NSF Grant Funds 'Collaborative Exploration'

Math and computer science Professor Chad Westphal says he’s learned a lot from fellow Wabash science professors Scott Feller, Jim Brown, Dennis Krause, and Lon Porter.

“They have this magic touch with students. From them I've picked up how to make good things happen on this campus.”

The $113,000 research grant Westphal received last fall from the National Science Foundation is going to make even better things happen in the mathematics department. Won in competition with top-flight research universities, it involves developing new techniques in computational mathematics. But it's also a template for how the liberal arts can enrich science, how science can inform the liberal arts, and how students can learn “the human element” of research from scientists as committed to teaching as they are to discovery.

Westphal calls it “collaborative exploration.”

That’s not the subject of his grant, Adaptively Weighted Finite Element Methods for PDEs and Optimal Least-Squared Metrics.

But Westphal says students will learn that human element—“what it’s like to be a professional”—as they engage in an experience most current faculty didn’t have until grad school.

He says Wabash students are well prepared for the work.

“Big research institutions focus on training graduate students and postdocs, and they do a very good job at that. That’s how I learned this stuff. But at a place like Wabash, the undergraduates are at the top of the totem pole. They’re used to close interaction with faculty.

“My challenge is to give them exposure to research while also discovering something meaningful in the field in computational mathematics. I treat them like graduate students and we work on that level.”

Westphal says that although the human element of research can’t simply be taught in the classroom, it can be observed and absorbed.

It begins with focus.

“In research, you’re focusing on this one project. You've got to do it today and tomorrow and the next day for weeks on end. You've got one problem that you've got your mind wrapped around.

“Most undergraduates have never have had that scale of project before.”

There’s failure.

“When you're on the front lines of doing things for the first time, the process is really slow. You hit a lot of dead ends. You ask a lot of dumb questions that you eventually find out were dumb questions, but that you had to ask.

“And there are lots of little failures. You've got to hit a wall. You've got to back up and move again, hit another wall. You almost blindly work your way around a lot of things. Every once in a while, you step out into the light, your eyes dilate, and it's scary, but then you realize you’ve found something important.”

Westphal says it’s best for students to experience such failure in the relatively safe environment of Wabash. Most important, he says, they must learn that “science is a team sport.”

“You have to be able to concentrate alone, but you’ve also got to be able to work in groups and communicate. The process works the best when you have two or three people working together. You talk through ideas. You get confused. You say, ‘What did we do last time we had something like this?’ You feed off of each other.”

Working with Westphal, students learn that “there are people behind all this stuff.

“We’ll go to conferences, meet other scientists, or we’ll go through journals and I’ll say, ‘This guy here, he’s a big player.’ It sounds like gossip, but you’ve got to know these things. You’ve got to know how to navigate, to know what research groups are putting out good work we need to be paying attention to and understanding.

“What we do at Wabash—and in my experience is done best at schools like Wabash—is to get undergraduates really plugged into the research process, to make them real ‘boots on the ground’ where they're working on open-ended problems.”

Westphal’s open-ended problem is in computational math.

He and his students aim to design a new class of robust adaptive algorithms with potential applications in fluid mechanics, and weather and climate modeling, among many others.

“What drives me is finding the reason why things often don’t work the way that they’re supposed to, and then figuring out what the problems are, and how to solve those in an elegant way,” Westphal says.

For the next three years, thanks to the NSF grant, two students for each of the next three summers will be figuring out problems with him, solving them in an elegant way, and learning how to be scientists in the best liberal arts tradition.