Structurally, both micro- and macro- cortical networks are highly complex.
When analyzed functionally in real time, whether locally or globally, the complexity of these networks really challenges my comprehension. It seems that being able to manipulate mathematical models of brain networks should prepare a scientist to better conceptualize the dynamic function of in vivo networks.
I've looked at mathematical concepts such as random matrix theory, Bayesian networks, hidden-hierarchical Markov chains, chaos and nonlinear dynamics; are any of these better suited than the others, or is a combined approach utilizing techniques from various disciplines more appropriate? Additionally, what kind of relevant course work should a hopeful neuroscientist invest in to perform these kinds of operations?
Since no-one knows what a "real understanding of cortical networks" will look like, this is a difficult question. But at a minimum, you need courses on nonlinear differential equations, bifurcation theory, multiple time-scale dynamical systems, stochastic processes, and the Fokker-Planck equation. Good luck!
I would say linear algebra and algorythmy.
But it depends on the approach..
I would say Linear Algebra too. It´s a very good start to deal with the ever growing potential to register large neuronal population. Try this course: https://www.youtube.com/watch?v=ZK3O402wf1c&list=PL49CF3715CB9EF31D
If you are interested in models of vision, you have to learn the basic ideas and notions of Differential Geometry, since the transformation of information in retina,LGN and visual cortex is local.-12.09.2014
I appreciate all of these great answers. Looks like I still have a lot of work to do!
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