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

休斯顿大学的四名教师计划为本科生开设一个夏季研究经验网站。 每年夏天都有两个主题。 在第一年，E。迪恩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，其中涉及计算近似梯度。 本主题将有一个计算组件。 S.季将带领两名学生在复杂的几何研究通过看映射的单位球在C2.Proposed主题的第二个夏天是环的运营商的内积空间，和几何结构在矩阵空间;这个主题也将有一个计算组件。 两名学生将在D.布莱切 Canic将指导两名学生进行双曲守恒律模型和应用的研究，包括在计算中使用软件包。学生将学习口头和书面表达自己的想法，并与所有主要教师、研究生和其他部门的教师和访客互动。 这些主题适合正在上升的高年级学生和大三学生，他们有一门高级微积分课程，无论是微分方程，复变量还是现代代数。这个REU网站的一个独特的特点是主题的选择，重点是分析，应用分析和几何。 设计和监督这项研究的教员都是这些领域的活跃研究人员，其中的关键人员具有监督本科生研究的一些经验，以及指导本科生、妇女和代表性不足的少数民族学生的经验。 除了在全国范围内为学生做广告外，该组织还建议在得克萨斯州，特别是在少数民族占多数的大学，广泛招募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.