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Fields and Galois Theory

Librairie Eyrolles - Paris 5e
Disponible en magasin

Fields and Galois Theory

Fields and Galois Theory

John M. Howie - Collection Springer Undergraduate Mathematics Series (SUMS)

226 pages, parution le 31/12/2005

Résumé

The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra.

This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection.

Topics covered include:

  • rings and fields
  • integral domains and polynomials
  • field extensions and splitting fields
  • applications to geometry
  • finite fields
  • the Galois group
  • equations

Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.

L'auteur - John M. Howie

University of St. Andrews, UK

Sommaire

  • Preface
  • Contents
  • Rings and Fields
  • Integral Domains and Polynomials
  • Field Extensions
  • Applications to Geometry
  • Splitting Fields
  • Finite Fields
  • The Galois Group
  • Equations and Groups
  • Some Group Theory
  • Groups and Equations
  • Regular Polygons
  • Solutions
  • Bibliography
  • List of Symbols
  • Index
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Caractéristiques techniques

  PAPIER
Éditeur(s) Springer
Auteur(s) John M. Howie
Collection Springer Undergraduate Mathematics Series (SUMS)
Parution 31/12/2005
Nb. de pages 226
Format 17,5 x 23,5
Couverture Broché
Poids 395g
Intérieur Noir et Blanc
EAN13 9781852339869
ISBN13 978-1-85233-986-9

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