MATLAB is a numerical computing and programming environment which is widely used in mathematics, engineering, and the sciences. It supports many add-on toolboxes for specialized applications ranging from signal processing to finance. MATLAB is available to students at no cost through software licensing.

Octave is a free MATLAB clone released under the GNU General Public License (GPL). Octave is mostly compatible with MATLAB, but it does not support MATLAB's specialized toolboxes.

Gnuplot is a powerful command line driven plotting utility with a steep learning curve. It is free, open source software, but, despite its name, is not released under the GPL. If you want to use Octave to produce plots, you will need to install gnuplot.

Sage is a powerful mathematics package supporting algebra, calculus, numerical methods, plotting, and much, much more. It is free software released under the GPL. If you are familiar with the programming language Python, you should feel immediately at home with Sage.

Sage in the cloud: Use Sage and other mathematical tools online.

Mathematica is a commercial computer algebra system available at no cost to students through software licensing.

Maple is a commercial computer algebra system available at no cost to students through software licensing.