My first 236 lecture was last night. The class was much fuller than I had anticipated with more than twice as many students as my 165 class. Once beyond introductory material, we began reviewing proofs by induction. One thing that surprised me was the idea that the carefully-crafted structures of 165 were not necessarily THE model for this course, but just one approach of many. This makes me wonder why 165 is so pedantic about proof structure. If it is not to be the model for other proofs within CS courses, what is it for?
I noticed that some of the examples (unit digits of powers of 3, or 12^n-1 = k*11) could be proven without induction -- maybe even better so. I suppose I would have preferred examples that couldn't be proven (or were very difficult to prove) without using induction. Still, there is value in looking at a problem from a fresh perspective.
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Good question about CSC165. I guess I'm one of the most reluctant, while at the same time most frequent, implementers of that rigid CSC165 structure.
Some of my colleagues have convinced me that many students need the rigid structure as a model that allows them to assess proofs. Once they have it "down" they can move on to more flexible proofs that contain the same components.
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