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  3. Knot Theory
  • This book is no longer available to purchase from Cambridge Core
  • Cited by 120
Publisher:
Mathematical Association of America
Online publication date:
January 2012
Print publication year:
1993
Online ISBN:
9781614440239
DOI:
https://doi.org/10.5948/UPO9781614440239
Subjects:
Mathematics, Geometry and Topology
Series:
Carus Mathematical Monographs
Information

Book description

Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced study will find a worthwhile overview, and the reader will need no training beyond linear algebra to understand the mathematics presented. The interplay between topology and algebra, known as algebraic topology, arises early in the book, when tools from linear algebra and from basic group theory are introduced to study the properties of knots. Livingston guides you through a general survey of the topic showing how to use the techniques of linear algebra to address some sophisticated problems, including one of mathematics' most beautiful topics, symmetry. The book closes with a discussion of high-dimensional knot theory and a presentation of some of the recent advances in the subject—the Conway, Jones, and Kauffman polynomials. A supplementary section presents the fundamental group, which is a centerpiece of algebraic topology.

Reviews

The author's book would be a good text for an undergraduate course in knot theory...The topics in the book are nicely tied together...The topics and the exercises together can provide an opportunity for many undergraduates to get a real taste of what present day mathematics is like.

Source: Mathematical Reviews

This monograph by Charles Livingston is a most accessible introductory survey of serious, mathematical twentieth century knot theory ... At a time when non-trivial topics are required for so many student projects, no school library with a mathematics section should be without this book. It is a thoroughly well written, well thought out account of a subject of current mathematical research which anyone of a mathematical orientation can enjoy.

Source: Mathematical Gazette

Knot Theory is a concise, comprehensive, and well-written introduction to the definitions, theorems, techniques, and problems of knot theory … the expository sections of the text are quite well organized.

Source: The Mathematics Teacher

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