External Influences on U.S. Undergraduate Mathematics Curricula: 1950-2000 - Discrete Mathematics

Discrete Mathematics

In a nutshell, the story of the Discrete Mathematics course is that the computer science community devised and promoted this course, asked the mathematical community to teach it, and the mathematical community did so – a clear case of openness to the world outside mathematics.

The computer science community had decided as early as 1968 that its majors should study a discrete mathematics course [1].  Corresponding interest in such a course in the mathematical community was, around this time, only flickering to life.  One notable example was a Discrete Mathematics course at Swarthmore pioneered by Eugene Klotz in 1970-71, soon to be joined by Steve Maurer.  But CBMS figures show only about 1000 enrollments in such a course in 1970 in the union of mathematics, computer science, statistics, operations research, and other mathematical science departments.  Most of these courses were taught in computer science departments according to Anthony Ralston, a mathematics Ph.D. who was also prominent in the computer science world as chair of computer science at the State University of New York at Buffalo [53]. 

In order to confirm how interest in this course was distributed between computer science and mathematics departments, we examined, with the help of WorldCat, all English language books with “Discrete Mathematics” or “Discrete Structures” in their titles published between 1973, when the first such book appeared, and 1988.  Some of these books are probably too advanced for undergraduate use at many universities, but it is unlikely that this search missed any significant number of undergraduate texts usable for a Discrete Mathematics course. 

Our search turned up 42 books that had at least one author working at an American institution.  Until 1984, at most two authors were people whose professional activities were mainly in a mathematics department or research lab.  All the rest were working in computer science environments.  We determined the loci of professional activity partly from examining the frontmatter of the textbooks mentioned above, partly from email contacts with the authors, and partly from our personal knowledge of some of the authors.  Starting in 1984, mathematical authors began to predominate.

Although computer scientists can be said to have invented this course through their early curriculum recommendations and textbooks, in time they became increasingly interested in leaving the teaching of it to mathematics departments [36].  Ralston was the ambassador who, more than anyone else, furthered this transfer of duties.  In a series of workshops, talks, articles and committee activity around 1980, he urged mathematics departments to create discrete mathematics courses [52].  As noted above, a few years after Ralston’s burst of advocacy, discrete mathematics books written by mathematical authors began to appear.  And by the Fall of 2000, enrollments in discrete mathematics courses in mathematics departments reached approximately 31,000 according to CBMS.

If one wishes to trace the influences on the Discrete Mathematics course back to before the creation of the academic computer science community, one might ask why that community exists in the first place.  The reason, obviously, lies in the existence and explosive development of computers, which in turn depended on work in mathematics, but also on contributions from electrical engineers and intense encouragement from commercial and military circles.