Fields and Galois Theory / Edition 1

Fields and Galois Theory / Edition 1

by John M. Howie
     
 

ISBN-10: 1852339861

ISBN-13: 9781852339869

Pub. Date: 09/26/2007

Publisher: Springer London

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

…  See more details below

Overview

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.

Product Details

ISBN-13:
9781852339869
Publisher:
Springer London
Publication date:
09/26/2007
Series:
Springer Undergraduate Mathematics Series
Edition description:
1st ed. 2005. Corr. 2nd printing 2007
Pages:
226
Product dimensions:
7.00(w) x 10.00(h) x 0.51(d)

Table of 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.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >