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Table of contents (10 chapters)
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Arithmetic Theory of Fields
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Abstract Theory Quadratic Forms
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Arithmetic Theory of Quadratic Forms over Fields
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Abstract Theory of Quadratic Forms over Rings
Keywords
About this book
J.W.S. Cassels, The Mathematical Gazette, 1965
"Anyone who has heard O'Meara lecture will recognize in every page of this book the crispness and lucidity of the author's style;... The organization and selection of material is superb... deserves high praise as an excellent example of that too-rare type of mathematical exposition combining conciseness with clarity...
R. Jacobowitz, Bulletin of the AMS, 1965
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Authors and Affiliations
About the author
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
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2000
Softcover ISBN: 978-3-540-66564-9Published: 14 December 1999
eBook ISBN: 978-3-642-62031-7Published: 06 December 2012
Series ISSN: 1431-0821
Series E-ISSN: 2512-5257
Edition Number: 1
Number of Pages: XIV, 344
Number of Illustrations: 1 b/w illustrations
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