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Okay, my turn to ask for help....
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
Re: Galois Groups
You have to learn a whole lot of things before trying to tackle Galois Theory. Start with groups and work your way up to rings and fields. But this is abstract algebra, it is nothing easy.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."