Field And Galois Theory

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Fields And Galois Theory

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Author : John M. Howie
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-11

Fields And Galois Theory written by John M. Howie 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 2007-10-11 with Mathematics categories.

A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews

Field And Galois Theory

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Author : Patrick Morandi
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-07-25

Field And Galois Theory written by Patrick Morandi 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 1996-07-25 with Mathematics categories.

The purpose of this book is twofold. First, it is written to be a textbook for a graduate level course on Galois theory or field theory. Second, it is designed to be a reference for researchers who need to know field theory. The book is written at the level of students who have familiarity with the basic concepts of group, ring, vector space theory, including the Sylow theorems, factorization in polynomial rings, and theorems about bases of vector spaces. This book has a large number of examples and exercises, a large number of topics covered, and complete proofs given for the stated results. To help readers grasp field.

Field And Galois Theory

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Author : Patrick Morandi
language : en
Publisher:
Release Date : 1996-07-01

Field And Galois Theory written by Patrick Morandi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-01 with categories.

Field Theory

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Author : Steven Roman
language : en
Publisher: Springer
Release Date : 2013-12-20

Field Theory written by Steven Roman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Mathematics categories.

Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory.

Galois Theory For Beginners

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Author : Jörg Bewersdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Galois Theory For Beginners 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 2006 with Mathematics categories.

Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. This book follows the historical development of the theory, emphasizing concrete examples along the way. It is suitable for undergraduates and beginning graduate students.

Galois Theory

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Author : David A. Cox
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-24

Galois Theory written by David A. Cox and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-24 with Mathematics categories.

An introduction to one of the most celebrated theories of mathematics Galois theory is one of the jewels of mathematics. Its intrinsic beauty, dramatic history, and deep connections to other areas of mathematics give Galois theory an unequaled richness. David Cox’s Galois Theory helps readers understand not only the elegance of the ideas but also where they came from and how they relate to the overall sweep of mathematics. Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel’s theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami. Anyone fascinated by abstract algebra will find careful discussions of such topics as: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois’s results about irreducible polynomials of prime or prime-squared degree Abel’s theorem about geometric constructions on the lemniscate With intriguing Mathematical and Historical Notes that clarify the ideas and their history in detail, Galois Theory brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike.

Galois Theory Of Algebraic Equations

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Author : Jean-pierre Tignol
language : en
Publisher: World Scientific Publishing Company
Release Date : 2001-04-02

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 2001-04-02 with Mathematics categories.

New Edition available hereGalois' 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.

Foundations Of Galois Theory

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Author : M.M. Postnikov
language : en
Publisher: Elsevier
Release Date : 2014-07-10

Foundations Of Galois Theory written by M.M. Postnikov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.

Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.

Lectures In Abstract Algebra

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Author : N. Jacobson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Lectures In Abstract Algebra written by N. Jacobson 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 present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a number of objectives in mind. First and foremost has been that of presenting the basic field theory which is essential for an understanding of modern algebraic number theory, ring theory, and algebraic geometry. The parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen sional field extensions and Galois theory, general structure theory of fields, and valuation theory. Also the results of Chapter IlIon abelian extensions, although of a somewhat specialized nature, are ofinterest in number theory. A second objective of our ac count has been to indicate the links between the present theory of fields and the classical problems which led to its development.

Algebra Fields And Galois Theory

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Author : Falko Lorenz
language : en
Publisher:
Release Date : 2008-05-01

Algebra Fields And Galois Theory written by Falko Lorenz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-01 with Algebra categories.