Programs to help learn math
MATLAB is of course famous as the main software to be used for doing math homework. It costs $99 for students, and has add-ons that are about $30 each.
SAGE is an open source, community focused alternative to MATLAB. Free, and written in Python. (Two birds with one stone.)
For me, SAGE seems like an obvious choice to try out.
Scilab and Octave are other open source alternatives.
R is an open source tool for doing statistics.
Here is a list of open source alternatives to AutoCAD: http://www.osalt.com/autocad
Programming
It is still hard to say which languages to focus on. SAGE is written in python, which is nice, because all the time spent working with that program will benefit anything you might want to do with python.
SAGE requires LaTex (I got MacTex, 1GB)
Eventually, an IDE is going to be necessary. I used to use Eclipse, which was OK, but heavy and bulky. I am not trying NetBeans, which supports Java, Ruby, Python, C++, PHP...seems pretty helpful to me.
Komodo is a professional IDE for programming, but it is $300. The trial is for 21 days.


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