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

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

Theano is a Python library that allows you to define, optimize, and efficiently evaluate mathematical expressions involving multi-dimensional arrays. It is built on top of NumPy. Its features include tight integration with NumPy, transparent use of a GPU, dynamic C code generation and lot more.

Theano - Optimizing compiler for evaluating mathematical expressions on CPUs and GPUs.

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.
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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

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


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

Newton does anything from numerical calculation to symbolic math parsing. Send a GET request to newton with a url-encoded math expression and your preferred operation. Get back a JSON response with your problem solved.

newton-api - A really micro micro-service for advanced math

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

Magic textboxes where you can type math as easily as writing. MathQuill renders LaTeX math as semantically rich HTML and presents it as human-readable math by styling with CSS. Showcasing the power of the HTML DOM, this math is WYSIWYG editable. 

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