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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.
In the past decade, there has been some interest shown in solving discriminant analysis problems using mathematical programming techniques. In this paper, we present a quadratic program which is used to obtain a linear discriminant function. This would provide an alternative to the conventional statistical approach.