EMSW21 - RTG: Numerical Mathematics for Scientific Computing

EMSW21 - RTG：科学计算的数值数学

• 批准号: 0602235
• 负责人: Margaret Wright
• 金额: $ 247.62万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-09-15 至 2012-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0602235&HistoricalAwards=false
• 关键词: EMSW21; RTG; Numerical; Mathematics; Scientific

For at least two decades, high-level reports on the health of mathematical sciences research in the United States have recommended creation of a more direct path between this research and its users. The most obvious means for improving this connection is software, which is ubiquitous in science, engineering, business, medicine, as well as everyday life. Mathematics embodied in software can quickly bring new knowledge, insights, and methods to bear in contexts ranging from detecting tumors to finding the best travel route to deciding how to invest. The role of software as standard-bearer for the mathematical sciences is especially important for industry, where mathematical discoveries tend to be applied only if they have been transformed into software. Successful production of high-quality, timely mathematical software brings an array of complex intellectual challenges requiring training not only in mathematics, but also in software development and the needs of application areas. Accordingly, the goal of this Research Training Group is to produce mathematical scientists with a deep, hands-on understanding of mathematical algorithms and their instantiation in software; in addition, we intend to make the crucial elements of the training program broadly available. The faculty involved with this activity, from the Courant Institute of Mathematical Sciences at New York University, and the Applied Physics and Applied Mathematics Department at Columbia University, represent a variety of experiences in applied and computational mathematics, numerical algorithms and software, and real-world applications. Our belief is that the combined expertise of these researchers will provide a rich source of common insights that currently exist in relative isolation. The Research Training Group will provide, for undergraduates, Ph.D. students, and postdoctoral researchers: (1) training that explores in depth the relationships among mathematical modeling, algorithm design, software choices, and the hardware environment; (2) understanding of how algorithm and software design may be affected, even driven, by the nature of problems and the contexts in which they need to be solved; (3) hands-on experience of designing software that succeeds when it can and fails gracefully when it cannot. At all levels, participants will experience individual and team involvement with mathematical software development. The undergraduate part of the program will include an enhanced curriculum and summer research experiences directly connecting the mathematical sciences with real-world applications. Ph.D. student training will include joint mentoring by faculty with expertise in applied and computational mathematics and scientific software, an enhanced curriculum that builds on the strengths of the two universities, and internships in government and industrial research laboratories. Postdocs will join longer-term projects with emphasis on applications, and will also be involved in undergraduate and graduate student training. Our hope is that the experiences of this Research Training Group will be helpful in developing other programs with similar goals.

至少二十年来，关于美国数学科学研究健康状况的高级别报告一直建议在这项研究与其用户之间建立一条更直接的路径。 改善这种联系最明显的手段是软件，它在科学、工程、商业、医学以及日常生活中无处不在。 软件中的数学可以迅速带来新的知识、见解和方法，从检测肿瘤到找到最佳旅行路线，再到决定如何投资。 软件作为数学科学的旗手的角色对工业来说尤其重要，因为数学发现只有转化为软件才能得到应用。 高质量，及时的数学软件的成功生产带来了一系列复杂的智力挑战，不仅需要在数学，而且在软件开发和应用领域的需求培训。 因此，这个研究培训小组的目标是产生数学科学家，对数学算法及其在软件中的实例化有深入的，动手的理解;此外，我们打算广泛提供培训计划的关键要素。 参与这项活动的教师来自纽约大学的柯朗数学科学研究所和哥伦比亚大学的应用物理和应用数学系，他们在应用数学和计算数学、数值算法和软件以及实际应用方面都有丰富的经验。我们相信，这些研究人员的综合专业知识将为目前相对孤立的共同见解提供丰富的来源。 研究训练小组将为本科生提供博士学位。学生和博士后研究人员： (1)深入探讨数学建模、算法设计、软件选择和硬件环境之间关系的培训; (2)理解算法和软件设计如何受到问题的性质和需要解决的环境的影响，甚至驱动; (3)设计软件的实践经验，当它可以成功时，当它不能优雅地失败时。 在所有级别，参与者将体验个人和团队参与数学软件开发。 该计划的本科部分将包括一个增强的课程和夏季研究经验，直接连接数学科学与现实世界的应用。 博士学生的培训将包括由在应用和计算数学及科学软件方面具有专长的教师联合指导，加强两所大学的优势课程，以及在政府和工业研究实验室实习。 博士后将加入长期项目，重点是应用程序，也将参与本科生和研究生的培训。 我们希望这个研究培训小组的经验将有助于制定具有类似目标的其他方案。