In one of my math magazines "Focus" there is a very intersting article about Experimental Mathematics. This is what I am trying to do. The article is an interview with Doron Zeilberger. Ironically, I just went to a talk by him the other day at DePaul. Great speaker: very loud, he would scream at you and then laugh that he was waking you up with the loud screaming. very funny and also slightly alarming ;)
ok. this article really has my interest. Here are the key take-aways for me from the interview:
1. Think about using computers and algorithms to do mathematics quickly and efficiently
2. programming gives you insight and understanding (re: mathematics)
3. He finds examples to work with in combinatorics and the theory of special functions. These examples can be used to train the computer to discover conjectures. This is experimental mathematics.
4. Trying to prove the conjectures without any human intervention is called Automatic Theorem Proving. Very interesting!
5. the Wilf-Zeilberger algorithmic proof theory is contained in all computer algebra systems and it is a collection of algorithms that can discover, and then prove, binomial coefficient "n choose k" counts the number of k-element subsets of an n-element set.
4. There is a journal by the name Experiential Mathematics and some books coming out. I'll keep my eye on them.