Mathematical Sciences/GIG: "Research and Training in Computational Harmonic Analysis"

数学科学/GIG：“计算调和分析的研究和培训”

• 批准号: 9631359
• 负责人: Richard Rochberg
• 金额: $ 15万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9631359&HistoricalAwards=false
• 关键词: Mathematical; Sciences; GIG; Research; Training

Abstract Rochberg et al The analysis group in the Mathematics Department is currently expanding the components of its research and training program related to new computational tools in analysis, particularly those in harmonic analysis associated with wavelets. In addition to furthering the group's advanced research in those areas, the support described will enable them to develop a Bachelors/Masters level curriculum titled "Mathematical method in multimedia signal processing". The support will also allow them, in cooperation with other units of the University, to create a signal processing working group which will serve as a training ground for undergraduates, advanced degree candidates, and postdoctoral researchers. Wavelets and related techniques of waveform analysis were first introduced as theoretical tools in mathematics and mathematical physics. In addition to becoming a very active area of mathematical research they have also proved to be an extremely fertile source of new numerical techniques of broad utility. This proposal will allow to develop a curriculum which will mix theoretical and computational work and which will enable us to bring students to state-of-the-art understanding in both the theory and the applications of these exciting new mathematical and computational tools.

数学系的分析小组目前正在扩展其与分析中的新计算工具相关的研究和培训计划的组成部分，特别是与小波相关的谐波分析。除了进一步推进该小组在这些领域的先进研究外，所述的支持将使他们能够开发名为“多媒体信号处理中的数学方法”的学士/硕士课程。这项资助还将使他们能够与大学的其他单位合作，成立一个信号处理工作组，作为本科生、高级学位候选人和博士后研究人员的培训基地。小波和相关的波形分析技术最初是作为数学和数学物理的理论工具引入的。除了成为一个非常活跃的数学研究领域外，它们还被证明是具有广泛用途的新数值技术的极其丰富的来源。该提案将允许开发一个课程，将理论和计算工作相结合，这将使我们能够让学生了解这些令人兴奋的新数学和计算工具的理论和应用。