Today I noticed a student in a graduate course being somewhat hesitant in presenting an induction proof. Next induction proof, hesitant again. It seems that some of the students, who are not from a CS or Math background, feel a bit insecure about proofs.

What to do? Make them prove!

So now I’m looking through online resources that will meet the following criteria:

- introductory enough for non-Math, non-CS people, who have had very little exposure to proving
- advanced, thorough, and challenging enough for graduate students from science/engineering disciplines
- convey the elegance of rigorous proof, and
- let them have fun proving

Thus far, I was most amused by the list of unacceptable proof techniques I found here.

I found some material on proof techniques, but what I found is either too basic, too concise, or too technical…

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This one looked pretty good.

http://www.risc.uni-linz.ac.at/education/courses/ws2009/TSW/Buchberger-Proof-Techniques.pdf

but maybe isn’t challenging enough. When I reached the last page I thought:

Where is strong, structural or well-founded induction, co-induction…?