Equation Editor 1.3 (J. McKenzie Alexander)

LaTeX equation editor.

FreeMat 3.2 (OpenSource)

From the site: "FreeMat is a free environment for rapid engineering and scientific prototyping and data processing. It is similar to commercial systems such as MATLAB from Mathworks, and IDL from Research Systems, but is Open Source. FreeMat includes several novel features such as a codeless interface to external C/C++/FORTRAN code, parallel/distributed algorithm development (via MPI), and plotting and visualization capabilities. FreeMat is available under the GPL license. Supported platforms include Linux, Windows and Mac OS X."

GAUSS 8.0 (Aptech systems)

From the site: GAUSS is a "Mathematical and Statistical System to Apple's MacOS X. This release of GAUSS 6.0 for Mac is compatible with both "Panther" (10.3) and Apple's new operating system "Tiger" (10.4) and now features a native Cocoa GUI. GAUSS 6.0 for MacOS X provides all of the robust computational features that have become the hallmark of GAUSS as a powerful and flexible matrix programming language."

IDL 6.4 (Research Systems)

From the page: "IDL ,the Interactive Data Language , is the ideal software for data analysis, visualization, and cross-platform application development. IDL combines all of the tools you need for any type of project, from "quick-look," interactive analysis and display to large-scale commercial programming projects."

LiveMath Maker 3.5.9 (Theorist Interactive, LLC)

From the site: "Our flagship Computer Algebra System product. LiveMath is a computer algebra system. LiveMath Maker is a computer program you use to MAKE (and explore and experiment with and create) LiveMath. Any LiveMath you make with LiveMath Maker may be shared with the world via the World Wide Web, using the FREE LiveMath Plug-In for Netscape/Explorer."

Also from the site: "Create Web-Sharable Mathematics with this Easy-to-Use Computer Algebra and Graphing System."

A viewer is available on the companie's site.

Maple 12.0 (MapleSoft)

Maple is a powerhouse in the mathematics and mathematical computation and programming systems. See the site for more information.

Mathematica 6.0.3 (Wolfram Research)

Mathematica is a powerful multipurpose mathematical computation development environment. Statistical and neural networks modules are available.

MathEQ Expression Editor 4.0.7 (Theorist Interactive, LLC)

This program is feature-rich, a good replacement for MathType 3.7 (not yet available natively for OS X).

From the site: "[MEQEE] is the desktop publishing solution for adding mathematical expressions to your scientific documents. Whether you're creating web-pages, papers, exams, multimedia presentations, or even homework assignments, MathEQ will help you give your document a professional scientific look without having to spend a lot of time."

Also from the site: "Create Professional Looking Mathematical Expressions for your Scientific Documents using this Powerful Typesetting Application."

MathMagic 5.54 (n'Pine)

Does what MathType did for OS 9. Cross platform equation editor. Personal and Pro editions available.

mathStatica 1.5 (mathStatica)

From the site: "mathStatica was designed to solve the algebraic / symbolic problems that are of primary interest in mathematical statistics. It does so by building upon the symbolic computational power of Mathematica to create a sophisticated toolset specially designed for doing mathematical statistics. By contrast, packages like SPSS, Systat, SAS, Gauss, JMP and S-Plus provide a numerical / graphical toolset. They can illustrate, they can simulate, and they can find approximate numerical solutions to numerical problems, but they generally cannot find exact symbolic solutions to statistical problems. Features include: a complete suite of functions for manipulating PDFs, automated expectations, probability, density plotting, automated transformations (functions of RVs), symbolic MLE, numerical MLE, automated Pearson curve fitting, Johnson curve fitting, Gram-Charlier expansions, nonparametric kernel density estimation, moment conversion formulae, component-mix and parameter-mix distributions, stable distributions, copulae, random number generation, asymptotics, sufficient statistics, decision theory, order statistics, Fisher Information, h-statistics, k-statistics, polykays, and much more."

MathType 5.1 (Design Science)

From the company's site: " Design Science MathType™ for Windows and Macintosh is a powerful interactive tool that will revolutionize the way you create print and web-based documents that contain math. MathType works with any word processor, presentation program, page layout program, HTML-authoring tool, plus other types of software, to create equations for research papers, class materials, web pages, slide presentations, journal articles and books."

MATLAB 7.4 (MathWorks)

MATLAB is, in part, a multipurpose mathematical computation development environment. Statistical modules including time series (Curve Fitting Toolbox 1.1.1) are available.

Octave 2.9.14 (GNU)

From the site: “GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language”. For more information, see the page about Octave.

SAGE 3.0.5

From the site: “General and Advanced Pure and Applied Mathematics. Use SAGE for studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.”

SciLab 4.1.1 (INRIA)

For Mac OSX. Another free MATLAB implementation, similar to Octave and FreeMat.

Smile full edition (SmileLab) 3.2.3 (Satimage)

See description in the Programming section.

Neural Networks applications:

1. ‣See Mathematica and MATLAB.
   

2. ‣Neural Networks 1.0.2 (to work with Mathematica, by Wolfram)
   

3. ‣Neural Network Toolbox 5.1 (to work with MATLAB, by MathWorks)