K. Rosen, Discrete Mathematics and its Applications, 3rd Ed. McGraw-Hill, 1995. Good intro material, sometimes a little loose on definitions but gets the ideas across quickly.
Knuth, The Art of Computer Programming. vol 1.
C.L.Liu, Elements of Discrete Mathematics, McGraw-Hill, 1977. C.L.Liu, Intro to Combinatorial Mathematics, McGraw-Hill, 1968. Classics. Instead of taking 10 different classes in the math 2 department, you can read these. Same content as Rosen but a lot deeper.
R. Graham, D. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, 1988. An excellent expansion of parts of vol. 1 of The Art of Programming. Binomials, recurrences, asymptotics, etc.