On Oct 26, 2010, at 4:21 PM, Richard O'Keefe wrote:
Number theory would probably be out except maybe in a 2nd or 3rd year course leading to cryptography.
Number theory is one of those weird cases. They are discrete structures, but advanced number theory uses a lot of complex analysis and "calculus" on other complete spaces, like the p-adics.
Difference equations show up in Knuth's "Concrete Mathematics", his tome on discrete mathematics. The theory of difference equations is the discrete analogue to the theory of differential equations. Surprisingly, the continuous/differential case is more general, since integral solutions can be modeled by constant functions.
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