Abstract:  Over the last decade neurophysiologists have found that learning-
related synaptic changes in several systems are sensitive to the relative
timing between pre- and post-synaptic spike events.  The temporal resolution
involved is on a scale of a few tens of milleseconds.  This spike-timing-dependent
plasticity (STDP) stands in contrast to earlier experimental results that lacked 
this time resolution, and hence described synaptic plasticity in terms of 
correlations between pre- and post-synaptic events estimated over many spikes.
Rate-based learning models, involving statistical averages, are conveniently 
described by deterministic differential or difference equations.  STDP learning
models, on the other hand, have intrinsic random components, and their dynamics 
are properly described in terms of stochastic dynamical systems.  Synaptic
strengths evolving under STDP and the iterative statistical estimators in stochastic
approximation algorithms from machine learning share a common dynamical description
in terms of a, usually intractable, master equation and it approximations. I will
discuss viable and non-viable approximate solution techniques for the ensemble dynamics,
and an exact solution for a particular STDP learning rule observed in rat hippocampal neurons.