Jo Ellis-Monaghan and Greta Pangborn team up to co-direct mathematics and computer science projects, to impressive results
By Buff Lindau
Two professors working in complex fields are recruiting more students than ever to engage in independent research projects outside the classroom. Jo Ellis-Monaghan, and Greta Pangborn have teamed up over the last six years to co-direct projects with a number of students that have yielded published journal articles for all involved. And the collaboration has helped students succeed in going on to prestigious graduate programs.
Ellis-Monaghan, associate professor of mathematics, whose specialty is algebraic combinatorics, graph theory and applied combinatorics, spent last spring as a funded invited Visiting Fellow at the Isaac Newton Institute at Cambridge University, U.K. Pangborn, associate professor of computer science, who specializes in operations research, has made a series of presentations on combinatorics, and has a number of publications, many co-authored by Saint Michael’s students.
Together with their colleague Michael Battig, Ellis-Monaghan and Pangborn earned a National Science Foundation grant of $600,000 to fund scholarships for math and computer science students at Saint Michael’s.
Their students are doing original independent research projects and get superb and unique opportunities not otherwise available to them. Most textbook lab assignments are extremely well-defined, Pangborn said. They don’t expect students “to reformat existing data, define metrics, balance conflicting parameters or even define the actual problem.”
Some of the problems these professors and their students explore result in mathematical and computer designs that can solve problems in science or industry. They have been able to produce computer algorithms which can be applied to problems in computer chip design, DNA design, statistical mechanics of all sorts, tumor migration, social demographics, magnetization, “nearest neighbor interactions” and more. Only through mathematics and CS collaborations can they tackle these problems.
“Nearest neighbors” are models of social demographics that can reveal through a small sample or segment what behavior emerges from a large system. This model has been applied to epidemiology, where, for instance, “if you know the transmission rate of a disease, how long people will be sick, whether they’re immune after they’ve recovered, you can then set up a nearest neighbor model to see if you are going to catch the disease, and from analysis of the transmission, you can determine the global rate of the system,” Ellis-Monaghan said.
With the combined forces of math and CS, “You only need to know microscale properties to determine outcomes—you don’t have to know the global scope,” said Ellis-Monaghan. This tool can now be applied with today’s huge computing capacity in innumerable situations.
Like calculus is to physics, graph theory is to computer science, Ellis-Monaghan explained. You simply can’t do computer science without graph theory. At the same time, effective simulations have only become possible with the growth of computing capacity—thus collaboration is essential, and often moves beyond these two realms to include biology, chemistry and physics.
“Our students love this kind of collaborative experience,” the professors said. They have enthusiasm and fearlessness about tackling unknown problems, and “they’re willing to go out and learn the tools they need to tackle those problems.” Working with problems focused on the concrete world “gives them a meaningful context for the computer science and mathematics they’re learning.”
The success of these projects can also be seen in the numbers of students continuing this kind of work. “All of the math and CS students who have worked with us over the last 10 years have gone onto graduate school, to such places as UVM Medical School, Rensselaer, Colorado State, Boston University and elsewhere.” These collaborations apply in industry as well as in the advancement of pure science.
