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Jeff Burdges
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There are nice options if your university's students all took calculous in high school. In that case, you might try some light weight mixture of elementary differential equations, recurrence relations, generating functions, and game theory.

You start out by explaining how differential equations arise in various branches of science. You next introduce recurrence relations explaining the distinction between discrete and continuous mathematics, indicating how they arise in science and game theory. You then remind them about Taylor series and introduce the method of generating functions, showing that differential equations are used in solving discrete problems too.

In this way, you could provide a cohesive course that builds upon itself like mathematics is want to do, requires computational homeworks, seriously discusses the notion of infinity, touches upon numerous applied topics, and shows how mathematics can be simultaneously convergent, surprising, and useful by introducing generating functions.

If they're very quick, there is considerable flexibility for discussing algorithm running times and P != NP, or Dirichlet series generating functions and the Riemann Zeta function, or whatever.

You'd want to verify that elementary differential equations and Taylor series are still part of the AP Calculous AB syllabus, as well as the percentage of incoming students who've had that course. You should however suppress anything that requires multi-variable calculous that only falls under the AP Calculous BC syllabus, which presumably few student's took.

Jeff Burdges
  • 565
  • 1
  • 4
  • 9