Discrete Mathematics: A Gateway to Advanced Mathematics

Intermediate—Fall

Your voice will produce a mostly continuous sound signal when you read this sentence out loud. As it appears on the page, however, the previous sentence is composed of 79 distinct characters, including letters and a punctuation mark. Measuring patterns—whether continuous or discrete—is the raison d’être of mathematics, and different branches of mathematics have developed to address the two sorts of patterns. Thus, a course in calculus treats motion and other continuous rates of change. In contrast, discrete mathematics addresses problems of counting, order, computation, and logic. We will explore these topics and their implications for mathematical philosophy and computer science. The form of this seminar will be that of a (mathematical) writing workshop. We will work collaboratively to identify and reproduce the key formal elements of mathematical exposition and proof as they appear in both the discrete mathematics literature and each other’s writing. This seminar is a must for students interested in advanced mathematical study and highly recommended for students with an interest in computer science, law, logic, or philosophy.