Galois theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Galois_theory


00:01:11 1 Application to classical problems
00:02:52 2 History
00:03:00 2.1 Pre-history
00:07:49 2.2 Galois' writings
00:08:31 2.3 Aftermath
00:08:41 3 Permutation group approach to Galois theory
00:09:44 3.1 First example: a quadratic equation
00:09:53 3.2 Second example
00:11:24 4 Modern approach by field theory
00:11:36 5 Solvable groups and solution by radicals
00:12:44 5.1 A non-solvable quintic example
00:13:43 6 Inverse Galois problem
00:15:24 7 See also
00:15:59 8 Notes
00:19:12 9 References
00:22:05 10 External links
00:23:55 A non-solvable quintic example
00:25:21 Inverse Galois problem
00:27:18 See also



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SUMMARY
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In mathematics, Galois theory provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is in some sense simpler and better understood.
The subject is named after Évariste Galois, who introduced it for studying the roots
of a polynomial and characterizing the polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is solvable by radicals if its roots may be expressed by a formula involving only integers, nth roots and the four basic arithmetic operations.  
The theory has been popularized (among mathematicians) and developed by Richard Dedekind, Leopold Kronecker and Emil Artin, and others, who, in particular, interpreted the permutation group of the roots as the automorphism group of a field extension.
Galois theory has been generalized to Galois connections and Grothendieck's Galois theory.