Topology and Its Applications

拓扑及其应用

• 批准号: 0442740
• 负责人: William Basener
• 金额: --
• 依托单位: Rochester Institute of Tech
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-03-15 至 2009-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0442740&HistoricalAwards=false
• 关键词: Topology; Its; Applications

Mathematical Sciences (21). The goal of this proposal is to write a cross-disciplinary textbook to make a variety of applications of topology accessible to undergraduate STEM students. The textbook is based on a prototype applied topology course taught twice by the Principal Investigator at the Rochester Institute of Technology (R.I.T.) and attended by students majoring in mathematics, physics, engineering, computer science, and information technology. Applications of topology have enabled two great revolutions in the 20th century; Nash equilibria in economics, and dynamical systems and chaos in differential equations. In other fields, such as condensed matter physics, string theory, robotics, DNA, chemistry, astronomy, and relativity, topology is playing an important role in expanding the frontiers of knowledge. The materials being developed close the gap between teaching of topology and its uses in real-world phenomena, and facilitate collaboration between topologists and scientists. The applications make topology courses more exciting for students, putting them at the edge of research knowledge in several applications, and they improve the pedagogy of topology by adding relevance. The materials are being tested and reviewed at a variety of small colleges, engineering schools, and larger universities. The applications are disseminated nationally through articles in exposition-focused journals, through faculty development workshops at national conferences, and as sections in a topology textbook to be published by John Wiley and Sons Inc. The journal articles are written so that they can be used as supplementary material in topology courses using a traditional topology textbook.

数学科学（21）。本提案的目标是编写一本跨学科教科书，使STEM本科生能够访问拓扑的各种应用。该教材基于一门应用拓扑学课程的原型，该课程由罗彻斯特理工学院（R.I.T.）的首席研究员教授两次，学生的专业包括数学、物理、工程、计算机科学和信息技术。拓扑学的应用使20世纪发生了两次伟大的革命；经济学中的纳什均衡，微分方程中的动力系统和混沌。在其他领域，如凝聚态物理、弦理论、机器人、DNA、化学、天文学和相对论，拓扑学在拓展知识前沿方面发挥着重要作用。正在开发的材料缩小了拓扑教学与其在现实世界现象中的应用之间的差距，并促进了拓扑学家和科学家之间的合作。这些应用程序使拓扑学课程对学生来说更加令人兴奋，使他们在一些应用中处于研究知识的边缘，并且通过增加相关性来改进拓扑学的教学方法。这些材料正在各种小型学院、工程学院和大型大学进行测试和审查。这些应用程序通过以博览会为重点的期刊上的文章、全国会议上的教师发展讲习班以及约翰威利父子公司即将出版的拓扑教科书中的章节在全国范围内传播。期刊文章的撰写是为了使它们可以作为使用传统拓扑教科书的拓扑课程的补充材料。