Computer Algebra Systems and Undergraduate Mathematics Curriculum

Abstract

In recent decades, we faced a number of changes in undergraduate mathematics curriculum. This process was a bit different in each country but the general idea was to accommodate in undergraduate mathematics curriculum topics that are relevant to our times. In many countries, selected topics that usually were taught in university were moved to the high school curriculum and some classical mathematical topics disappeared completely from high school and even from university. This is quite strange, but such changes very rarely addressed issues of using computers in teaching mathematics. Now that computers have become commodity items, generation of complex graphical structures and difficult calculations has become fast; we have inexpensive and fast access to a globally connected network, it is reasonable to ask: what computational topics should be added to the undergraduate mathematics curriculum, what will be the outcome of such change and what skills would gain our students? The main objective of this paper is to analyze teaching of mathematics from a computing point of view; to highlight changes or at least potential changes in the mathematics curriculum that follow from using computer applications and especially Computer Algebra Systems; to investigate some of the changes in how we teach mathematics; and to describe new skills that our students acquire from these changes.