Theory Of Algebraical Expressions
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Galois Theory Of Algebraic Equations
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Author : Jean-Pierre Tignol
language : en
Publisher: World Scientific
Release Date : 2001
Galois Theory Of Algebraic Equations written by Jean-Pierre Tignol and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as ?group? and ?field?. A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the most technical details can be skipped by readers who are interested primarily in a broad survey of the theory.This book will appeal to both undergraduate and graduate students in mathematics and the history of science, and also to teachers and mathematicians who wish to obtain a historical perspective of the field. The text has been designed to be self-contained, but some familiarity with basic mathematical structures and with some elementary notions of linear algebra is desirable for a good understanding of the technical discussions in the later chapters.
General Theory Of Algebraic Equations
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Author : Etienne Bézout
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
General Theory Of Algebraic Equations written by Etienne Bézout and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Mathematics categories.
This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.
Galois Theory Of Algebraic Equations
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Author : Jean-Pierre Tignol
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-12-28
Galois Theory Of Algebraic Equations written by Jean-Pierre Tignol and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-28 with Mathematics categories.
The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as "group" and "field". A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory. In this second edition, the exposition has been improved throughout and the chapter on Galois has been entirely rewritten to better reflect Galois' highly innovative contributions. The text now follows more closely Galois' memoir, resorting as sparsely as possible to anachronistic modern notions such as field extensions. The emerging picture is a surprisingly elementary approach to the solvability of equations by radicals, and yet is unexpectedly close to some of the most recent methods of Galois theory.
Introduction To The Theory Of Algebraic Equations Classic Reprint
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Author : Leonard Eugene Dickson
language : en
Publisher: Forgotten Books
Release Date : 2016-08-15
Introduction To The Theory Of Algebraic Equations Classic Reprint written by Leonard Eugene Dickson and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-15 with Mathematics categories.
Excerpt from Introduction to the Theory of Algebraic Equations But, of all the sources, the lectures and publications of Professor Bolza have been of the greatest aid to the author. In particular, the examples 65) of the group of an equation have been borrowed with his permission from his lectures. The present elementary presentation of the theory is the out come oi lectures delivered by the author in 1897 at the University of California, in 1899 at the University of Texas, and twice in 1902 at the University of Chicago. 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.
Introduction To The Theory Of Algebraic Equations
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Author : Leonard Eugene Dickson
language : en
Publisher: Wentworth Press
Release Date : 2019-02-21
Introduction To The Theory Of Algebraic Equations written by Leonard Eugene Dickson and has been published by Wentworth Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with History categories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Treatise On The Theory Of Algebraical Equations
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Author : Robert Murphy
language : en
Publisher:
Release Date : 1839
A Treatise On The Theory Of Algebraical Equations written by Robert Murphy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1839 with Equations, Theory of categories.
A History Of Abstract Algebra
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Author : Jeremy Gray
language : en
Publisher: Springer
Release Date : 2018-08-07
A History Of Abstract Algebra written by Jeremy Gray and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-07 with Mathematics categories.
This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
A Treatise On The Theory Of Algebraical Equations
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Author : John Hymers
language : en
Publisher:
Release Date : 1811
A Treatise On The Theory Of Algebraical Equations written by John Hymers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1811 with Algebra categories.
Algebraic Theories
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Author : Leonard Dickson
language : en
Publisher: Courier Dover Publications
Release Date : 2004
Algebraic Theories written by Leonard Dickson 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 2004 with Algebra categories.
This in-depth introduction to classical topics in higher algebra provides rigorous, detailed proofs for its explorations of some of mathematics' most significant concepts, including matrices, invariants, and groups. Algebraic Theories studies all of the important theories; its extensive offerings range from the foundations of higher algebra and the Galois theory of algebraic equations to finite linear groups (including Klein's "icosahedron" and the theory of equations of the fifth degree) and algebraic invariants. The full treatment includes matrices, linear transformations, elementary divisors and invariant factors, and quadratic, bilinear, and Hermitian forms, both singly and in pairs. The results are classical, with due attention to issues of rationality. Elementary divisors and invariant factors receive simple, natural introductions in connection with the classical form and a rational, canonical form of linear transformations. All topics are developed with a remarkable lucidity and discussed in close connection with their most frequent mathematical applications.
Algebraic Equations
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Author : Edgar Dehn
language : en
Publisher:
Release Date : 1930
Algebraic Equations written by Edgar Dehn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1930 with Mathematics categories.
This text focuses on the basics of algebraic theory, giving detailed explanations of integral functions, permutations, and groups, and Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.