Abstract or Additional Information
Inspired by Glenn Young's talk last week and my Graph Theory class, I will present a short talk on generating functions. As expressed in the first sentence of Herbert Wilf's classic text on the subject "A generating function is a clothesline on which we hang up a sequence of numbers for display". Generating functions play an important role in Probability in that they are a perfect-record keeping device for moments of distributions (recall the first moment is the mean and the second the standard deviation of the distirbution). As well, they are quite useful tools in proofs, solving recursions, or counting.
In addition to many beautiful examples. we will consider some algebraic and analytic properties of GFs. This talk will be accessible to anyone that understands capital sigma represents a sum and will be a great motivator for those that find the Series chapter in Calculus II dreadful and dull.