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ABSTRACT
Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees, food webs, networks), cellular automata (pattern formation, diffusion limited aggregation), fractals (both measurement and generation of self-similar structures), finite difference equations and deterministic chaos (logistic growth, predator–prey, SIR epidemiology), combinatorics and probability (genetics and evolution), information theory (biodiversity, sequence logos), and Boolean logic (operons) are available to adopt, adapt, and implement. An emphasis has been placed on modules that are freely available, that have been educationally vetted, and that run on a variety of operating systems. Most modules are easy to use, graphically visual, and amenable to modification. In this paper, two different approaches are stressed: (1) “glass box models” that allow students to see equations associated with each cell in a spreadsheet and to modify/extend those models with minimal effort; and (2) agent-based models that emphasize “bottom-up” modeling and that instantiate the power of massively parallel simulation and address the misconceptions of a “centralized mind-set.”
ACKNOWLEDGEMENTS
This article is dedicated to Ranjan Roy, who team taught finite mathematics with me, who passed away in 2020. His scholarship, passion for mathematics, and compassion for students were truly amazing to witness and to benefit from as a friend and colleague. I am particularly thankful to three colleagues who have been supportive of my education in finite mathematics over the past 40 years: Midge Cozzens, Fred Roberts, and Bob Stark. In addition, Evelyn Fox Keller was my mentor for a Mina Shaughnessy Scholarship, Martha Bertman was my collaborator from 1975 to 1979 at Clarkson University, and editors Jo Ellis-Monaghan and Raina Robeva have edited so much of my work over the years that they are implicitly co-developers of my work. I am sure that many ideas expressed herein are derivative from discussions with the eight of them and I cannot distinguish the particular origins. Numerous former students were significant co-developers of many software packages described inside as were so many colleagues that I can only name a few in this limited space: Tony Weisstein, John Calley, Rama Viswanathan, Vince Strief, Virginia Vaughan, Jenn Spangenberg, Glenn Ledder, Stephen Everse, Noppadon and Jutarat Khiripet, and Ed Louis. They converted so many expectations into actual fruition of usable software that were graphically rich and educationally informed. Glenn Ledder did a close editing of the whole manuscript for which I am deeply grateful as he comes from a very different mathematical perspective. Also, three anonymous reviewers provided line by line suggestions for revision of the whole manuscript and to them I am deeply grateful for their careful and useful suggestions.
DISCLOSURE STATEMENT
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
John R. Jungck
John R. Jungck is a professor of biological sciences and mathematical sciences at the University of Delaware. He is known as the founder of the BioQUEST Curriculum Consortium. He is the Education Editor of the Bulletin of Mathematical Biology, is an editorial board member of Evolutionary Bioinformatics and the American Journal of Undergraduate Research, and is the former Editor of Biology International, Bioscene: Journal of College Biology Teaching, BioQUEST Library, and American Biology Teacher.