Mathematical Sciences: REU: Experimental Mathematics

数学科学：REU：实验数学

• 批准号: 9000624
• 负责人: Paul Goodey
• 金额: $ 2.4万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-04-01 至 1991-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9000624&HistoricalAwards=false
• 关键词: Mathematical; Sciences; REU; Experimental; Mathematics

In this Research Experiences for Undergraduates project, six students will work with faculty advisors relating advances in computational technology to mathematical research. The emphasis of the work will be on computational aspects of two areas: group theory and dynamics. Following initial orientation, students will break up into teams, concentrating on one of the two themes. The interplay between experimentation and theory will enable the students to deal, at an early stage, with complicated examples which cannot be done by hand. These will lead to a better understanding of groups, dynamical systems and their underlying structure. Students concentrating on group theory will be introduced to fundamental concepts of computational group theory through permutation groups and exposure to CAYLEY and other programming languages capable of symbolic manipulation. Dynamical systems will build on students' basic courses in calculus and linear algebra to investigate properties of orbits such as period doubling and saddle node bifurcations, Mandelbrot sets and the generation of fractal images using iterated functions systems. As the students become more familiar with computer experimentation, they will be exposed to problem areas and unsolved problems on which they will focus their attention for the remainder of the activity. Interspersed with the research program will be an evening lecture series in the sciences, history and literature.

在这个本科生研究经验项目中，六名学生将与教师顾问合作，将计算技术的进步与数学研究联系起来。 这项工作的重点将是两个领域的计算方面：群论和动力学。 在完成初步培训后，学生将分成小组，专注于两个主题之一。 实验与理论之间的相互作用将使学生能够在早期阶段处理无法手工完成的复杂示例。 这些将有助于更好地理解群体、动力系统及其底层结构。 专注于群论的学生将通过置换群并接触 CAYLEY 和其他能够进行符号操作的编程语言，了解计算群论的基本概念。 动力系统将建立在学生微积分和线性代数基础课程的基础上，研究轨道的性质，例如周期倍增和鞍节点分岔、曼德尔布罗特集以及使用迭代函数系统生成分形图像。 随着学生对计算机实验越来越熟悉，他们将接触到问题领域和未解决的问题，他们将在剩余的活动中集中注意力。 与研究计划穿插的是科学、历史和文学方面的晚间系列讲座。