Concrete Mathematics: A Foundation for Computer Science

I don't think there is a definitive answer for your question because computer science is a relative new area of knowledge and “fundamental books” are still being published. If I had to say one text that is the fundamental one, I would go with a paper: “On Computable Numbers, with an Application to the Entscheidungsproblem” [1], by Alan Turing. --- But if you just started your course in Computer Science, then I will give you some “bookshelf advice" based on my experience. I had the pleasure to study all the books I am going to recommend you, and most of them I was able to read cover-to-cover during the university years. And they are also in my bookshelf for reference. The book order does not represent rank of importance. * “Introduction to the Theory of Computation”, by Michael Sipser. * I also recommend the “Elements of the Theory of Computation”, by Christos Papadimitriou. * Another good complement is “Introduction to Automata Theory, Languages and Computation”, by Hopcroft and Ullman. (Thanks, @reacweb, for the reminder.) * “Graph Theory”, by Reinhard Diestel.…

Concrete Mathematics is (as it says itself) intended for first year grad students. It is certainly good, but it is NOT for a "complete noobie". I am in a similar situation, and am finding Vellman's "How to Prove It" extremely useful. Having poked around the edges of math for about a year, I finally realized that proofs are central to mathematical maturity... No more eyes crossing when I read a new CS textbook!

I left school when I was 16 to do homeschool, which turned out to be nothing more than my parents buying me books when I asked for them and nothing more. I did my GED and dropped out of college, so I think that I can relate to how you feel. There's a huge inferiority complex that comes from having less education than others. Filling in the gaps is difficult but I've found that whenever I fill something in, I've benefited pretty quickly. Lately I realized that I sucked at systems programming concepts, so I've been reading about that, which has been really helpful. I make a living as a programmer, but I have to continually be studying to try and fill in gaps before I'm hurt by lack of knowledge.…