Juan Carrillo, a senior double majoring in mathematics and computer science, won a “meritorious poster award” at the Mathematics Association of America Southern California-Nevada meeting on Apr. 2. His project aimed at developing a more intuitive understanding of puzzling fibonomial coefficients in mathematics formulas.
The award capped a four-year process of working closely with mentors to develop his research skills, Carrillo says. He entered Loyola Marymount University as a computer science major, but soon added an applied mathematics major and sought out research opportunities.
“The most important thing I’ve experienced at LMU is the professional relationships with professors and mentors,” he explains. “I started doing research freshman year because I had a mentor. I told him I’d like to do something interesting in math and computers, and we discussed options.”
The work on fibonomial coefficients began this year after winter break when Carrillo asked one of his instructors, Curtis D. Bennett, Ph.D., professor of mathematics, for a research project to work on outside of class. Bennett gave Carrillo a choice of research projects. He chose fibonomial coefficients, which have perplexing properties when integers are inserted into the formula. His poster attempted to explain in a more elegant way what previous studies had suggested about the mysterious equation.
“The formula is counting something. The question was: We know what this equation looks like and how to manipulate it, but can we figure out what it’s counting?” Carrillo says.
Carrillo spent considerable time designing his poster, titled “New Combinatorial Interpretation of Fibonomial Coefficients,” to make the concept easy to grasp.
“It was pretty exciting to win,” he says. “One of the judges told me I had gone out of my way to make sure my research was very approachable and intuitive.”
Carrillo, who grew up in the San Fernando Valley, plans to apply to graduate school. He hopes his future career can duplicate the experience he had at LMU: Working as a team, exchanging ideas with others and coming up with solutions to problems.
“I really like tutoring,” he says. “I like explaining concepts to people. I’d like to be a professor at a research university or a researcher at a tech company in R&D. I see myself continuing to do research.”
He calls graduation “bittersweet.”
“I like the academic environment,” he says. “The professors are very approachable at LMU. I can ask them very academic questions or career-oriented ones. That has really paid off for me, and that is one of the strengths of this university.”