There's no way I can just give you a list of all the references you will need during the contest. Any textbooks you've had in a class can be especially useful, because you've worked through a good part of them and know what they hold. Make sure that they're close at hand on friday, and start with them.
The art of using a library is a whole subject in itself, but I can give you a few tips. Once you've scanned through your own textbooks, make a list of the things you want to research and do things systematically. You'll most likely be looking for textbooks, not current research or conference proceedings. Remember: Keep it simple. Start with the basics. Find the general classification that your problem falls into, and learn as much as you can. Then try to creatively apply that knowledge to the specific problem that the MCM has given you.
All that being said, there are a number of books that do cover a lot of territory and have information that could be applied to many past problems. These books are generally about solving problems, often with examples of computer programs included to make your life easier.
· Numerical Recipies in C: The Art of Scientific Computing, William H. Press
This is a truly fantastic book. It gives you a start on just about every continuous modeling technique that can be programmed. Interpolation, solving ordinary and partial differential equations, linear algebra, all with the code ready to be typed in. There are editions of the book in other languages to suit your preference.
· Numerical Methods that Work, Forman Acton
Another really first rate book. Very practical -- a great place to start.
· Introduction to Algorithms, Thomas H. Cormen, Leiserson, Rivest
· Numerical Analysis, Richard L Burden, J. Douglas Faires, Albert C. Reynolds
· Matrix Computations, Gene H. Golub, Charles F. Van Loan
· Introduction to Automata Theory, Languages, and Computation, John E. Hopcroft
· Computer Graphics: Principles and Practice, James D. Foley