Helping Undergraduates See Mathematics in the Material World

July 23, 2010

Maria Emelianenko

Undergraduate education in STEM disciplines has been a focus of nationwide attention in recent years, and while few would question the importance of increasing students' interest in science and technology, many still hesitate to involve undergraduates in formal research. This is especially noticeable in interdisciplinary areas, such as the mathematics of materials, where students have to make considerable effort to attain the necessary level of knowledge in both fields. My experience has convinced me that this is exactly the type of activity that can ignite students' passion for scientific learning and discovery. Provided that a mutually enriching student�mentor relationship can be created, this activity holds great promise for success. It is well worth the trouble!

I had the opportunity to organize a minisymposium on undergraduate research for the 6th SIAM Conference on Mathematical Aspects of Materials Science, held in Philadelphia, May 23�26, 2010. The first session of its kind at a SIAM materials meeting, it was made possible by generous support from SIAM. The (student) speakers focused on results obtained in collaboration with mathematics and materials science faculty mentors; papers on the work had either appeared or were about to be submitted for publication in refereed journals. Three of the four students in the group were past or current participants in the Computational Science Training for Undergraduates in the Mathematical Sciences (CSUMS) initiative at George Mason University.

The NSF-supported year-long CSUMS (http://math.gmu.edu/urcm/) and the summer-long Research Experience for Under-graduates (http://math.gmu.edu/reu/) programs at GMU run in tandem, providing a unique opportunity for students to get research experience while giving participating faculty a chance to involve students in their projects with partial summer support. Students learn the fundamentals of applied and computational mathematics by taking a special course in numerical PDEs, and they are trained in LaTeX and scientific software, such as MATLAB and AUTO. In addition, they have ample opportunities to present their work at national and regional conferences. Nineteen students have made it through the GMU CSUMS program so far, and eight are currently enrolled. Each summer, the REU program admits eight students from around the county and a K�12 teacher to an intensive nine-week training program emphasizing analytical and numerical problem-solving techniques with applications to bio-inspired and materials systems.

The minisymposium provided great examples of the significant contributions undergraduates can make through materials-related projects. Mike Atkins, a senior from GMU, has worked with mentors Yuri Mishin and Daniel Anderson on a precise characterization of the solid�liquid interface thickness by combining molecular dynamics and phase-field simulation methods to a block of partially melted copper. His work, which has been submitted to the journal SIAM Undergraduate Research Online, helped him land a summer internship at NIST, along with several GMU-wide awards. Tom Stephens, another graduating senior at GMU, significantly improved standard phase diagram calculations by using low-discrepancy sampling together with adaptive minimization ideas that he arrived at independently while working with the author over the summer. He has had one paper published in SIURO and is now completing a journal paper on the results he presented in the minisymposium. Both of these students started as mathematics majors and got interested in materials-related research while participating in the GMU CSUMS program.

As a materials engineering student working with faculty member Anthony Rollett at Carnegie Mellon University, minisymposium participant Wren Chan was introduced to mathematical theory while using novel level set methods to simulate grain boundary motion in models of Al�Cu alloys. James O'Beirne, another GMU CSUMS student, has worked with faculty mentors Thomas Wanner and Evelyn Sander; a math/computer science major, O'Beirne got interested in the mathematics of materials while modeling phase separation in ternary alloys. He is currently involved in the development of a large-scale software package for materials applications as part of an internship at NIST. All four of these students plan to enroll in PhD programs.

While this list by no means exhausts all the contributions made by undergraduate students in materials-related areas, it exemplifies an important tendency--students not previously interested in the field become extremely motivated and perform at unexpectedly high levels when placed in a dynamic, competitive research environment, with opportunities to contribute to an understanding of important real-life phenomena. This new-found passion for science is reflected in their career choices. Of the nine students in the first-year CSUMS cohort, all but one have gone on to take graduate courses, six are pursuing doctoral degrees in computational science or applied mathematics, and two others have completed master's degrees. Several REU students from the first group eventually applied to graduate schools as well; one of them, Kyle Pounder of St. Mary's College of California, received a national Sigma Xi research award, and another, Angela Dapolite of Clarkson University, completed an honors thesis based on her REU project. It is noteworthy that fewer than half of the students had seriously considered graduate school before they started the programs--clearly, students' career choices are greatly influenced by the availability of structured learning environments like those provided by the CSUMS and REU programs. These programs play a crucial role, attracting students by providing financial support as well as opportunities to present their work at thematic conferences.

Only two REU programs in mathematics (other than GMU's) offer materials-related research at the moment. This past year, the GMU REU received more than 180 applications for eight positions, with many students indicating an interest in materials research. We can only hope that more funding will become available to increase the number of opportunities we can offer such students. And despite the disturbing news that NSF has discontinued the CSUMS program, with no word on possible renewal, this hope lives on.

Maria Emelianenko is an assistant professor of the mathematical sciences at George Mason University.

• See more news from this issue