EMSW21-RTG: Integrated Research Training in the Mathematical Sciences

该项目将对本科生、研究生和博士后助理进行跨学科的培训，该项目将建模、分析和计算与当代实验研究相结合。从科学上讲，总体主题是大型多尺度非线性系统以及分析它们所需的数学和数值方法。我们对高度非线性、高噪声、具有大量组件并在广泛的空间和时间尺度上发展的应用感兴趣。这些模型在物理上是真实的，但难度太大，以至于直接的数值模拟不能真实地再现它们想要描述的过程。我们的研究目标是提供更深入的分析，这总是涉及到将建模、计算和分析与当代实验研究相结合。我们项目的核心是学生和博士后在跨学科研究团队中的指导参与。与此同时，我们将开展的活动将覆盖广泛的受众，并将研究、指导和广泛的教育经验结合在一起。具体的例子有应用数学日和小型研讨会。这项努力还将包括创新的课程改革，这些课程将提供有指导的过渡，既将增加对数学研究生院感兴趣并为之做好准备的学生数量，也将为我们的研究生和博士后助理为在学术界或行业的职业生涯做好准备。此外，我们将开发创新的招聘和留住组件，以及对该计划的仔细管理和评估。

This project will train undergraduates, graduate students, and postdoctoral associates in an interdisciplinary program that integrates modeling, analysis, and computations with contemporary experimental research. Scientifically, the overarching theme is large multi-scale nonlinear systems and the mathematical and numerical methods needed to analyze them. We are interested in applications that are highly nonlinear, noisy, have a large number of components, and evolve over an extensive range of spatial and temporal scales. The models are physically realistic but are so difficult that direct numerical simulations are not able to faithfully reproduce the processes they are intended to describe. Our research objective is to provide a more in-depth analysis, and this invariably involves integrating modeling, computations, and analysis with contemporary experimental research.The core of our program is mentored participation of students and postdocs in an interdisciplinary research team. At the same time, the activities we will develop will reach a wide audience and combine research, mentoring, and broad education experiences. Specific examples are Applied Math Days and mini-symposia. Also included in this effort will be innovative curricular changes that will provide mentored transitions that will both increase the number of students interested in, and prepared for, graduate school in mathematics and which will also prepare our graduate students and postdoctoral associates for careers in academia or industry. In addition we will develop innovative recruitment and retention components, as well as careful management and assessment of the program.