An introduction to single neuron and populations of neurons computations for graduate students interested in studying how nerve cells integrate and transmit signals and how perception, cognition and memory emerges from the integrated actions of populations or circuits of nerve cells. The course covers basic notions of electrical and biochemical properties of single neurons, the electrical and chemical communication between neurons, the anatomy, physiology and function of each of the major brain structures and systems and how behavior emerges from their actions.
Emphasis will be given on mathematical descriptions and computational techniques used to study and understand neurons and network of neurons such as:Hodgkin-Huxley models, cable theory, integrate-and-fire neurons, multicompartmental modeling, firing rate models, various types of neural networks (feedforward, associative, linear recurrent, stochastic, etc.), central pattern generators, topographic maps, receptive fields, elements of information theory (entropy and mutual information, etc.), spike-train statistics, reverse-correlation methods, rate vs temporal processing, population vector coding, adaptation and learning (Hebbian learning, LTP/LTD, STDP, supervised, unsupervised learning), classical conditioning, reinforcement learning (Markov decision processes, actor-critic model, etc).