When starting to write documents with lots of equations or starting to think about solving some equations numerically, the question usually arises which software to use. One can either start with commercial software (which might have the best quality) or use software which is free. Here are some suggestions for free software which works well for an advanced seminar paper at the bachelor or master level, for a bachelor or master thesis or the beginning of a PhD - or even beyond.
Writing Papers
* MikTeX, LyX and the like
Standard software like MS Word will not do the job if there are as many equations as in a standard economic paper these days. So something based on LaTeX will be very useful. One can either become a LaTeX addict and type text and equations in "raw code" or use an editor where the screen shows nice integrals and the like, i.e. where there is no necessity to type something like \int_a^b \! f(x) \, dx.
Those, who decide to start writing their thesis with LaTeX, might find this template for a LaTeX document very useful.
One free software which seems to perform a good job is
which uses MikTeX as the underlying version LaTeX. Intalling and using it worked easily for me (even though I stick to commercial software as I have been using it for years now).
For those who want to work with Lyx, this template for Lyx documents should help you to get started.
* Writing in MS Word
If there is no chance to avoid writing a paper in Word, please use this template as a starting point. It gives you an automatic (!) table of contents which dramatically increases the readability of your document.
Numerical solutions
When it comes to numerical solutions, there are various commercial software packages as well. For students, they can be pretty expensive. Alternatives are provided by the following free programmes.
http://www.gnu.org/software/octave/
http://www.scilab.org/
The first one claims to be able to run all programmes that run in matlab. It worked for simple examples I checked. The second one looks more professional but I did not work with it. When writing this line, I discovered a wikipedia entry on (not necessarily free) numerical software - see http://en.wikipedia.org/wiki/List_of_numerical_analysis_software