Hi guys, 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.