EMSW21-RTG: Analysis and Differential Equations

EMSW21-RTG：分析和微分方程

• 批准号: 1044944
• 负责人: Panagiotis Souganidis
• 金额: $ 10万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1044944&HistoricalAwards=false
• 关键词: EMSW21; RTG; Analysis; Differential; Equations

This is a one year Research Training Group (RTG) type of project in Analysis and Differential Equations at the Department of Mathematics of the University of Chicago. The project funds graduate students and visitors and the organization of a summer course aimed towards advanced undergraduates, graduate students and young postdocs in mathematics, engineering and sciences. Analysis and differential equations are central, deep and rich fields of mathematics. From an applied perspective, differential equations are the most fundamental mathematical models in all of science and engineering. They describe phenomena from quantum mechanics to weather prediction and climate and are the basic theoretical tools in science and technology. The exponential improvement in the capabilities of modern computers allows for the practical use of increasingly complex systems of differential equations. Although recent results have solved numerous outstanding problems, many still remain open. The understanding of the mathematical properties of these models is essential. The need in both academia and industry for young, well-trained mathematicians in these areas is ever growing.The PIs along with others in the mathematical community believe that there is a severe shortage of US PhDs trained in (applied) analysis and differential equations. The goal of the proposed one year project is to provide the seed towards developing a well-rounded and modern educational program to increase the number of American researchers working in the applied analysis and differential equations and to improve the quality of the training of future mathematical scientists (working in either academia or industry). Having support for graduate students working in this general area will increase the number of students willing to work in applied analysis. The expectation is that the proposed summer course will serve as a model of the type of educational activity needed to attract more researchers to differential equations as well as to educate student and postdocs in engineering and sciences.

这是芝加哥大学数学系的分析和微分方程项目的一年研究培训小组（RTG）类型。该项目为研究生和访客提供了资金，以及针对高级本科生，研究生和年轻的数学，工程和科学博士后的夏季课程的组织。分析和微分方程是数学的中心，深层和丰富的领域。 从应用的角度来看，微分方程是所有科学和工程学中最基本的数学模型。他们描述了从量子力学到天气预测和气候的现象，是科学和技术的基本理论工具。现代计算机功能的指数改进允许实际使用越来越复杂的微分方程系统。尽管最近的结果解决了许多罕见的问题，但许多问题仍然保持开放。对这些模型的数学特性的理解至关重要。在这些领域，年轻，训练有素的数学家的学术界和行业的需求一直在增长。数学社区中的PI与其他人一起认为，在（应用）分析和微分方程式培训的美国博士学位非常短缺。拟议的一年项目的目标是为制定一个全面的现代教育计划提供种子，以增加在应用分析和微分方程中工作的美国研究人员的数量，并提高未来数学科学家的培训质量（在学术界或行业中工作）。支持在这个一般领域工作的研究生将增加愿意在应用分析中工作的学生数量。期望拟议的夏季课程将成为吸引更多研究人员进入微分方程的教育活动类型的模型，并在工程和科学领域教育学生和博士后。