Physical Knots Knotting Linking And Folding Geometric Objects In Mathbb R 3
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Physical Knots Knotting Linking And Folding Geometric Objects In Mathbb R 3
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Author : Jorge Alberto Calvo
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Physical Knots Knotting Linking And Folding Geometric Objects In Mathbb R 3 written by Jorge Alberto Calvo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Knot theory categories.
The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volumediscusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering,physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.
Physical Knots
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Author : Jorge Alberto Calvo
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-11-15
Physical Knots written by Jorge Alberto Calvo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-15 with Mathematics categories.
Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volume discusses critical questions and new ideas in the areas of knotting and folding of curves in surfaces in three-dimensional space and applications of these ideas to biology, chemistry, computer science, and engineering. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering, physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.
Quandles
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Author : Mohamed Elhamdadi
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-27
Quandles written by Mohamed Elhamdadi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-27 with Knot theory categories.
From prehistory to the present, knots have been used for purposes both artistic and practical. The modern science of Knot Theory has ramifications for biochemistry and mathematical physics and is a rich source of research projects for undergraduate and graduate students and professionals alike. Quandles are essentially knots translated into algebra. This book provides an accessible introduction to quandle theory for readers with a background in linear algebra. Important concepts from topology and abstract algebra motivated by quandle theory are introduced along the way. With elementary self-contained treatments of topics such as group theory, cohomology, knotted surfaces and more, this book is perfect for a transition course, an upper-division mathematics elective, preparation for research in knot theory, and any reader interested in knots.
A History Of Folding In Mathematics
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Author : Michael Friedman
language : en
Publisher: Birkhäuser
Release Date : 2018-05-25
A History Of Folding In Mathematics written by Michael Friedman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-25 with Mathematics categories.
While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.
Energy Of Knots And Conformal Geometry
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Author : Jun O'Hara
language : en
Publisher: World Scientific
Release Date : 2003
Energy Of Knots And Conformal Geometry written by Jun O'Hara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a "canonical configuration" of a knot in each knot type. It also considers this problem in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting thorough numerical experiments.
Visual Thinking In Mathematics
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Author : Marcus Giaquinto
language : en
Publisher: Clarendon Press
Release Date : 2007-07-05
Visual Thinking In Mathematics written by Marcus Giaquinto and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Philosophy categories.
Visual thinking - visual imagination or perception of diagrams and symbol arrays, and mental operations on them - is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures. Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking.
Topology And Physics
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Author : Chen Ning Yang
language : en
Publisher: World Scientific
Release Date : 2019-01-09
Topology And Physics written by Chen Ning Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-09 with Science categories.
'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems … The book explores many interesting and novel topics that lie at the intersection between gravity, quantum fields, condensed matter, physical cosmology and topology … A rich, well-organized, and comprehensive overview of remarkable and insightful connections between physics and topology is here made available to the physics reader.'Contemporary PhysicsSince its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably — resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences — finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.
Mathematics Of Dna Structure Function And Interactions
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Author : Craig John Benham
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-29
Mathematics Of Dna Structure Function And Interactions written by Craig John Benham 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 2010-04-29 with Medical categories.
Propelled by the success of the sequencing of the human and many related genomes, molecular and cellular biology has delivered significant scientific breakthroughs. Mathematics (broadly defined) continues to play a major role in this effort, helping to discover the secrets of life by working collaboratively with bench biologists, chemists and physicists. Because of its outstanding record of interdisciplinary research and training, the IMA was an ideal venue for the 2007-2008 IMA thematic year on Mathematics of Molecular and Cellular Biology. The kickoff event for this thematic year was a tutorial on Mathematics of Nucleic Acids, followed by the workshop Mathematics of Molecular and Cellular Biology, held September 15--21 at the IMA. This volume is dedicated to the memory of Nicholas R. Cozzarelli, a dynamic leader who fostered research and training at the interface between mathematics and molecular biology. It contains a personal remembrance of Nick Cozzarelli, plus 15 papers contributed by workshop speakers. The papers give an overview of state-of-the-art mathematical approaches to the understanding of DNA structure and function, and the interaction of DNA with proteins that mediate vital life processes.
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.
Vortex Dynamics
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Author : P. G. Saffman
language : en
Publisher: Cambridge University Press
Release Date : 1995-02-24
Vortex Dynamics written by P. G. Saffman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-24 with Mathematics categories.
Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary.