Hardcover ISBN:  9780821844656 
Product Code:  GSM/90 
List Price:  $64.00 
MAA Member Price:  $57.60 
AMS Member Price:  $51.20 
Electronic ISBN:  9781470411596 
Product Code:  GSM/90.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 

Book DetailsGraduate Studies in MathematicsVolume: 90; 2008; 255 ppMSC: Primary 11; 12; 15;
The arithmetic theory of quadratic forms is a rich branch of number theory that has had important applications to several areas of pure mathematics—particularly group theory and topology—as well as to cryptography and coding theory. This book is a selfcontained introduction to quadratic forms that is based on graduate courses the author has taught many times. It leads the reader from foundation material up to topics of current research interest—with special attention to the theory over the integers and over polynomial rings in one variable over a field—and requires only a basic background in linear and abstract algebra as a prerequisite. Whenever possible, concrete constructions are chosen over more abstract arguments. The book includes many exercises and explicit examples, and it is appropriate as a textbook for graduate courses or for independent study. To facilitate further study, a guide to the extensive literature on quadratic forms is provided.
ReadershipGraduate students interested in number theory and algebra. Mathematicians seeking an introduction to the study of quadratic forms on lattices over the integers and related rings.

Table of Contents

Chapters

Chapter 1. A brief classical introduction

Chapter 2. Quadratic spaces and lattices

Chapter 3. Valuations, local fields, and $p$adic numbers

Chapter 4. Quadratic spaces over $\mathbb {Q}_p$

Chapter 5. Quadratic spaces over $\mathbb {Q}$

Chapter 6. Lattices over principal ideal domains

Chapter 7. Initial integral results

Chapter 8. Local classification of lattices

Chapter 9. The localglobal approach to lattices

Chapter 10. Lattices over $\mathbb {F}_q[x]$

Chapter 11. Applications to cryptography

Appendix. Further reading


Additional Material

Reviews

Basic Quadratic Forms is a great introduction to the theory of quadratic forms. The author is clearly an expert on the area as well as a masterful teacher. ... It should be included in the collection of any quadratic forms enthusiast.
MAA Reviews 
Gerstein's book contains a significant amount of material that has not appeared anywhere else in book form. ... It is written in an engaging style, and the author has struck a good balance, presenting enough proofs and arguments to give the flavor of the subject without getting bogged down in too many technical details. It can be expected to whet the appetites of many readers to delve more deeply into this beautiful classical subject and its contemporary applications.
Andrew G. Earnest for Zentralblatt MATH


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The arithmetic theory of quadratic forms is a rich branch of number theory that has had important applications to several areas of pure mathematics—particularly group theory and topology—as well as to cryptography and coding theory. This book is a selfcontained introduction to quadratic forms that is based on graduate courses the author has taught many times. It leads the reader from foundation material up to topics of current research interest—with special attention to the theory over the integers and over polynomial rings in one variable over a field—and requires only a basic background in linear and abstract algebra as a prerequisite. Whenever possible, concrete constructions are chosen over more abstract arguments. The book includes many exercises and explicit examples, and it is appropriate as a textbook for graduate courses or for independent study. To facilitate further study, a guide to the extensive literature on quadratic forms is provided.
Graduate students interested in number theory and algebra. Mathematicians seeking an introduction to the study of quadratic forms on lattices over the integers and related rings.

Chapters

Chapter 1. A brief classical introduction

Chapter 2. Quadratic spaces and lattices

Chapter 3. Valuations, local fields, and $p$adic numbers

Chapter 4. Quadratic spaces over $\mathbb {Q}_p$

Chapter 5. Quadratic spaces over $\mathbb {Q}$

Chapter 6. Lattices over principal ideal domains

Chapter 7. Initial integral results

Chapter 8. Local classification of lattices

Chapter 9. The localglobal approach to lattices

Chapter 10. Lattices over $\mathbb {F}_q[x]$

Chapter 11. Applications to cryptography

Appendix. Further reading

Basic Quadratic Forms is a great introduction to the theory of quadratic forms. The author is clearly an expert on the area as well as a masterful teacher. ... It should be included in the collection of any quadratic forms enthusiast.
MAA Reviews 
Gerstein's book contains a significant amount of material that has not appeared anywhere else in book form. ... It is written in an engaging style, and the author has struck a good balance, presenting enough proofs and arguments to give the flavor of the subject without getting bogged down in too many technical details. It can be expected to whet the appetites of many readers to delve more deeply into this beautiful classical subject and its contemporary applications.
Andrew G. Earnest for Zentralblatt MATH