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I am a senior in high school intending on becoming a physicist. I would like to know what books/textbooks I should buy and start working on to get ahead in university. I am particularly talking about math books. I have a few goals:

1.Prepare myself for university

2.Have a good knowledge of the subjects that I will learn at university before they are taught

3.Getting into the juicy quantum mechanics math as soon as possible without skipping anything (I think that I would like to make a career out of research in fundamental QM)

4.Be able to do summer research in physics at my university (you can as early as 1st year)

I know that I at least should get books in (I know I must be forgetting subjects):

1.Calculus (I currently have just about no calculus training. Could I benefit from Spivak?)

2.Trig

3.Vectors

4.Algebra

What physics books should I buy?

I am also looking for a QM book that is harder than those I have currently read (mostly a non-mathematical hodge-podge of books with a few chapters on QM).

I have Dirac's QM book as well as Shankar's. These are both too hard for me now.

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# Schools Personal pre-university curriculum

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