Rational Quadratic Forms
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Rational Quadratic Forms
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Author : J. W. S. Cassels
language : en
Publisher: Courier Dover Publications
Release Date : 2008-08-08
Rational Quadratic Forms written by J. W. S. Cassels and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-08 with Mathematics categories.
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.
The Arithmetic Theory Of Quadratic Forms
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Author : Burton W Jones
language : en
Publisher: American Mathematical Soc.
Release Date : 1950-12-31
The Arithmetic Theory Of Quadratic Forms written by Burton W Jones and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950-12-31 with Forms, Binary categories.
This monograph presents the central ideas of the arithmetic theory of quadratic forms in self-contained form, assuming only knowledge of the fundamentals of matric theory and the theory of numbers. Pertinent concepts of p -adic numbers and quadratic ideals are introduced. It would have been possible to avoid these concepts, but the theory gains elegance as well as breadth by the introduction of such relationships. Some results, and many of the methods, are here presented for the first time. The development begins with the classical theory in the field of reals from the point of view of representation theory; for in these terms, many of the later objectives and methods may be revealed. The successive chapters gradually narrow the fields and rings until one has the tools at hand to deal with the classical problems in the ring of rational integers. The analytic theory of quadratic forms is not dealt with because of the delicate analysis involved. However, some of the more important results are stated and references are given.
Ternary Quadratic Forms And Norms
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Author : O. Taussky
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Ternary Quadratic Forms And Norms written by O. Taussky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
This book covers topics including the Redei-Reichardt theorem, automorphs of ternary quadratic forms, facts concerning rational matrices leading to integral ternary forms representing zero, characteristics polynomials of symmetric matrices, and Gauss' theory of ternary quadratic forms.
The Sensual Quadratic Form
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Author : John Horton Conway
language : en
Publisher: Cambridge University Press
Release Date : 1997
The Sensual Quadratic Form written by John Horton Conway and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Quadratic forms are presented in a pictorial way, elucidating many topics in algebra, number theory and geometry.
Binary Quadratic Forms
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Author : Duncan A. Buell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Binary Quadratic Forms written by Duncan A. Buell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
The Sensual Quadratic Form
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Author : John Horton Conway
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-12-31
The Sensual Quadratic Form written by John Horton Conway and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-31 with categories.
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.
The Arithmetic Theory Of Quadratic Forms
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Author : Burton Wadsworth Jones
language : en
Publisher: MAA Press
Release Date : 1950
The Arithmetic Theory Of Quadratic Forms written by Burton Wadsworth Jones and has been published by MAA Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Mathematics categories.
Quadratic Forms With Applications To Algebraic Geometry And Topology
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Author : Albrecht Pfister
language : en
Publisher: Cambridge University Press
Release Date : 1995-09-28
Quadratic Forms With Applications To Algebraic Geometry And Topology written by Albrecht Pfister and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-28 with Mathematics categories.
A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Basic Quadratic Forms
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Author : Larry J. Gerstein
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Basic Quadratic Forms written by Larry J. Gerstein and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Introduction To Quadratic Forms
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Author : Onorato Timothy O'Meara
language : en
Publisher:
Release Date : 1963
Introduction To Quadratic Forms written by Onorato Timothy O'Meara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Forms, Quadratic categories.