Discrete Calculus through generating functions (Wai Yan Pong, Cal State Dominguez Hills)

Discrete Calculus studies discrete structures, such as sequences and graphs, using techniques similar to those used in Calculus for continuous functions. The basic idea of generating functions is to associate a function with a sequence so that the coefficients of the power series expansion of the function represent the terms of the sequence. They provide a systematic way to encode information about a sequence or a combinatorial structure in a single function, which can then be manipulated algebraically to obtain various types of results. In this talk, we will examine a few well-known results about binomial coefficients, Stirling numbers and Bernoulli numbers using both Discrete Calculus and generating functions as well as the interaction between them.