Ravi Mohan's Blog

Sunday, December 16, 2007

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.

7 comments:

Anonymous said...

Which books are you using ?

Binil said...

Ravi,

Will you be posting material from your "course" on this blog?

Thanks,
Binil

Ravi said...

@anonymous,

I am not using any books (if I were I could just give my students the books!)

I am drawing a little on my notes (from years ago) but mostly on my experience of what works and what doesn't, what needs to be learned first, what next and so on. Think learning music vs learning for an exam.

@Binil,

posting material is not likely (though I might if I discover something particularly interesting).

This isn't a formal "course" just a very intense, very student specific and very dynamic person to person "knowledge transfer" - very antithetical to written descriptions I would imagine

Anonymous said...

aho my friend ...

Your RSS feed is really active these days ... :)

It's really nice to know that, there are a lot (few?) more people understanding that there's a lot (infinite?) more out there ....

Don't digress on Indian universities ... Things are pretty much the same in this part of the world too ...

I used to think that Universities were supposed to be for "knowledge", and not for "Industry specific knowledge". A better way of saying "Job Guaranteed !".

Did you hear that, they (MIT) are gonna retire 6.001 in favor of Python ? It (almost) bought tears into my eyes ...

Why ? Why ? Why ? ,,,

What are we coming to ?? ... Where are we going ?? ...

Think about it ...

Computer Science ... Nothing to do with Computer's ... Not really about science ...

What could possibly be pure'er than Scheme ...

So long my friend ... May the force be with you ...

Click.. Click...

P S said...

Hello Ravi,
I have been a frequent Visitor to your Blogs since i met you in a Trivandrum-Blore Flight.This blog have infact caught me, Now i am really interested to learn maths as you had told me 1.5 year back that Math is the Basic Fundamental of Software Engineering. Can you teach me too?
-Regards
P S Walia

Ravi said...

@PS,
Hi,
I remember we had an interesting conversation!

As for the teaching, I don't have a conceptual objection but logistics is an issue. Since I don't have an "office" (I work out of home) there are issues about how when and where. If I could find a few more "students", perhaps I could structure this as a series of lectures but I'd still need to work out space(where) and time(when -perhaps a lecture per week or something. maybe a good time to kick off an algorithms interest group?).

PS: I am out of town (and so have intermittent net access) till mid Jan so response time may vary. Just FYI.

P S said...

Hello Ravi,

I understand the logistics part which may currently play the real spoilsport, but i am sure that if your list of students are little more, then some or the other thing can work out. So count me in your list and let me know in case you are starting.

-Regards
P S Walia