These are all things I would like a firm theoretical grasp of. The problem is most of the algebra books and precalc books I've seen only emphasize memorization of the techiques, which is a skill I already have. I'd like theorems, proofs, and definitions of elementary math. The closest thing to such a book I've read is Courant's WIM, but even he already assumes you know a lot of this stuff, like exponents (which I do, but not why they work). Likewise, I'd like a firm grasp of Euclidean geometry for the mathematically mature.

Can anyone reccommend titles?