Fun stuff we did

Its past midnight and I am on the 4th floor of the library. Today was the last day of Math 549 lecture. That class rocked. I am excited that over the break I will be exploring the topic of various lattice paths. We discussed today the Mobius inversion formula and the posets. Dr. Clark's way of using exponential generating function is cool and the way the composition formula is derived algebraically helps one understand why it works and its easy to come up with the Bell Numbers and fixed partition formulae. Similarly when he does graphs he exploits the formula --> number of automorphisms* number of labellings = n! for a n vertex connected graph. Similarly he shows how it can be used in case of permutations where he does it for Stirling number of first kind of cases. Then he later generalizes for multivalued functions. His book is remarkably good and the kind of examples he uses to elucidate the theory makes it a solid pedagogical material that I am sure will bound to influence many other books when it gets published.