Educational Mission
In today’s high-tech marketplace, global competition and transparency in the flow of goods and services throughout the world have had an immediate and profound effect on the balance of trade, the outsourcing of labor, and our world’s financial systems [2]. There are concerns, however, that over the long term, our nation’s competiveness will be significantly hampered without increased attention and investment in Science, Technology, Engineering, and Mathematics (STEM) fields [1, 3, 5, 6]. Indeed a strong indicator of our nation’s vibrancy, economic sustainability, and security is the strength of its STEM workforce.
While educators, policy makers, and academics largely agree on the crucial role our STEM workforce plays in our nation’s health, many households have yet to embrace this idea [4]. This gap is particularly pronounced in the mathematical sciences, where young students seem largely unaware of the rich career opportunities available. Indeed, a mathematics or statistics degree can prepare students for high-paying and influential careers in finance, insurance, risk management, operations research, computational science & engineering, signal, image, & natural language processing, bioinformatics & computational biology, information science, and machine learning, to name a few. A math or statistics major is also a great choice for careers that are not directly math related, such as business, law, and medicine, where admission rates for these majors are relatively high.
To help address the gap between our national interests and household participation in the mathematical sciences, we have developed BYU’s Interdisciplinary Mentoring Program in Analysis, Computation, and Theory or IMPACT, which serves as a national model for other universities. Indeed we are working toward a multi-faceted approach to attracting and retaining new talent into the mathematical sciences through:
1. Undergraduate and graduate research in (primarily) interdisciplinary fields,
2. A modernized curriculum that cuts through the jargon of particular disciplines and reveals the common mathematical, statistical, and computational structures behind key scientific principles, methods and processes,
3. Socialization and team-building amongst horizontally and vertically integrated groups of undergraduates, graduate students, and faculty, and
4. Industrial cooperation that will provide internship and career opportunities for our students.
Research in the IMPACT program is funded through grants, industrial sponsorship, and the generosity of private donors. Continued support from each of these sources is necessary sustain this program.
Research Opportunities
For many students, the research focus on specific applications is important. Not only does it give them concrete examples that align with their individual interests and intuition, but it also motivates the need for deeper and more abstract mathematics. Through the use of modern computational tools and advanced technology, we have found that students can be quickly trained to begin substantial research projects as undergraduates. Furthermore, as they develop computational expertise, they find themselves well equipped to meaningfully contribute to research groups. As our students are guided though the program, and as their analytical and computational sophistication matures, they will have the capacity to take on harder problems and do so with less supervision. Within a year, it is expected that students will be contributing to publishable quality work and in many instances preparing their research for publication in a refereed scientific journal.
Our students are also exposed to a myriad of other projects through close working quarters with other students in different research areas, as well as our continually reinforcing the mathematical, statistical, and computational connections between different problems in our weekly seminars and specialized courses designed for this program.
Interdisciplinary research projects in the IMPACT program come principally from the following 3 areas: (i) the actuarial, investment, and management sciences, (ii) human, biological, and organizational systems, and (iii) the physical sciences and engineering. We have identified these three application areas to be fertile recruiting ground for (good) students.
Modernized Curriculum
The aim of IMPACT is more than simply building an interdisciplinary research group. Projects from our program feed the undergraduate and graduate curriculum with examples that cut through application-specific jargon and focus attention on the common mathematical themes underlying seemingly disparate problems. This helps students to see mathematics as an intellectual core of scientific pursuit rather than some kind of esoteric or tangential offshoot. Indeed it is through abstraction and mathematical rigor that we are able to effectively communicate the ubiquity and prominence of ideas such as approximation, estimation, optimization, prediction, decision and control in the world’s most pressing scientific problems.
Horizontal and Vertical Integration
Mathematical science students with interests in computational biology, population dynamics, finance, economics, fluid dynamics, operations research, defense systems, or the policy sciences, can all take a common core of courses that focuses on the mathematical issues surrounding the formulation and computation of prediction and decision processes; examples include courses in optimization, dynamical systems, modeling & simulation, numerical analysis, and probability & statistics. Introducing application-specific projects for student researchers allows us to keep the curriculum focused on the central theory at the intersection of all of these applications, and does so without sacrificing the pedagogical advantage of concrete examples used to feed a wide variety of student interests. Moreover, engaging all of these “horizontal” application areas simultaneously within the IMPACT program keeps the mathematics focused on the underlying theoretical principles rather than allowing it to become dominated by any one particular application. By vertically integrating teams of undergraduates, graduate students, and faculty, all members of the group participate as teacher-scholars by helping one another to learn and grow through collaboration and hard work. This vertical structure gives younger students numerous opportunities for help and guidance, and it also gives the more senior students opportunities to reinforce their understanding by teaching. A spirit of community is a crucial component in the IMPACT Program.
Industrial Cooperation
In addition to basic research, IMPACT develops relationships with industrial partners to provide opportunities for students to connect their work to industry. Industrial cooperation not only provides opportunities for internships, employment, and entrepreneurship, but it provides for rapid deployment of mathematical and statistical methods and tools developed in research projects.
References
[1] Council of Graduate Schools. Graduate Education: The backbone of American competitiveness and innovation, Washington D.C., 2007.
[2] Thomas L. Friedman The World Is Flat: A Brief History of the Twenty-First Century, Farrar, Straus and Giroux, 2007.
[3] Bill Gates. How to Keep America Competitive. Washington Post, pg. B7, February 25, 2007.
[4] Alison Kadlec and Will Friedman with Amber Ott. Important, but not for me: Parents and students talk about math, science, and technology education. Public Agenda, 2007.
[5] National Research Council. Rising Above The Gathering Storm: Energizing and Employing America for a Brighter Economic Future. National Academies Press, 2007, Washington D.C.
[6] National Science Board. Science and engineering indicators, Volume 1, 2008. Washington D.C.
