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.
Download or read book Quadratic Forms and Their Classification by Means of Invariant factors written by Thomas John I'Anson Bromwich and published by . This book was released on 1906 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quadratic Forms and Their Classification by Means of Invariant factors written by Thomas John I'Anson Bromwich and published by . This book was released on 1906 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book QUADRATIC FORMS AND THEIR CLASSIFICATION BY MEANS OF INVARIANT FACTORS written by T. J. I'A. BROMWICH and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quadratic Forms and Their Classification by Means of Invariant factors written by Thomas John I'Anson Bromwich and published by . This book was released on 1960 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 330 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.
Download or read book Quadratic Forms and Their Classification by Means of Invariant factors written by Thomas John I'Anson Bromwich and published by . This book was released on 1906 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quadratic Forms written by T J I Bromwich and published by . This book was released on 2019-06-24 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: IN writing this tract, the chief difficulty has been to compress the material so as not to entirely outrun the prescribed limits of space.The theory is developed in an order which may seem unusual to readers already acquainted with other methods of treatment; but my object has been to obtain a fairly complete account in the minimum of space. If the methods of Weierstrass or Darboux had been adopted, a long and rather tedious discussion would have been needed for certain determinantal theorems (Arts. 24, 25), before the real problem of reduction could have been attacked. Further, the singular case would then have required an entirely separate discussion, of which the only satisfactory account is both involved and laborious.Both of these objections are avoided by the method used here, which is due in substance to Kronecker. And, in addition, the method lends itself to geometrical explanations (see Arts. 1, 13, 17 and Appendix) and is well adapted for the actual reduction of numerical examples, when once the roots of the fundamental determinant are known (see Arts. 2, 16, 19, 22). I hope that a frequent appeal to geometry may serve to make the algebra more easily understood.The omission of any account of Weierstrass's and Darboux's methods would be a serious blot, if the tract were intended to be exhaustive rather than suggestive; in particular Darboux's treatment of the case of unequal rootsl must always be regarded as a model of algebraical elegance. But accounts of these methods are already available to a certain extent (for references, see Art. 38); and consequently an exposition is less necessary here.I have devoted Chapter V to an exhibition of some applications of the theory; these may serve to convince the reader of its utility; and a glance at the table given in Art. 23 will shew that families containing more than four variables could not be exhaustively classified without the aid of invariant-factors. Indeed, even the case of four variables was not fully worked out (in spite of the assistance derived from space intuition) until Sylvester took the first step in the general theory by classifying the contacts of quadric surfaces (see Arts. 11, 18).In conclusion, my best thanks are due to the editors for giving me the opportunity of writing this tract; and to Mr. Leathem in particular for reading the manuscript and proofs. His care has enabled me to detect and remove many difficulties and ambiguities; but it is only too likely that others remain to be found after publication. The addition of the Appendix is due to Mr. Leathem's suggestion.The printing of the University Press stands in no need of praise from me; but I must thank the officials for their excellent reproductions of my drawings, and for their careful superintendence of the press-work in general.
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.
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:
Download or read book Quadratic Forms and Their Classification written by T. J.I'A. Bromwich and published by . This book was released on 1971 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Algebraic and Arithmetic Theory of Quadratic Forms written by Ricardo Baeza and published by American Mathematical Soc.. This book was released on 2004 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.
Download or read book Introduction to Quadratic Forms written by O. Timothy O'Meara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "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." Bulletin of the AMS
Download or read book Bilinear Algebra written by Kazimierz Szymiczek and published by Routledge. This book was released on 2017-11-22 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving 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.
Download or read book Quaternion Algebras written by John Voight and published by Springer Nature. This book was released on 2021-06-28 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Download or read book Quadratic Forms and Their Classification by Means of Invariant Factors Vol 3 Classic Reprint written by T. J. I'A Bromwich and published by Forgotten Books. This book was released on 2017-10-16 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Quadratic Forms and Their Classification by Means of Invariant Factors, Vol. 3 The theory is developed in an order which may seem unusual to readers already acquainted with other methods of treatment; but my object has been to obtain a fairly complete account in the minimum of space. If the methods of Weierstrass or Barboux had been adopted, a long and rather tedious discussion would have been needed for certain determinantal theorems (arts. 24, before the real problem of reduction could have been attacked. Further, the singular case would then have required an entirely separate discussion, of which the only satisfactory account1 is both involved and laborious. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
