Quadratic Forms In Infinite Dimensional Vector Spaces

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Quadratic Forms in Infinite Dimensional Vector Spaces

Author : Herbert Gross
Publisher : Springer Science & Business Media
ISBN 13 : 1475714548
Total Pages : 419 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Quadratic Forms in Infinite Dimensional Vector Spaces by : Herbert Gross

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) .

Quadratic Forms in Infinite Dimensional Vector Spaces

Author : Springer
Publisher :
ISBN 13 : 9781475714555
Total Pages : 438 pages
Book Rating : 4.7/5 (145 download)

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Book Synopsis Quadratic Forms in Infinite Dimensional Vector Spaces by : Springer

Download or read book Quadratic Forms in Infinite Dimensional Vector Spaces written by Springer and published by . This book was released on 2014-01-15 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quadratic Forms in Infinite Dimensional Vector Spaces

Author : H. Gross
Publisher :
ISBN 13 : 9781489935434
Total Pages : 436 pages
Book Rating : 4.9/5 (354 download)

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Book Synopsis Quadratic Forms in Infinite Dimensional Vector Spaces by : H. Gross

Download or read book Quadratic Forms in Infinite Dimensional Vector Spaces written by H. Gross and published by . This book was released on 2014-09-01 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quaternion Algebras

Author : John Voight
Publisher : Springer Nature
ISBN 13 : 3030566943
Total Pages : 877 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Quaternion Algebras by : John Voight

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.

K-theory and Algebraic Geometry

Author : Bill Jacob
Publisher : American Mathematical Soc.
ISBN 13 : 0821803409
Total Pages : 444 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis K-theory and Algebraic Geometry by : Bill Jacob

Download or read book K-theory and Algebraic Geometry written by Bill Jacob and published by American Mathematical Soc.. This book was released on 1995 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 of two - also available in a set of both volumes.

Quadratic Forms, Linear Algebraic Groups, and Cohomology

Author : Skip Garibaldi
Publisher : Springer Science & Business Media
ISBN 13 : 1441962115
Total Pages : 348 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Quadratic Forms, Linear Algebraic Groups, and Cohomology by : Skip Garibaldi

Download or read book Quadratic Forms, Linear Algebraic Groups, and Cohomology written by Skip Garibaldi and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.

Topological Vector Spaces I

Author : Gottfried Köthe
Publisher : Springer Science & Business Media
ISBN 13 : 3642649882
Total Pages : 470 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Topological Vector Spaces I by : Gottfried Köthe

Download or read book Topological Vector Spaces I written by Gottfried Köthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are intro duced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces.

Octonions, Jordan Algebras and Exceptional Groups

Author : Tonny A. Springer
Publisher : Springer
ISBN 13 : 3662126222
Total Pages : 212 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Octonions, Jordan Algebras and Exceptional Groups by : Tonny A. Springer

Download or read book Octonions, Jordan Algebras and Exceptional Groups written by Tonny A. Springer and published by Springer. This book was released on 2013-12-21 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1963 Göttingen notes of T. A. Springer are well known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra.

An Introduction to the Theory of Linear Spaces

Author : Georgi E. Shilov
Publisher : Courier Corporation
ISBN 13 : 0486139433
Total Pages : 320 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Introduction to the Theory of Linear Spaces by : Georgi E. Shilov

Download or read book An Introduction to the Theory of Linear Spaces written by Georgi E. Shilov and published by Courier Corporation. This book was released on 2012-12-03 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory treatment offers a clear exposition of algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. Numerous examples illustrate many different fields, and problems include hints or answers. 1961 edition.

Mathematical Methods in Physics

Author : Philippe Blanchard
Publisher : Springer Science & Business Media
ISBN 13 : 1461200490
Total Pages : 469 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Mathematical Methods in Physics by : Philippe Blanchard

Download or read book Mathematical Methods in Physics written by Philippe Blanchard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Introduction to Quadratic Forms over Fields

Author : Tsit-Yuen Lam
Publisher : American Mathematical Soc.
ISBN 13 : 0821810952
Total Pages : 577 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Quadratic Forms over Fields by : Tsit-Yuen Lam

Download or read book Introduction to Quadratic Forms over Fields written by Tsit-Yuen Lam and published by American Mathematical Soc.. This book was released on 2005 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.

Aspects of Symmetry

Author : Sidney Coleman
Publisher : Cambridge University Press
ISBN 13 : 9780521318273
Total Pages : 424 pages
Book Rating : 4.3/5 (182 download)

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Book Synopsis Aspects of Symmetry by : Sidney Coleman

Download or read book Aspects of Symmetry written by Sidney Coleman and published by Cambridge University Press. This book was released on 1988-02-18 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: For almost two decades, Sidney Coleman has been giving review lectures on frontier topics in theoretical high-energy physics at the International School of Subnuclear Physics held each year at Erice, Sicily. This volume is a collection of some of the best of these lectures. To this day they have few rivals for clarity of exposition and depth of insight. Although very popular when first published, many of the lectures have been difficult to obtain recently. Graduate students and professionals in high-energy physics will welcome this collection by a master of the field.

Elementary Linear Algebra

Author : Howard Anton
Publisher : John Wiley & Sons
ISBN 13 : 1118474228
Total Pages : 800 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Elementary Linear Algebra by : Howard Anton

Download or read book Elementary Linear Algebra written by Howard Anton and published by John Wiley & Sons. This book was released on 2013-11-04 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Linear Algebra: Applications Version, 11th Edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus.

A Course of Higher Mathematics

Author : V. I. Smirnov
Publisher : Elsevier
ISBN 13 : 148314013X
Total Pages : 336 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis A Course of Higher Mathematics by : V. I. Smirnov

Download or read book A Course of Higher Mathematics written by V. I. Smirnov and published by Elsevier. This book was released on 2016-06-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Series of Monographs in Pure and Applied Mathematics, Volume 59: A Course of Higher Mathematics, III/I: Linear Algebra focuses on algebraic methods. The book first ponders on the properties of determinants and solution of systems of equations. The text then gives emphasis to linear transformations and quadratic forms. Topics include coordinate transformations in three-dimensional space; covariant and contravariant affine vectors; unitary and orthogonal transformations; and basic matrix calculus. The selection also focuses on basic theory of groups and linear representations of groups. Representation of a group by linear transformations; linear representations of the unitary group in two variables; linear representations of the rotation group; and Abelian groups and representations of the first degree are discussed. Other considerations include integration over groups, Lorentz transformations, permutations, and classes and normal subgroups. The text is a vital source of information for students, mathematicians, and physicists.

The Mathematical Heritage of Hermann Weyl

Author : Raymond O'Neil Wells
Publisher : American Mathematical Soc.
ISBN 13 : 0821814826
Total Pages : 344 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Mathematical Heritage of Hermann Weyl by : Raymond O'Neil Wells

Download or read book The Mathematical Heritage of Hermann Weyl written by Raymond O'Neil Wells and published by American Mathematical Soc.. This book was released on 1988 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hermann Weyl was one of the most influential mathematicians of the twentieth century. Viewing mathematics as an organic whole rather than a collection of separate subjects, Weyl made profound contributions to a wide range of areas, including analysis, geometry, number theory, Lie groups, and mathematical physics, as well as the philosophy of science and of mathematics. The topics he chose to study, the lines of thought he initiated, and his general perspective on mathematics have proved remarkably fruitful and have formed the basis for some of the best of modern mathematical research. This volume contains the proceedings of the AMS Symposium on the Mathematical Heritage of Hermann Weyl, held in May 1987 at Duke University. In addition to honoring Weyl's great accomplishments in mathematics, the symposium also sought to stimulate the younger generation of mathematicians by highlighting the cohesive nature of modern mathematics as seen from Weyl's ideas. The symposium assembled a brilliant array of speakers and covered a wide range of topics. All of the papers are expository and will appeal to a broad audience of mathematicians, theoretical physicists, and other scientists.

The Geometry of Infinite-Dimensional Groups

Author : Boris Khesin
Publisher : Springer Science & Business Media
ISBN 13 : 3540772634
Total Pages : 304 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis The Geometry of Infinite-Dimensional Groups by : Boris Khesin

Download or read book The Geometry of Infinite-Dimensional Groups written by Boris Khesin and published by Springer Science & Business Media. This book was released on 2008-09-28 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.

A Modern Introduction to Linear Algebra

Author : Henry Ricardo
Publisher : CRC Press
ISBN 13 : 1439894612
Total Pages : 672 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis A Modern Introduction to Linear Algebra by : Henry Ricardo

Download or read book A Modern Introduction to Linear Algebra written by Henry Ricardo and published by CRC Press. This book was released on 2009-10-21 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful Concepts and Results at the Heart of Linear AlgebraA one- or two-semester course for a wide variety of students at the sophomore/junior undergraduate levelA Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. Concrete, easy-to-understand examples m