Assisted by Francis Y. C. Fung
Softcover ISBN:  9781470448424 
Product Code:  CAR/26 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
eBook ISBN:  9781614440253 
Product Code:  CAR/26.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
Softcover ISBN:  9781470448424 
eBook: ISBN:  9781614440253 
Product Code:  CAR/26.B 
List Price:  $95.00 $72.50 
MAA Member Price:  $71.25 $54.38 
AMS Member Price:  $71.25 $54.38 
Assisted by Francis Y. C. Fung
Softcover ISBN:  9781470448424 
Product Code:  CAR/26 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
eBook ISBN:  9781614440253 
Product Code:  CAR/26.E 
List Price:  $45.00 
MAA Member Price:  $33.75 
AMS Member Price:  $33.75 
Softcover ISBN:  9781470448424 
eBook ISBN:  9781614440253 
Product Code:  CAR/26.B 
List Price:  $95.00 $72.50 
MAA Member Price:  $71.25 $54.38 
AMS Member Price:  $71.25 $54.38 

Book DetailsThe Carus Mathematical MonographsVolume: 26; 1997; 152 ppMSC: Primary 11
John Horton Conway's unique approach to quadratic forms was the subject of the Hedrick Lectures that he gave in August of 1991 at the Joint Meetings of the Mathematical Association of America and the American Mathematical Society in Orono, Maine. This book presents the substance of those lectures.
The book should not be thought of as a serious textbook on the theory of quadratic forms. It consists rather of a number of essays on particular aspects of quadratic forms that have interested the author. The lectures are selfcontained and will be accessible to the generally informed reader who has no particular background in quadratic form theory. The minor exceptions should not interrupt the flow of ideas. The afterthoughts to the lectures contain discussion of related matters that occasionally presuppose greater knowledge.

Table of Contents

Chapters

The first lecture. Can you see the values of $3x^2+6xy5y^2$?

Afterthoughts. ${PSL}_2(Z)$ and Farey Fractions

The second lecture. Can you hear the shape of a lattice?

Afterthoughts. Kneser’s gluing method: Unimodular lattices

The third lecture. $\dots $and can you feel its form?

Afterthoughts. Feeling the form of a fourdimensional lattice

The fourth lecture. The primary fragrances

Afterthoughts. More about the invariants: The $p$adic numbers

Postscript. A taste of number theory


Reviews

Absolutely fascinating from beginning to end.
Ian Stewart, New Scientist 
This is a book rich in ideas. They seem to burst forth from almost every page ... I suspect that the author's hope that "even the experts will find some new enlightenment here" will be realized.
The Mathematics Teacher 
A very original book ... The lectures are selfcontained for the graduate reader ... full of new ideas, and thus of real interest also to experts.
Zentralblatt fur Mathematik


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
John Horton Conway's unique approach to quadratic forms was the subject of the Hedrick Lectures that he gave in August of 1991 at the Joint Meetings of the Mathematical Association of America and the American Mathematical Society in Orono, Maine. This book presents the substance of those lectures.
The book should not be thought of as a serious textbook on the theory of quadratic forms. It consists rather of a number of essays on particular aspects of quadratic forms that have interested the author. The lectures are selfcontained and will be accessible to the generally informed reader who has no particular background in quadratic form theory. The minor exceptions should not interrupt the flow of ideas. The afterthoughts to the lectures contain discussion of related matters that occasionally presuppose greater knowledge.

Chapters

The first lecture. Can you see the values of $3x^2+6xy5y^2$?

Afterthoughts. ${PSL}_2(Z)$ and Farey Fractions

The second lecture. Can you hear the shape of a lattice?

Afterthoughts. Kneser’s gluing method: Unimodular lattices

The third lecture. $\dots $and can you feel its form?

Afterthoughts. Feeling the form of a fourdimensional lattice

The fourth lecture. The primary fragrances

Afterthoughts. More about the invariants: The $p$adic numbers

Postscript. A taste of number theory

Absolutely fascinating from beginning to end.
Ian Stewart, New Scientist 
This is a book rich in ideas. They seem to burst forth from almost every page ... I suspect that the author's hope that "even the experts will find some new enlightenment here" will be realized.
The Mathematics Teacher 
A very original book ... The lectures are selfcontained for the graduate reader ... full of new ideas, and thus of real interest also to experts.
Zentralblatt fur Mathematik