On daily basis I need to check (and re-check and re-check...) some definitions and main theorems that are not in my research area. Usually I accomplish this by a Google-search and/or a visit to our library. Unfortunately this doesn't work too well as the local library is a small one and internet seems to be a contradictive entity on its own.

Are there any must-to-have mathematical encyclopedia that one should invest to when starting to work in a math-oriented research field? I'm mainly interested in discrete mathematics and logic, but it definitely wouldn't hurt to have a wider scope in the book (say, for example, optimization, calculus and some probability theory).

I'm not interested in any study material, but a (probably very heavy) book with short listing / explanation of the basic definitions and the useful theories from different areas.

Any suggestions?