Mathematical software is software used to model, analyze, or calculate numeric, symbolic, or geometric data.
SAGE is open source math software which is provided for free of charge. You can use it for studying many things about mathematics, including algebra, calculus, elementary to very advanced number theory, numerical computation, commutative algebra,...
FreeMat is an environment for rapid engineering and scientific processing. It is similar to commercial systems such as MATLAB from Mathworks and IDL from Research Systems, but is Open Source.
GEONEXT is dynamic mathematics software that provided for free of charge as learning and teaching tool. The software can be used for learning, teaching from elementary school up to calculus at high schools.
GeoGebra is free and multi-platform dynamic mathematics software for learning and teaching. It has received several educational software awards in Europe and the USA.