Intuitive approach to algebra?

I’m studying maths at uni and I’ve just had a course in Galois Theory.

While I have understood the importance of the subject and while I can demonstrate most of the theorems, I can’t get my head around some basic ideas.

For example, what does it really mean for a group to be solvable?

I’ve “understood” Galois Theorem (about solvability by radicals and solvability of groups), but, for example, what’s missing in A_5? Why is A_4 solvable? Why are Dihedral Groups solvable? Why one even felt the need to give a name to a chain of groups whose factors are abelian?

submitted by /u/maurocanta
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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs

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