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

数学系的分析小组目前正在扩大其研究和培训计划的组成部分，这些内容涉及分析中的新计算工具，特别是与小波相关的调和分析。除了促进该小组在这些领域的高级研究外，所述的支持还将使他们能够开发一门名为“多媒体信号处理中的数学方法”的学士/硕士课程。这项支持还将使他们能够与大学其他单位合作，创建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。小波和波形分析的相关技术最初是作为数学和数学物理中的理论工具而被介绍的。除了成为数学研究的一个非常活跃的领域外，它们还被证明是新的具有广泛实用价值的数值技术的极其肥沃的来源。这项建议将允许开发一门将理论和计算工作结合在一起的课程，这将使我们能够让学生在这些令人兴奋的新数学和计算工具的理论和应用方面获得最先进的理解。

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.