General Theory Of Algebraic Equations
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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.
The General Theory Of Relativity
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Author : Anadijiban Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26
The General Theory Of Relativity written by Anadijiban Das 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 2012-06-26 with Science categories.
The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einstein’s field equations spherically symmetric solutions and experimental confirmations static and stationary space-time domains black holes cosmological models algebraic classifications and the Newman-Penrose equations the coupled Einstein-Maxwell-Klein-Gordon equations appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.
Lie Equations Vol I
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Author : Antonio Kumpera
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Lie Equations Vol I written by Antonio Kumpera 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 2016-03-02 with Mathematics categories.
In this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that theory, based on the differential calculus in the analytic spaces of Grothendieck, was recently given by B. Malgrange. The first approach adopts Malgrange's idea in defining jet sheaves and linear operators, although the brackets and the non-linear theory arc treated in an essentially different manner. The second approach is based on the theory of derivations, and its relationship to the first is clearly explained. The introduction describes examples of Lie equations and known integrability theorems, and gives applications of the theory to be developed in the following chapters and in the subsequent volume.
General Theory Of C Algebras
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Author :
language : en
Publisher: Elsevier
Release Date : 2001-07-11
General Theory Of C Algebras written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-11 with Mathematics categories.
General Theory of C*-Algebras
Introduction To The Theory Of Algebraic Equations
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Author : Leonard Eugene Dickson
language : en
Publisher: Merchant Books
Release Date : 2009
Introduction To The Theory Of Algebraic Equations written by Leonard Eugene Dickson and has been published by Merchant Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Equations, Theory of categories.
An Unabridged, Digitally Enlarged Printing Of The First Edition Presented In Two Parts, With Appendix And Index. PART ONE: The Lagrange-Cauchy-Abel theory of general algebraic equations - PART TWO: Galois' theory of algebraic equations, whether with arbitrary or special coefficients. There are numerous illustrative examples, as well as sets of elementary exercises. This work requires little dependence on any branch of mathematics beyond elementary algebra.
Algebra
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Author : Siegfried Bosch
language : en
Publisher: Springer
Release Date : 2018-11-02
Algebra written by Siegfried Bosch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.
The material presented here can be divided into two parts. The first, sometimes referred to as abstract algebra, is concerned with the general theory of algebraic objects such as groups, rings, and fields, hence, with topics that are also basic for a number of other domains in mathematics. The second centers around Galois theory and its applications. Historically, this theory originated from the problem of studying algebraic equations, a problem that, after various unsuccessful attempts to determine solution formulas in higher degrees, found its complete clarification through the brilliant ideas of E. Galois. The study of algebraic equations has served as a motivating terrain for a large part of abstract algebra, and according to this, algebraic equations are visible as a guiding thread throughout the book. To underline this point, an introduction to the history of algebraic equations is included. The entire book is self-contained, up to a few prerequisites from linear algebra. It covers most topics of current algebra courses and is enriched by several optional sections that complement the standard program or, in some cases, provide a first view on nearby areas that are more advanced. Every chapter begins with an introductory section on "Background and Overview," motivating the material that follows and discussing its highlights on an informal level. Furthermore, each section ends with a list of specially adapted exercises, some of them with solution proposals in the appendix. The present English edition is a translation and critical revision of the eighth German edition of the Algebra book by the author. The book appeared for the first time in 1993 and, in later years, was complemented by adding a variety of related topics. At the same time it was modified and polished to keep its contents up to date.
Lie Equations
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Author : Antônio Kumpera
language : en
Publisher:
Release Date : 1972-01-01
Lie Equations written by Antônio Kumpera and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-01-01 with Differential equations categories.
The Theory Of Equations
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Author : William Snow Burnside
language : en
Publisher: Forgotten Books
Release Date : 2016-06-26
The Theory Of Equations written by William Snow Burnside and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-26 with Mathematics categories.
Excerpt from The Theory of Equations: With an Introduction to the Theory of Binary Algebraic Forms Many attempts have been made to arrive at similar general formulas for equations of the fifth and higher degrees; but it may now be regarded as established by the researches of modern analysts that it is not possible by means of radical signs, and other signs of operation employed in common algebra, to ex press the root of an equation of the fifth or any higher degree in terms of the coefficients. 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 Algebraic Geometry
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Author : Serge Lang
language : en
Publisher: Courier Dover Publications
Release Date : 2019-03-20
Introduction To Algebraic Geometry written by Serge Lang 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 2019-03-20 with Mathematics categories.
Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
Galois Theory For Beginners A Historical Perspective Second Edition
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Author : Jörg Bewersdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-15
Galois Theory For Beginners A Historical Perspective Second Edition written by Jörg Bewersdorff 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 2021-07-15 with Education categories.
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular n n-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.