# Monthly Archives: January 2005

## A Good Problem

… a mathematical problem should be difficult in order to entice us, yet not completely inaccessible lest it mock our efforts. It should be a guidepost on the tortuous path to hidden truths, ultimately rewarding us by the satisfaction of … Continue reading

## ~p V q

This week, I have to teach predicate calculus to first year computer science students, in addition to the vector calculus for engineering students. I find that I really have nothing to value-add for logic. Perhaps it is because I’ve never … Continue reading

Posted in Teaching | 1 Comment

## Irresistible Integrals

A book by George Boros and Victor Moll. The authors bill the book as a guide to the evaluation of integrals, but it strucked me as a nice guide to old-fashioned (nineteen century) analysis, in the spirit of Gauss and … Continue reading

Posted in Books, Calculus/Analysis | 1 Comment

## Immortality

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean. – G.H. Hardy (1877-1947), A … Continue reading

## Maple vs Excel

AIME 1994 Find n for which $\lfloor \log_2 1 \rfloor + \lfloor \log_2 2 \rfloor + \lfloor \log_2 3 \rfloor + \ldots + \lfloor \log_2 n \rfloor = 1994$. A fairly straightforward problem that can be worked out quickly once … Continue reading

Posted in Problems | 1 Comment

## Abelian Functions and the Development of Mathematics

Taken from Pi and the AGM: When I was a student, abelian functions were, as an effect of the Jacobian tradition, considered the uncontested summit of mathematics and each of us was ambitious to make progress in this field. And … Continue reading

${n \choose r}$ is the number of ways of picking r objects out of n possibilities without order. A simple but elegant identity is this ${n+1 \choose r }= {n \choose r} + {n \choose r-1}$ which appears when … Continue reading