A modern approach to discrete structures

Abstract

In this paper, we present a new paradigm for a freshman course in discrete structures. Historically, a freshman course in discrete structures is taught by presenting a variety of topics in a modular fashion. Topics typically include logic, sets, functions, induction, recursion, algorithms, graphs, probability, counting, proofs, and Boolean algebra, to name a few. Students are expected to follow, digest, and retain such knowledge, often for several years before applying it in junior- and/or senior-level courses. In the Department of Computer Science and Engineering at the State University of New York at Buffalo, the success of a traditional course in discrete structures has been marginal, at best. The alternative approach that we present provides a focused educational experience covering key components of discrete structures. Specifically, we present a unifying thread of modern computer architectures and their algorithms, where critical components of discrete structures are presented in context. In addition, we provide freshman students with an opportunity to take ownership of the educational process. To date, results of this new paradigm have been extremely promising.