Well, if you're looking for an introduction to the basics of mathematics (which I would recommend for anyone looking to delve deeper into any specific area), you can't really beat 'How to Prove It' by Velleman. It covers the fundamental concepts of mathematical analysis and proof-writing (and, perhaps more importantly, reading proofs) and will help give you a great grounding for further reading, especially in the areas of discrete mathematics, set theory, and probability. I can't recommend it enough as an enjoyable introduction to the field.

Also, for a good probability textbook, I would point you to 'Probability and Random Processes' by Grimmett and Stirzaker. It may be a bit hard-going at first (which is why I recommend How to Prove It to get you used to rigorous maths), but it is a very thorough text that also happens to concentrate on many areas of interest to the average programmer (Markov chains and the like). Together with the companion book of exercises, it should be fantastic for self-teaching, too.

In calculus, you have so many options that I can only really suggest you go out and find one that you like. I used 'Early Transcendentals' by Stewart in my first year Calculus lectures and it's served as a good reference ever since, particularly for basic vector / multi-dimensional calculus. But, like I say, just look around.