So, if this is the last picture I get to post you before the end of the competition I hope you enjoy it.
Here are some magic-skills for you - Take a look, and I've put a little theory if you want to read it below...

The magic? Well I'll tell you a little bit about it :) :
The main use is through the 'rune-burning' that's been mentioned briefly (a take on traditional ideas where runes would be written on paper and burnt - in the world of Mathema they just sear them into the air) .
Runes guide the magic (that will either come from the person or from the Mathema device) and can be one or a 'path' of several.. depending on what you want to do.
If your keeping up with the characters and thinking 'I don't know the chap on the far left' - that's Thomas Swithin; he's only really a sub-character but I added him in here because his rune-skills are kind of special... usually only one 'path' can be used at a time, but Thom can split it.
Good luck all :)