eBook ISBN:  9781614440239 
Product Code:  CAR/24.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
eBook ISBN:  9781614440239 
Product Code:  CAR/24.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 

Book DetailsThe Carus Mathematical MonographsVolume: 24; 1993; 240 pp
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 readers 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's most beautiful topics—symmetry. The book closes with a discussion of highdimensional 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.

Table of Contents

Chapters

Chapter 1. A century of knot theory

Chapter 2. What is a knot?

Chapter 3. Combinatorial techniques

Chapter 4. Geometric techniques

Chapter 5. Algebraic techniques

Chapter 6. Geometry, algebra, and the Alexander polynomial

Chapter 7. Numerical invariants

Chapter 8. Symmetries of knots

Chapter 9. Highdimensional knot theory

Chapter 10. New combinatorial techniques


Reviews

The author makes it clear that there are many unanswered questions still lying around. This may have the effect of attracting students into the field, but, more importantly, any student reading the book can see the interconnectedness and openendedness of knot theory in very concrete terms and, hence, appreciate better the interconnectedness and openendedness of mathematics as a whole.
William Dunbar, Mathematical Reviews


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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 readers 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's most beautiful topics—symmetry. The book closes with a discussion of highdimensional 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.

Chapters

Chapter 1. A century of knot theory

Chapter 2. What is a knot?

Chapter 3. Combinatorial techniques

Chapter 4. Geometric techniques

Chapter 5. Algebraic techniques

Chapter 6. Geometry, algebra, and the Alexander polynomial

Chapter 7. Numerical invariants

Chapter 8. Symmetries of knots

Chapter 9. Highdimensional knot theory

Chapter 10. New combinatorial techniques

The author makes it clear that there are many unanswered questions still lying around. This may have the effect of attracting students into the field, but, more importantly, any student reading the book can see the interconnectedness and openendedness of knot theory in very concrete terms and, hence, appreciate better the interconnectedness and openendedness of mathematics as a whole.
William Dunbar, Mathematical Reviews