Introduction to Computational Neuroscience Applied Mathematics
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Course outline:
  1. Single compartment neurons – passive properties

  2. The behavior and modeling of ion channels

  3. The Hodgkin-Huxley action potential

  4. The diversity of voltage gated ion channels, and effects upon neuron spiking

  5. The cable equation

  6. Compartmental models of neurons; the NEURON simulation environment

  7. Models of synapses, including facilitation and depression
  8. The cable theory of dendritic spines

  9. Reduction of the Hodgkin-Huxley model to an integrate and fire neuron

  10. Implementing integrate and fire neuron models

  11. Coupled integrate and fire neuron models – mutual excitation and inhibition

  12. The autapse – a simple recurrent memory

  13. Firing rate models

  14. The Hopfield associative memory

  15. Network models (synchronization, rhythms)

  16. Hebbian learning

  17. Long term potentiation

  18. Plasticity models