For computer science, I would recommend starting with discrete mathematics. A good book is the Rosen book, which my university uses. From there, you can move on to Concrete Mathematics, Introduction to Algorithms, and Introduction to the Theory of Computation. I can't speak much about Introduction to Algorithms - it's still on my wish list. But the other two are very good. That should cover the basics of computer science.
From there, you can go down any route. Some major fields in computer science are theoretical computer science (logic, automata theory), computational theory (computability theory and complexity theory), algorithms and data structures, computer architectures (parallel processing), operating systems, computer networks, graphics, vision, databases, AI...You would have to decide what interests you the most and investigate that particular topic area in more depth.