Introduction to Quadratic Forms
Author: Onorato Timothy O’Meara
Publisher: Springer
Published: 2013-12-01
Total Pages: 354
ISBN-13: 366241922X
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Author: Onorato Timothy O’Meara
Publisher: Springer
Published: 2013-12-01
Total Pages: 354
ISBN-13: 366241922X
DOWNLOAD EBOOKAuthor: Tsit-Yuen Lam
Publisher: Addison-Wesley
Published: 1980
Total Pages: 344
ISBN-13: 9780805356663
DOWNLOAD EBOOKAuthor: Larry J. Gerstein
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 274
ISBN-13: 0821844652
DOWNLOAD EBOOKThe 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 self-contained 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.
Author: J. W. S. Cassels
Publisher: Courier Dover Publications
Published: 2008-08-08
Total Pages: 429
ISBN-13: 0486466701
DOWNLOAD EBOOKExploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.
Author: Kazimierz Szymiczek
Publisher: Routledge
Published: 2017-11-22
Total Pages: 508
ISBN-13: 1351464205
DOWNLOAD EBOOKGiving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.
Author: Johannes Buchmann
Publisher: Springer Science & Business Media
Published: 2007-06-22
Total Pages: 328
ISBN-13: 3540463682
DOWNLOAD EBOOKThe book deals with algorithmic problems related to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory. The book explains applications to cryptography and requires only basic mathematical knowledge. The author is a world leader in number theory.
Author: Yoshiyuki Kitaoka
Publisher: Cambridge University Press
Published: 1999-04-29
Total Pages: 292
ISBN-13: 9780521649964
DOWNLOAD EBOOKProvides an introduction to quadratic forms.
Author: Herbert Gross
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 432
ISBN-13: 1475714548
DOWNLOAD EBOOKFor about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. Here we present in a systematic fashion half of the results found du ring this period, to wit, the results on denumerably infinite spaces (" ~O- forms") . Certain among the resul ts included here had of course been published at the time when they were found, others appear for the first time (the case, for example, in Chapters IX, X, XII where I in clude results contained in the Ph.D.theses by my students w. Allenspach, L. Brand, U. Schneider, M. Studer). If one wants to give an introduction to the geometric algebra of infinite dimensional quadratic spaces, a discussion of ~ -dimensional 0 spaces ideally serves the purpose. First, these spaces show a large nurober of phenomena typical of infinite dimensional spaces. Second, most proofs can be done by recursion which resembles the familiar pro cedure by induction in the finite dimensional Situation. Third, the student acquires a good feeling for the linear algebra in infinite di mensions because it is impossible to camouflage problems by topological expedients (in dimension ~O it is easy to see, in a given case, wheth er topological language is appropriate or not) .
Author: John Horton Conway
Publisher: American Mathematical Soc.
Published: 1997-12-31
Total Pages: 152
ISBN-13: 1470448424
DOWNLOAD EBOOKJohn Horton Conway's unique approach to quadratic forms was the subject of the Hedrick Lectures that he gave in August of 1991 at the Joint Meetings of the Mathematical Association of America and the American Mathematical Society in Orono, Maine. This book presents the substance of those lectures. The book should not be thought of as a serious textbook on the theory of quadratic forms. It consists rather of a number of essays on particular aspects of quadratic forms that have interested the author. The lectures are self-contained and will be accessible to the generally informed reader who has no particular background in quadratic form theory. The minor exceptions should not interrupt the flow of ideas. The afterthoughts to the lectures contain discussion of related matters that occasionally presuppose greater knowledge.
Author: Daniel B. Shapiro
Publisher: Walter de Gruyter
Published: 2000
Total Pages: 440
ISBN-13: 9783110126297
DOWNLOAD EBOOKNo detailed description available for "Compositions of Quadratic Forms".