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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

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.)

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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