Numerical Computation
GNU Octave: GNU Octave is a freeware version of Matlab and is mostly compatible with Matlab. It is part of the GNU Project.
Matlab: Matlab is supported by the Math Center.
Other programs used for numerical computations include Maple, Mathematica, and R. See below:
Wikipedia’s list of numerical software programs
NAG Numerical Libraries: A library of commercially available routines in a variety of programming languages.
Symbolic Computation
Mathematica: Mathematica is supported by the Math Center.
GNU Maxima: Other programs used for symbolic computations include Matlab (using the symbolic math toolbox) and Symbolic C++.
Wikipedia’s list of computer algebra systems
Graphing
Gnuplot: An interactive graphing program. There is a version of Gnuplot, called GnuTeX that outputs code in LaTeX’s picture environment that can be inserted in a LaTeX document.
Other programs that are used for graphing and representing data are all of the numerical computation, symbolic computation, and statistical software packages listed on this page.
Wikipedia’s list of graphing programs
Statistics
R is an implementation of the S programming language and environment for statistical computing and graphics. It is a GNU project and is freely available for download.
S-Plus is a commercial implementation of the S programming language that was developed at Bell Labs for statistical computing and graphics.
SAS is a powerful commercially available program used for statistical analysis. It is available on the machines in the ITS computer labs.
SPSS is a commercially available program for statistical analysis. It is available on the machines in the ITS computer labs
Other programs used for statistical analysis include Matlab, GNU Octave, Stata, Minitab and Excel.
Wikipedia’s list of statistical packages
Optimization
Decision Tree for Optimization Software: This site helps you identify ready-to-use software for your optimization problem. Some of the software is free, some is only commercially available.
NEOS guide is an online source for optimization.
APPSPACK is a derivative-free optimization software.
TeX
TeXShop is a freely available implementation of TeX for Mac OS X machines.
MiKTeX is a freely available implementation of TeX for Windows machines.
Comprehensive TeX Archive Network (CTAN) is the primary repository for TeX-related software.
University of Pennsylvania’s Mathematics TeX documentation
General and Other
Wavelab is a collection of Matlab functions to implement a variety of algorithms related to wavelet analysis.
DSWeb Dynamical Systems Software is a list of software available on dynamical systems theory.
Penn State’s Mathematics Software List
Netlib is a collection of mathematical software, papers, and databases.