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PROFESSOR: I guess, my
goal in every lecture

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is to get some light
bulbs to go on,

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and that can be a
challenging thing for--

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I think it's a challenging
thing for a teacher,

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but it's a wonderful
thing when it happens.

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And so, I mean, to do that,
I think the first step is

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you've got to get the kids
engaged in the problem,

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and whether that
involves sometimes

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humorous demonstration
of the problem,

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or you drawing on
anecdotes, or examples--

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getting them thinking
about the problem

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and ideally a little puzzled,
I think, is the first step.

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And then hopefully taking
them through some examples

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or related problems can get
them to that point aha point

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where I don't actually have
to tell them the solution.

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They see it for themselves.

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Combinatorics is very
well suited to that,

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because there are so
many patterns that

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come up over and over again,
whether it's the Fibonacci

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sequence, or Pascal's Triangle,
or the Catalan numbers,

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or any other
phenomenon that appears

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in many different guises
throughout combinatorics.

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So it's natural
for acheiving them.