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Author : Onorato Timothy O’Meara
Publisher : Springer
ISBN 13 : 366241922X
Total Pages : 354 pages
Book Rating : 4.6/5 (624 download)
Download or read book Introduction to Quadratic Forms written by Onorato Timothy O’Meara and published by Springer. This book was released on 2013-12-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tsit-Yuen Lam
Publisher : Addison-Wesley
ISBN 13 : 9780805356663
Total Pages : 344 pages
Book Rating : 4.3/5 (566 download)
Download or read book The Algebraic Theory of Quadratic Forms written by Tsit-Yuen Lam and published by Addison-Wesley. This book was released on 1980 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. W. S. Cassels
Publisher : Courier Dover Publications
ISBN 13 : 0486466701
Total Pages : 429 pages
Book Rating : 4.4/5 (864 download)
Download or read book Rational Quadratic Forms written by J. W. S. Cassels and published by Courier Dover Publications. This book was released on 2008-08-08 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploration 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 : Larry J. Gerstein
Publisher : American Mathematical Soc.
ISBN 13 : 0821844652
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)
Download or read book Basic Quadratic Forms written by Larry J. Gerstein and published by American Mathematical Soc.. This book was released on 2008 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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 : John Horton Conway
Publisher : American Mathematical Soc.
ISBN 13 : 1470448424
Total Pages : 152 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Sensual (quadratic) Form written by John Horton Conway and published by American Mathematical Soc.. This book was released on 1997-12-31 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: John 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 : Duncan A. Buell
Publisher : Springer Science & Business Media
ISBN 13 : 1461245427
Total Pages : 249 pages
Book Rating : 4.4/5 (612 download)
Download or read book Binary Quadratic Forms written by Duncan A. Buell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega,nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can be done in what is essentially a two dimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number the ory. In consequence, this elegant, yet pleasantly simple, theory has been neglected even as some of its results have become extremely useful in certain computations. I find this neglect unfortunate, because binary quadratic forms have two distinct attractions. First, the subject involves explicit computa tion and many of the computer programs can be quite simple. The use of computers in experimenting with examples is both meaningful and enjoyable; one can actually discover interesting results by com puting examples, noticing patterns in the "data," and then proving that the patterns result from the conclusion of some provable theorem.
Author : W. Scharlau
Publisher : Springer Science & Business Media
ISBN 13 : 3642699715
Total Pages : 431 pages
Book Rating : 4.6/5 (426 download)
Download or read book Quadratic and Hermitian Forms written by W. Scharlau and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic forms. On the basis of their work, Minkowski, Siegel, Hasse, Eichler and many others crea ted the impressive "arithmetic" theory of quadratic forms, which has been the object of the well-known books by Bachmann (1898/1923), Eichler (1952), and O'Meara (1963). Parallel to this development the ideas of abstract algebra and abstract linear algebra introduced by Dedekind, Frobenius, E. Noether and Artin led to today's structural mathematics with its emphasis on classification problems and general structure theorems. On the basis of both - the number theory of quadratic forms and the ideas of modern algebra - Witt opened, in 1937, a new chapter in the theory of quadratic forms. His most fruitful idea was to consider not single "individual" quadratic forms but rather the entity of all forms over a fixed ground field and to construct from this an algebra ic object. This object - the Witt ring - then became the principal object of the entire theory. Thirty years later Pfister demonstrated the significance of this approach by his celebrated structure theorems.
Author : Johannes Buchmann
Publisher : Springer Science & Business Media
ISBN 13 : 3540463682
Total Pages : 328 pages
Book Rating : 4.5/5 (44 download)
Download or read book Binary Quadratic Forms written by Johannes Buchmann and published by Springer Science & Business Media. This book was released on 2007-06-22 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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 : Herbert Gross
Publisher : Springer Science & Business Media
ISBN 13 : 1475714548
Total Pages : 419 pages
Book Rating : 4.4/5 (757 download)
Download or read book Quadratic Forms in Infinite Dimensional Vector Spaces written by Herbert Gross and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: For 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 : Max-Albert Knus
Publisher : Springer Science & Business Media
ISBN 13 : 3642754015
Total Pages : 536 pages
Book Rating : 4.6/5 (427 download)
Download or read book Quadratic and Hermitian Forms over Rings written by Max-Albert Knus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book.
Author : Yoshiyuki Kitaoka
Publisher : Cambridge University Press
ISBN 13 : 9780521649964
Total Pages : 292 pages
Book Rating : 4.6/5 (499 download)
Download or read book Arithmetic of Quadratic Forms written by Yoshiyuki Kitaoka and published by Cambridge University Press. This book was released on 1999-04-29 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to quadratic forms.
Author : Eva Bayer-Fluckiger
Publisher : American Mathematical Soc.
ISBN 13 : 0821827790
Total Pages : 311 pages
Book Rating : 4.8/5 (218 download)
Download or read book Quadratic Forms and Their Applications written by Eva Bayer-Fluckiger and published by American Mathematical Soc.. This book was released on 2000 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume outlines the proceedings of the conference on 'Quadratic Forms and Their Applications' held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.
Author : Daniel B. Shapiro
Publisher : Walter de Gruyter
ISBN 13 : 9783110126297
Total Pages : 440 pages
Book Rating : 4.1/5 (262 download)
Download or read book Compositions of Quadratic Forms written by Daniel B. Shapiro and published by Walter de Gruyter. This book was released on 2000 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Compositions of Quadratic Forms".
Author : Krishnaswami Alladi
Publisher : Springer Science & Business Media
ISBN 13 : 1461474884
Total Pages : 298 pages
Book Rating : 4.4/5 (614 download)
Download or read book Quadratic and Higher Degree Forms written by Krishnaswami Alladi and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.
Author : Goro Shimura
Publisher : Springer Science & Business Media
ISBN 13 : 1441917322
Total Pages : 245 pages
Book Rating : 4.4/5 (419 download)
Download or read book Arithmetic of Quadratic Forms written by Goro Shimura and published by Springer Science & Business Media. This book was released on 2010-08-09 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
Author : Albrecht Pfister
Publisher : Cambridge University Press
ISBN 13 : 0521467551
Total Pages : 191 pages
Book Rating : 4.5/5 (214 download)
Download or read book Quadratic Forms with Applications to Algebraic Geometry and Topology written by Albrecht Pfister and published by Cambridge University Press. This book was released on 1995-09-28 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Author : Claus M. Ringel
Publisher : Springer
ISBN 13 : 3540391274
Total Pages : 390 pages
Book Rating : 4.5/5 (43 download)
Download or read book Tame Algebras and Integral Quadratic Forms written by Claus M. Ringel and published by Springer. This book was released on 2006-11-14 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:
