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Thursday, May 14, 2020 | History

2 edition of Applications of knot theory found in the catalog.

Applications of knot theory

American Mathematical Society. Short course

Applications of knot theory

American Mathematical Society, Short Course, January 4-5, 2008, San Diego, California

by American Mathematical Society. Short course

  • 363 Want to read
  • 34 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Knot theory -- Congresses,
  • DNA -- Structure -- Congresses

  • Edition Notes

    Includes bibliographical references and index.

    StatementDorothy Buck, Erica Flapan, editors.
    GenreCongresses
    SeriesProceedings of symposia in applied mathematics -- v. 66. -- AMS short course lecture notes, Proceedings of symposia in applied mathematics -- v. 66., Proceedings of symposia in applied mathematics
    ContributionsBuck, Dorothy, 1973-, Flapan, Erica, 1956-
    Classifications
    LC ClassificationsQA612.2 .A465 2008
    The Physical Object
    Paginationx, 186 p. :
    Number of Pages186
    ID Numbers
    Open LibraryOL23943169M
    ISBN 100821844660
    ISBN 109780821844663
    LC Control Number2008044393

    In mathematics, the braid group on n strands (denoted), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see § Introduction).Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result. theory of braids, because there is an excellent survey by Birman and Brendle [5] on this topic. We have also avoided 4-dimensional questions, such as the slice-ribbon conjecture (Problem in [41]). Although these do have a signi cant in uence on elementary knot theory, via unknotting numberCited by:

    In Thomson's theory, knots such as the ones in Figure 1a (the unknot), Figure 1b (the trefoil knot) and Figure 1c (the figure eight knot) could, in principle at least, model atoms of increasing complexity, such as the hydrogen, carbon, and oxygen atoms, respectively. For knots to be truly useful, however, mathematicians searched for some. 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.

    Introduces knot theory, providing insights into recent applications in DNA research and graph theory. The book offers fundamental facts about the theory, such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. Introduces knot theory, providing insights into recent applications in DNA research and graph theory. The book offers fundamental facts about the theory, such as .


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Applications of knot theory by American Mathematical Society. Short course Download PDF EPUB FB2

Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as to problems in computer science, biological and medical research, and mathematical physics. This book is directed to a broad audience of researchers, beginning graduateBrand: Birkhäuser Basel.

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 by: The first is that knot theory is a treasure chest of examples for several different branches of topology, geometric group theory, and certain flavours of algebra.

The second is a list of engineering and scientific applications: untangling DNA, mixing liquids, and the structure of the Sun's corona. The Knot Book. by Colin Adams I recommend this book to anyone learning about mathematical knot theory for the first time.

It assumes only a general background in mathematics yet contains a great deal to occupy even the expert. Also it has chapters on the recent applications of knot theory to other fields such as physics, chemistry and biology. It's used a bit in the study of DNA and proteins, as well as cryptology and other encryption-type problems.

Also has some use in GPS applications and motion-planning in robotics. "The Knot Book" is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and by: 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. Over the past years, knot theory has rekindled its historic ties with biology, chemistry, and physics as a means of creating more sophisticated descriptions of the entanglements and properties of natural phenomena--from strings to organic compounds to DNA.

This volume is based on the AMS Short Course, Applications of Knot Theory.2/5(2). Knot theory has a lot of applications. I suggest you take a look at “Applications of Knot theory” by Buck and Flapan.

It has applications in DNA synthesis, chemical synthesis, Quantum computing, statistical physics, string theory, fluid dynamics. This book is directed to a broad audience of researchers, beginning graduate students, and senior undergraduate students in these fields.

The book contains most Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as to problems in computer science, biological and medical /5(4).

The second half of this volume is focused on three particular applications of knot theory. 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.

$\begingroup$ In my experience, the "applications" of knot theory to these fields are fairly elementary and really don't use any deep theory, but I'd love to be proven wrong. Knot theory is a concept in algebraic topology that has found applications to a variety of mathematical problems as well as to problems in computer science, biological and medical research, and mathematical physics.

This book is directed to a broad audience of researchers, beginning graduate students, and senior undergraduate students in these fields.5/5(2).

This book is an introduction to hyperbolic geometry in dimension three, and its applications to knot theory and to geometric problems arising in knot theory. It has three parts. The first part covers basic tools in hyperbolic geometry and geometric structures on 3-manifolds.

The book starts with an introductory chapter giving basic definitions required from knot theory, and motivating some of the problems discussed in this book. The first example of a hyperbolic knot, identified by Riley, is the unique prime knot with crossing number four, known as File Size: 5MB.

This book makes me see that knot theory is almost too pretty and too profound to be true. So much other math comes into it — matrices, determinants, polynomials, continued fractions — even e.

It’s an amazing field, connected with other amazing fields, and the book does it all justice. 1 Knot Theory Knot theory is an appealing subject because the objects studied are familiar in everyday physical space.

Although the subject matter of knot theory is familiar to everyone and its problems are easily stated, arising not only in many branches of mathematics but also in such diverse fields as biology, chemistry, and physics.

Abstract. In this chapter we give an overview of some recent connections between knot theory and graph theory. After giving a quick overview of classical links, links in thickened surfaces and virtual links, we explain some of the ways in which embedded graphs can be Author: Joanna A.

Ellis-Monaghan, Iain Moffatt. The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas.

He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. Knot theory, in mathematics, the study of closed curves in three dimensions, and their possible deformations without one part cutting through another.

Knots may be regarded as formed by interlacing and looping a piece of string in any fashion and then joining the ends. The first question that. Knot theory is the mathematical branch of topology that studies mathematical knots, which are defined as embeddings of a circle in 3-dimensional Euclidean space, R3.

This is basically equivalent.Knot theory is a popular subfield of mathematics with new and exciting applications. Here, we will briefly describe the application of knot theory to building a quantum computer and to the study of DNA, but first we need a bit of background information.

What is a knot? Take a piece of string, make a knot in it, and glue the ends together.Knot Theory and Its Applications.

Kunio Murasugi. Birkhäuser, - Mathematics - pages. 1 Review. From inside the book. What people are saying - Write a review. User Review - Flag as inappropriate.

Amazing book! By far the best book on knot theory that I have ever read. Helped me a lot in my own research in knot theory.5/5(1).