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Maths Recap

Obviously with the summer been and gone (well almost, some still have a couple of weeks left) it's back to Uni for everyone. Having had a quick flick through last years notes though, I feel like i've forgotten everything.

I'm not wanting to go as far as 'revising' past papers etc, as I feel that serves a different purpose. I'm trying to establish the theories behind all the topics again to keep my mind fresh for when the term starts, but have no real idea how to do this. When it's come down to revising etc it's always been past papers, learn from mistakes and repeat until i've got the hang of it. I've struggled to recap on the theories behind the Maths to keep it fresh in my mind, though. Does anyone have any tips on how to get it to sink in again?

Anyone?

Original post by Schmucks

Anyone?

Um, I wouldn't say forget everything but they will go over this (A-level) stuff at uni. And make you prove what you used to take for granted. Maths at uni is a bit like "starting again". That's the mentality I would recommend.

Basically, A-level maths goes up to the end of the 1600s, then stops. A lot has happened in the meantime. More or less, people realised that things they hadn't thought needed to be demonstrated, actually should really be proved.

Secondly, people realised that there existed abstract concepts, of a qualitative (as opposed to quantitative) nature, which had a legitimate claim to count as precise mathematical concepts. The prototypical straw that broke the camel's back was probably Galois' realization that "groups" were just the thing needed to explain hard-headed eventualities in the theory of polynomials. Namely, the quadratic formula (for quadratic equations) can be extended in a natural way to provide a (complicated) cubic formula for cubic equations. But this extension cannot go on forever. A coherent explanation of why it cannot go on forever is due to group theory, a field of mathematics that was invented by Galois.

And that's just the purely mathematical side of things. Don't forget applications (there are some pretty cool ones), although I am not as knowledgeable about that sort of thing.