With costs for academic mathematics software approaching $1,000 for a single license, it doesn't take a numbers whiz to realize that a free, open source option is probably a better alternative. Sage is an entire mathematics system licensed under the GPL and available as a free download for Windows (running VMWare), Mac OS X, and Linux.

Sage covers everything from basic algebra all the way up to complex math processes like graph theory and exact linear algebra. It's designed for both research and studying, and is also plenty robust for classroom settings. In fact, the Web site has several resources for teaching with Sage, complete with lesson plans and worksheets.

If you work with statistics, then you should look at R, an open-source language for statistical analysis. It's jam-packed with features, and has a strong community that offers both assistance and numerous extension packages.

When people talk about big, successful open-source projects, they often think about software that can be used in large organizations. So we hear a great deal about the Linux operating system, the MySQL database, and even Ruby on Rails as a framework for developing Web applications. There's more to the story, though.