Introduction

A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development in ancient cultures. By contrast, a course in finite mathematics is sometimes presented as a fast-paced news reel of facts and formulae, often memorized by the students, with the text offering only passing mention of the motivating problems and original work that eventually found resolution in the modern concepts of induction, recursion and algorithm. This chapter focuses on the pedagogy of historical projects, which offer excerpts from original sources, place the material in context, and provide direction to the subject matter.

Each historical project is centered around a publication of mathematical significance, such as Blaise Pascal's “Treatise on the Arithmetical Triangle” [2, vol. 30] from the 1650s or Alan Turing's 1936 paper “On Computable Numbers with an Application to the Entscheidungsproblem” [3]. The projects are designed to introduce or provide supplementary material for topics in the curriculum, such as induction in a discrete mathematics course, or compilers and computability for a computer science course.