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

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~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

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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

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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

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Maple vs Excel

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

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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

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Binomial Coefficients

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

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