ENGLISH

Fields and Galois Theory

By John M. Howie

Book information

Publisher
Springer
Year
2006
ISBN
1852339861, 9781852339869
Language
english
Format
PDF
Filesize
943 kB (965238 bytes)
Series
Springer Undergraduate Mathematics Series
Edition
1
Pages
234\234
Topic
Mathematics\\Algebra
Library
Kolxo3
Orientation
portrait
Paginated
yes
Scanned
no
Time added
2011-07-22 07:35:22

Description

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.

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