Virtually every student who chooses to learn how to do computations on a computer ends up taking a course in numerical analysis. Compared to numerical analysis, the field of computer algebra is relatively young and has fewer active researchers. The commercial success of systems like Maple combined with the obvious wider range of applications (again compared to numerical computations) show an enormous potential for the future. We dare to predict that, just as numerical analysis is routinely taught at the undergraduate level, introductory courses in symbolic computation will be just as common and essential.
The MSCS department at UIC offers "MCS 320", an undergraduate course aimed at introducing students to use mathematical software. Ideally, this course will be taken before the "MCS 471" (numerical analysis). Based on five recent successful offerings of this course, valuable experience was acquired on what should and what can be taught in an introductory course in symbolic computation. Compared to the canonical and mandatory list of topics expected to be covered in any first numerical analysis course, we can outline a typical list of topics, balancing the mathematical (im)maturity of the students, the needs of other math courses, and taking into account future trends and current research developments.
Maple Conference 2005. Wilfrid Laurier University. July 17-21, 2005. Waterloo Ontario, Canada. Book of Proceedings. Edited by Ilias Kotsireas. Pages 500-509, Maplesoft, 2005.