Authors: Russ Miller
Addresses: Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY, USA
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.
Keywords: discrete mathematics; asymptotic analysis; parallel algorithms; models of computation; divide-and-conquer; parallel prefix; summation; recursion; induction; sorting; graph theory.
International Journal of Teaching and Case Studies, 2018 Vol.9 No.1, pp.33 - 47
Received: 13 Jan 2017
Accepted: 11 Aug 2017
Published online: 14 Feb 2018 *