The question of the advisability of incorporating discrete mathematics into the mathematics curriculum is addressed by examining the different types of courses typically offered in the first two years of college and the appropriateness of including discrete mathematics topics in these courses. The introductory section explains how the advent of the computer, with its capacity for easily performing extended numerical computations, has made discrete calculations less laborious than continuous functions. This section goes on to enumerate various reasons for teaching discrete math topics. The next sections provide analyses of the advantages and disadvantages of including discrete topics in particular courses, offer examples of ways to present these topics, and review trends in mathematics education with respect to: (1) the calculus sequence; (2) applied calculus; (3) differential equations and linear algebra; (4) finite mathematics; (5) statistics; (6) survey of mathematics for liberal arts students; (7) remedial mathematics; and (8) geometry. A discussion is then presented of the problems associated with incorporating discrete mathematics in the curriculum, such as the national trend towards separate courses on discrete math for math majors; the conservatism of of mathematicians; and the reluctance of the publishing industry to put out innovative texts. A list of discrete math topics is appended. (LAL)