Tim Chartier

Mathematics and Sports: Bracketology: How can math help?

Every year, people across the United States predict how the field of 65 teams will play in the Division I NCAA Men’s Basketball Tournament by filling out a tournament bracket for the postseason play. This article discusses two popular rating methods that are also used by the Bowl Championship Series, the organization that determines which college football teams are invited to which bowl games. The two methods are the Colley Method and the Massey Method, each of which computes a ranking by solving a system of linear equations. The article also discusses how both methods can be adapted to take late season momentum into account. All the methods were used to produce brackets in 2009 and their results are given, including a mathematically-produced bracket that was better than 97% of the nearly 4.5 million brackets submitted to ESPN’s Tournament Challenge.

Devastating Roundoff Error

twined. While some of the math used by Homeland Security scientists is extremely complex, most of it is accessible on rather elementary levels, commonly taught in colleges and universities around the world. Linear Algebra, Discrete Math, and Differential Equations are all common courses at the undergraduate level, yet they serve as a foundation for much of the homeland security research conducted at LLNL. With computers in use daily in the lives of all Americans, it is no surprise that mathematics and supercomputing, in the hands of research scientists like those at LLNL, will help shape the future of the complex world of homeland security. •

Digital field scholarship and the liberal arts: results from a 2012---13 sandbox

We summarize a recent multi-institutional collaboration in digital field scholarship involving four liberal arts colleges: Davidson College, Lewis & Clark College, Muhlenberg College, and Reed College. Digital field scholarship (DFS) can be defined as scholarship in the arts and sciences for which field-based research and concepts are significant, and digital tools support data collection, analysis, and communication; DFS thus gathers together and extends a wide range of existing scholarship, offering new possibilities for appreciating the connections that define liberal education. Our collaboration occurred as a sandbox, a collective online experiment using a modified WordPress platform (including mapping and other advanced capabilities) built and supported by Lewis & Clark College, with sponsorship provided by the National Institute for Technology in Liberal Education. Institutions selected course-based DFS projects for fall 2012 and/or spring 2013. Projects ranged from documentary photojournalism to home energy efficiency assessment. One key feature was the use of readily available mobile devices and apps for field-based reconnaissance and data collection; another was our public digital scholarship approach, in which student participants shared the process and products of their work via public posts on the DFS website. Descriptive and factor analysis results from anonymous assessment data suggest strong participant response and likely future potential of digital field scholarship across class level and gender. When set into the context of the four institutions that supported the 2012–2013 sandbox, we see further opportunities for digital field scholarship on our and other campuses, provided that an optimal balance is struck between challenges and rewards along technical, pedagogical, and practical axes. Ultimately, digital field scholarship will be judged for its scholarship and for extending the experimental, open-ended inquiry that characterizes liberal education.

REVERSE ENGINEERING College Rankings

H ow did you choose where to attend college? You probably talked to family members, guidance counselors, and friends; visited a variety of schools, and weighed differences such as size, type of institution, location, price, and reputation. At some point you probably consulted rankings of colleges and universities such as those produced by U.S. News & World Report. In 2007, the publisher of U.S. News stated that the rankings website received more than 10 million views within 72 hours of its release. U.S. News has been publishing rankings since 1983. The magazine divides schools into four categories: national universities, national liberal arts colleges, regional universities, and regional colleges. Within each category, the institutions are ranked using up to 16 key measures of quality in areas such as faculty resources, selectivity, fi nancial resources, retention, alumni giving, and academic reputation. Most of the information comes in the form of hard data. But the academic reputation score comes from surveys of college and university presidents and high school guidance counselors. Not only are the U.S. News rankings quite well known; they are also some of the most controversial. Several schools, such as Reed College, have refused to participate in the rankings. The largest controversy occurred in 2007 when 12 college and university presidents wrote a letter calling for schools to no longer use the rankings in their promotional materials and to refuse to fi ll out the reputational survey, which, according to the U.S. News website, accounts for 22.5 percent of a college’s overall score. More than 50 other college and university presidents signed the letter after it was published. Further objections to these rankings include their lack of transparency and their failure to refl ect the full experience of students at their respective institutions. The popularity and controversy of these rankings raise some questions that are worth exploring mathematically. Given the data and the fi nal rankings for the institutions, we can fi nd the approximate weights and scores by using techniques from linear algebra. Although we may not produce the exact formula, we may uncover some interesting information along the way. In particular, we can investigate how important the reputational survey is in the ranking. What would happen to the rankings if we omit it?