Awesome Computational Mathematics

         

A curated list of tools, frameworks, libraries, and educational resources for computational mathematics. Computational mathematics involves the use of mathematical models, numerical analysis, and algorithms to solve real-world problems computationally.

Contents

• General Resources
• Symbolic Computation
• Numerical Methods
• Optimization
• Matrix Computation
• Visualization Tools
• Libraries and Frameworks
• Educational Resources
• Community and Forums
• Contribute
• License

General Resources

• What is Computational Mathematics? - An overview of computational mathematics and its applications.
• Numerical Recipes - A comprehensive resource for numerical methods and algorithms.
• The SIAM Community - The Society for Industrial and Applied Mathematics.

Symbolic Computation

• SymPy - A Python library for symbolic mathematics, including calculus, algebra, and equation solving.
• Maxima - An open-source computer algebra system for symbolic computation.
• Mathematica - A powerful platform for symbolic computation and advanced mathematics.
• Maple - A symbolic computation software with a focus on engineering and scientific applications.

Numerical Methods

• SciPy - A Python library for numerical integration, optimization, and linear algebra.
• GNU Scientific Library (GSL) - A library for numerical computing in C and C++.
• NLopt - A library for nonlinear optimization using numerical methods.
• SUNDIALS - A suite of solvers for ordinary differential equations (ODEs) and nonlinear systems.

Optimization

• COIN-OR - A collection of open-source tools for mathematical optimization.
• CVXPY - A Python library for convex optimization.
• Gurobi - A high-performance solver for linear and nonlinear programming.
• Pyomo - A Python-based optimization modeling framework.

Matrix Computation

• LAPACK - A library for linear algebra, supporting matrix factorizations and solutions.
• Eigen - A C++ library for linear algebra and numerical computations.
• Armadillo - A high-performance C++ library for linear algebra and matrix operations.
• NumPy - A Python library for array operations and linear algebra.

Visualization Tools

• Matplotlib - A Python library for creating static, animated, and interactive plots.
• Plotly - A library for creating interactive and publication-quality visualizations.
• ParaView - A visualization tool for analyzing large-scale data.
• D3.js - A JavaScript library for creating dynamic and interactive visualizations.

Libraries and Frameworks

• SageMath - A comprehensive open-source system for mathematical computation.
• Octave - An open-source alternative to MATLAB, focusing on numerical computations.
• MATLAB - A high-level language and environment for numerical and symbolic computations.
• Julia - A high-performance programming language for technical computing.

Educational Resources

• Numerical Methods for Engineers - An MIT OpenCourseWare on numerical methods.
• Khan Academy: Linear Algebra - A beginner-friendly course on linear algebra concepts.
• 3Blue1Brown: Essence of Linear Algebra - A video series that visually explains linear algebra.
• Computational Mathematics Textbooks - A Springer series on computational mathematics.

Community and Forums

• Stack Exchange: Mathematics - A Q&A platform for mathematics discussions.
• r/Mathematics - A subreddit for discussing math topics and resources.
• SymPy Community - A chatroom for SymPy users and developers.
• Numerical Analysis Forum - Discussions on numerical analysis and computational methods.

Contribute

Contributions are welcome. Please ensure your submission fully follows the requirements outlined in CONTRIBUTING.md, including formatting, scope alignment, and category placement.

Pull requests that do not adhere to the contribution guidelines may be closed.

License