If one is more interested in understanding how algorithms in the biological brain solve problems (theoretically, particularly the mathematical aspect), and possibly in building brain-inspired computation (applied theory, particularly neurorobotics), then is it suggested to focus more on studying computational neuroscience rather than artificial neural nets/machine learning? It seems the latter one is more oriented toward any algorithms just to solve problems via computer simulations without the constraints of biological brains, though there are still large areas for theory of machine learning and artificial neural nets.
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Computational neuroscience and neural networks are both studied on this MSc at the University of Sussex. When I took the course in 2004/5, the Neural Networks module was compulsory, and the Computational Neuroscience was optional in the 2nd semester, so that would suggest the course designers (world leaders in biologically inspired computing) thought that studying neural networks first might aid the study of computational neuroscience. I think some of the other subjects taught on the course would be of interest to you, e.g. evolving genetic algorithms for robot control (see Rodney Brooks – and the iRobot corporation).
Lastly to answer the question(!), I think you probably need some understanding of (simple) neural networks (artificial or otherwise) to understand more in-depth concepts in computational neuroscience.
Neural networks constitute one (very important) level of organization that is modelled computationally in brain research. Computational neuroscience attempts to make these as biologically realistic as possible, often creating models that operate at multiple levels, such as having the neural networks exhibit electrochemical dynamics - something that is obviously not the goal of standard machine learning research. Thus, in a sense, studying computational neuroscience will necessarily make you more of an expert in artificial neural networks than studying machine learning ever will. The type of neural networks used in machine learning are much too basic to explain the brain. However, machine learning texts could give you insight into, well, how information about the environment could potentially be saved in the brain. Computational neuroscience as a field is still in its infancy, especially what concerns modelling learning in the brain. Even Chris Eliasmith's spiking neural network model Spaun (which is quite impressive!) has been criticized by Henry Markram (the guy that got 1 billion Euro from the EU for the Human Brain Project) for being biologically unrealistic. In short, you won't get around the basic ANN theory in studying computational neuroscience, and you will expand on it significantly in biological terms. However, you might want to check out machine learning texts to see how neural networks could possibly store patterns.