Mathematical Sciences: A Research Initiation for Undergraduates Via Differential Equations, Difference Equations and Chaos

对五名从事数学研究的本科生的资助将由本科生研究体验奖提供支持。学生将进行数值分析，研究差分方程组，并研究由连续地图迭代过程模拟的混沌。研究的重点将集中在差分方程解的振动性和对称性在混沌平面动力学中的作用。该计划将持续八周。休斯顿大学(UH)的教职员工也将参加该项目。这将通过几种方式完成。首先，休斯顿大学将提供一名教员与学生一起研究微分方程式和混沌问题。来自福尔曼大学的另一名教员将教授必要的混沌入门材料。她的薪水将由UH支付。每周五上午，学生们将在密歇根大学参观动力学实验室以及物理系、机械工程系和化工系的实验室，在那里通过实验观察混沌动力学。该计划的部分研究部分将涉及将UH开发的软件转移到TSU正在开发的PC环境中，该软件用于研究对称映射和动力学的迭代。对这些映射的研究可以在许多层面上进行，从群表示中的证明定理到二次映射中的参数探索。此外，UH将为三名REU学生提供资金，让他们与来自TSU的五名学生合作。还计划举办一项积极的讲座、咨询和社会活动方案。将鼓励学生在少数民族教授协会年会上介绍他们的工作成果。

Support for five undergraduate students engaged in mathematical research will be supported by this Research Experiences for Undergraduates award. The students will perform numerical analysis, investigate difference equations and engage in studies of chaos as modeled by the process of iteration of continuous maps. The main focus of the research will be on the oscillatory behavior of difference equations and the role of symmetry in chaotic planar dynamics. The program will run for eight weeks. Faculty from the University of Houston (UH) will also participate in the program. This will be done in several ways. First, the University of Houston will provide a faculty member to work with the students on problems of differential equations and chaos. A second faculty member from Furman University will teach the necessary introductory material on chaos. Her salary will be paid by UH. Students will spend each Friday morning at UH visiting laboratories such as the Dynamics Laboratory and laboratories in the Departments of Physics, Mechanical Engineering and Chemical Engineering where chaotic dynamics is observed experimentally. A portion of the program's research component will involve transferring of software, which has been developed at UH to study iterates of mappings and dynamics with symmetry, to the PC environment which is being developed at TSU. A study of these mappings can be made at many levels, from proving theorems in group representations to parameter exploration in quadratic maps. In addition, UH will provide funds for three REU students to work with the five from TSU. An active program of colloquium lectures, counselling and social events is also planned. Students will be encouraged to present the results of their work at the annual meeting of the Association of Minority Professors.