ALGORITHMIC ANALYSIS OF STOCHASTIC MODELS The Changing Face of Mathematics

V. Ramaswami
AT&T Labs, Research
180 Park Avenue, E-233
Florham Park, NJ 07932, USA
email: vramaswami@att.com

The progress in computing and communications technologies
made in the last quarter of the past Century has not only
ushered in the ``Information Age,'' but it has also influenced
the basic sciences, including mathematics, in fundamental ways.
Thanks to the significantly increased computing power,
mathematicians can now augment classical techniques of analysis,
proof and solution with an algorithmic approach in a manner that
enables the consideration of more complex models with wider
applicability, and also obtain results with greater practical value
to engineering.
While providing powerful tools to the mathematician, the
technologies, nevertheless, are also posing new challenges
and problems, and opening many new vistas for further
mathematical research. Among the areas exemplifying all these,
a notable one is algorithmic methods for stochastic models based
on ``the matrix (operator) analytic method.'' This lecture is an overview
of these methods.