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Galois theory, named after Évariste Galois, 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.
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Ideas for introducing Galois theory to advanced high school students
I recently came across a YouTube video by "not all wrong" called Galois-Free Guarantee! | The Insolubility of the Quintic that I think offers a lot of good ideas for making this material accessible to …