
#1
Jul2212, 11:50 PM

P: 10

I've always want to understand the mind and its inner working. After lots of consideration I've narrowed my choice down to computational neuroscience. I know it's a hardcore science but I'd like to know more about it. How much math is required? What disciplines would suit it best?
Every suggestions count 



#2
Jul2312, 01:46 AM

Mentor
P: 5,350

Mind or brain? If you want to understand the mind then something like cognitive neuroscience or psychology would probably be better for you.




#3
Jul2312, 01:58 AM

P: 771

There are two points here. The first, which is rather blunt (but important, I think), is that you really shouldn't be narrowing down your interests to this extent without being familiar with the field already, in which case you would have decent understanding of the prerequisites. Myself, I became interested in computational neuroscience as a result of my interest in the biological underpinnings of reinforcement learning and working memory processes (largely, basal ganglia and PFC circuitry). Having immersed myself in the literature already, I found the mathematical approach to subject to be the most intuitive and informative, so I naturally gravitated to computational neuroscience (having already had a background in mathematics helped).
As far as the math goes, there are a few prerequisites that are absolutely nonnegotiable, and a few that depend on what level of abstraction you're interested in (neuron modelling, systems/network modelling, cognitive modelling, etc). The essential prerequisites are a solid understanding of calculus (up to multivariable and vector calculus), basic linear algebra, ODE's (you can go quite a ways in neuroscience without PDE's), and probability/statistics. For all practical purposes, some knowledge of dynamical systems is essential (in many branches of computational neuroscience, you can't even get your foot in the door without it). Additionally, you'll want to be very comfortable with at least one programming language (Matlab and python are very common for "general purpose", though there are software packages dedicated specifically to certain types of neuronal modelling). In certain areas like computational vision research, where the goal is to understand exactly how a population of neurons are coding for a specific stimulus, the prerequisites for statistics are much higher, and you'll want all the experience with generalized linear models and bayesian statistics that you can get. Biologically realistic neuron modelling, in turn, usually involves much more sophisticated theory in differential equations and dynamical systems (though you should learn all you can about both regardless of what you're doing). In computational cognitive neuroscience (my interest), the prerequisites get a little trickier because the models are much more abstract, and so you can draw upon some pretty surprising areas of mathematics (I read a paper recently that applied some fairly deep concepts in differential geometry to the modelling of visual processes...and was published in a journal of physiology, go figure). Some people (often in cognitive psychology) are only interested in throwing together the occasional neural network, in which case some basic calculus and linear algebra is enough. More rigorous work tends to draw very strongly from dynamical systems, and references biophysically realistic modelling enough that you'll need to understand every that was said about it above. 



#4
Jul2712, 06:53 PM

P: 606

Computational Neuroscience.
Interesting post Number Nine. I've found the amount of maths required in computational neuroscience to be disappointingly low, but then I've come from a strong mathematical background. More correctly, I'd probably say it's been disappointingly handwavy, like you would expect from an engineer rather than a mathematician. It's certainly at the level that people with backgrounds in engineering or computer science can get straight into it.
To be fair, some of the maths is quite technical (e.g. weiner series for cell responses), but I've never once seen it explained properly in a computational neuroscience setting. 



#5
Jul2812, 07:01 PM

P: 771





#6
Jul2812, 09:54 PM

Sci Advisor
P: 8,007





#7
Jul2912, 08:01 AM

P: 606





#8
Jul2912, 08:21 AM

P: 1,666





#9
Jul2912, 10:42 AM

P: 606





#10
Jul2912, 11:00 AM

PF Gold
P: 4,210

What Jack speaks of is often the Physicist's route to comp neuro. But physicists don't need to be mathematicians to do nonlinear science.




#11
Jul2912, 11:36 AM

P: 1,666

Note I said "excel". That's the difference. Oh, you can study computational neuroscience without a lot of math, without a passion for math, and just do meodicre work but that's not excelling, not groundbreaking, not rocking the foundation of neuroscience. There is in my opinion only one thing in the entire Universe that can create the apparent unlimited diversity of the human mind and that is nonlinear dynamics. It has to be the key to understanding the brain, consciousness, and mind. But it will take more than just a cursory understanding to turn this key. Something more is needed and that is where the passion not for neuroscience but math will come in.
So I'm not a science advisor in here, just an ordinary Joe and my ordinary Joe opinion is in order to rock the foundation of neuroscience, have a passion and love for math and neuroscience, then major in math. 



#13
Jul2912, 01:19 PM

P: 606

http://www.pnas.org/content/109/29/11735.full I think to some extent you have to make a decision in computational neuroscience as to whether you will actually work with biological data and sacrifice using too much mathematics or stick with mathematics and risk having no biologists take you seriously. 



#14
Jul2912, 02:32 PM

PF Gold
P: 4,210

My route too. You don't have to appeal to biologists though. Think of them as the ones who are providing experimental data for you. We have journals like Chaos and Physics Review E. Our audience really is nonlinear scientists.




#15
Jul2912, 02:40 PM

P: 1,666





#16
Jul2912, 03:25 PM

P: 606





#17
Jul2912, 03:36 PM

PF Gold
P: 4,210





#18
Jul2912, 03:52 PM

P: 606

Without concrete quantitative predictions, there's not much to verify or falsify in an experiment. Sometimes I feel like biology papers are just stabbing around in the dark with no real hypothesis to test (or at least no hypothesis that is strictly defined before you get the results of the experiment). I definitely believe mathematical models are an important part of understanding the brain. 


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