Introduction to Quadratic Forms

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Springer Science & Business Media, Dec 14, 1999 - Mathematics - 344 pages
From the reviews: "O'Meara treats his subject from this point of view (of the interaction with algebraic groups). He does not attempt an encyclopedic coverage ...nor does he strive to take the reader to the frontiers of knowledge... . Instead he has given a clear account from first principles and his book is a useful introduction to the modern viewpoint and literature. In fact it presupposes only undergraduate algebra (up to Galois theory inclusive)... The book is lucidly written and can be warmly recommended.
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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Contents

II
1
III
14
IV
20
V
28
VI
30
VII
37
VIII
41
IX
42
XXVIII
157
XXIX
158
XXX
172
XXXI
173
XXXII
186
XXXIII
190
XXXV
203
XXXVI
205

X
44
XI
52
XII
54
XIII
59
XIV
65
XV
82
XVI
88
XVII
100
XVIII
112
XIX
113
XX
118
XXI
129
XXII
131
XXIII
137
XXIV
141
XXV
142
XXVI
149
XXVII
154
XXXVII
208
XXXVIII
220
XXXIX
239
XL
246
XLI
250
XLII
279
XLIII
280
XLIV
284
XLV
285
XLVI
297
XLVII
305
XLVIII
311
XLIX
321
L
323
LI
336
LII
337
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About the author (1999)

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.

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