Fractal Geometry: Summer Workshops and Other Outreach

在接下来的四年中，研究人员将继续并扩大耶鲁大学连续两次关于分形几何的夏季研讨会的持续和成功系列，并开展相关的推广工作。 预期的研讨会参与者是高中，社区学院和大学教师有兴趣提供分形几何课程的非科学的学生。 自1993年以来，耶鲁大学一直非常成功地开设了这样一门课程。 分形几何为这些学生提供了一个数学的分支，它是最近的，是可视化的，是基于计算机的，具有真实的数学内容（与杰出的在世数学家的作品相联系），并鼓励学生探索和发现。 此外，分形几何的巨大应用范围从科学和工程扩展到艺术和人文学科。 科学之外的应用使这门课程对文科学生最有吸引力。 一般来说，学生们从这门课程中走出来的感觉是，数学是他们可以接近的东西，是活的，很好，是与他们自己的兴趣有关。 然而，教授这门课程是相当具有挑战性的。 使它如此吸引人的应用程序超出了大多数数学家的训练范围。 讲习班的目的是调查分形几何和一些应用的细节足以使其他教师将这种材料在自己的课程。 这一课程规划将得到支持基础设施的帮助。 这些想法将通过其他推广活动传播到更广泛的地区，包括在卫星地点举办类似的讲习班和制作一盘介绍这些课程的录像带。 此外，提议者还准备了一个网页classes.yale.edu/math190a/Fractals/Welcome.htmlto支持讲习班，并作为参加者参加其课程的资源。提议者的主要目标是在已经取得的成就的基础上再接再厉。 具体而言，（i）完善这些讲习班，吸引来自更大地区的参与者，并建立支持基础设施，（ii）扩大和完善上述网站，作为分形几何远程学习课程的基础，（iii）开发和发展另一个网站，强调分形的使用，并扩展即将出版的书“分形，图形，《数学教育》，2002年。 这个网站的一个初步版本已经在网上，网址是：http：//classes.yale.edu/math190a/Fractals/Panorama/Welcome.html（iv）准备一个简单的实验和课堂活动的实验手册，说明分形几何的基本概念，（v）发展一个推广网络，在其他地方扩大这些讲习班，并通过其他媒体传播这些想法，包括录像带。

For each of the next four years, the investigators will continue and expand an ongoing and successful series of two successive summer workshops on Fractal Geometry at Yale University, and develop related outreach efforts. The intended workshop participants are high school, community college, and college teachers interested in offering fractal geometry courses for non-science students. Such a course has been run very successfully at Yale since 1993. Fractal geometry presents these students with a branch of mathematics that is recent, is visual, is computer-based, has real mathematical content (in contact with the works of eminent living mathematicians), and encourages student exploration and discovery. In addition, the tremendous range of applications of fractal geometry extends beyond science and engineering to arts and humanities. The applications outside science make the course most attractive to liberal arts students. Generally, students come out of this course with a feeling that mathematics is something they can approach, is alive and well, and is relevant to their own interests. Yet teaching this course is quite challenging. The very applications that make it so appealing are outside the training of most mathematicians. The purpose of the workshops is to survey fractal geometry and some applications in detail sufficient to enable other teachers to incorporate this material in their own courses. This lesson planning will be aided by a support infrastructure. These ideas will be spread to a wider area through other outreach activites, including establishing similar workshops at satellite sites and producing a videotape illustrating these courses. In addition, the proposers have prepared a webpagehttp://classes.yale.edu/math190a/Fractals/Welcome.htmlto support the workshops and to be a resource for the participants in their courses.The proposers' main goal is to build on what has already been achieved. Specifically, (i) to refine these workshops, draw participants from a larger area, and establish a support infrastructure,(ii) to expand and elaborate the above-mentioned website for use as the basis for Distance Learning courses on fractal geometry,(iii) to develop and grow another website that emphasizes the uses of fractals and extends the brief "Panorama" chapter of the forthcoming book "Fractals, Graphics, and Mathematics Education," MAA 2002. A preliminary version of this site already is online athttp://classes.yale.edu/math190a/Fractals/Panorama/Welcome.html(iv) to prepare a lab manual of simple experiments and classroom activities, illustrating basic concepts of fractal geometry, and(v) to develop an outreach network for growing these workshops at other locations and disseminating these ideas through other media, including a videotape.