In the second term of 2007 I will teach an introductory course on mathematical modelling in the neurosciences as part of the 4th year MMath (masters in mathematics) program. Below is the entry in the maths PYDC page.
Please feel free to contact me if you have any questions.
INTRODUCTION TO THEORETICAL NEUROSCIENCE
Commitment: 30 one-hour lectures.
Prerequisites: Calculus and standard methods for the solution of differential equations. Basic knowledge of stochastic calculus (Langevin, Fokker-Planck and master equations) and probability theory would be an advantage.
Content: Neuroscience is a highly active multidisciplinary field of research in which analytical methods play an important role. This course introduces some of the basic concepts in cellular neuroscience and provides an overview of the fundamental approaches used in the modelling of electrical activity in the nervous system. The topics covered span the spatial and temporal scale from rapid signalling at synapses to emergent dynamic states of networks of coupled neurons, specifically: propagation of action potentials in axonal fibres; synaptic transduction including the statistics of vesicle release, short- term synaptic dynamics and spike-time-dependent learning; the subthreshold neuronal response to excitatory and inhibitory synaptic drive, dendritic filtering and cable theory, the role of voltage-gated channels and the firing properties of neurons; and finally, the dynamic states of networks of coupled neurons such as persistent memory and oscillations.
Aims: To provide a grounding in the basic theory of neuroscience as well as to highlight the most active areas in modern brain research, with particular emphasis on models that are of relevance to experiment.
Objectives: At the end of the course the participants will be familiar with major topics of research in the neurosciences and have the necessary analytical techniques for the pursuit of research in this field or in other related fields in biophysics.
Books: No single book will be used; wherever possible the original scientific articles will be introduced and discussed. However, as background reading the following books may be of interest:
P Dayan and LF Abbott, Theoretical NeuroscienceMIT Press (2001).
W Gerster and WM Kistler, Spiking Neuron ModelsCambridge University Press (2002).
ER Kandel, TMJ Schwartz and TM Jessel, Principles of Neural SciencesElsevier (1991).
C Koch, Biophysics of Computation Oxford University Press (1999).
Assessment: 3 hour exam.