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My plan is to read how to prove it, spivak calculus, a probability book, and maybe something about linear algebra in the 4 months I have off. (I already have taken linear algebra, but I'd want a more theoretical book)

I've been considering replacing one of these books with learning Euclids Elements, as I noted that Newton's intellect peaked after reading this book. As someone who has never taken geometry before, would it be worth doing geometry in my summer for my major?

I plan on studying very hard, 10+ hours a day, 6-7 days a week.