In this project teams of undergraduates are undertaking substantive research projects that contain both mathematical and computational aspects. To prepare the students for their research experiences, the PI team at Rennselaer Polytechnic Institute (RPI) is offering a sequence of educational components. These include both a new course, "Research in Applied and Computational Mathematics," and a special topics course that serves as a "capstone-like" experience. Additional activities are also being implemented to develop and then sustain each group of students as a cohort. For example, to enable students to gain a broad perspective of i) contemporary research in computational science and mathematics, and ii) some of the associated methods and tools, the project team is instituting an interdisciplinary seminar in computational mathematics, consisting of expository talks accessible to advanced undergraduate students given by prominent computational scientists from universities, national laboratories, and industry. Through the combination of their research and coursework students gain a deep and broad understanding of a research area in applied and computational mathematics. The project also features a significant partnership between RPI and Howard University that supports two students from Howard to be in residence at RPI annually for a spring term (tuition waived) and summer as part of the undergraduate cohort. Faculty mentors at Howard join with RPI colleagues to oversee the continuation of the research projects in the fall term.
The intellectual merit of the project lies in the mentored participation of undergraduates in a research project. The organization and components of the program provide an environment in which creativity, invention, and scientific communication skills are promoted and developed. The educational and professional experiences of the participants are also enhanced through regular interaction with scientists and engineers, both theoretical and experimental, from other academic, industrial and government laboratory facilities. The broader impacts of the project are found in the partnership with Howard University and the increased diversity of the student cohort. But more importantly the partnership offers the opportunity to nurture longer term collaborations among faculty with similar research interests at both institutions that form the basis for continued undergraduate student research experiences. Additionally, the new courses and seminar series also serve as models that other institutions may adopt or adapt. Such curricular changes provide mentored transitions that increase the number of students interested in, and prepared for, graduate school in mathematics. The project is supported by the MPS Division of Mathematical Sciences, the MPS Office of Multidisciplinary Activities, and the EHR Division of Undergraduate Education.
We developed and implemented a successful mentoring program for our undergraduates, that integrates mathematics with computations. The CSUMS program (as designed by DMS and DUE) had the foresight to provide student funding over an extended period of time (12 months versus the usual 3 months for the Research Experiences for Undergraduates (REU) program). This allowed our students the time needed to undertake a research project that produces meaningful results, and the ability to present their work at one or more national conferences. Evidence for our success includes the large number of CSUMS supported students who have gone on to graduate school. Over the funding period, our graduates have entered PhD programs at Arizona, Brown, Courant, Duke, Maryland, Northwestern, and Princeton. Moreover, the first three CSUMS students have received their PhD from Brown, Courant, and Duke. Another indicator of our success is the large number of visits we have had to our CSUMS web-site. While CSUMS was a program supported by DMS, using the search word "CSUMS" always resulted in us being listed first or second (when we came in second, the one listed first was the NSF site for CSUMS). In fact, it still receives several new visitors each week, mostly from the US and China. An important component of our program has been to help the undergraduates develop their communication skills. This included weekly presentations in our summer research seminar, and they also presented 17 talks and 8 posters at national research conferences (with one of our students winning a best poster award). Moreover, for three years we organized and ran two CSUMS mini-symposia at the Society for Industrial and Applied Mathematics (SIAM) National Meeting (with speakers from the various CSUMS program across the country). In terms of intellectual merit, the core of our program was a mentored participation of undergraduates in a research project. The organization and components of the program provided a mentored research environment that was designed so that creativity, invention, and scientific communication skills were promoted and developed. The program also significantly broadened the educational and professional experiences of the students as they regularly interacted with scientists and engineers, both theoretical and experimental, from other academic, industrial and government laboratory facilities. As for the broader impacts, the activities we developed reached a wide audience and combined research, mentoring and broad educational experiences. Specific examples were the CSUMS mini-symposia at the SIAM national meetings, the high traffic web-site we built, and the impact our students have in the PhD programs they entered at the highly ranked universities across the country.
