best Writing on Mathematics 2017 by Mircea Pitici Pdf

The year's finest mathematics writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2017 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here Evelyn Lamb describes the excitement of searching for incomprehensibly large prime numbers, Jeremy Gray speculates about who would have won math’s highest prize—the Fields Medal—in the nineteenth century, and Philip Davis looks at mathematical results and artifacts from a business and marketing viewpoint. In other essays, Noson Yanofsky explores the inherent limits of knowledge in mathematical thinking, Jo Boaler and Lang Chen reveal why finger-counting enhances children’s receptivity to mathematical ideas, and Carlo Séquin and Raymond Shiau attempt to discover how the Renaissance painter Fra Luca Pacioli managed to convincingly depict his famous rhombicuboctahedron, a twenty-six-sided Archimedean solid. And there’s much, much more. In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.