Below is a selection of high quality free math software. Many of them are distributed under a GNU license and work on multiple platforms (Linux, Windows, etc)
Maxima Algebra system with emphasis on symbolic computations.
Octave High level language, mostly oriented to numerical methods. It's fairly compatible with MATLAB. It was created for use in chemical engineering problem solving.
R Statistical and graphics package.It's similar to the "S" system developed at Bell labs (The main author of "S", is part of the development team of "R")
Scilab User friendly numerical package.
Gnuplot Very comprehensive scientific plotting program. Can be used from a command line or via scripts that allow automation of many tasks.
We found the links in GnuWin, a website dedicated to software of the GNU kind.
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