I recently moved from Mac OS X to Ubuntu, and I'd like to (as much as possible) only use free software on my new machine. As a theoretical ecologist, I used to rely a lot on Mathematica, and even though there is a Linux version out there, I'd really rather use something free.
Some people have mentioned Maxima and sympy (both are fine with me), but I'd really love to hear about other alternatives, and people's experiences with any of these packages.
http://en.wikipedia.org/wiki/Category:Free_mathematics_software
http://en.wikipedia.org/wiki/List_of_numerical_libraries
http://en.wikipedia.org/wiki/List_of_numerical_analysis_software
there is pretty much everything you can get for free here.
Ubuntu ships with python (by default),and there are plenty of useful python packages available. You would find numpy and matplotlib very useful since you are coming from mathematica.
