Mathematics majors Katie Kucich, Larissa Hjort and David Parker are good friends. They’ve been preceptorial colleagues, classmates and study partners during their four years at the University of San Diego.
That’s why it’s fitting when they competed in February’s Consortium for Mathematics and Its Applications (COMAP) Math Modeling competition, a problem-solving activity that attracts more than 16,000 undergraduate student teams worldwide, that they did so as a collective unit.
“We’re all seniors, we’ve worked on projects together so we came in already knowing each other’s work style. We knew we’d be able to work well together,” Kucich said.
Familiarity and camaraderie, a healthy retention of USD’s math curriculum and the ability to survive a competition that lasted five full days all paid off. Kucich, Hjort and Parker (pictured above, left to right) learned this month that they earned an honorable mention designation in the prestigious competition.
“This was a nice reward for four years of really hard work,” Hjort said. “It was a very good experience to see that we could apply what we know about math. It wasn’t just what we learned in class. This experience really showed how I can use math in a real-world application.”
Math Professor and USD’s COMAP Competition Advisor Diane Hoffoss said the team, one of seven 2012 USD entrants (21 students total), earned the university’s fifth honorable mention recognition since it first entered in 2002. The event has four awards categories: outstanding, meritorious, honorable mention and successful participant. A USD team has yet to earn the top mark, but three teams have claimed meritorious honors, including two in 2006. Due to the competition’s difficult nature thousands of entrants worldwide are unable to finish by the deadline, thus recognition as a “successful participant” is an accomplishment. USD’s other six teams earned the latter distinction by completing one of two math problem choices available.
“No matter what, I feel I really accomplished a lot because of the time and effort I put into it,” said Janet Chao, a biophysics major, who was on a USD team with John Dawdy and Stanley Zhou.
Kucich, Hjort and Parker and two other teams chose Problem A: The Leaves of a Tree. The objective was to build a mathematical model to describe and classify leaves. Four USD teams selected Problem B: Camping along the Big Long River. The objective was to create a math model that effectively determined a method for the public to better enjoy the hypothetical river and whitewater rafting fun while considering the necessity of camping.
This year’s other USD competitors, whose majors include math, physics, computer science and economics, were: Alex Hill, Ashley Klahr and Erin Williams; Brent Allman, Nick Lipperd and Carolynn Stuart; Ryan DeMuse, Dawei Teng and Chris Yip; Dean Henze, Nick Otto and Veronica Rindge; and Sam Allsop, Paul Locker and Tim Welsh.
Kucich, Hjort and Parker tackled their work, which they titled, “Make Like a Tree and ‘Leaf,’” by developing a math model through allometric relationships to evaluate individual leaf mass.
To do it, they created leaf and tree profiles for 12 tree species. The leaf profiles focused on average leaf size and approximated shape. The tree profile consisted of the diameter at breast height, tree height range, and crown width and crown shape, according to their final report. Several equations helped break down Problem A into a more manageable situation. In all, their model successfully predicted a reasonable mass for three tree species.
Team members consumed multiple energy drinks and snacks and had pillows available for short naps. They powered through their work on multiple computer screens, wrote out formulas on a long whiteboard in a Serra Hall classroom and more. The dedication shown by all seven teams to this competition was noteworthy.
“The hardest part was just deciding how to go about the problem and what aspects of the problem would we answer,” Hjort said.
Added Kucich: “We started in one direction and then went completely in another direction. We were still working on it Sunday, but then it all came together that night and on Monday we felt really good about it. Once we had the data in place, the equations weren’t that complex. It was just a matter of getting the data and figuring out that’s the way we wanted to go. I typed everything in LaTeX as they were researching and coming up with the equations.”
Hjort focused on research and development tasks and Parker suggested and implemented the allometric equation approach.
“Our original approach was to use computer-generated ideas to estimate the leaves on a tree, but we soon realized that wasn’t a feasible approach, so we started again,” Parker said. “We wanted to use something else that would be easily calculable and useful. Through the alometry equation, we took a lot of statistical data and saw what relationships we could make. We found some that worked.”
Their teamwork, utilizing individual strengths for the betterment of the whole, was key for what was their first time competing in the COMAP event.
“I was inspired by my teammates,” Parker said. “It’s a well-oiled machine. We know each other so well.”
— Ryan T. Blystone
Some photos courtesy of Diane Hoffoss