Early math education for college

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I plan to go the path of mathematics in college. I've always been an adept at solving problems and writing proofs.

I'm only 17 and doing self-study. I checked out from the university library the second volume of Calculus by Apostol and Principles of Mathematical Analysis by Rudin. These should be good for a few months of study, but am I going in the wrong direction as a freshman undergraduate? I'm still not sure what kind of maturity is expected of an undergraduate doing pure math.

So what should I study in preparation for my first year?

(I would have posted this in the sticky, but there are too many important and specific questions in there. I won't clutter.)
 
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I plan to go the path of mathematics in college. I've always been an adept at solving problems and writing proofs.

I'm only 17 and doing self-study. I checked out from the university library the second volume of Calculus by Apostol and Principles of Mathematical Analysis by Rudin. These should be good for a few months of study, but am I going in the wrong direction as a freshman undergraduate? I'm still not sure what kind of maturity is expected of an undergraduate doing pure math.

So what should I study in preparation for my first year?

(I would have posted this in the sticky, but there are too many important and specific questions in there. I won't clutter.)
As far as what is expected, it depends on where you are going to go to college. At the school I went to they don't really expect anything. You have to at least be ready to take pre-calculus. I myself only started college doing Multivariable Calc and didn't take Analysis until the begging of my second year. At somewhere like Caltech they expect you to be able to handle Apostol. So if you can handle Apostol and Rudin you are doing more than fine.

Of course if you want to stand out then what you are doing is great. However depending on where you go they might or might not let you get accelerated. You should find out how things work at the school you plan to go. At my school I was able to start with multivariable calc and finished my lower division classes my first year. I took analysis (2 quarters), complex analysis (undergraduate), differential geometry (2 quarters), linear algebra (upper division), topology all in my second year and that spring quarter I took my first graduate class, Graduate complex analysis. So even though I did not start as advanced and with as much maturity as you will I'm still doing fairly well (I'm in my third year right now) and because my school let me take alot of classes at the same time my maturity level rose really fast.

II think at some schools they make you start with calculus your first year. They might waive that requirement if you can demonstrate that you have the mathematical maturity to go onto more advanced subjects, but this is what you need to find out about.

Just out of curiosity: where are you planning to go for college? Are you a senior in HS or a junior?
 
  • #3
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To answer your question, I'm looking at UGA and UT. I have friends in both areas, and I love both locations. I currently live in Athens, so UGA would be nearby, but Austin is nice too.

I'm in home school. I haven't had much formal math instruction.
 
  • #4
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To answer your question, I'm looking at UGA and UT. I have friends in both areas, and I love both locations. I currently live in Athens, so UGA would be nearby, but Austin is nice too.

I'm in home school. I haven't had much formal math instruction.
Well, like I said before if you can handle Apostol and Rudin, that should be more than enough.

In my opinion the best preparation is to go in with the mindset of wanting to learn math. Work hard and doing good in you classes should follow. Plus if you are good at proofs, then you should have no problem.

Really most schools don't expect you to be that advanced, but if you are then that's great for you.

Well, this is just me, so let's see what other people think.
 
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