Dynamic visualization in advanced undergraduate courses

The advent of inexpensive computing technology has dramatically changed the way many mathematicians do mathematics, and the way many students and teachers learn and teach mathematics. This is an ongoing revolution, and no end is in sight. Among the many different ways that computing technology may be employed in mathematics, one of the most intriguing ones is for interactive and dynamic visualization. It started in the 1980s when then first personal computers became available, with such visionary work as e.g. [1]. The technical revolution continues at an ever faster pace. Nowadays one needs little more than a JAVAenabled WWW-browser and an internet connection to do truly exciting mathematics. And we still are looking forward to many possibilities that currently we only dream about—such as instant computations and rendering in 3D. The author's dream is an instant computation of curvature and geodesic spheres for control and subRiemannian geometry, manipulating theses instantaneously by dragging the mouse.