Summer Research Experiences for Undergraduates: Topics in Geometry, Analysis, Number Theory and Numerical Analysis

休斯顿大学的四名教职员工计划运营一个面向本科生的暑期研究体验网站。每个暑假都会探讨两个主题。在第一年，E.Dean将指导两名学生研究数值优化问题，包括一个简单的流体流动控制模型，该模型涉及计算近似梯度。本主题将包含计算部分。季羡林将带领两名学生通过研究C2中单位球的映射来研究复杂几何。第二个暑期的主题是内积空间上的算子环，以及矩阵空间中的几何结构；本主题还将包含计算部分。两名学生将在D.Blecher的指导下从事这一领域的工作。S，CANIC将指导两名学生研究双曲守恒定律模型和应用，包括在计算中使用软件包。学生将学习口头和书面表达他们的想法，并将与所有关键教师以及研究生和其他系教职员工和来访者进行互动。这些主题适合大四学生和上过微积分、微分方程、复变量或现代代数课程的大三学生。这个REU网站的一个显著特点是主题的选择，重点放在分析、应用分析和几何上。设计和将指导这项研究的教职员工都是这些领域的活跃研究人员，其中关键人员有一定的本科生研究指导经验，以及本科生、女性和少数民族学生的指导经验。除了在全国范围内发布招生广告，该组织还提议在德克萨斯州广泛招聘学生，特别是在少数族裔占多数的大学，以获得一批有才华的学生参与者。

Four faculty members at the University of Houston plan to run a summer Research Experiences for Undergraduates site. Two topics will be explored each summer. During the first year, E. Dean will supervise two students in research on numerical optimization problems, including a simple model of control of fluid flows, which involves calculating approximate gradients. This topic will have a computational component. S. Ji will lead two students in research in complex geometry by looking at mappings of the unit ball in C2.Proposed topics for the second summer are rings of operators on inner product spaces, and geometric constructions in matrix spaces; this topic will also have a computational component. Two students will work in this area under the direction of D. Blecher. S, Canic will supervise two students in research on hyperbolic conservation law models and applications, including the use of software packages in computing.Students will learn to present their ideas orally and in writing, and will interact with all the key faculty and with graduate students and other department faculty and visitors. The topics are suitable for rising seniors and for juniors who have had a course in advanced calculus and either differential equations, complex variables or modern algebra.A distictive feature of this REU site is the selection of topics, with a focus on analysis, applied analysis and geometry. The faculty who have designed and will supervise the research are all active researchers in these areas.The key personnel have, among them, some experience in supervising undergraduate research, and experience in mentoring of undergraduates and of women and underrepresented minority students. As well as advertising nationally for students, the group proposes to recruit extensively in Texas, especially in minority-majority colleges, to obtain a good mix of talented student participants.