If you can teach game theory, that could be good. It's bread and butter for mathematical economics and political science (even ecologists learn it now) -- I think the subject illustrates the point that math is not limited in application to situations which involve numbers. In addition to being useful, it's very elementary to solve games (although the fundamental fact that mixed strategy Nash equilibria exist requires topology to prove, it doesn't provide an algorithm for finding them -- actually solving games is more combinatorial). Proving that sets of strategies are/are not Nash equilibria can introduce students to the concept of a formal mathematical proof in a setting which I think is straightforward.
Unfortunately, I can't think of a textbook that would be good, but maybe someone else knows one.