RTG: Research Training in Applied Mathematics at Columbia University

这个研究培训小组(RTG)项目是由应用物理和应用数学系、数学系和哥伦比亚大学工程与应用科学学院联合开展的。它的目标是创建现代应用数学的尖端研究和培训计划。通过极大地丰富学员的研究和教育经验，并通过直接结合工程与应用科学学院和整个大学的关键教育和研究活动，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(通过暑期研究计划)，启发美国未被充分代表的群体的数学事业。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主题；(Ii)为本科生和研究生以及博士后学者提供的连贯的应用数学研究和职业发展指导学习计划；以及(Iii)应用数学和科学计算本科和研究生课程现代化的系统计划。高级研究人员和受训人员将组成小组，解决具有挑战性和回报的数学和计算问题，包括新的复杂(可能是随机)结构中的线性和非线性波传播，材料发现的物理和数据使能算法，混合反问题和成像，机器学习的数学理论，大数据集的调和分析，以及不确定性量化。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。该RTG项目的高级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广泛和多样化的经验将对学员的职业成长起到无价的作用。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.