Collaborative Research: Complex Analysis Projects with accompanying applets

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的合作项目。该项目团队正在制作一组本科生复杂分析研究项目，并附带计算机应用程序。这个集合将允许本科生在复杂分析中探索应用和当前的研究主题。该文集有几个目的：(1)作为高级顶峰课程的资源；(2)作为标准本科复杂分析课程的补充，目的是帮助学生小组或单独探索研究主题；以及(3)作为希望开始探索复杂分析研究领域的高级本科生的小型或独立学生研究项目的资源。例如，本科生将能够开始研究复杂分析的主题，如极小曲面、圆填充、复杂动力学、流体流动和调和映射。随附的计算机小程序正在帮助学生探索基本结果和与这些主题相关的开放问题。这个项目有巨大的潜力产生广泛的影响，远远超出参与该项目的学校。这些材料和小应用程序对于那些想要做本科生研究，但在没有足够资源或研究机会有限的机构的学生特别有帮助。它将为这些学生提供与数学研究相关的背景、经验和兴奋。

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.