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The Resource A classical introduction to Galois theory, Stephen C. Newman
A classical introduction to Galois theory, Stephen C. Newman
Resource Information
The item A classical introduction to Galois theory, Stephen C. Newman represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item A classical introduction to Galois theory, Stephen C. Newman represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 "This book provides an introduction to Galois theory and focuses on one central theme  the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematics, and a fundamental question to be considered is: For a given polynomial equation (over a given field), does a solution in terms of radicals exist? That the need to investigate the very existence of a solution is perhaps surprising and invites an overview of the history of mathematics. The classical material within the book includes theorems on polynomials, fields, and groups due to such luminaries as Gauss, Kronecker, Lagrange, Ruffini and, of course, Galois. These results figured prominently in earlier expositions of Galois theory, but seem to have gone out of fashion. This is unfortunate since, aside from being of intrinsic mathematical interest, such material provides powerful motivation for the more modern treatment of Galois theory presented later in the book. Over the course of the book, three versions of the Impossibility Theorem are presented: the first relies entirely on polynomials and fields, the second incorporates a limited amount of group theory, and the third takes full advantage of modern Galois theory. This progression through methods that involve more and more group theory characterizes the first part of the book. The latter part of the book is devoted to topics that illustrate the power of Galois theory as a computational tool, but once again in the context of solvability of polynomial equations by radicals"
 Language
 eng
 Extent
 1 online resource.
 Contents

 A CLASSICAL INTRODUCTION TO GALOIS THEORY; CONTENTS; PREFACE; 1 CLASSICAL FORMULAS; 1.1 Quadratic Polynomials; 1.2 Cubic Polynomials; 1.3 Quartic Polynomials; 2 POLYNOMIALS AND FIELD THEORY; 2.1 Divisibility; 2.2 Algebraic Extensions; 2.3 Degree of Extensions; 2.4 Derivatives; 2.5 Primitive Element Theorem; 2.6 Isomorphism Extension Theorem and Splitting Fields; 3 FUNDAMENTAL THEOREM ON SYMMETRIC POLYNOMIALS AND DISCRIMINANTS; 3.1 Fundamental Theorem on Symmetric Polynomials; 3.2 Fundamental Theorem on Symmetric Rational Functions; 3.3 Some Identities Based on Elementary Symmetric Polynomials
 Isbn
 9781118336847
 Label
 A classical introduction to Galois theory
 Title
 A classical introduction to Galois theory
 Statement of responsibility
 Stephen C. Newman
 Language
 eng
 Summary
 "This book provides an introduction to Galois theory and focuses on one central theme  the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematics, and a fundamental question to be considered is: For a given polynomial equation (over a given field), does a solution in terms of radicals exist? That the need to investigate the very existence of a solution is perhaps surprising and invites an overview of the history of mathematics. The classical material within the book includes theorems on polynomials, fields, and groups due to such luminaries as Gauss, Kronecker, Lagrange, Ruffini and, of course, Galois. These results figured prominently in earlier expositions of Galois theory, but seem to have gone out of fashion. This is unfortunate since, aside from being of intrinsic mathematical interest, such material provides powerful motivation for the more modern treatment of Galois theory presented later in the book. Over the course of the book, three versions of the Impossibility Theorem are presented: the first relies entirely on polynomials and fields, the second incorporates a limited amount of group theory, and the third takes full advantage of modern Galois theory. This progression through methods that involve more and more group theory characterizes the first part of the book. The latter part of the book is devoted to topics that illustrate the power of Galois theory as a computational tool, but once again in the context of solvability of polynomial equations by radicals"
 Assigning source
 Provided by publisher
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 1952
 http://library.link/vocab/creatorName
 Newman, Stephen C.
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA214
 Literary form
 non fiction
 Nature of contents

 standards specifications
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 ebrary
 http://library.link/vocab/subjectName

 Galois theory
 MATHEMATICS / Applied
 Mathematics
 Galois theory
 Label
 A classical introduction to Galois theory, Stephen C. Newman
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 A CLASSICAL INTRODUCTION TO GALOIS THEORY; CONTENTS; PREFACE; 1 CLASSICAL FORMULAS; 1.1 Quadratic Polynomials; 1.2 Cubic Polynomials; 1.3 Quartic Polynomials; 2 POLYNOMIALS AND FIELD THEORY; 2.1 Divisibility; 2.2 Algebraic Extensions; 2.3 Degree of Extensions; 2.4 Derivatives; 2.5 Primitive Element Theorem; 2.6 Isomorphism Extension Theorem and Splitting Fields; 3 FUNDAMENTAL THEOREM ON SYMMETRIC POLYNOMIALS AND DISCRIMINANTS; 3.1 Fundamental Theorem on Symmetric Polynomials; 3.2 Fundamental Theorem on Symmetric Rational Functions; 3.3 Some Identities Based on Elementary Symmetric Polynomials
 Dimensions
 unknown
 Extent
 1 online resource.
 Form of item
 electronic
 Isbn
 9781118336847
 Lccn
 2012005885
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Specific material designation
 remote
 Stock number
 10.1002/9781118336816
 System control number

 (OCoLC)775780317
 (OCoLC)ocn775780317
 Label
 A classical introduction to Galois theory, Stephen C. Newman
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 A CLASSICAL INTRODUCTION TO GALOIS THEORY; CONTENTS; PREFACE; 1 CLASSICAL FORMULAS; 1.1 Quadratic Polynomials; 1.2 Cubic Polynomials; 1.3 Quartic Polynomials; 2 POLYNOMIALS AND FIELD THEORY; 2.1 Divisibility; 2.2 Algebraic Extensions; 2.3 Degree of Extensions; 2.4 Derivatives; 2.5 Primitive Element Theorem; 2.6 Isomorphism Extension Theorem and Splitting Fields; 3 FUNDAMENTAL THEOREM ON SYMMETRIC POLYNOMIALS AND DISCRIMINANTS; 3.1 Fundamental Theorem on Symmetric Polynomials; 3.2 Fundamental Theorem on Symmetric Rational Functions; 3.3 Some Identities Based on Elementary Symmetric Polynomials
 Dimensions
 unknown
 Extent
 1 online resource.
 Form of item
 electronic
 Isbn
 9781118336847
 Lccn
 2012005885
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Specific material designation
 remote
 Stock number
 10.1002/9781118336816
 System control number

 (OCoLC)775780317
 (OCoLC)ocn775780317
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