Samples of new material include chaotic dynamical systems and fractals (via iterations in Newton's method) in first year calculus; the singular value decomposition in first year linear algebra; the defect or residual in the numerical solution of differential equations; the unwinding number in complex variables; polynomial elimination and resultants in computer algebra (this is a revitalization of nineteenth century mathematics, made possible by technology; indeed the computer algebra course was wholly new to Western when I introduced it). The programs written for the HP48S for truncated power series algebra, and their description in FYEMUS, provide an example I am particularly proud of.
Regarding new methods and tools, I pioneered the use of programmable symbolic-capable calculators for engineering mathematics. I also introduced Matlab to numerical analysis courses (both for engineers and scientists), and Maple to computer scientists, physicists, applied mathematicians, and engineers.
In 1995 I used the Web and HTML tools to help deliver my Maple course, while I was at Simon Fraser University working on the Organic Mathematics Project under the auspices of the National Centre for Excellence in Telelearning. I was co-chair of the project and chair of the workshop. See the paper ``What is Organic Mathematics'', appended to this dossier, and section 4.1 below for more details on this, perhaps the most `high-powered' of my experiments with technology in teaching.
I do not neglect the `low-tech' route, either. Recently I have introduced the idea of handing out ``classic'' papers in numerical analysis and asking the students to read and summarize, as part of their assignments. This experiment has proved very successful, with some students counting this as the best part of the course.