The organizers of SIAM’s Modeling Across the Curriculum project, under the leadership of VP for education Peter Turner, have conducted two workshops. The first resulted in a report that focused on the development of math modeling-based high school courses in STEM subjects and on a larger role for math modeling in undergraduate curricula.
The second workshop, designed to develop some of the recommendations that arose in the first, was held in January of this year. In a keynote address, Joan Ferrini-Mundy, the National Science Foundation’s assistant director for Education and Human Resources, questioned the 50 workshop participants about the growing field of big data, and specifically about the implications for education.
Big Data—What Is It?
Big Data has become a Big Deal. In industry, people are hired as data analysts or data scientists. In response, universities are creating programs to train students for jobs in these fields. And, of course, agencies, among them NSF, have created major research programs in big data (including the ongoing Big Data Initiative launched by the Obama administration in 2012; see NSF update below). Some would claim that massive data sets and the information that can be mined from them will supplant traditional modeling and simulation as a means of discovery. Although we doubt that this will happen, big data is clearly emerging as a field of study. The tools created in that research will have an impact on the work of scientists and engineers; already, we are seeing an impact on business applications.
As is often the case with emerging fields, big data is not clearly defined. What do we mean by “data-enabled science” or “data science”? What courses are required for a degree in this field?
More particularly, what does mathematics have to say about data science? Obviously, statistics is a longstanding player here, as is computer science, with its supporting areas of machine learning, databases, and so on. What should a data science program look like? What topics should be covered? Should someone trained in data science know, say, linear algebra?
A measure of the growing importance of this area is the recent creation of several data science centers. Three prominent new ones come to mind—one supported by the Sloan Foundation, another by the Simons Foundation, and a third at UC Berkeley. With time, answers to the “What is it?” question will emerge as research is focused around this theme. Centers will define research topics; education programs will be established to serve the demand for people trained in this area. We can look at other emerging research areas for clues.
Another area that seems to invite the “What is it?” question is uncertainty quantification. I am reminded of the comment made at SIAM’s first conference on UQ (2012) by a prominent senior SIAM member who teaches probability and statistics: “UQ—I thought that’s what I had been doing for the past 30 years!”
The field as defined by the SIAM Activity Group on Uncertainty Quantification focuses on quantifying uncertainty in output from large computational simulations, typically governed by partial differential equations, given uncertainties in parameters, data, and even the model itself. Techniques like MCMC (Markov Chain Monte Carlo) play a major role in this area.
The growth of this area of research has been amazing. Fifteen years ago, John Guckenheimer led a study that produced a SIAM report on uncertainty quantification, which led in turn to a small SIAM workshop on the topic. These efforts attracted sufficient attention that the Chronicle of Higher Education ran an article, “To Improve Their Models, Mathematicians Seek a ‘Science of Uncertainty’” (April 16, 1999), featuring Guckenheimer and Jim Glimm.
Nevertheless, UQ occupied a small corner of SIAM conferences—typically as a theme in the CS&E conferences—until 2011, when SIAG/UQ was created. The group’s second conference, held at the beginning of April, shows how the research area has grown. The 560 participants came from a diverse set of disciplines. The program featured well-known speakers from applied mathematics, such as Andrew Stuart, and statistics, James Berger being one example, as well as various application disciplines. Geosciences was a featured application area, represented on the organizing committee by Marcia McNutt, who was director of the United States Geological Survey when the conference was organized and is currently editor-in-chief of Science.
We expect that more detailed answers to the “What is it?” question will be forthcoming. At the conference, SIAG/UQ chair Max Gunzburger raised the issue with regard to SIAM/ASA Journal on Uncertainty Quantification. The editorial board can be counted on to have a good understanding of what constitutes UQ, but questions remain about the criteria for articles appropriate for the journal, especially with regard to supporting areas. When, for example, is a paper on numerical methods for stochastic differential equations appropriate for the journal? We expect to hear more on this issue, and more about sessions at this lively conference, in a future issue of SIAM News.
Back to Math Modeling and Education
Education—beginning at K–12 and continuing through postsecondary levels—has become an increasing emphasis for the math sciences community in recent years. This is due, in part, to the interest of the Obama administration in STEM education, with its stated goal of training more people in the STEM disciplines.
For SIAM, the focus has been on aspects of education clearly related to mathematics and its applications, especially modeling. Along with the Modeling Across the Curriculum workshops mentioned at the beginning of this article, SIAM is the publisher of a new guidebook on modeling. Undertaken to help prospective mentors of high school teams competing in the SIAM-run Moody’s Mega Math Challenge, the guidebook is a resource for anyone seeking a background in mathematical modeling. In the words of authors Karen Bliss, Katie Fowler, and Ben Galluzzo, the guidebook is intended for students and teachers who want “to learn how to model.” It is designed to “demystify the process of how a mathematical model can be built.”
Undergraduate education (at least in the early years) and K–12 education are relatively new topics for SIAM. Driven by calls for the inclusion of applications and modeling in math curricula, and spurred by the activities of the energetic SIAM Education Committee, such topics are likely to see continuing emphasis in upcoming years.
NSF Updates: Big Data Program
The National Science Foundation has issued an updated solicitation for its Critical Techniques and Technologies for Advancing Big Data Science & Engineering (BIGDATA) program. Details can be found here.
The deadline for full proposals is June 9, 2014.
The solicitation invites two types of proposals: “Foundations” (F), for those developing or studying fundamental techniques, theories, methodologies, and technologies of broad applicability to big data problems; and “Innovative Applications” (IA), for those developing techniques, methodologies, and technologies of key importance to a big data problem that directly impacts at least one specific application.
All proposals must address critical challenges for big data management, big data analytics, or scientific discovery processes impacted by big data. These techniques, methodologies, and technologies can be computational, statistical, or mathematical in nature; proposals can focus on novel theoretical analysis or experimental evaluation of these techniques and methodologies.
||Jim Crowley is the executive director of SIAM.