  Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we
first show how the ordering of the non-commuting operators intrinsic to that
algebra gives rise to generalizations of the classical Stirling Numbers of
Combinatorics. These may be expressed in terms of infinite, but {\em
row-finite}, matrices, which may also be considered as endomorphisms of
$\C[[x]]$. This leads us to consider endomorphisms in more general spaces, and
these in turn may be expressed in terms of generalizations of the
ladder-operators familiar in physics.
