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.

中文翻译：

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 教育


SIAM 评论，第 66 卷，第 4 期，第 749-749 页，2024 年 11 月。

在本期中，教育部分介绍了两篇文章。第一篇论文“沙堆和沙丘：颗粒物质的数学模型”由 Piermarco Cannarsa 和 Stefano Finzi Vita 撰写，回顾了沙堆和沙丘形成的数学模型。在自然界和日常生活中，各种材料以颗粒的聚集形式出现，例如沙子、砾石、新雪、大米、糖等。在更大的尺度上，颗粒状材料表现出新的和更复杂的现象，这些现象仍未被完全理解。它与固体、液体或气体的特性非常不同，因为它可以根据系统的能量表现出与其中一种或另一种相似的特性。它的建模有助于理解复杂的自然现象，例如沙丘迁移、侵蚀、山体滑坡和雪崩，并有助于环境保护计划的制定。此类模型在农业、建筑、能源生产以及化学、制药、食品和冶金行业的各种应用中也很重要。即使还没有一个足够整合的颗粒材料动力学通用模型，但最近随着适应更具体情况的新理论模型的引入，已经取得了重大进展。在本文中，在进行了一般性描述和一些历史评论之后，作者仅限于考虑在小强度垂直源的作用下桌子上一堆沙子生长的问题，而忽略了风的影响，风在沙丘形成中起着重要作用。尽管如此，即使对于这样一个看似简单的情况，也确实出现了许多有趣的现象，并以一种易于理解的方式进行了描述。 随附的真实生活经历图片使阅读真正有趣，而数字插图则对现象的复杂性带来了更好的直觉。作者还指出了可供进一步学习的文献。这篇文章组织得很好，写得很工整，并提出了突出一些主要方面的主题。对现有模型的审查可以成为应用数学和偏微分方程硕士课程研究项目的起点。高等数学学生也可以使用它以经济实惠的方式学习颗粒材料的差分模型。第二篇论文“培养具有数学建模技能的员工队伍”由 Ariel Cintrón-Arias、Ryan Andrew Nivens、Anant Godbole 和 Calvin B. Purvis 发表。本科数学学位占美国所有授予学位的很小一部分，而且这部分正在停滞不前，而 2016 年至 2026 年期间统计学家和数学家的就业增长预计将是可观的。因此，数学训练的增长需求变得势在必行。作者讨论了全国范围内 STEM 专业人士的培养，并认为数学建模课程可以吸引更多学生学习数学专业和辅修专业。它们还提供了三个公共数据存储库的一些亮点，这些存储库可以与数学建模说明一起使用。然后提出了与高需求技能相关的数学建模通用辅修课程，并提供了一些选定的教育资源。最后，讨论了授予作者所在机构的国家科学基金会资助的结果，该资助旨在帮助和鼓励学生进行数学建模。 本文可以作为获得大学管理人员支持将数学建模整合到 STEM 课程的宝贵工具。