Greg Convertito and George Thekkedath, members of the Class of 2016, were awarded Certificates for Outstanding Presentations at the Mathematical Association of America’s (MAA) annual MathFest competition held recently at the Connecticut Convention Center in Hartford.
The competition is billed as a “celebration of mathematics” and gives students from colleges and universities globally the opportunity to demonstrate their facility, creativity and skill in math. This year’s MathFest featured student presentations from some of the top institutions in the United States, Canada and the United Kingdom, among them Yale, the University of Notre Dame, Duke, Columbia, Princeton, Dartmouth, and the University of California, Los Angeles.
It’s unusual for first-year students to be awarded Certificates for Outstanding Presentations, but neither David Cruz-Uribe, professor of mathematics and Convertito’s adviser, nor Gregory Kelsey, visiting assistant professor of mathematics and Thekkedath’s adviser, were surprised. Cruz-Uribe called Convertito “one of the best students I’ve ever worked with. His enthusiasm and his mathematical spirit are just amazing.” Similarly, Kelsey said he was “very pleased and impressed” with Thekkedath’s ability and the quality of his presentation. “It speaks to his ability to communicate his ideas.”
The MAA student chapters program was launched in January 1989 to encourage students to continue their studies in the mathematical sciences, provide opportunities to meet other students at national meetings, and provide career information in the mathematical sciences. There are approximately 550 student chapters on college and university campuses nationwide.
Both Convertito, of Fairfield, CT, and Thekkedath, of Lawrenceville, GA, participated in this summer’s 10-week Interdisciplinary Science Program at Trinity, an innovative academic program designed to broaden and enrich the study of science and mathematics, under the leadership of Alison Draper, director of the Science Center and lecturer in Interdisciplinary Science. As such, both students were in Hartford when the MAA get-together was taking place.
The title of Thekkedath’s project, which he began in the spring semester, was “Geometry and Mass Transit Distance.” In his presentation, Thekkedath covered the basic ideas behind taxicab geometry and how shapes change due to the constraints of the taxicab metric and how that differs from Euclidean geometry. In addition, he looked at the mass-transit distance to understand how adding a subway into taxicab geometry can change the distance between two points. Lastly, to put the idea in perspective, he investigated how traffic density within an area can affect the mass-transit distance.
According to Thekkedath, taxicab geometry is essentially a form of geometry in which a mathematician measures distance by taking the absolute difference between two coordinates. It’s sometimes referred to as “Manhattan geometry” because the movements are vertical and horizontal, as they would be in a city. Thus, the applications of Thekkedath’s research can be applied to urban geography.
Thekkedath described MathFest as “a rewarding experience,” one that enabled him to see different projects and to appreciate the “universal applicability of mathematics.” Although he said it was a bit nerve-wracking to present his project at a conference where mathematicians from around the world were gathered, he credited Kelsey and Cruz-Uribe with preparing both students for the competition.
Although Kelsey said it can be “tricky working with first-year students because they don’t have all the tools,” he noted that Thekkedath caught on very quickly. He pointed out that Thekkedath had given a talk at Manhattan College a few months ago, an experience that helped him overcome any jitters he might have had.
Convertito, whose project was titled “Rationality of Calculus Optimization Problems,” said he submitted his abstract to the MAA in the spring and thought it was “very cool” that it was accepted. However, he didn’t realize until he got to the annual meeting how unusual it was for undergraduates to be participating at that high level.
His project description: “Beginning with the generalization of a basic optimization problem from Calculus I, we attempted to find all possible rational solutions assuming integer initial conditions. The original problem reduced to finding solutions to solving a Pythagorean-like Diophantine equation a2 + 3b2 = c2. We solved this by generalizing a classical method of generating Pythagorean triples, producing four cases involving the parity of a, b, and c.”
Convertito said Cruz-Uribe gave him the problem in December, thinking it would take a week to solve. In actuality, it took the whole semester. But by the time MathFest arrived, it was “totally done.”
Cruz-Uribe praised Convertito for “rising to the challenge,” saying the research was something that he’d expect from a graduate student and not from a first-year student. Said Cruz-Uribe: “I was really pleased that [Greg] was recognized for that.”
In addition to the student presentations, MathFest included lectures by renowned mathematicians, mini-courses, workshops and a class on The Mathematics of Games and Puzzles. Students were treated to Math Jeopardy, lectures, panel presentations, social activities, a 5K fun run, and the problem-solving competition.
George Thekkedath '16, is featured on the home page.