Education

SIAM Review, Volume 66, Issue 4, Page 749-749, November 2024.
In this issue the Education section presents two contributions. The first paper, “Sandpiles and Dunes: Mathematical Models for Granular Matter,” by Piermarco Cannarsa and Stefano Finzi Vita, presents a review of mathematical models for formation of sand piles and dunes. In nature and everyday life various materials appear as conglomerates of particles, like, for instance, sand, gravel, fresh snow, rice, sugar, etc. On larger scales, granular material exhibits new and more complex phenomena which are still not fully understood. It is very different from that of a solid, liquid, or gas in the sense that it can show characteristics similar to one or the other depending on the energy of the system. Its modeling can help in understanding complex natural phenomena such as dune migration, erosion, landslides, and avalanches, and can contribute to the development of environmental protection programs. Such models are also important in various applications in agriculture, construction, energy production, as well as in the chemical, pharmaceutical, food, and metallurgical industries. Even if a sufficiently consolidated general model for the dynamics of granular materials is not available yet, significant progress has been made recently with the introduction of new theoretical models adapted to more specific situations. In this article, after a general description and some historical comments, the authors limit themselves to considering the problem of the growth of a pile of sand on a table under the action of a vertical source of small intensity, neglecting the effects of wind, which has an important role in dune formation. Still, even for such an apparently simpler case, many interesting phenomena do arise and are described in an easily accessible way. Accompanying pictures of real-life experiences make the reading truly enjoyable, and numerical illustrations bring even better intuition on the complexity of phenomena. The authors also indicate literature for further learning. This article is well organized, neatly written, and presents the subject highlighting some of the major aspects. This review of existing models can become a starting point for research projects in a Master's program of applied mathematics and partial differential equations. It could also be used by advanced mathematics students to learn differential models of granular material in an affordable way. The second paper, “Developing Workforce with Mathematical Modeling Skills,” is presented by Ariel Cintrón-Arias, Ryan Andrew Nivens, Anant Godbole and Calvin B. Purvis. Undergraduate mathematics degrees constitute a very small portion of all awarded degrees in the U.S., and this portion is stagnating, while the job growth between 2016 and 2026 for Statisticians and Mathematicians is expected to be substantial. So the need for growth in mathematical training becomes imperative. The authors discuss the nationwide production of STEM professionals and argue that mathematical modeling curricula could attract more students to mathematical majors and minors. They also provide some highlights of three public data repositories that can be used along with instruction in mathematical modeling. Then a generic minor in mathematical modeling related to skills in high demand is proposed and some selected educational resources are provided. Finally the outcomes of a National Science Foundation grant awarded to the authors' institution designed to assist and encourage students in mathematical modeling are discussed. This article may serve as a valuable tool to obtain support from university administrators for integrating mathematical modeling into STEM curricula.