I have been tasked to write a maths essay on a topic of my choice. One of the areas that seems appealing is chaos theory and possibly nonlinear dynamical systems as a whole. However, what I wonder is whether the maths might be too complicated.
The plan was to try to look at bits of maths where order came out of chaos, such as Ramsey Numbers, a more advanced look at probability which strays away from combinatorics, or catastrophes.
Is this at all possible, given time? If so, could anyone point me towards a few sources which go over the maths of the above topics, for neither have I found any nor do I want just a superficial knowledge of the matters.