Collaborative Research: Complex Analysis Projects with accompanying applets

协作研究：带有附带小程序的复杂分析项目

• 批准号: 0633266
• 负责人: Michael Dorff
• 金额: $ 3.64万
• 依托单位: Brigham Young University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-01 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0633266&HistoricalAwards=false
• 关键词: Collaborative; Research; Complex; Analysis; Projects

Mathematical Sciences (21) This project is a collaboration among Brigham Young University, The University of Tennessee, Ball State University, and The United States Air Force Academy. The project team is producing a collection of undergraduate complex analysis research projects with accompanying computer applets. This collection will allow undergraduate students to explore applications and current research topics in complex analysis. The collection has several purposes: (1) to serve as a resource for senior capstone courses; (2) to serve as a supplement for a standard undergraduate complex analysis course with the objective of helping students explore research topics either in a group or individually; and (3) to serve as a resource for small or independent student research projects for advanced undergraduate students who would like to begin exploring some research areas in complex analysis. For example, undergraduate students will be able to begin researching topics in complex analysis such as minimal surfaces, circle packing, complex dynamics, fluid flows, and harmonic mappings. The accompanying computer applets are helping the students explore the basic results and the open questions related to these topics. There is great potential for a broad impact of this project, well beyond the schools involved in the project. The materials and applets will be especially helpful for students who want to do undergraduate research, but who are at institutions without sufficient resources or with limited research opportunities. It will provide these students with the background, experience, and excitement that is associated with research in mathematics.

数学科学（21）这个项目是杨百翰大学，田纳西大学，鲍尔州立大学和美国空军学院之间的合作。该项目组正在制作一系列本科生复杂分析研究项目，并附带计算机小程序。这个集合将允许本科生探索复杂分析中的应用和当前的研究主题。该集合有几个目的：（1）作为高级顶点课程的资源;（2）作为标准本科复杂分析课程的补充，帮助学生以小组或个人的方式探索研究课题;以及（3）作为高年级本科生的小型或独立学生研究项目的资源，他们希望开始探索一些复杂分析的研究领域。例如，本科生将能够开始研究复杂分析的主题，如最小曲面，圆包装，复杂的动力学，流体流动和谐波映射。随附的计算机小程序正在帮助学生探索与这些主题相关的基本结果和开放性问题。这个项目有很大的潜力产生广泛的影响，远远超出了参与该项目的学校。这些材料和小程序将特别有助于那些想做本科研究的学生，但他们所在的机构没有足够的资源或研究机会有限。它将为这些学生提供与数学研究相关的背景，经验和兴奋。