27 January 2008

Street Fighting Mathematics

18.098/6.099. Street Fighting Mathematics, a course currently being offered during MIT's Independent Activities Period, by Sanjoy Mahajan. (I got a call from MIT asking me for money tonight; I donated some; that got me thinking about the Institute so I poked around the web site a bit.)

The course description is as follows:
The art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Application to mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.)
Personally, I always thought the epsilons and deltas were harming me. The text (a draft version of which can be found on the course web page) stresses the idea that approximate answers, heuristics, etc. are more valuable than they are often claimed to be, which is a question that Mahajan also took on in his PhD thesis, which is a combination of a version of such a textbook and some extended examples on what one might call "research-level" problems, one of which is a probabilistic model of the primes which it is too late at night to seriously read.

From a quick poke around the web page, it looks like Mahajan also offered a similar, but more physics-oriented course in IAP 2006, as well as TAing a couple more substantial courses in the same vein at Caltech called "Order-of-Magnitude Physics". (The MIT IAP course meets three hours a week for four weeks and carries one-quarter the credit that a "normal" course at MIT would carry; the Caltech courses appear to have met three hours a week for ten weeks. As such, they have more problem sets. But they're also more physics-y, which may be good or bad depending on how you feel about physics.


Michael Livshits said...

Speaking about these harmful epsilons and deltas, you don't have to put up with them any longer. You can take an approach to calculus via algebra and uniform estimates. I tried to explain it to the John Armstong, "The Unapologetic Mathematician,"
in my remarks about his proof of
the chain rule
, but he didn't like the idea, maybe you will. Sanjoy was quite interested, by the way.

meep said...

He did something like this when he taught at Mathcamp.

Michael Livsgits said...

Who is "he?" John or Sanjoy? And when was the mathcamp?