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© 2000

Introduction to Quadratic Forms

Book

Part of the Classics in Mathematics book series (volume 117)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Arithmetic Theory of Fields

    1. O. Timothy O’Meara
      Pages 1-41
    2. O. Timothy O’Meara
      Pages 41-54
    3. O. Timothy O’Meara
      Pages 54-81
  3. Abstract Theory Quadratic Forms

    1. O. Timothy O’Meara
      Pages 82-112
    2. O. Timothy O’Meara
      Pages 112-153
  4. Arithmetic Theory of Quadratic Forms over Fields

    1. O. Timothy O’Meara
      Pages 154-189
    2. O. Timothy O’Meara
      Pages 190-207
  5. Abstract Theory of Quadratic Forms over Rings

    1. O. Timothy O’Meara
      Pages 208-239
    2. O. Timothy O’Meara
      Pages 239-284
    3. O. Timothy O’Meara
      Pages 284-335
  6. Back Matter
    Pages 336-342

About this book

Introduction

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.

Keywords

Arithmetic Theory of Fields Arithmetic Theory of Rings Lattice Quadratic Forms algebra finite field number theory

Authors and affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

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.

Bibliographic information

  • Book Title Introduction to Quadratic Forms
  • Authors O. Timothy O'Meara
  • Series Title Classics in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-62031-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-02984-7
  • Softcover ISBN 978-3-540-66564-9
  • eBook ISBN 978-3-642-62031-7
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XIV, 344
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as Volume 117 in the series: Grundlehren der mathematischen Wissenschaften
  • Topics Number Theory
    Linear and Multilinear Algebras, Matrix Theory
    Group Theory and Generalizations
  • Buy this book on publisher's site
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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