ESP Biography

Here's the way this goes: someone thinks of a counting problem, like "how many ways can you make change for n cents?" The answer is some sort of sequence - one number for each n. Usually it's fairly hopeless to try to find a nice formula for each number, but we can often figure out how fast the sequence grows (and therefore compare it to other sequences). Our main tool will be something called the generating function. I'll go over how this works by going through a couple of examples, and then we'll come up with a few problems of our own to tackle.