Department of Mathematics

  MATH 3370, Mathematical Neuroscience

This course is an introduction to computational and mathematical neuroscience, i.e., study of biological nervous systems in terms of biophysical and mathematical models. We shall discuss methods that have been developed in modeling and analyzing complex dynamics of single neurons and large-scale networks. Emphasis will be made on how to characterize properties of the synaptic connectivity pattern in a given brain area, and how this, as well as intrinsic cellular properties and neuromodulators, determines the network behavior. Two main themes are (1) to understand the rhythmogenesis and the functions of synchronous neuronal firings and various oscillatory modes; and (2) to describe synaptic plasticity during development or learning. The course will be self-contained, and will duly take into account the backgrounds of those from neuroscience and mathematics alike.

  MATH 3375, Computational Neuroscience

This course offers an introduction to modeling methods in neuroscience. It illustrates how models can extend and evaluate neuroscience concepts. Basic techniques of modeling biophysics, excitable membranes, small network and large scale net work systems will be introduced. The course begins with a consideration of mathematical models of excitable membranes, including the Hodgkin- Huxley model and simplifications such as the Morris-Lecar and FitzHugh-Nagumo models. It will provide hands-on laboratory experience in modeling membranes, neurons, and neural networks. The course explores the use of differential equations, numerical simulation and graphical techniques for modeling neural systems. The range of topics includes simulations of electrical properties of membrane channels, single cells, neuronal networks and cognitive simulation. Students will be afforded laboratory experience in computer modeling, and they will develop computational neuroscience models in the course. Prerequisites for the course include basic knowledge of calculus, neuroscience, and some computer programming.