Hi Matt,
I've been using Mathematica throughout my PhD and as someone who's fumbling their way through applied maths I've been pretty impressed with it as a package.
It is relatively easy to use, in that the commands are fairly intuitive, there is a huge help function, with the explanations of the majority of commands well explained and usually in understandable english and example code. Also there are a large number of forums where problems are discussed and existing code can be easily modified for a more specific purpose.And most importantly the visual output is really nice, 3D diagrams can be rotated or manipulated in most ways, most of the graphs produced usually look good enough for publication.
There is a pretty decent but slightly dated book (in that some of the code doesn't work without adjustments for the newest version of Mathematica) for it's use in structural geology
Also Dr Kieran Mulchrone might have some better advice than me on the topic
Hope this helps,
Dave
