Tuesday, July 05, 2005

100 math problems

Brad deLong has an interesting challenge: 100 interesting math problems for non-science majors who need to learn real math

His number 2 is the Drake Equation. Fascinating as that is, he would be better served to generate student interest if he used the Date Equation

Other related problem to look at would be the Date Rate equation - which estimates the mean time between dates, given the estimated number of available dates.

Another problem is the "marriage optimisation problem" - namely how to decide when to pick a partner, under the conservative estimate of wanting to choose one lifetime partner as well as possible.
This is a somewhat non-trivial problem to formulate, and therefore left as an exercise to the student...
But the answer, as I recall it is simple: Estimate the total number of potential partners you will meet in your life; after you have met 1/e of them, pick the next one who is as good or better than all the previous ones. Marry that one.

The catch: there is a finite probability you let the best one go; your criteria may possibly change; and your estimate of the number of eligible partners is almost certain to be wrong.

Interestingly this explains one of the more ubiquitous phenomena around: why high school couples almost always break up at university. It also sheds some light on divorce patterns, and the problems associated with changing social environments (especially jobs) and moving to big cities.
Something interesting there, especially if linked to game theory problems of the equilibria for "cheaters" in populations with iterated interactions.


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