Software is discrete mathematics

Abstract

A three-year study collected information bearing on the question of whether studying mathematics improves programming skills. An analysis of the data revealed significant differences in the programming effectiveness of two populations of students: (1) those who studied discrete mathematics through examples focused on reasoning about software and (2) those who studied the same mathematical topics illustrated with more traditional examples. Functional programming played a central role in the study because it provides a straightforward framework for the presentation of concepts such as predicate logic and proof by induction. Such topics can be covered in depth, staying almost entirely within the context of reasoning about software. The intricate complexities in logic that mutable variables carry with them need not arise, early on, to confuse novices struggling to understand new ideas. In addition, because functional languages provide useful and compact ways to express mathematical concepts, and because the choice of notation in mathematics courses is often at the discretion of the instructor (in contrast to the notational restrictions often fiercely guarded by the faculty in programming courses), discrete mathematics courses, as they are found in most computer science programs, provide an easy opportunity to enhance the education of students by exposing them to functional programming concepts.