Tools for teaching computational mathematics

So called “computer algebra” or “symbolic computation” systems such as Maple, and Mathematica have become complete mathematical computation workspaces with a large and constantly expanding built-in “knowledge base”. They aim to provide exact mathematical answers to mathematical questions, and have opened the way for so called “experimental” computer-assisted mathematics in both the pure and applied fields. Furthermore, it has been only recently (perhaps the last 5 to 10 years or so) that personal computers have been quick enough that one might feasibly experiment with mathematics applicable to a second year student at a cognitively satisfying speed for the learner. The author has designed a second year mathematics course to introduce students to computer algebra systems, and has written textbooks to go with the course: “An Introduction to Mathematical Computing with Maple”, and “An Introduction to Mathematical Computing with Mathematica”. We discuss the process of creation of both the course and the books, and the differences between our approach, and prior approaches.