Mathematical Sciences: REU: Experimental Mathematics

在这个本科生研究经验项目中， 学生将与教师顾问有关的进展， 计算技术到数学研究。 重点 的工作将在计算方面的两个领域： 理论和动力学。 在初步指导后，学生 将分成几个小组集中讨论两个主题之一 实验和理论之间的相互作用将使 学生在早期阶段处理复杂的例子 这是手工无法完成的。 这些将导致一个更好的 了解群体、动力系统及其基础 结构 学生集中在群论将被介绍给 计算群论的基本概念， 置换群和接触到CAYLEY和其他编程 能够进行符号操作的语言。 动力系统 将建立在学生的微积分和线性基础课程 代数来研究轨道的性质， 二重和鞍结分支，Mandelbrot集和 使用迭代函数系统生成分形图像。 随着学生对计算机的熟悉， 实验，他们将接触到问题领域， 未解决的问题，他们将集中注意力， 剩下的活动。 穿插在研究项目中的将是一个晚上 科学、历史和文学系列讲座。

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.