I have developed several colloquium talks that I enjoy giving for undergraduate audiences. Below are descriptions of some of my favorites. I would love to give a talk for your students!
In a 1991 article in the Mathematical Intelligencer, David Robbins made the following proclamation.
This talk is accessible to anyone who has seen matrices, determinants, and Pascal's triangle. |
Matching problems are everywhere: high school seniors work hard to match themselves with colleges and universities around the country, medical students are matched with hospitals for their residencies, law students are matched with judicial clerkships, and a committee of doctors matches donated organs to transplant recipients. In these examples (and many others) we want to construct something called a stable matching. In particular, we do not want to have a college admissions process in which a student attending one college would prefer to be at the college across the river, while the college across the river would prefer that student to one of its own. In this talk I first describe a natural algorithm for constructing a stable matching from the preferences of the people or institutions being matched, and the advantages and disadvantages of variants of this algorithm. I then describe some remarkable structure on the set of all stable matchings (for a given set of preferences), which lets you "add" and "multiply" stable matchings.
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In March of 2005 Doron Zeilberger declared,
No special background is required to enjoy this talk, but certain parts will be easier to understand if you have seen sequences and limits. |