My course on the Theory of Partitions will focus on introducing the
students to the Omega computer package (implemented in Mathematica) that
has been developed by Peter Paule, Axel Riese and me. I believe that this
package can be used with a minimal knowledge of Mathematica. It will be
my intention to instruct the students early on in what they need to know.
It is my hope to pose some of the problems that occupied MacMahon when he
developed the theory early in the century. The problems are still
interesting; however, MacMahon's method (called Partition Analysis by him)
was sufficiently unwiledy that he was able to make only minimal progress
with his projects. Paule, Riese and I have established that Partition
Analysis is, in fact, an algorithm which we have implemented. Thus we are
able to do calculations that took MacMahon days or weeks.