Stochastic Processes in the Natural Sciences (2007 2nd semester)
The course is designed to provide a broad,
application-agnostic, introduction to stochastic methods
in the physical sciences and in biology. The first part,
covering approximately three-fourths of the course
duration, deals with the algebra of stochastic variables,
the calculus of stochastic processes, Markov processes,
the master equation with techniques of exact and
approximate solutions, the diffusion approximation of the
master equation, the related Fokker-Planck and Langevin
descriptions, and ends with stochastic field theories.
Depending on feedback, applications in statistical
mechanics, chemical kinetics, and population dynamics are
discussed. In the second part, an elementary introduction
is given to the Bayesian interpretation of probability,
Bayesian inference, and the maximum entropy method.
Depending on feedback, applications in data analysis,
image restoration, and file compression are given. A
detailed syllabus is available.
Numerical Mathematics (2008 1st semester)
This is a first course in numerical methods for science
undergraduates and is meant to complement the usual
mathematical methods course. The emphasis is on
understanding the mathematics which underlies numerical
algorithms. The main topics covered are interpolation,
differentiation and integration, solutions of systems of
equations, optimisation and ordinary and partial
differential equations. Evaluation is based on
assignments and a short project. The course has its own
wiki site.
Classical Mechanics (2008 2nd semester)
This is a graduate level course in classical mechanics,
with an emphasis on Hamiltonian and continuum mechanics.
The course follows the texts of Landau and Lifshitz and
Jose and Maritan. The course has its own wiki site.