Speaker
Description
There are several fundamental mathematical concepts, including some very simple definitions and some fairly straightforward theorems, which occur in many different contexts in university-level mathematics courses, even though it is not always easy for students to recognize these mathematical concepts and to notice how they occur in different courses.
One such concept is the product rule for the derivative of a function, which is essentially the same in mathematical content (but not in form) for pointwise products of real-valued functions, products of complex-valued functions, scalar products of vector-valued function in inner product spaces, cross-product of functions in 3-space, matrix product of matrix-valued functions. These product rules are taught in different courses at different times, but are more or less the same formula (except maybe for syntax) and use essentially the same proof.
Another such concept is the notion of triangle inequality, which occurs in courses of geometry, linear algebra, analysis of one real variable, and higher-dimensional analysis, although in different forms where students may not understand the similarity.
This talk tries to give some unifying framework.
