# Stability of Marriages

On 2014 May 22, I had the pleasure of doing a presentation for the Sydney University Mathematics Society (SUMS), the topic was on the “stability of relationships and college admission”. Most of the contents were based on a particular algorithm presented in this article in the 60’s (yes, the 60’s)

http://www.econ.ucsb.edu/~tedb/Courses/Ec100C/galeshapley.pdf

The basic motivation is: imagine a set of $n$ students who can bbe ranked (unambiguously) by $n$ universities. We can start pairing the students with their desired unis, even though not everyone can get their first preference.

Based on this set up, we wish to find stable and optimal paring between the students and universities. The precise definitions of “stable” and “optimal” can be found in the above link. And of course, this problem can be easily modified into a “boys propose to girls” romantic marriage problem.

My talk is much light-hearted, since I only had 5 minutes to explain everything, so I left out the crucial proof of the algorithm, and instead, I used an example to illustrate all the important features. (There is even an Alpha-Male pun in there).

In retrospect, everyone had a great laugh, so my efforts to conjure up jokes did pay off!

My Beamer slides can be found here: