Comment by nextos

A key subject is Logic. Logic is the Calculus of CS and should be your first stop. I recommend:

* Logic for Computer Scientists by Uwe Schoening

* Logic in Computer Science by M. Huth and M. Ryan

The first one is short, very elegant and doable. The second one is a bit longer, but also at freshman level.

There are PDFs circulating on the Internet. Skim through those before buying a hardcopy.