There are some really good suggestions here. I would like to add that learning calculus properly is of the utmost importance. It's no exaggeration when I say that this is unquestionably the single best, most profitable action you can take. Any one of these books can change your life.

1. Spivak Calculus

2. Apostol Calculus vol. I and II

3. Courant and Johns, Introduction to Calculus and Analysis vol. I, IIA and IIB

For the more casual computer science or physics major, I'd go with choice 3 which resembles the Feynmann lectures the most. All the rigour of the other two is there but in a more digestible form. It's hard for someone not accustomed to hard maths to digest long proofs, it could give you a bad case of indigestion. It's more a function of patience. Courant and Johns get to the point much more quickly while Spivak and Apostol take their time to do everything thoroughly. Courant and Johns does do everything thoroughly but they are kinder to the reader and delay lengthy rigoourous proofs as long as possible while giving plenty of motivation and intuition.

Also I strongly recommend any books by Ray Smullyan particularly his introduction to mathematical logic. "A Beginner's Guide to Mathematical Logic"