My recommendation for mathsy people is two very different books: Skiena, recommended above, and "Introduction to algorithms" by Cormen, Leiserson, Rivest, and Stein. Skiena is informal, discursive, and strategic. CLRS is formal, mathematical, and tactical. They complement each other nicely.

[EDITED to add: CLRS and Sedgewick are quite similar in style and content. I find CLRS more rigorous and analytical, which is good in a complement to Skiena. Personally I'd prefer CLRS even without Skiena, but I can see why others might not. I should also say that I haven't seen the latest edition of either book, and that I have a copy of CLRS but not of Sedgewick, which I therefore don't know as well and may be being unfair to.]