Today a guest post from Periklis Papakonstantinou, coincidentally not unrelated to Bill's post earlier this week. I'll be back with a special post on Sunday.
I'm teaching in an undergrad program that is half computer science and half business at Rutgers, but the CS part taught there is the real thing (I assume for Business too). This term I taught a very theoretical course in cryptography and I realized that (1) the students enjoyed it and (2) that they were lacking basic reasoning skills. I ended up teaching for a few weeks how one can structure basic logic arguments. I am not sure if they appreciated things like the hybrid argument but I believe I convinced them that without rigorous thinking one cannot think clearly.
So, I decided to teach a much more fun class (hopefully next year) titled "How to solve it" -- à la Pólya. The goal is students to develop rigorous problem-solving skills. At the same time, I'd like to use this course as an excuse to introduce basic concepts in combinatorics, linear algebra, and theoretical stats. I'm not sure whether the original book by Polya is appropriate for this and that's why I thought of reaching out to my peers for suggestions. Any ideas and thoughts on possible texts, topics, or notes would be greatly appreciated.