  One of the "deepest" theorems in mathematics is Endre Szemer\'edi's theorem
about the inevitability of arithmetical progressions. Here we try to nibble at
it, by doing "finite" analogs. This is already interesting for its own sake,
but we believe that it has the potential to lead to extremely interesting
sharpening of the currently rather weak bounds. Let's hope!
  Along with introducing the theory behind the finite analogs of Szemer\'edi's
Theorem, full Maple, Mathematica, and Java code is provided. See paper for
further details.
