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!

License