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.
