CSUMS: Development of an Ongoing Program of Undergraduate Computational Mathematics Research

计算数学在现代科学的基础设施中起着至关重要的作用。为了促进计算和数学科学技能的发展，在这个csums项目中，研究者和他的同事们在乔治梅森大学建立了一个正在进行的本科生研究项目。该项目涉及一些有才华的本科生，他们有几个重叠的研究机会，这些机会都依赖于计算数学。本科数学专业的学生与知名教授一起研究计算数学的即时问题，这些问题在材料科学、天文学、空间气象、动力系统建模、生物物理学、神经科学、金融数学、统计学和流体动力学等领域有直接的应用。来自数学科学系和计算与数据科学系的五名共同研究人员，以及其他20名具有指导高中生和本科生经验的教授。每个csum队列在核心知识核心班一起工作，每年轮换，此后不久专门从事与核心相关的几个特定研究项目之一。学生由终身教授或终身教授指导，并在年底前制作一份海报和一篇描述他们研究的书面论文。这个项目解决了激励和教育下一代计算科学家的重要需求。由于当代科学对计算建模的严重依赖，计算数学专家对于美国科学的发展将是必要的。该项目通过让今天的数学专业学生参与重要的本科应用研究，帮助培养训练有素的计算数学家。研究经验使他们更有可能在研究生阶段取得成功，完成计算机领域的高级学位。乔治梅森大学的csums项目让学生接触到关键竞争力领域的有趣的、可计算的研究问题，包括材料科学、计算流体动力学、金融数学以及生物和物理科学的其他几个领域。此外，当学生们还在制定自己的职业方向时，这个项目就教育他们计算技能的价值。该项目得到了MPS数学科学部、MPS多学科活动办公室和本科教育EHR部门的支持。

SauerDMS-0639300 Computational mathematics plays a critical role in theinfrastructure of modern science. To foster the development ofcomputational and mathematical science skills, in this CSUMSproject the investigator and his colleagues establish an ongoingprogram of undergraduate research at George Mason University. The program involves selected talented undergraduates in severaloverlapping research opportunities that share a reliance oncomputational mathematics. Undergraduate mathematics majors workwith established professors on timely problems of computationalmathematics with immediate applications in materials science,astronomy, space weather, dynamical systems modeling, biophysics,neuroscience, financial mathematics, statistics, and fluiddynamics. The five co-investigators on the project, from theDepartment of Mathematical Sciences and the Department ofComputational and Data Sciences, are joined by 20 otherprofessors with experience in mentoring high-school andundergraduate students. Each CSUMS cohort works together in acentral knowledge core class, to rotate from year to year, andshortly thereafter specializes to one of several particularresearch projects related to the core. Students are supervisedby tenured/tenure track faculty and produce a poster and awritten thesis describing their research by the end of the year. This project addresses the important need to inspire andeducate the next generation of computational scientists. Due tothe heavy reliance of contemporary science on computationalmodeling, experts in computational mathematics will be necessaryfor the advancement of science in the U.S. This project assistsin the creation of well-trained computational mathematicians byinvolving today's mathematics majors in significant appliedresearch at the undergraduate level. Research experiences makethem more likely to succeed at the graduate level, in thecompletion of advanced degrees in computational areas. The CSUMSprogram at George Mason University exposes the student tointeresting, computationally accessible research problems incritical competitiveness areas, including materials science,computational fluid dynamics, financial mathematics, and severalother areas in the biological and physical sciences. Additionally, the program educates students about the value ofcomputational skills while they are still formulating theircareer directions. The project is supported by the MPS Divisionof Mathematical Sciences, the MPS Office of MultidisciplinaryActivities, and the EHR Division of Undergraduate Education.