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?



Suggestions for mathematics encyclopedia
The suggesstion by Peter Humphries in the comments is good. This book contains a nice overview of many fields in mathematics, although you might find that it does not contain the level of detail you're looking for.


There is also Springer's online Encyclopaedia of Mathematics at <http://eom.springer.de> that might be what you're looking for. Personally though, I usually do a google search and end up at Wikipedia, or look into a reference book of a specific field, for example Blackadar's "Operator Algebras".


