Teaching Mathematics

I've just taken up an assignment to mentor one of my friends in maths/proof/logic.

My "student" has no background in maths or logic (if you ignore the negative knowledge gained by sitting through a bachelors degree in Engineering in India's f***ed up educational system), but is a good programmer.

The expected post condition is that my "student" will be able to read and work out mathematical proofs, design an experiment, analyze an existing research paper, work out an algorithm for a given task, understand basic calculus and linear algebra and in general gain the ability to conduct independent research in Machine Vision. I (and some others, like my friend Rajesh, for e,g.) have worked out some of these "how to"s over the last few years, mostly by brute force search of the landscape, discovering pitfalls by falling into them (and making a careful map, which it is now time to pass on).

"How to work out a proof" for example is rarely taught (well) in a classroom setting and I have had to synthesize knowledge from many sources to come up with a workable technique. I can save my "student" hundreds of hours of work.

Teaching is how one crystallizes one's knowledge. I've always enjoyed teaching but what I've done earlier was in a many to one to many format, involving speaking to a group of people in using a blackboard to derive a proof or a projector to display code.

The one to one format will be a new experience. I spent a few hours today working out a "syllabus" and it looks very good, even if I do say so myself :-)

Update : I plan to teach first order logic and proofs first, probably using books by Velleman, Polya, and Doets and Van Ejck.