SageMath is a free, open-source mathematics software system that is based on Python. It is intended to be an "open source alternative to Magma, Maple, Mathematica, and MATLAB." You can download it (for free!) here. You can also run it in the cloud here.
Here are some useful links for learning and using SageMath:
Wolfram Mathematica is a computer algebra system used in many scientific, engineering, mathematical, and computing fields. Mathematica is particularly well-suited to computations involving calculus. Dartmouth has a site license for Mathematica: you can download it (for free!) here.
Here are some useful links for learning and using Mathematica: