ABSTRACT:
How do you divide the rent among roommates fairly? My friend's
dilemma was a question that mathematics could answer, both elegantly
and constructively. We show how it and other "fair division" questions
--- the
most famous of which is the problem of Steinhaus: how do you cut a cake
fairly? --- motivate a host of mathematical ideas. They provide
excellent examples of how mathematics can address an old class of
problems in new ways, and conversely, how problems in the social
sciences can motivate new mathematics--- where topology, geometry, and
combinatorics meet social applications, and where research by
undergraduates has played a big role.
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BIOGRAPHICAL SKETCH: Francis Edward Su is a Professor of Mathematics at
Harvey Mudd College. He earned his Ph.D. from Harvard University, and
has held visiting positions at Cornell and MSRI. His research is
in geometric combinatorics and applications to the social sciences, and
he has co-authored nearly a couple dozen papers with
undergraduates. He also has a passion for teaching and
popularizing mathematics. From the MAA, he received the 2001 Hasse
Prize for expository writing, the 2004 Alder Award for distinguished
teaching, and was the 2006 Leitzel Lecturer. He also serves on
editorial boards of the American Mathematical Monthly and Math
Horizons. In his spare time he enjoys working on his "Math Fun Facts"
website, which receives nearly 4,000 hits every day, and is active in a
unique Christian community in LA known as Mosaic.
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