The Resource A classical introduction to Galois theory, Stephen C. Newman

A classical introduction to Galois theory, Stephen C. Newman

Label
A classical introduction to Galois theory
Title
A classical introduction to Galois theory
Statement of responsibility
Stephen C. Newman
Creator
Contributor
Provider
Subject
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
Instantiates
Publication
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
Publication
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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