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Sensual (Quadratic) Form
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John Horton Conway
The distinguished mathematician John Conway presents quadratic forms in a pictorial way that enables the reader to understand them mathematically without proving theorems in the traditional fashion. One learns to sense their properties. In his customary enthusiastic style, Conway uses his theme to cast light on all manner of mathematical topics ...
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A Course in Arithmetic
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Jean-Pierre Serre
Serre's "A Course in Arithmetic" is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level. "...The book is ...
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Arithmetic of Quadratic Forms
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Kitaoka
The aim of this book is to provide an introduction to quadratic forms that builds from basics up to the most recent results. Professor Kitaoka is well known for his work in this area, and in this book he covers many aspects of the subject, including lattice theory, Siegel's formula, and some results involving tensor products of positive definite ...
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Binary Quadratic Forms: An Algorithmic Approach
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Johannes Buchmann, Ulrich Vollmer
This book deals with algorithmic problems related to binary quadratic forms, such as finding the representations of an integer by a form with integer coefficients, finding the minimum of a form with real coefficients and deciding equivalence of two forms. In order to solve those problems, the book introduces the reader to important areas of number ...
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Ternary Quadratic Forms and Norms
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O Taussky, Taussky O
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Quadrangular Algebras
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Richard M Weiss
This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the ...
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Variations on a Theme of Euler: Quadratic Forms, Elliptic Curves and Hopf Maps
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Takashi Ono
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Quadratic Forms with Applications to Algebraic Geometry and Topology
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Albrecht Pfister, J W S Cassels (Editor), N J Hitchin (Editor)
This volume has grown out of lectures given by Professor Pfister over many years. The emphasis here is placed on results about quadratic forms that give rise to interconnections between number theory, algebra, algebraic geometry and topology. Topics discussed include Hilbert's 17th problem, the Tsen-Lang theory of quasi algebraically closed fields ...
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Introduction to Quadratic Forms
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Timothy O O'Meara, O T O'Meara
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 ...
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From Polynomials to Sums of Squares
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Terence H Jackson
"From Polynomials to Sums of Squares" describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is ...
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Rational Quadratic Forms
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by
J W S Cassels
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Singular Quadratic Forms in Perturbation Theory
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Volodymyr Koshmanenko
This monograph is devoted to the systematic presentation of the method of singular quadratic forms in the perturbation theory of self-adjoint operators. The concept of a singular (nowhere closable) quadratic form, a key notion of the present volume, is treated from different points of view such as definition, properties, relations with regular ...
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Quadratic Forms in Infinite Dimensional Vector Spaces
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Dr. Herbert Gross
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Quaternary Quadratic Forms: Computer Generated Tables
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Gordon L Nipp
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Integral Quadratic Forms
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G L Watson
This tract gives a fairly elementary account of the theory of quadratic forms with integral coefficients and variables. It assumes a knowledge of the rudiments of matrix algebra and of elementary number theory, but scarcely any analysis. It is therefore intelligible to beginners and helps to prepare them for the study of the advanced work on ...
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Algebraic L-theory and topological manifolds
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A A Ranicki
This book presents a definitive account of the applications of the algebraic L-theory to the surgery classification of topological manifolds. The central result is the identification of a manifold structure in the homotopy type of a Poincare duality space with a local quadratic structure in the chain homotopy type of the universal cover. The ...
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From Polynomial to Sums of Squares
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T. H. Jackson
This text and software describes a "journey" through algebra and number theory based on the central theme of factorization. It begins with basic knowledge of rational polynomials, gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The treatment is made very concrete throughout the main text with ...
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Squares
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by
Rajwade
Many classical and modern results and quadratic forms are brought together in this book. The treatment is self-contained and of a totally elementary nature requiring only a basic knowledge of rings, fields, polynomials, and matrices, such that the works of Pfister, Hilbert, Hurwitz and others are easily accessible to non-experts and undergraduates ...
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Spaces of Orderings and Abstract Real Spectra
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Murray Marshall
This work should be of interest to both students and professionals in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice-ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained, as is the important application to minimal ...
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Introduction to Quadratic Forms
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O T O'Meara
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Tame Algebras and Integral Quadratic Forms
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Claus M Ringel
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Bilinear Algebra: An Introduction to the Algebraic Theory of Quadratic Forms
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Kazimierz Szymiczek, Szymiczek Szymiczek
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, ...
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Higher Spinor Classes
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J F Jardine
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Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups
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by
Alexander Hahn
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The arithmetic theory of quadratic forms.
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by
Burton Wadsworth Jones
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