Xingjie Li, a new Prager Assistant Professor of Applied Mathematics, strives to be provably right, but she also knows the value of being purposely wrong.
In her research, Li works to produce mathematical descriptions of the structure and dynamics of crystalline materials. Her goal is not to make a stronger alloy or a more efficient conductor. Instead she focuses on perfecting the numerical models of aspects of crystal structure.
“We mathematicians want to describe things rigorously,” says Li, who earned her Ph.D. at the University of Minnesota in May. “We try to prove every statement.”
Li is not so exacting, however, that she’d let a little thing like being right interfere with teaching. When she taught calculus classes at Minnesota she says she’d sometimes teach by not only showing the correct solution to a problem, but also a wrong solution. There’s pedagogical value in showing what not to do.
“In my own experience, if I do something wrong and then I analyze why I did it incorrectly I can remember the mistake and next time try my best not to make that mistake again,” she said. “It’s very helpful for a student to learn new things. It can help them to develop some skills to analyze why it’s wrong.”
A passion for analysis, in either research or teaching, is Li’s motivation. She’s had it at least since she was an undergraduate at Fudan University in her hometown of Shanghai. In pursuit of her bachelor’s degree, she delved deeply into numerical analysis, a discipline in which mathematicians develop algorithms to finely approximate the solutions to otherwise unsolvable equations.
In the latter half of her undergraduate education she worked on numerical analysis algorithms to solve Maxwell’s equations, which describe electricity and magnetism.
“And then I analyzed these new algorithms,” she said.
In her graduate work at Minnesota, Li worked on developing and analyzing a mathematical model of a simple crystal structure at multiple scales. She also investigated the computational application of the model to benchmark problems in the field.
At Brown during her position’s three-year term, she will join a community that shares similar interests. In fact, her introduction to Providence came by attending a conference on “Heterostructured Nanocrystalline Materials” at the Institute for Computational and Experimental Research in Mathematics at the end of May. There she rubbed elbows with new Brown colleagues Vivek Shenoy and Eric Chason from the School of Engineering.
Here she plans to continue her current work but she also is inspired to work on new ideas with potential collaborators in the Division of Applied Mathematics. Govind Menon, for example is interested in nanomaterials that assemble themselves. Chi-Wang Shu, meanwhile has developed intriguing methods for numerical analysis of nonlinear partial differential equations.
So let the rigorous analysis, and the fruitful recognition of error, begin.