Mathematical areas of research within the Bitcoin field? I'm doing my IB math SL internal assessment on bitcoins. We have to incorporate a lot of math into a 6-12 page essay on our topic. What parts of Bitcoin involve or can be modeled by mathematics, such as calculus/probability/statistics?

I'm hoping to find at least a few equations I can discuss in my writings. I'm fairly good with math, but I'm not a complete expert, so if you would take that in to consideration with your answers that would be great! :) Thanks!
You could approach bitcoin and maths under many and different aspects. 
You could talk about cryptography (hash function, elliptic curve digital signature,...) or about the economy. 
You could talk about probability (mining, solo vs pool,...).