12/05/21 22:13:12.40
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Brent Everitt, University of York, England
URLﾘﾝｸ(www-users.york.ac.uk)
Symmetries of Equations: An Introduction to Galois Theory
Brent Everitt, version 1.12, December 19, 2007.
Department of Mathematics, University of York, York YO10 5DD, England.
Contents
1. What is Galois Theory? .......3
（抜粋）
"Evarist´e Galois started thinking about the deeper problem: why
don’t these formulae exist? Thus Galois theory was originally motivated by the desire to understand, in a
much more precise way than they hitherto had been, the solutions to polynomial equations.
Galois’ idea was this: study the solutions by studying their “symmetries”. Nowadays, when we hear
the word symmetry, we normally think of group theory rather than number theory. Actually, to reach
his conclusions, Galois kind of invented group theory along the way. In studying the symmetries of the
solutions to a polynomial, Galois theory establishes a link between these two areas of mathematics."
（引用おわり）