Download or read book Knot Projections written by Noboru Ito and published by CRC Press. This book was released on 2016-11-03 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot Projections offers a comprehensive overview of the latest methods in the study of this branch of topology, based on current research inspired by Arnold’s theory of plane curves, Viro’s quantization of the Arnold invariant, and Vassiliev’s theory of knots, among others. The presentation exploits the intuitiveness of knot projections to introduce the material to an audience without a prior background in topology, making the book suitable as a useful alternative to standard textbooks on the subject. However, the main aim is to serve as an introduction to an active research subject, and includes many open questions.
Download or read book Knot Projections written by Noboru Ito and published by CRC Press. This book was released on 2016-11-03 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot Projections offers a comprehensive overview of the latest methods in the study of this branch of topology, based on current research inspired by Arnold’s theory of plane curves, Viro’s quantization of the Arnold invariant, and Vassiliev’s theory of knots, among others. The presentation exploits the intuitiveness of knot projections to introduce the material to an audience without a prior background in topology, making the book suitable as a useful alternative to standard textbooks on the subject. However, the main aim is to serve as an introduction to an active research subject, and includes many open questions.
Download or read book Linknot written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Knot Theory written by Charles Livingston and published by Cambridge University Press. This book was released on 1993 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses only linear algebra and basic group theory to study the properties of knots.
Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Combinatorial Group Theory written by Roger C. Lyndon and published by Springer. This book was released on 2015-03-12 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
Download or read book The Statistical Mechanics of Interacting Walks Polygons Animals and Vesicles written by E. J. Janse van Rensburg and published by OUP Oxford. This book was released on 2015-05-14 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers. This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account of constructive methods in models of adsorbing, collapsing, and pulled walks, animals and networks, and for models of walks in confined geometries. Additional topics include scaling, knotting in lattice polygons, generating function methods for directed models of walks and polygons, and an introduction to the Edwards model. This essential second edition includes recent breakthroughs in the field, as well as maintaining the older but still relevant topics. New chapters include an expanded presentation of directed models, an exploration of methods and results for the hexagonal lattice, and a chapter devoted to the Monte Carlo methods.
Download or read book Knots written by Gerhard Burde and published by Walter de Gruyter. This book was released on 2013-11-27 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known.
Download or read book Applications of Knot Theory written by American Mathematical Society. Short Course and published by American Mathematical Soc.. This book was released on 2009 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology."--BOOK JACKET.
Download or read book Knots Molecules and the Universe written by Erica Flapan and published by American Mathematical Soc.. This book was released on 2015-12-22 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Knot Theory written by William Menasco and published by Elsevier. This book was released on 2005-08-02 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics
Download or read book Physical and Numerical Models in Knot Theory written by Jorge Alberto Calvo and published by World Scientific. This book was released on 2005 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year.This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.
Download or read book High dimensional Knot Theory written by Andrew Ranicki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.
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 Expeditions in Mathematics written by Tatiana Shubin and published by MAA. This book was released on 2011 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second volume based on lectures for pre-college students given by prominent mathematicians in the Bay Area Mathematical Adventures (BAMA). This book reflects the flavor of the BAMA lectures and the excitement they have generated among the high school and middle school students in the Silicon Valley. The topics cover a wide range of mathematical subjects each treated by a leading proponent of the subject at levels designed to challenge and attract students whose mathematical interests are just beginning. In addition, the treatments given here will intrigue and enchant a more mature mathematician. It is hoped that the publication of these lectures will expose students outside of the San Francisco Bay Area to interesting mathematical topics and treatments outside of their normal experience in the classroom. Mathematical educators are encouraged to offer the students in their own localities similar opportunities to come into contact with exciting adventures in mathematics.
Download or read book Mathematics of Bioinformatics written by Matthew He and published by John Wiley & Sons. This book was released on 2011-03-16 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Bioinformatics: Theory, Methods, and Applications provides a comprehensive format for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. Each chapter is divided into a number of sections based on the bioinformatics topics and related mathematical theory and methods. Each topic of the section is comprised of the following three parts: an introduction to the biological problems in bioinformatics; a presentation of relevant topics of mathematical theory and methods to the bioinformatics problems introduced in the first part; an integrative overview that draws the connections and interfaces between bioinformatics problems/issues and mathematical theory/methods/applications.
Download or read book Philosophy of Mathematics written by James Robert Brown and published by Routledge. This book was released on 2010-03-17 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.
