Galois theory

I seem to have been quite successful in scaring some students in the last two classes on Galois theory. My intention was pretty innocent: showing that the simple problem of finding formulas for the roots of cubic, quartic, quintic ... polynomials led step by step to an elaborate abstract theory, namely Galois theory. If you sat through these classes without any real idea of what was going on, then you can imagine how Cauchy must have felt when he saw Galois' theory exposed in a few densely written pages: he didn't understand a word. You also should develop some respect for the genius of Galois who dreamed up this whole area before he got himself killed at 20.
What I will not do is cover this material in the final. The problem is that if I had announced this in advance, then the classes would have been empty -(.
In any case, those of you with some background in algebra should have seen how the abstract theory evolved in the 18th century, and that it evolved from very concrete problems, in our case the solvability of polynomials by radicals. As for those of you without this background: I hope I haven't put you off too much, and maybe you'll attend a course on abstract algebra one day to fill in these gaps.