Quadratic Forms and Their Applications PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Quadratic Forms and Their Applications PDF full book. Access full book title Quadratic Forms and Their Applications by Eva Bayer-Fluckiger. Download full books in PDF and EPUB format.
Author: Eva Bayer-Fluckiger Publisher: American Mathematical Soc. ISBN: 0821827790 Category : Mathematics Languages : en Pages : 330
Book Description
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: Eva Bayer-Fluckiger Publisher: American Mathematical Soc. ISBN: 0821827790 Category : Mathematics Languages : en Pages : 330
Book Description
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: Albrecht Pfister Publisher: Cambridge University Press ISBN: 0521467551 Category : Mathematics Languages : en Pages : 191
Book Description
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: Johannes Buchmann Publisher: Springer Science & Business Media ISBN: 3540463682 Category : Mathematics Languages : en Pages : 328
Book Description
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: Michael Barot Publisher: ISBN: 9783030056285 Category : Forms, Quadratic Languages : en Pages :
Book Description
This monograph presents combinatorial and numerical issues on integral quadratic forms as originally obtained in the context of representation theory of algebras and derived categories. Some of these beautiful results remain practically unknown to students and scholars, and are scattered in papers written between 1970 and the present day. Besides the many classical results, the book also encompasses a few new results and generalizations. The material presented will appeal to a wide group of researchers (in representation theory of algebras, Lie theory, number theory and graph theory) and, due to its accessible nature and the many exercises provided, also to undergraduate and graduate students with a solid foundation in linear algebra and some familiarity on graph theory.
Author: Larry J. Gerstein Publisher: American Mathematical Soc. ISBN: 9780821884072 Category : Mathematics Languages : en Pages : 280
Book Description
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: Achill Schurmann Publisher: American Mathematical Soc. ISBN: 082184735X Category : Mathematics Languages : en Pages : 183
Book Description
"Starting from classical arithmetical questions on quadratic forms, this book takes the reader step by step through the connections with lattice sphere packing and covering problems. As a model for polyhedral reduction theories of positive definite quadratic forms, Minkowski's classical theory is presented, including an application to multidimensional continued fraction expansions. The reduction theories of Voronoi are described in great detail, including full proofs, new views, and generalizations that cannot be found elsewhere. Based on Voronoi's second reduction theory, the local analysis of sphere coverings and several of its applications are presented. These include the classification of totally real thin number fields, connections to the Minkowski conjecture, and the discovery of new, sometimes surprising, properties of exceptional structures such as the Leech lattice or the root lattices." "Throughout this book, special attention is paid to algorithms and computability, allowing computer-assisted treatments. Although dealing with relatively classical topics that have been worked on extensively by numerous authors, this book is exemplary in showing how computers may help to gain new insights."--BOOK JACKET.
Author: Kazimierz Szymiczek Publisher: CRC Press ISBN: 9789056990763 Category : Mathematics Languages : en Pages : 508
Book Description
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.
Author: Richard S. Elman Publisher: American Mathematical Soc. ISBN: 9780821873229 Category : Mathematics Languages : en Pages : 456
Book Description
This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.
Author: Duncan A. Buell Publisher: Springer Science & Business Media ISBN: 1461245427 Category : Mathematics Languages : en Pages : 249
Book Description
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: Eva Bayer-Fluckiger
Author: Eva Bayer-Fluckiger
Author: Albrecht Pfister
Author: Johannes Buchmann
Author: Michael Barot
Author: Larry J. Gerstein
Author: Achill Schurmann
Author: Kazimierz Szymiczek
Author: Richard S. Elman
Author: 
Author: Duncan A. Buell