Fractal Geometry: Summer Workshops and Other Outreach

在接下来的四年里，研究人员将继续并扩大耶鲁大学连续两次成功举办的关于分数几何的夏季研讨会，并开展相关的外联工作。研讨会的参与者是高中、社区大学和大学教师，他们对为非理科学生提供分形几何课程感兴趣。自1993年以来，耶鲁大学一直非常成功地开设了这样的课程。分形几何为这些学生提供了一个新的、可视化的、基于计算机的、具有真实数学内容(与杰出的在世数学家的作品相联系)的数学分支，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延伸到艺术和人文。科学之外的应用使这门课程对文科学生最具吸引力。一般来说，学生在学完这门课后会觉得数学是他们可以接近的东西，是活生生的，与他们自己的兴趣相关。然而，教授这门课程相当具有挑战性。让它如此吸引人的应用程序本身，不是大多数数学家所受的训练。研讨会的目的是详细介绍分形几何和一些应用，以使其他教师能够将这些材料纳入他们自己的课程。这一课程计划将得到支持基础设施的帮助。这些想法将通过其他外联活动传播到更广泛的领域，包括在卫星站点设立类似的讲习班，并制作说明这些课程的录像带。此外，提倡者还准备了一个支持研讨会的webpagehttp://classes.yale.edu/math190a/Fractals/Welcome.htmlto，作为课程参与者的资源。提倡者的主要目标是在已有成果的基础上再接再厉。具体地说，(I)改进这些讲习班，从更大的领域吸引参与者，并建立辅助基础设施；(Ii)扩大和完善上述网站，作为有关分形几何的远程学习课程的基础；(Iii)开发和发展另一个网站，强调分形学的应用，并扩展即将出版的新书“分形学、图形学和数学教育”中简短的“全景”一章，MAA 2002。该网站的初步版本已经上线athttp://classes.yale.edu/math190a/Fractals/Panorama/Welcome.html(iv)，以编写一份简单实验和课堂活动的实验室手册，说明分形几何的基本概念，以及(V)开发一个外联网络，以便在其他地点举办这些讲习班，并通过其他媒体，包括录像带传播这些想法。

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.