Knots : mathematics with a twist
Author(s)
Bibliographic Information
Knots : mathematics with a twist
Harvard University Press, 2002
- : pbk
- Other Title
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Noeuds : genèse d'une théorie mathématique
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Note
"Originally published as Nœuds : genèse d'une théorie mathématique, Editions du Seuil, 1999" -- T.p. verso
Includes bibliographical references. (p. 127)
Description and Table of Contents
- Volume
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ISBN 9780674009448
Description
This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject. A guide to the basic ideas and applications of knot theory, Knots takes us from Lord Kelvin's early - and mistaken - idea of using the knot to model the atom, almost a century and a half ago, to the central problem confronting knot theorists today: distinguishing among various knots, classifying them, and finding a straightforward and general way of determining whether two knots - treated as mathematical objects - are equal.
- Volume
-
: pbk ISBN 9780674013810
Description
Ornaments and icons, symbols of complexity or evil, aesthetically appealing and endlessly useful in everyday ways, knots are also the object of mathematical theory, used to unravel ideas about the topological nature of space. In recent years knot theory has been brought to bear on the study of equations describing weather systems, mathematical models used in physics, and even, with the realization that DNA sometimes is knotted, molecular biology.
This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject. A guide to the basic ideas and applications of knot theory, Knots takes us from Lord Kelvin's early-and mistaken-idea of using the knot to model the atom, almost a century and a half ago, to the central problem confronting knot theorists today: distinguishing among various knots, classifying them, and finding a straightforward and general way of determining whether two knots-treated as mathematical objects-are equal.
Communicating the excitement of recent ferment in the field, as well as the joys and frustrations of his own work, Alexei Sossinsky reveals how analogy, speculation, coincidence, mistakes, hard work, aesthetics, and intuition figure far more than plain logic or magical inspiration in the process of discovery. His spirited, timely, and lavishly illustrated work shows us the pleasure of mathematics for its own sake as well as the surprising usefulness of its connections to real-world problems in the sciences. It will instruct and delight the expert, the amateur, and the curious alike.
Table of Contents
Preface 1. Atoms and Knots Lord Kelvin -- 1860 2. Braided Knots Alexander -- 1923 3. Planar Diagrams of Knots Reidemeister -- 1928 4. The Arithmetic of Knots Schubert -- 1949 5. Surgery and Invariants Conway -- 1973 6. Jones's Polynomial and Spin Models Kauffman -- 1987 7. Finite-Order Invariants Vassiliev -- 1990 8. Knots and Physics Xxx? -- 2004? Notes Works Cited
by "Nielsen BookData"