RTG: Research Training in Applied Mathematics at Columbia University

这个研究训练组（RTG）项目是哥伦比亚大学应用物理与应用数学系、数学系和工程与应用科学学院共同努力的结果。它的目标是在现代应用数学领域建立一个前沿的研究和培训项目。通过大量丰富学员的研究和教育经验，并直接与工程与应用科学学院和整个大学的关键教育和研究计划相结合，这些活动将对哥伦比亚大学的应用数学教育和培训产生重大影响。RTG项目将吸引来自纽约大都会地区和全国各地的高中生和本科生（通过暑期研究项目），为美国代表性不足的群体激发数学事业。该项目包括三个主要组成部分：(i)一组工程应用前沿的应用数学研究课题；（ii）为本科生和研究生以及博士后学者提供连贯的应用数学研究和职业发展指导学习计划；（三）系统规划应用数学和科学计算的本科和研究生课程现代化。高级研究人员和学员将组成小组，解决具有挑战性和有价值的数学和计算问题，包括新型复杂（可能是随机的）结构中的线性和非线性波传播、材料发现的物理和数据支持算法、混合逆问题和成像、机器学习的数学理论、大数据集的谐波分析和不确定性量化。他们将与哥伦比亚大学的顶尖工程师合作，将他们的数学和计算发现与非线性光学和光子学、材料科学、医学成像、气候建模和一般数据科学的应用联系起来。这个RTG项目的资深成员致力于培养和指导本科生、研究生和博士后学者。他们在教学和指导方面的丰富经验对学员的专业成长将是无价的。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This Research Training Group (RTG) project is a joint effort of the Department of Applied Physics and Applied Mathematics, the Department of Mathematics, and the School of Engineering and Applied Sciences at Columbia University. It aims to create a cutting-edge research and training program in modern applied mathematics. By substantially enriching research and educational experiences for trainees, and by directly coupling into key educational and research initiatives in the School of Engineering and Applied Sciences and across the University, the activities will have a significant impact on applied mathematics education and training at Columbia. The RTG project will engage high school as well as undergraduate students from the New York metropolitan area and across the country (through the Summer Research Program), inspiring mathematical careers for underrepresented groups in the United States.The project includes three main ingredients: (i) a group of research topics in applied mathematics at the frontier of engineering applications; (ii) a coherent mentoring-learning program on applied mathematics research and career development for undergraduate and graduate students as well as postdoctoral scholars; and (iii) a systematic plan to modernize undergraduate and graduate curriculum in applied mathematics and scientific computation. The senior investigators and the trainees will form groups to tackle challenging and rewarding mathematical and computational problems, including linear and nonlinear wave propagation in novel complex (and possibly random) structures, physics- and data-enabled algorithms for material discovery, hybrid inverse problems and imaging, mathematical theory of machine learning, harmonic analysis of large data sets, and uncertainty quantification. They will collaborate with leading engineers at Columbia to connect their mathematical and computational discoveries with applications in nonlinear optics and photonics, materials science, medical imaging, climate modeling, and general data science. The senior members of this RTG project are strongly committed to training and mentoring undergraduates, graduate students, and postdoctoral scholars. Their extensive and varied experiences in teaching and mentorship will be invaluable to the professional growth of the trainees.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.