October 8th, 2008
Turning US News college rankings into 7-dimensional analytic geometry
No really, I’m not kidding. Two researchers from UC Berkeley and Carnegie Mellon thought that the methods employed by US News and World Report to rank the nation’s top universities was just a bit too arbitrary. As Science News reports in a great article to share with high school and undergrad math students,
They imagined each university as a point in seven-dimensional space, with one dimension for each factor that U.S. News considers…Techniques they’d developed for a completely different problem — aligning gene sequences to understand evolutionary changes — could be adapted to do just that, they realized.
Because each universities ranking could be represented as a vector and a student’s relative priorities for school selection could also be represented as a vector in 7-dimensional space, the researchers were able to show that different priorities (research funding vs. alumni giving, for example) could result in significant changes in the rankings:
The top schools, they found, were top pretty much regardless of one’s priorities. Harvard and Princeton and Yale, for example, were always in the top five, because they were strong across the board on all the criteria.
Schools that were a bit more uneven could vary wildly, though. Penn State, for example, was 48 according to the magazine’s criteria, but it could also be as high as 1 or as low as 59.
The article does a nice job of distilling out the toughest mathematical pieces of their research; anyone wanting to dig a little deeper can view their full results published at ArXiv.org. While it’s an exercise in interesting math, it’s also probably not a bad starter for higher-end high school math classes, students in which are already starting to put in early decision applications.
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| 10/09/08
