integral operators of singular type, invariant subspaces of multiple weighted
shift operators, Hardy-type spaces of analytic operator-valued functions,
digital image processing.
Mathematical foundations of data protection
Modern methods of data protection rely on an essential theoretical background,
including, in particular, the general algebra, more precisely, its part
dealing with the theory of finite algebraic systems: groups, rings, and fields.
This part in turn borders with the number theory, with the coding theory
and cryptography. The presented information permits to serve
as the basis for other training courses and to be used in
the further practical work.
Introduction to computer algebra
Computer algebra deals with algorithms that differ significantly from
the ones used in computational mathematics, since calculations are usually
are produced without rounding. The results and methods of computer algebra
are widely are used in the modern mathematical software systems such as
Maple, Mathematica, MatLab.