## Calculus without Limits in Tehran

Here is the poster

and the group photo

Interestingly, this group included students from humanities, engineering, and also a mathematician and a physicist.

The mathematician had to be told that there was a separate course on calculus without limits for post-graduates in mathematics. In this course, tried out at USM, I thought I would go into details of the philosophy of mathematics. But the students did not understand even the formal mathematics I sought to criticise. Hence, half the people dropped out because they found the pre-test too tough (since it tested them on basic concepts (complete metric space, Lebesgue integral, Schwartz derivative) related to limits, and the failure of the formal definition of the derivative, whichever way one looks at it (as in elementary analysis or in the Schwartz theory).

In that USM test, the one and only one question which everyone could manage was a question taken from a school exam, related to differentiability and continuity. They had all memorised that a differentiable function must be continuous, without a thought to the Schwartz theory (which enables discontinuous functions to be differentiated) or to the meaning of the differential equations of physics, when one encounters discontinuous phenomena such as shock waves (especially those cases which cannot be handled by the simple-minded technique of going over to integral formulations). Also, if one is doing physics, it has to be refutable, one cannot jump about between different definitions of the derivative. The physicist, at least, was convinced.