Pure maths is a lot of following rules and once you know how the rules work, it's pretty easy to solve almost everything :o) And I agree with you about matrices for solving quadratics - they are such an elegant way of getting to the solution. Mind you I was the only one in my O Level Maths group to think so - even the guy who later went on to do a maths degree didn't really get them! I seem to remember vector operations can be expressed in matrix form, but don't quote me on that - I did A Level Maths (Pure and Applied) as separate subjects nearly 20 years ago! From getting an unclassified mark in my mocks in the January, I got B grades in the actual papers. There were a lot of tears of frustration in my classes in those years, but it was worth it when the Head of Maths saw me on results day - he'd a huge grin on his face, showed me the slip, then said "How the f*ck did you manage that?" - and added that he was proud of me! So it is possible to have the brain explosion that clears the fog...

And talking of fog - quantum mechanics. If you really, really want to go there, take it from a scarred survivor of a year of classes in the subject at University (where I was studying Materials Science and Metallurgy because I thought it would be easier than Physics - ha!) - prepare yourself for an interesting experience. It wasn't really the maths that was tough, it was understanding the concepts behind it. A grasp of probability theory might also help... I think. I've blocked the experience from my long term memory, although allegedly, it was one of the papers I passed when I failed my second year.

I'm sure someone with more knowledge will be along shortly to expound better :o)