Classics in Mathematics

Introduction to Quadratic Forms

Authors: O'Meara, O. Timothy

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About this book

Timothy O'Meara was born on January 29, 1928. He was educated at the University of Cape Town and completed his doctoral work under Emil Artin at Princeton University in 1953. He has served on the faculties of the University of Otago, Princeton University and the University of Notre Dame. From 1978 to 1996 he was provost of the University of Notre Dame. In 1991 he was elected Fellow of the American Academy of Arts and Sciences. O'Mearas first research interests concerned the arithmetic theory of quadratic forms. Some of his earlier work - on the integral classification of quadratic forms over local fields - was incorporated into a chapter of this, his first book. Later research focused on the general problem of determining the isomorphisms between classical groups. In 1968 he developed a new foundation for the isomorphism theory which in the course of the next decade was used by him and others to capture all the isomorphisms among large new families of classical groups. In particular, this program advanced the isomorphism question from the classical groups over fields to the classical groups and their congruence subgroups over integral domains. In 1975 and 1980 O'Meara returned to the arithmetic theory of quadratic forms, specifically to questions on the existence of decomposable and indecomposable quadratic forms over arithmetic domains.

About the authors

Biography of  O. Timothy O'Meara

Timothy O'Meara was born on January 29, 1928. He was educated at the University of Cape Town and completed his doctoral work under Emil Artin at Princeton University in 1953. He has served on the faculties of the University of Otago, Princeton University and the University of Notre Dame. From 1978 to 1996 he was provost of the University of Notre Dame. In 1991 he was elected Fellow of the American Academy of Arts and Sciences.

O'Mearas first research interests concerned the arithmetic theory of quadratic forms. Some of his earlier work - on the integral classification of quadratic forms over local fields - was incorporated into a chapter of this, his first book.

Later research focused on the general problem of determining the isomorphisms between classical groups. In 1968 he developed a new foundation for the isomorphism theory which in the course of the next decade was used by him and others to capture all the isomorphisms among large new families of classical groups. In particular, this program advanced the isomorphism question from the classical groups over fields to the classical groups and their congruence subgroups over integral domains.

In 1975 and 1980 O'Meara returned to the arithmetic theory of quadratic forms, specifically to questions on the existence of decomposable and indecomposable quadratic forms over arithmetic domains.

Reviews

"The exposition follows the tradition of the lectures of Emil Artin who enjoyed developing a subject from first principles and devoted much research to finding the simplest proofs at every stage." - American Mathematical Monthly

Table of contents (10 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-642-62031-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-540-66564-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Quadratic Forms
Authors
Series Title
Classics in Mathematics
Copyright
2000
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-62031-7
DOI
10.1007/978-3-642-62031-7
Softcover ISBN
978-3-540-66564-9
Series ISSN
1431-0821
Edition Number
1
Number of Pages
XIV, 344
Number of Illustrations and Tables
1 b/w illustrations
Additional Information
Originally published as Volume 117 in the series: Grundlehren der mathematischen Wissenschaften
Topics