Generating Functions: Applications and Techniques

Abstract

Generating functions, one of the important topics in undergraduate discrete mathematics, are useful in a wide range of disciplines in mathematics. However, most of the undergraduate students feel that it is difficult to apply them. In this paper, we first introduce the background necessary for our discussion, then we demonstrate, through examples, how generating functions can be used in certain series, probability theory, and some counting problems. A BASIC program performing some counting calculations can be obtained from the authors upon request.