Foundations of Galois Theory

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Publisher : Elsevier
ISBN 13 : 1483156478
Total Pages : 122 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Foundations of Galois Theory by : M.M. Postnikov

Download or read book Foundations of Galois Theory written by M.M. Postnikov and published by Elsevier. This book was released on 2014-07-10 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Galois Theory

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Publisher :
ISBN 13 :
Total Pages : 109 pages
Book Rating : 4.:/5 (18 download)

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Book Synopsis Foundations of Galois Theory by : Michail M. Postnikov

Download or read book Foundations of Galois Theory written by Michail M. Postnikov and published by . This book was released on 1995 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Classical Introduction to Galois Theory

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Publisher : John Wiley & Sons
ISBN 13 : 1118336844
Total Pages : 296 pages
Book Rating : 4.1/5 (183 download)

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Book Synopsis A Classical Introduction to Galois Theory by : Stephen C. Newman

Download or read book A Classical Introduction to Galois Theory written by Stephen C. Newman and published by John Wiley & Sons. This book was released on 2012-05-29 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the foundations and modern applications of Galois theory Galois theory is widely regarded as one of the most elegant areas of mathematics. A Classical Introduction to Galois Theory develops the topic from a historical perspective, with an emphasis on the solvability of polynomials by radicals. The book provides a gradual transition from the computational methods typical of early literature on the subject to the more abstract approach that characterizes most contemporary expositions. The author provides an easily-accessible presentation of fundamental notions such as roots of unity, minimal polynomials, primitive elements, radical extensions, fixed fields, groups of automorphisms, and solvable series. As a result, their role in modern treatments of Galois theory is clearly illuminated for readers. Classical theorems by Abel, Galois, Gauss, Kronecker, Lagrange, and Ruffini are presented, and the power of Galois theory as both a theoretical and computational tool is illustrated through: A study of the solvability of polynomials of prime degree Development of the theory of periods of roots of unity Derivation of the classical formulas for solving general quadratic, cubic, and quartic polynomials by radicals Throughout the book, key theorems are proved in two ways, once using a classical approach and then again utilizing modern methods. Numerous worked examples showcase the discussed techniques, and background material on groups and fields is provided, supplying readers with a self-contained discussion of the topic. A Classical Introduction to Galois Theory is an excellent resource for courses on abstract algebra at the upper-undergraduate level. The book is also appealing to anyone interested in understanding the origins of Galois theory, why it was created, and how it has evolved into the discipline it is today.

Foundations of Galois Theory

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Publisher : Pergamon
ISBN 13 : 9780080096865
Total Pages : 0 pages
Book Rating : 4.0/5 (968 download)

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Book Synopsis Foundations of Galois Theory by : Mikhail Mikhaĭlovich Postnikov

Download or read book Foundations of Galois Theory written by Mikhail Mikhaĭlovich Postnikov and published by Pergamon. This book was released on 1962 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent mathematician, this text offers advanced undergraduate and graduate students a virtually self-contained treatment of the basics of Galois theory. The source of modern abstract algebra and one of abstract algebra's most concrete applications, Galois theory serves as an excellent introduction to group theory and provides a strong, historically relevant motivation for the introduction of the basics of abstract algebra. This two-part treatment begins with the elements of Galois theory, focusing on related concepts from field theory, including the structure of important types of extensions and the field of algebraic numbers. A consideration of relevant facts from group theory leads to a survey of Galois theory, with discussions of normal extensions, the order and correspondence of the Galois group, and Galois groups of a normal subfield and of two fields. The second part explores the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concluding with the unsolvability by radicals of the general equation of degree n [greater than or equal] 5. Book jacket.

Fields and Galois Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1852339861
Total Pages : 230 pages
Book Rating : 4.8/5 (523 download)

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Book Synopsis Fields and Galois Theory by : John M. Howie

Download or read book Fields and Galois Theory written by John M. Howie and published by Springer Science & Business Media. This book was released on 2007-10-11 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Foundations of Galois Theory

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Foundations of Galois Theory by : Mikhail Mikhailovich Postnikov

Download or read book Foundations of Galois Theory written by Mikhail Mikhailovich Postnikov and published by . This book was released on 1962 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Course in Galois Theory

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Publisher : Cambridge University Press
ISBN 13 : 9780521312493
Total Pages : 180 pages
Book Rating : 4.3/5 (124 download)

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Book Synopsis A Course in Galois Theory by : D. J. H. Garling

Download or read book A Course in Galois Theory written by D. J. H. Garling and published by Cambridge University Press. This book was released on 1986 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.

Exploratory Galois Theory

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Publisher : Cambridge University Press
ISBN 13 : 9780521544993
Total Pages : 224 pages
Book Rating : 4.5/5 (449 download)

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Book Synopsis Exploratory Galois Theory by : John Swallow

Download or read book Exploratory Galois Theory written by John Swallow and published by Cambridge University Press. This book was released on 2004-10-11 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. The text is appropriate for traditional lecture courses, for seminars, or for self-paced independent study by undergraduates and graduate students.

Galois Theory for Beginners

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Publisher : American Mathematical Soc.
ISBN 13 : 0821838172
Total Pages : 202 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Galois Theory for Beginners by : Jörg Bewersdorff

Download or read book Galois Theory for Beginners written by Jörg Bewersdorff and published by American Mathematical Soc.. This book was released on 2006 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of p-adic Teichmüller Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 1470412268
Total Pages : 529 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Foundations of p-adic Teichmüller Theory by : Shinichi Mochizuki

Download or read book Foundations of p-adic Teichmüller Theory written by Shinichi Mochizuki and published by American Mathematical Soc.. This book was released on 2014-01-06 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the foundation for a theory of uniformization of p-adic hyperbolic curves and their moduli. On one hand, this theory generalizes the Fuchsian and Bers uniformizations of complex hyperbolic curves and their moduli to nonarchimedian places. That is why in this book, the theory is referred to as p-adic Teichmüller theory, for short. On the other hand, the theory may be regarded as a fairly precise hyperbolic analog of the Serre-Tate theory of ordinary abelian varieties and their moduli. The theory of uniformization of p-adic hyperbolic curves and their moduli was initiated in a previous work by Mochizuki. And in some sense, this book is a continuation and generalization of that work. This book aims to bridge the gap between the approach presented and the classical uniformization of a hyperbolic Riemann surface that is studied in undergraduate complex analysis. Features: Presents a systematic treatment of the moduli space of curves from the point of view of p-adic Galois representations.Treats the analog of Serre-Tate theory for hyperbolic curves.Develops a p-adic analog of Fuchsian and Bers uniformization theories.Gives a systematic treatment of a "nonabelian example" of p-adic Hodge theory. Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.

Galois Theory of Difference Equations

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Publisher : Springer
ISBN 13 : 354069241X
Total Pages : 182 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Galois Theory of Difference Equations by : Marius van der Put

Download or read book Galois Theory of Difference Equations written by Marius van der Put and published by Springer. This book was released on 2006-11-14 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.

Galois Groups and Fundamental Groups

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Publisher : Cambridge University Press
ISBN 13 : 1139481142
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Galois Groups and Fundamental Groups by : Tamás Szamuely

Download or read book Galois Groups and Fundamental Groups written by Tamás Szamuely and published by Cambridge University Press. This book was released on 2009-07-16 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.

Galois Theory

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Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (111 download)

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Book Synopsis Galois Theory by : Emil Artin

Download or read book Galois Theory written by Emil Artin and published by . This book was released on 1948 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Abstract Algebra

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110605252
Total Pages : 613 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Abstract Algebra by : Celine Carstensen-Opitz

Download or read book Abstract Algebra written by Celine Carstensen-Opitz and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-02 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects.

Algebraic Theories

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Publisher : Courier Corporation
ISBN 13 : 048615520X
Total Pages : 275 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Algebraic Theories by : Leonard Dickson

Download or read book Algebraic Theories written by Leonard Dickson and published by Courier Corporation. This book was released on 2014-03-05 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Galois Theories

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Publisher : Cambridge University Press
ISBN 13 : 9780521803090
Total Pages : 360 pages
Book Rating : 4.8/5 (3 download)

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Book Synopsis Galois Theories by : Francis Borceux

Download or read book Galois Theories written by Francis Borceux and published by Cambridge University Press. This book was released on 2001-02-22 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops Galois theory in a more general context, emphasizing category theory.

Whom the Gods Love

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Publisher :
ISBN 13 :
Total Pages : 323 pages
Book Rating : 4.:/5 (78 download)

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Book Synopsis Whom the Gods Love by : Leopold Infeld

Download or read book Whom the Gods Love written by Leopold Infeld and published by . This book was released on 1948 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: