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I'm going to graduate this May with a degree in Electrical Engineering. While I've done pretty well, my passion was never in EE and I'd like to aim for graduate school in Computational Neuroscience. When I look at the background and methodology employed by many favorite (current) researchers, I'm realizing that the best preparation would have been a double major in Math and Physics (the common Theoretical route, I assume?).

My specific interests involve interpreting biologically-plausible artificial neural networks as nonlinear dynamical systems and interpreting their activity to understand their function. While there are many researchers in this field, two great examples are Surya Ganguli (former Theoretical Physicist) and Eric Shea Brown.

I'm surely not the first engineering major to switch their focus towards Theoretical Physics, so I was hoping I could get some general advice on those who have transitioned. While neuroscience in practice doesn't look much like physics, the problem solving strategy of applying an abstract mathematical framework to uncover a system's first principles is still required. Beyond gaining fluency with the necessary math (mathematical statistics/statistical mechanics, nonlinear dynamics, topology/abstract algebra relevant to nonlinear dynamics), I would really benefit from developing that aforementioned problem solving strategy.

Hoping anyone has some general advice or can point me in the right direction for engineers with a newfound passion for physics/mathematics!

Edit: I should note that "theoretical physics" isn't really the proper term for my future direction, but the undergraduate/master's level training in terms of math fluency, problem solving and critical thinking ability is quite similar. So I'm looking for advice to transition and obtain such skills.