Commons Math is a library of lightweight, self-contained mathematics and statistics components addressing the most common problems not available in the Java programming language. it has support for Linear Algebra, Probability Distributions, Numerical Algebra, Statistics, Transform methods, Least Square etc.

Commons Math: The Apache Commons Mathematics Library

Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors. Maxima yields high precision numerical results by using exact fractions, arbitrary-precision integers and variable-precision floating-point numbers. Maxima can plot functions and data in two and three dimensions.

Maxima - A Computer Algebra System

KaTeX is a fast, easy-to-use JavaScript library for TeX math rendering on the web. KaTeX renders its math synchronously and doesn't need to reflow the page. It's layout is based on Donald Knuth’s TeX, the gold standard for math typesetting. It has no dependencies and can easily be bundled with your website resources. It produces the same output regardless of browser or environment, so you can pre-render expressions using Node.js and send them as plain HTML.

KaTeX - Fast math typesetting for the web

SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization. SciPy provides modules for Statistics, Optimization, Numerical integration, Linear algebra, Fourier transforms, Signal processing, Image processing, ODE solvers. 
 Sourceforge location: <A HREF="http://sourceforge.net/projects/scipy/" target="_blank">http://sourceforge.net/projects/scipy/</A>

SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization.

SciPy - software for Mathematics, Science, and Engineering

MathJax is an open-source JavaScript display engine for LaTeX, MathML, and AsciiMath notation that works in all modern browsers. It was designed with the goal of consolidating the recent advances in web technologies into a single, definitive, math-on-the-web platform supporting the major browsers and operating systems. It requires no setup on the part of the user (no plugins to download or software to install), so the page author can write web documents that include mathematics and be confident that users will be able to view it naturally and easily. Simply include MathJax and some mathematics in a web page, and MathJax does the rest.

MathJax - Beautiful math in all browsers

NumPy is the fundamental package needed for scientific computing with Python. Numerical Python adds a fast and sophisticated N-dimensional array facility to the Python language. NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.

NumPy - fundamental package for scientific computing with Python

The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. The library provides a wide range of mathematical routines such as random number generators, special functions and least-squares fitting. There are over 1000 functions in total with an extensive test suite.
 
The complete range of subject areas covered by the library includes:
	<ul>
 <li>Complex Numbers</li>
 <li>Roots of Polynomials</li>
 <li>Special Functions</li>
 <li>Vectors and Matrices</li>
 <li>Permutations</li>
 <li>Sorting</li>
 <li>BLAS Support</li>
 <li>Linear Algebra</li>
 <li>Eigensystems</li>
 <li>Fast Fourier Transforms</li>
 <li>Quadrature</li>
 <li>Random Numbers</li>
 <li>Quasi-Random Sequences</li>
 <li>Random Distributions</li>
 <li>Statistics</li>
 <li>Histograms</li>
 <li>N-Tuples</li>
 <li>Monte Carlo Integration</li>
 <li>Simulated Annealing</li>
 <li>Differential Equations</li>
 <li>Interpolation</li>
 <li>Numerical Differentiation</li>
 <li>Chebyshev Approximation</li>
 <li>Series Acceleration</li>
 <li>Discrete Hankel Transforms</li>
 <li>Root-Finding</li>
 <li>Minimization</li>
 <li>Least-Squares Fitting</li>
 <li>Physical Constants</li>
 <li>IEEE Floating-Point</li>
 <li>Discrete Wavelet Transforms</li>
 <li>Basis splines</li>
 <li>Running Statistics</li>
 <li>Sparse Matrices and Linear Algebra</li>
 </ul>

The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. The library provides a wide range of mathematical routines such as random number generators, special functions and least-squares fitting. There are over 1000 functions in total with an extensive test suite.

GSL - GNU Scientific Library

OpenGL Mathematics (GLM) is a header only C++ mathematics library for graphics software based on the OpenGL Shading Language (GLSL) specifications. GLM provides classes and functions designed and implemented with the same naming conventions and functionality than GLSL so that anyone who knows GLSL, can use GLM as well in C++.

GLM - OpenGL Mathematics (GLM)

JGraphT is a Java graph library that provides mathematical graph-theory objects and algorithms. It includes directed, undirected, weighted, unweighted etc. Graphs could be created based on Strings, URLs, XML documents. 

jGraphT - Java graph library

The jsMath package provides a method of including mathematics in HTML pages that works across multiple browsers under Windows, Macintosh OS X, Linux and other flavors of unix. It overcomes a number of the shortcomings of the traditional method of using images to represent mathematics: jsMath uses native fonts, so they resize when you change the size of the text in your browser, they print at the full resolution of your printer, and you don't have to wait for dozens of images to be downloaded in order to see the mathematics in a web page. 

jsMath - A Method of Including Mathematics in Web Pages

ASCEND is an interactive environment for modeling, debugging, and solving large systems of nonlinear algebraic or differential equations. Oriented towards chemical engineering applications, it includes the largest open-source thermodynamic properties database. Its interactive design allows users to inspect and solve very difficult nonlinear systems. It includes plotting abilities and is scriptable. 

Ascend - ASCEND modelling environment

Qalculate! is a multi-purpose cross-platform desktop calculator. It is simple to use but provides power and versatility normally reserved for complicated math packages, as well as useful tools for everyday needs (such as currency conversion and percent calculation). Features include a large library of customizable functions, unit calculations and conversion, physical constants, symbolic calculations (including integrals and equations), arbitrary precision, uncertainty propagation, interval arithmetic, plotting, and a user-friendly interface (GTK+ and CLI).

Qalculate! - the ultimate desktop calculator 

JUNG is a software library that provides a common and extensible language for the modeling, analysis, and visualization of data that can be represented as a graph or network. Its basis in Java allows JUNG-based applications to make use of the extensive built-in capabilities of the Java API, as well as those of other existing third-party Java libraries.

JUNG: Java Universal Network/Graph Framework


la4j (Linear Algebra for Java) is an open source and 100% Java library that provides Linear Algebra primitives (matrices and vectors) and algorithms. The la4j library was initially designed to be a lightweight and simple tool for passionate Java developers. It has been started as student project and turned into one of the most popular Java packages for matrices and vectors.

la4j - Linear Algebra for Java

wxMaxima is a document based interface for the computer algebra system Maxima. wxMaxima provides menus and dialogs for many common maxima commands, autocompletion, inline plots and simple animations. 

wxMaxima - A gui for the computer algebra system Maxima built with wxWidgets

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