Topology and Its Applications

数学科学(21)。这项建议的目标是编写一本跨学科的教科书，使本科生能够接触到拓扑学的各种应用。这本教科书是基于罗切斯特理工学院(R.I.T.)首席研究员两次教授的应用拓扑学原型课程。数学、物理、工程、计算机科学和信息技术专业的学生参加。拓扑学的应用在20世纪促成了两场伟大的革命：经济学中的纳什均衡，以及微分方程中的动力系统和混沌。在其他领域，如凝聚态物理、弦论、机器人学、DNA、化学、天文学和相对论，拓扑学在扩展知识边界方面发挥着重要作用。正在开发的材料缩小了拓扑学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令人兴奋，使他们在几个应用程序中处于研究知识的边缘，并通过增加相关性改进了拓扑学的教学法。这些材料正在各种小型学院、工程学校和较大的大学进行测试和审查。这些申请通过在以博览会为重点的期刊上发表的文章，通过全国会议上的教师发展研讨会，以及将由John Wiley and Sons Inc.出版的拓扑学教科书中的章节在全国范围内传播。期刊论文的撰写是为了在使用传统拓扑学教科书的拓扑学课程中作为补充材料。

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.