Michael Bird, A16, Kathleen Cachel, A16, and Charles Colley,
E16 (From left to right,) winners of the 2014 Mathematical
Contest in Modeling contest, outside the Tisch Library.
Michael Bird, A16,Charles Colley, E16, and Kathleen Cachel, A16
Three Tufts students, Michael Bird (A16), Kathleen Cachel (A16),
and Charles Colley (E16), received the Outstanding Award in the
annual Mathematics Contest in Modeling (MCM) competition from
Consortium for Mathematics and Its Applications. Of 6,755
international teams of undergraduate students, only 13 teams
received the Outstanding Award designation.
The sophomores, who self-organized to form the 2014 Tufts team, are students in Mathematical Modeling and Computation (Math 87), a recent addition to the Department of Mathematics offerings. Math 87 serves as a key requirement in the new Applied Mathematics major. The course introduces students to both the concept of modeling physical systems and the manipulation of these models to answer questions about the underlying physical problem, says Department of Mathematics Associate Professor Scott MacLachlan, who teaches the course and was the team's faculty sponsor.
"The MCM is a challenging competition because it asks students to exercise a wide range of skills," says MacLachlan. "A successful paper will include detailed background research on the use of mathematical modeling for the problem at hand, specialization of these models to the particular questions posed, detailed computational results in support of their conclusions, and critical analysis of the mathematical models and computational results obtained. All of this must be presented clearly and concisely, in a compelling written document."
MacLachlan's participation is limited to preparing the team for the four-day contest. During the period in which the contest runs, the students cannot discuss the problem with anyone outside their team, including their faculty sponsor. This year's competition began on February 6, when the team saw the problems for the first time. By 8:00 pm, four nights later, they had to submit a copy of their paper via email, explaining their mathematical model and how it answers the questions posed.
"Many students are drawn to the competition because it shows them just how much mathematics is present in the world around us, as well as providing an intense experience beyond what is possible in the classroom environment," says MacLachlan.
After selecting one of two modeling problems to solve, the Tufts team was challenged to analyze the benefits and performance of a "keep right except to pass" rule for highway travel. Michael Bird, A16, a biochemistry and applied mathematics major, says he was originally convinced the problem was beyond him. "Charlie and Kathleen helped to get me off the ground in the first few hours of the competition", he said. "By the time I broke out of my 'this is impossible' haze, we'd found the Nagel-Schreckenberg model for traffic flow on a freeway, which we eventually adapted to create our model that was used for the paper."
However, says Bird, on Friday and Saturday the team still believed they had plenty of time. "By Sunday, we had spent hours in Eaton finishing the model and mining data from it, and then adapted it so we could test different rules for passing on a highway." Colley tested the models with different numbers of lanes, cars, max speeds, and accident rates, and realized the team wouldn't have usable data until some time in 2025. "We had to drop any further model building we were doing so that I could come up with a script that would run lots of the tests at once," says Bird, "and throw the results out as a neat table that Charlie could convert into the informative charts that make up much of the final paper." Earlier in the day the team spent hours trying to fix broken code that frequently became stuck in infinite loops.
As of Monday morning the team had not started writing the final paper, recalls Bird, who says they spent the entire day writing it in Hotung Café. The submitted paper was 17 pages, including citations. No code is included says Bird: "it's all about drawing conclusions from the data your model produced."
When Professor MacLachlan contacted team members on April 3 with the news that they had been awarded the highest rank given to solution papers, Bird was stunned. "At the time we were hoping we might be able to produce a paper that just about earned the rank of 'successful participant', the second lowest score above 'unsuccessful', says Bird. "I was convinced the Outstanding Award was some sort of belated April Fools joke for a few minutes after I saw it."
This team's achievement is particularly notable, says Maclachlan, since they are all sophomores, competing against many juniors and seniors. He adds that they brought a great enthusiasm to the contest. "They wrote a detailed and thoroughly researched report," adds Maclachlan. "They provided strong data in support of their conclusions, as well as critical commentary on their results."