Computational and Mathematical Neuroscience

Computational neuroscience investigates the brain at many different levels, from single cell activity, to small local network computation, to the dynamics of large neuronal populations. As such, this course introduces students to modeling and quantitative techniques used to investigate neural activity at these different levels.

Topics to be covered include:

Passive membrane properties, the Nernst potential, derivation of the Hodgkin-Huxley model, action potential generation, action potential propagation in cable and multi-compartmental models, probabilistic models for ion channel gating, reductions of the Hodgkin-Huxley model, phase plane analysis, linear stability of equilibria, bifurcation analysis, synaptic currents, excitatory and inhibitory network dynamics, firing rate models, neural coding.

No required textbook. Readings and homework problems will be selected from a number of different texts including:

1. Foundations of Cellular Neurophysiology by D. Johnston and S.M. Wu (MIT Press, 1999).
2. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems by P. Dayan and L. Abbott (MIT Press, 2005).
3. Biophysics of Computation by C. Koch (Oxford University Press, 1999).

Numerical implementation and analysis of the models presented in the lectures will be an integral part of the course. MATLAB experience helpful but not required. Course requirements will include homework assignments containing a combination of analytical and numerical-based problems, a longer-term modeling project and an oral presentation of the project to the class at the end of the semester.

Questions? Contact Victoria Booth, Departments of Mathematics and Anesthesiology, 4075 East Hall, vbooth@umich.edu

Course Requirements:

Course requirements will include homework assignments containing a combination of analytical and numerical-based problems, a longer-term modeling project and an oral presentation of the project to the class at the end of the semester.

Intended Audience:

MATLAB experience helpful but not required.

Class Format:

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