Making it all add up

 

 
 

When scholars apply mathematical principles to real-life problems, it’s called applied math, and according to Charles Epstein, the Francis J. Carey Term Professor of Mathematics, people are doing it all over campus—just not in his department.

With an interdisciplinary group of colleagues, Epstein has pulled together a Working Group in Applied Mathematics and Computational Science. The group’s new colloquium series recently brought math superstars Peter Lax and Stephen Smale to Penn, and continues next month with a visit from Princeton chemical engineer and guru of equation-free modeling Yannis Kevrekidis, who will speak on November 4.

“A lot of applied math at Penn is amorphous,” says Epstein. “There’s no department, and you can’t get a degree in it.” But throughout Penn people are incorporating sophisticated math into their work. In the Physics Department, they’re using it to pull apart string theory. At Wharton, they rely on it to build financial models and projections, and in the Engineering Department, it’s supplying the vital equations for figuring out how to make robots walk.

Epstein himself has taken his expertise out of the math department and applied it to medical imaging. Since 1998 he’s taught a course on the mathematical foundations of MRI and ultrasound. “A lot of people don’t realize that what makes them go is a good mathematical model,” says Epstein. “Different students get different things out of the course. They’re coming at it from different angles and they prove assertions in different ways.”

Epstein’s interest in applying his math led him in 2003 to spend a year in Penn’s Radiology Department as a visiting faculty member studying problems in nuclear magnetic resonance with Felix Wehrli, a professor of radiology, biochemistry and biophysics. “I wanted to do something that wasn’t just math, but had an interesting consequence,” explains Epstein.

For him, the meaning of math comes from its functional use, though he readily acknowledges that many pure mathematicians—known for their “pride in craft” and “lapidary tendency to polish”—would disagree. English mathematician G.H. Hardy, he says, went so far as to boast that he had never worked on anything that had any conceivable application. Often, though, the models mathematicians create become building blocks for applied work. “When Einstein sat down to do his work on relativity,” Epstein says, “he was lucky that the math had just been done. That gave him the tools to express his theory. The mathematicians developed this structure and he showed them how it was important. He put some meat on the bones.”

The goal of the colloquium series is to make applied math more accessible, and Epstein is confident that his “dream list” of speakers will do just that. The larger goal of the Applied Math group, which he formed with colleagues in the Schools of Arts and Sciences, Engineering and Medicine, as well as Wharton, is to find common ground and create a fully funded graduate group in applied math. By next year, says Epstein, a Masters degree program will be up and running, using both existing courses and several new beginning level courses.

Getting people from different disciplines to understand each other and to understand mathematical discourse can be a challenge, concedes Epstein. “One of the things I’ve learned is that when a mathematician writes an equal sign he means one thing and when an engineer writes it he means something else.”

For more information on the Working Group in Applied Mathematics and Computational Science and for a full schedule of colloquium and seminars, go to the web site at www.amcs.upenn.edu/.


Originally published on October 20, 2005