[chimeracoder]

I second CLRS - I just finished an algorithms course taught from that book, and I can't imagine a single textbook being more comprehensive.

I'm surprise nobody's mentioned Knuth, though maybe that goes without saying?

As for probability and statistics, I haven't really found anything (at an advanced) level that I've been happy with. Maybe it's because my background is in statistics, so it's a perception bias (I see the flaws more easily than with other subjects), but I think that most statistics textbooks are pretty rotten.

There are really only two that I'd recommend, and only one at a high level. Gelman & Hill is a great introduction to computational statistics at a high level, while still very readable (and enjoyable!)

http://www.amazon.com/Analysis-Regression-Multilevel-Hierarc...

Other than that, the only truly stellar statistics textbook I've ever seen was the one I used in my intro class in high school. It's sad, but it's a very true comment about the current state of most statistics textbooks (that I can find).

[nandemo]

Grandparent comment is asking for textbooks. The Art of Computer Programming is not considered a textbook, it's a treatise.

[spitfire]

> I'm surprise nobody's mentioned Knuth, though maybe that goes without saying?

Everyone's waiting for the complete book.