<p>Yikes, well I was intimidated when starting too – I guess I wanted to convey the one friendly thing about the math you’ll do, though, which is that it pays off tremendously to consider what it is you’re trying to do! As in, going into a first course in algebra and saying “OK, that’s just another structure I have to learn the properties of and grow familiar with” seems like a way to be less nervous to me at least =] I hope I was at least a bit helpful to the OP!</p>
<p>I’m also sorry, I sort of assumed the OP had calculus in high school! Which isn’t fair, different people come from very different backgrounds. </p>
<p>Yeah, enjoy break is good advice, if you’ve had some calculus. Nothing like being fresh and rested and happy. Because I found that if I looked at things in a calm way, my math load was never too much “material,” it’s just getting through it the first time that can be intimidating if you can’t stay calm.</p>
<p>If you want to know, the natural progression would be to learn some linear algebra (because the structures you deal with are simplest to work with, and give you good practice so you won’t find the ones in modern algebra as scary), multivariable calculus (which I actually think seemed LESS intimidating to me than single variable calculus did, since the ideas aren’t all terribly new), and some differential equations (certainly will be friendly, just more complex techniques to solve them). Then you’ll get to the stuff I went on about earlier. </p>
<p>Hey, a good exercise if you haven’t seen them much before is to practice a few epsilon-delta proofs. Proofs about limits from the definition of limit. I think it’s more important to break the ice with this sort of stuff than to get yourself too deep into any material. Toying around with a few exercises is often less annoying anyway! </p>
<p>Good luck.</p>