Mathematics and Scientific Computation

Resource

Wolfram MathWorld : The Web's Most Extensive Mathematics Resource
PlanetMath : a virtual community which aims to help make mathematical knowledge more accessible
zbMATH : the first resource for mathematics
Encyclopedia of Mathematics : an open access resource designed specifically for the mathematics community

GSL : the GNU Scientific Library, a numerical library for C and C++ programmers
PETSc : a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations
Colt : a set of Open Source Libraries for High Performance Scientific and Technical Computing in Java
AForge.NET : an open source C# framework designed for developers and researchers in the fields of Computer Vision and Artificial Intelligence - image processing, neural networks, genetic algorithms, fuzzy logic, machine learning, robotics, etc.
Theano : a Python library that allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently
Math.NET : an opensource initiative to build and maintain toolkits covering fundamental mathematics, targetting advanced but also every day needs of .Net developers

Sage : a free open-source mathematics software system
- SageMathCloud
- Sage Notebook
SpeQ Mathematics : a small, extensive mathematics program with a simple, intuitive interface
GeoGebra : an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school
Desmos : A beautiful, free, online graphing calculator
Mathway : Free math problem solver
- Mathway graphing calculator
Frink : a practical calculating tool and programming language designed to make physical calculations simple (It tracks units of measure (feet, meters, kilograms, watts, etc.) through all calculations, allowing you to mix units of measure transparently)

Maxima : 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, and sets, lists, vectors, matrices, and tensors
YACAS : Yet Another Computer Algebra System, an easy to use, general purpose Computer Algebra System, a program for symbolic manipulation of mathematical expressions
Mathomatic : a portable, command-line, educational CAS and calculator software
Mathics : A free, light-weight alternative to Mathematica, a free, general-purpose online computer algebra system featuring Mathematica-compatible syntax and functions

BLAS : Basic Linear Algebra Subprograms
- GotoBLAS2
- OpenBLAS : an optimized BLAS library based on GotoBLAS2
LAPACK : Linear Algebra PACKage
- CLAPACK : f2c'ed version of LAPACK
ATLAS : Automatically Tuned Linear Algebra Software
- GATLAS : GPU Automatically Tuned Linear Algebra Software
Eigen : a C++ template library for linear algebra
Armadillo : a C++ linear algebra library
CVM Class Library
JAMA : a Java Matrix Package
SuperLU : a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations
SuiteSparse : a suite of sparse matrix packages
TAUCS : a Library of Sparse Linear Solvers
MAGMA : Matrix Algebra on GPU and Multicore Architectures
CULA : a set of GPU-accelerated linear algebra libraries
ViennaCL : a free open-source linear algebra library for computations on many-core architectures (GPUs, MIC) and multi-core CPUs

CGAL : Computational Geometry Algorithms Library, efficient and reliable geometric algorithms in the form of a C++ library
OpenMesh : a generic and efficient data structure for representing and manipulating polygonal meshes
Boost.Geometry and Boost.Polygon
PCL : the Point Cloud Library, a standalone, large scale, open project for 2D/3D image and point cloud processing

BGL : the Boost Graph Library
GraphLab : a graph-based, high performance, open source distributed computation framework written in C++
GraphChi : Disk-based large-scale graph computation
JGraphT : a free Java graph library that provides mathematical graph-theory objects and algorithms
LEMON : Library for Efficient Modeling and Optimization in Networks, a C++ template library providing efficient implementations of common data structures and algorithms with focus on combinatorial optimization tasks connected mainly with graphs and networks
g2o : A General Framework for Graph Optimization, an open-source C++ framework for optimizing graph-based nonlinear error functions
TORO : a Tree-based netwORk Optimizer, an optimization approach for constraint-network

GLPK : GNU Linear Programming Kit
Clp : COIN-OR linear programming, an open-source linear programming solver written in C++
SCIP : Solving Constraint Integer Programs, the fastest non-commercial solvers for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP)
- SoPlex : an optimization package for solving linear programming problems (LPs) based on an advanced implementation of the primal and dual revised simplex algorithm
Ceres Solver : an open source C++ library for modeling and solving large, complicated optimization problems
levmar : Levenberg-Marquardt nonlinear least squares algorithms in C/C++
LINPACK : a collection of Fortran subroutines that analyze and solve linear equations and linear least-squares problems
NLopt : a free/open-source library for nonlinear optimization
Uncoptim : a C++ library for unconstrained optimization
Ipopt : Interior Point OPTimizer, a software package for large-scale nonlinear optimization
OPT++ : an Object-Oriented Nonlinear Optimization Library
minpack : a software for solving nonlinear equations and nonlinear least squares problems
COIN-OR : the Computational Infrastructure for Operations Research project, an initiative to spur the development of open-source software for the operations research community
The NEOS Server : a free internet-based service for solving numerical optimization problems

SPUDD : Stochastic Planning using Decision Diagrams
MADP Toolbox : The Multiagent decision process Toolbox, a free C++ software toolbox for scientific research in decision-theoretic planning and learning in multiagent systems (MASs)
Markov Decision Process (MDP) Toolbox for Matlab
hmdp : a C++ library and tools for solving Markov Decision Processes (MDPs) with hybrid discrete and/or continuous state-spaces

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