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Ok, this summer im self-studying Alg II so I can test out of it in August for my highschool. I was also planning on learning alot of pre-calc/calc from a friend, but I'm somewhat skeptical about it because he seems to not have that much time on his hands and I don't want to be a burden to him. The last thing I was going to study would be Alg II based Physics and some Calc based Physics (not to sure about the Calc based Physics, if anyone has a tremendousley good textbook PLEASE refer it too me).

If learning Pre-Calc/Calc from a friend doesn't work out then could anyone recommend a really fun and rigorous subject to me?

I'm looking along the lines of; Intro to Number Theory, Intermediate Counting & Probability, Abstract Algebra, Linear Algebra, Differential Geometry, and basically whatever else I would be capable of doing.

About 6 of the 12 weeks of summer I will be traveling, at camps, vacation, ect., so with the off time I have on my hands (which will be alot) I would really enjoy getting into a completely new and rigorous subject.

*Please keep in mind that I am in highschool, freshman to be exact, so please don't recommend a subject and textbook thats completely out of my league. Also, don't recommend Pre-Calc/Calc, I'm only interested in learning it this summer if my friend is teaching me. Otherwise I will just wait til my Sophomore year Calc course.

Thanks!