A Tufts team that competed in an international, four−day mathematical modeling competition in February placed in the top 15 percent of 2,775 participating teams, the competition organizers announced on Friday.
This year's Mathematical Contest in Modeling, in which three other Tufts teams participated, marked the third time Tufts has fielded successful competitors in the event.
The contest, which is held annually by the Consortium for Mathematics and Its Applications and this year took place Feb. 10 to Feb. 14, required participants to respond to one of two modeling problems: one in discrete mathematics and another in continuous mathematics.
Sophomores John Abel, Kim Stachenfeld and Jay Stotsky, all chemical engineering students, submitted a problem solution that achieved the title of "Meritorious Winner."
A team made up of juniors Stephen Bidwell and Victor Minden and senior Liam Clegg received "Honorable Mention," placing it in the top 45 percent of participants.
Two other teams — one consisting of sophomores Zach Himes, Brandon Dillow and Daniel Fortunato and another made up of sophomore Min Zhong, junior Yunlin Huang and senior Liwei Liao — successfully completed the competition but did not receive additional awards.
Abel's team chose to attempt to solve a problem that required the students to determine the minimum number of signal repeaters necessary to provide 1,000 people with uninterrupted service. Repeaters take weak radio signals, amplify them and translate them into different frequencies to avoid interference.
According to Abel and Stachenfeld, the team had limited experience with radio networks before receiving the problem details electronically the on the evening of the first day of the competition.
Their group camped out for the next 96 hours in South Hall, where they learned a new programming language called LaTeX in order to put together a 21−page solution without any outside help, Abel said.
"Not only did we have to determine where to place these repeater towers, but [also] to figure out the configuration of the system as a whole, which channels would be represented," Abel said.
Because of these variables, Stotsky said, there were different possible outcomes.
"In making the mathematical model, we did have to make some assumptions," Stotsky said. "So depending on what kind of model you were using or assumptions you make, you could actually get pretty different answers."
Though the team was not allowed to consult any in−person help during the competition, previous coaching and review sessions prepared group members for realizing the different variables and taking into account possible factors that they might encounter, according to Stachenfeld.
Responses were judged on whether or not the models were realistically functional.
"Our model was definitely functional in certain geological situations," Abel said, adding that terrain differences and other variables can affect functionality.
Stachenfeld said that the team fared well despite being unfamiliar with radio signals.
"At the start of the project we actually had no idea how a radio worked at all," Stachenfeld said. "We were actually very pleased."
Last year, a Tufts team received the highest award, the "Outstanding Winner" title. Despite no Tufts team reaching that level this year, having four teams compete successfully in the intense competition was a major feat, according to Professor of Mathematics Misha Kilmer, co−coach of the teams.
"We're happy with it, but I also think we're going to be coming for the number−one spot next year," Abel said. "We did well for our first year. We're eternally grateful for the help that we received before the contest."
Abel added that the fact that all four Tufts teams received at least a successful participant award shows the strength of Tufts' Department of Mathematics.
The department is proud of the students, Kilmer said.
"To be able to perform so well for the third year in a row is quite incredible," Kilmer said.
Kilmer and Assistant Professor of Mathematics Thomas Höft co−coached the Tufts teams for this year's competition.
Kilmer said the fact that all the members of Tufts' top team are sophomores is particularly noteworthy.
"The students performed exceptionally well under four days of intense pressure," she said. "Neither one of those problems were easy. … They were difficult for different reasons."
