Sage is a free open source mathematics software system spanning a huge range of mathematics including algebra, calculus, combinatorics, number theory and graph theory.
Maxima is a fairly complete computer algebra system written in lisp with an emphasis on symbolic computation. It is based on DOE-MACSYMA and licensed under the GPL. Its abilities include symbolic integration, 3D plotting, and an ODE solver.
The MathWorks is the world‘s leading developer of technical computing software for engineers and scientists in industry, government, and education.
An expanding collection of freely available, interactive Demonstrations in math, science, and many other areas--at all levels from elementary education to front-line research.
Mathematica is a fully integrated software environment for technical and scientific computing. Mathematica combines numerical and symbolic computation, visualization, and programming in a single, flexible interactive software system.