PROFESSOR: I guess, my goal in every lecture
is to get some light bulbs to go on,
and that can be a challenging thing for--
I think it's a challenging thing for a teacher,
but it's a wonderful thing when it happens.
And so, I mean, to do that, I think the first step is
you've got to get the kids engaged in the problem,
and whether that involves sometimes
humorous demonstration of the problem,
or you drawing on anecdotes, or examples--
getting them thinking about the problem
and ideally a little puzzled, I think, is the first step.
And then hopefully taking them through some examples
or related problems can get them to that point aha point
where I don't actually have to tell them the solution.
They see it for themselves.
Combinatorics is very well suited to that,
because there are so many patterns that
come up over and over again, whether it's the Fibonacci
sequence, or Pascal's Triangle, or the Catalan numbers,
or any other phenomenon that appears
in many different guises throughout combinatorics.
So it's natural for acheiving them.