I've just finished my high school education and cannot wait until I get to go to university - but I've got 3 whole months to endure first. Maths is ultimately my favorite subject but I'm just really interested in its applications at the moment - namely applications to the weird and wonderful phenomena in physics.
What are some relatively involved physics books (about M-theory, black holes, quantum mechanics etc) that are understandable to a student who has studied high school physics and maths?
I don't want really simple 'laymans' books, I feel like my education has put me slightly past that level. I was considering Brian Greene's book "the elegant universe"... I've already seen his documentaries (fabric of the cosmos); they were interesting but didn't really go into the kind of depth I was looking for. Everything seemed like magic with no real explanation. I want to begin to really understand what's going on rather than just read about it. (p.s. im not looking for a textbook). I know I'm being really picky but please help!
This is my mathematical background so I should be able to follow along with any books containing these concepts:
*Calculus (Derivatives and integration + some differential equations)
*Linear algebra at the first-year university level (I did a first-year course there in my spare time while still in high school)(vectors, linear independence, scalar product. Matrices, simultaneous equations, determinants, vector product, eigenvalues, eigenvectors. Equation of straight line & plane)
And most likely more but i can't recall it all now. It would definitely come back to me though.