[okmjuhb]

Not really "brand new" at all. It wouldn't be out of place in the first week of an Algebra course.

You don't really need much math background to understand the proof. At the top, where he writes pi = (top line of numbers, bottom line of numbers), he means the permutation that sends the first element to the second place, the second element to the third place, and so on.

If you think about it, every permutation can be split into cycles of this form (a -> b, b-> c, c->d, ..., e->a). One of these cycles, that's of length K, is called a "K-Cycle".

I think that's the only terminology you need to follow the proof.