Introductory discrete math textbook (pdf) courtesy of MIT. I prefer it to Rosen, which is currently recommended in the MIRI research guide, although I think there exist students who would do better with Rosen's book.

(How to tell which book you should choose? Well, since this one is Creative Commons, and therefore free, I'd try this one. If you find it's not saying enough words per theorem, try Rosen. If you think it's saying too many words per theorem, try these lecture notes. A recommendation to LW's list of best textbooks is forthcoming, which will contain a complete discussion.)

An earlier version of the book corresponds to these videos lectures, which I find to be excellent, as far as lectures go.