“It gets complicated very quickly,” said Swinarski, PhD, who managed the immense number of equations by turning to computers for help.
It proved an enduring interest. Today, his research program sits at the intersection of mathematics and computer science, two fields that are increasingly linked in the study of abstract questions but also more concrete topics like human health. Fordham’s joint major offering in the two fields, still awaiting state approval, is the latest sign of how they’re coming together.
“It’s not that they’re converging, it’s just that maybe the division between them has always been a little artificial,” said Swinarski, an assistant professor of mathematics who helped draw up the plans for the proposed joint major.
Advances in computing power are opening up lots of new possibilities in mathematics, as Swinarski came to appreciate while earning his doctorate at Columbia University. For his dissertation, he was trying to answer a question about string theory, concerned with infinitesimally small particles that are impossible to observe,.
“My adviser and I found a way to answer some very abstract questions with some very concrete calculations, but they were too difficult to do by hand,” he said.
This was the first time he had applied computers to algebraic geometry, and he was soon using computer programming to get results to many other math problems. “It just sort of snowballed,” he said.
Computers are an important part of his research program that involves students in a variety of projects at the Lincoln Center campus. Some projects have focused on economics, mathematical finance, and other areas; one current project, for which Swinarski wrote software, could lead to faster and more accurate analysis of large data sets.
Another project is applying math and computer programs—Visual Basic, Excel—to the subtleties of human physiology for the benefit of people suffering from emphysema and other conditions.
Swinarski and an undergraduate student, Jeremy Fague, are working with Columbia University Medical Center researchers to analyze the large data set gathered by placing 89 sensors on people’s chests, backs, and stomachs to measure changes in their chest volume while they exercised. They’re hoping this new data will offer better insight compared with data obtained from breathing tests administered while someone is at rest and lead to better ways to manage emphysema.
“The big question in pulmonary medicine is, ‘Why is this particular patient short of breath?’” Swinarski said. “Is it their lungs, is it their chest muscles, is it actually that they have poor circulation and this feels to them like they’re short of breath when actually their lungs are functioning fine (and) it’s the heart that’s the problem?”
“Answering the question is complicated for all those reasons,” and both math and computer science can be used to identify potential causes of the breathing problems, such as out-of-sync expansion of the chest and abdomen, Swinarski said.
The new computer science/mathematics joint major will give students more leeway for electives at the intersection of the two fields and better prepare them for working in today’s tech sector, Swinarski said.
For instance, problems in parametric statistics call for an extremely large number of computations because fewer assumptions are made about the variables in question. Because today’s computers are far better able to handle this kind of problem, it no longer needs to be relegated to the margins in the classroom, Swinarski said.
“If you take sort of a classic one-semester statistics course, that’s something you would maybe hear about for a week or two at the end of a semester,” he said. “Nowadays, with the explosion of data science in New York, this is the kind of thing we’d like to teach a whole second semester of statistics on.”