I was recently commissioned by one of my neuroscience professors to help him develop a new gameplan for possibly describing neural networks with dynamical systems theory. In his most recent paper on the subject, he used Hidden Markov Modeling to detect coherent rate patterns in populations of simultaneously recorded neurons, demonstrating that trial to trial variability is significant in neuronal testing and the commonly used methods of analysis sush as peristimulus time histograms which rely on across trial averages overlook relevant connectivity between neurons. The HMM showed the connected neuron ensembles progressing through a series of three or four firing rate states, which he hopes to demonstrate are attractor states. Essentially he's looking for me to do some research this summer and help him figure out where to go for a follow up experiment. I have a lot of time (I'm working on this all summer) and am looking for a place to really start learning the material i'd need to help develop some insights into the situation. I'm a third year undergrad math major and my background consists of undergraduate courses in multivariable Calculus up to Stoke's theorem, linear algebra, abstract algebra up to galois theory, real analysis, point-set topology, with a little bit of algebraic topology. It seems i'm looking to teach myself a good chunk of statistics and stochastic processes, but i think i'm also looking to understand more on dynamical systems in general. I'm not really sure exactly where to start and what course to plot so i was looking for your help and insights there, and any recommendations you might have with regards to readings would be most appreciated. Also if it is too much to learn in a summer (it may be, i'm not sure) a heads up would be well appreciated. I'm fairly bright, but hardly brilliant.