Some recent trends from research mathematics and their connections to teaching: Case studies inspired by parallel developments in science and technology

摘要

We will outline our ideas for teaching in the core mathematics disciplines.They are based on our own experience in teaching at a number of universities inthe USA, as well as in Europe. While some of the core ideas stay and havestayed relatively constant over a long period of time, they must be varied inaccordance with the needs and the demands of students, and they must constantlyupdated keeping an eye to current research and to modern international trendsin technology. Our thoughts and suggestions on the use of these trends inteaching have been tried out by the author, and they are now in textbooks, someby the author.