Karl-Dieter Crisman and I are organizing an MAA PREP workshop on Sage this summer. Sign up if you want to learn about Sage!
I’m the main author of the SageTeX package, which allows you to easily pull the results of Sage computations and plots into your LaTeX document. And since Sage is based on Python, you can write Python that writes LaTeX for you. This is really useful! SageTeX is a (admittedly small) component of an NSF grant for “integrating open mathematics software and open educational materials into the mathematics curriculum and classroom”.
Try it today. If you’re really curious, you can follow SageTeX development at bitbucket.
I maintain the KAIST Sage server(s). If you are interested in an account on the Memorial Day server, please email me. Otherwise, anyone can use the Groundhog Day server. (Read about the difference between the two servers.)
In 2007, I developed some Java applets that demonstrate the geometric operations of truncation, expansion, and snubification on the Platonic solids. My goal was to get all of the Archimedean solids this way; it turns out to be impossible, but I enjoyed making the applets and you may find them interesting.
That page also includes a little mini-essay on the freedoms and restrictions that mathematical software affords and imposes on you.
GeoGebra is a Java program with which you can easily make very cool interactive geometry demonstrations. Its focus is on elementary Euclidean geometry, but I’ve discovered that you can use it for an impressive variety of 2-dimensional graphics. It’s also extremely easy to make web pages with GeoGebra — see my pages on the complex cosine or polar plotting or Riemann sums for definite integrals. Try double-clicking on the applet to open the full GeoGebra program!
I’ve also published a (IMHO) very nice applet demonstrating the epsilon-delta definition of limits.
TikZ is a graphics system for TeX and friends. It’s very powerful, and somewhat similar to PSTricks. I highly recommend TikZ (and its lower-level engine, PGF) for all your graphics needs when writing LaTeX documents. Here are some examples of things I’ve made with TikZ:
Here are some old notes and other things I wrote back in grad school; according to server logs, they’re relatively popular and I should update and improve these sometime, but for now, here they are: