Softcover ISBN:  9781470471514 
Product Code:  STML/101 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470473112 
Product Code:  STML/101.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470471514 
eBook: ISBN:  9781470473112 
Product Code:  STML/101.B 
List Price:  $118.00 $88.50 
Softcover ISBN:  9781470471514 
Product Code:  STML/101 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470473112 
Product Code:  STML/101.E 
List Price:  $59.00 
Individual Price:  $47.20 
Softcover ISBN:  9781470471514 
eBook ISBN:  9781470473112 
Product Code:  STML/101.B 
List Price:  $118.00 $88.50 

Book DetailsStudent Mathematical LibraryVolume: 101; 2023; 129 ppMSC: Primary 55; 51; 20
This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links.
Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of nonelementary topics and a brief history of the subject, including many references.
ReadershipUndergraduate and graduate students interested in knot theory.

Table of Contents

Chapters

Knots and links, Reidmeister moves

The Conway polynomial

The arithemtic of knots

Some simple knot invariants

The Kauffman bracket

The Jones polynomial

Braids

Discriminants and finite type invariants

Vassiliev invariants

Combinatorial description of Vassiliev invariants

The Kontsevich integrals

Other important topics

A brief history of knot theory


Additional Material

Reviews

I found [this] book informative and interesting. It has the potential to encourage any beginner in lowdimensional topology to study knot theory. Thus, I strongly recommend this book as one of the elementary course books in knot theory.
Santanu Acharjee, MathSciNet 
This new addition to the Student Mathematical Library is an excellent concise introduction to knot theory and some of its associated algebra and topology. It is written clearly and simply, and well illustrated with many figures...Altogether, this book is ideal for selfstudy by undergraduates with an interest in topology.
John Stillwell (University of San Francisco),Notices of the AMS


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This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links.
Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of nonelementary topics and a brief history of the subject, including many references.
Undergraduate and graduate students interested in knot theory.

Chapters

Knots and links, Reidmeister moves

The Conway polynomial

The arithemtic of knots

Some simple knot invariants

The Kauffman bracket

The Jones polynomial

Braids

Discriminants and finite type invariants

Vassiliev invariants

Combinatorial description of Vassiliev invariants

The Kontsevich integrals

Other important topics

A brief history of knot theory

I found [this] book informative and interesting. It has the potential to encourage any beginner in lowdimensional topology to study knot theory. Thus, I strongly recommend this book as one of the elementary course books in knot theory.
Santanu Acharjee, MathSciNet 
This new addition to the Student Mathematical Library is an excellent concise introduction to knot theory and some of its associated algebra and topology. It is written clearly and simply, and well illustrated with many figures...Altogether, this book is ideal for selfstudy by undergraduates with an interest in topology.
John Stillwell (University of San Francisco),Notices of the AMS