namelesslady said:
At the risk of sounding like a giant nerd, maths really is a tops subject. We've just started calculas, and I didn't really like it at first, but it's all starting to make sense. It's so clever that you can figure out so much, with so little. Everything has a reason, and - it's just top shelf. Go maths, and my fellow enthusists!
Wow, I really do sound like a nerd.
Great to see people like you! We need more of you.
I'm going to be doing mathematics at university, myself (pure, applied and some stats). I'm especially interested in algebras, but I like analysis and the rest, too.
If you're at all keen (and plan to do maths at uni*), then I'd suggest you pick up 'Calculus' by Michael Spivak. This text starts from the beginning, but challenges even the best maths students. Because of that, you might also want to grab 'Calculus: Multivariate' by James Stewart, which has the benefit of probably being the text you will use in first year uni (though obviously if it isn't, you may want to buy the one that is, instead). You can uses Stewart's whenever you get stuck.
To be honest, Spivak's is probably more an introduction to analysis to bridge the gap between 1st and 2nd year uni. Still, if you're keen, and you REALLY want to explore maths thoroughly, not half-heartedly, it's a good investment.
Of course, these are both university textbooks, which means the price for both would be somewhere around $200. But hey - small price to pay for learning more maths faster, IMHO. Anyway, as I said, you'll refer to them all the time at uni, so it's not a waste, either.
My 2 cents.
*Why do maths at uni? Basically, if there's a single degree that's worth doing at uni, that's maths. It will equip you with a skillset that will last you for life and that employers, whoever they are, will highly value. You can then go and pursue engineering or commerce or whatever if you don't want to be working in informatics. Or you could simply do a maths degree combined with a commerce or engineering degree.
Some people say maths is useless and that they'll never use it. Well, ignoring the inherent beauty of maths and pursuing it simply for the sake of it, maths makes you 'smarter' and you can applying it to all sorts of fields - I would hardly call that useless (As you'll begin to understand when you come to things like exponential growth and decay - which is a simple model of a system. Such models almost always use differential equations, which are the backbone of many scientific and quantitative disciplines).
/end rant
EDIT: If you have any questions, feel free to ask me. And don't be perturbed by the mediocrity above.
