I study computer science at a university. My school offers several courses where various proofs are expected, but there is no course that introduces the fundamental concepts of proofs and how to write your own proofs. It's possible to "muddle through" some of these courses without really understanding proofs, but I want to spare myself the frustration and actually learn about them.
How can I learn about proofs for computer science?
I want to start at the very basics of proofs. I'm only interested in proofs as they relate to computer science, since I will have to spend my spare time on this. However, if I really do need to learn about mathematical proofs in general first, then so be it.
Note: Just reading the proofs in our course literature is not enough; this is what me and my classmates do right now, and none of us have any deeper understanding of what constitutes an actual proof.