Resources in Mathematics Education for Biology

Teaching Modules

• Educational Modules for Mathematical Epidemiology
• Educational Modules for COVID-19

Books and Book Chapters

• Undergraduate Mathematics for the Life Sciences: Models, Processes, & Directions (2013), ed. G.Ledder, J.Carpenter, T. Comar. MAA Notes.

  Preface, annotated Table of Contents, and editor's introduction.

  This book consists of individual chapters containing reports of experiences in math education for biology in the early 2010's. Much of the content will still be valid in the mid 2020's.

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• G.Ledder, M. Homp (2022) Mathematical Epidemiology

  This manuscript develops an individual-based and a continuous-time SEIR model in mathematical epidemiology with minimal prerequisites: algebra for the IBM and only Calculus I for the SEIR model. A variety of exercises are included, from basic exercises to more advanced challenge problems, to group projects. It now appears in a book on mathematics projects for undergraduate research: Mathematics Research for the Beginning Student, Volume 1: Accessible Projects for Students Before Calculus (2022), ed. E. Goldwyn, S. Ganzell, A. Wootton. Springer.

Papers

1. G. Ledder (2022), Mentoring Undergraduate Research in Mathematical Modeling, Bull. Math. Biol. 84:77, DOI: 10.1007/s11538-022-01040-4.

   This paper was invited by the Education editor of the journal. It presents a "theory" of undergraduate research in mathematical modeling based on my extensive experience working with undergraduate research students.

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2. G. Ledder (2021), Qualitative Analysis of a Resource Management Model and Its Application to the Past and Future of Endangered Whale Populations, CODEE 14, DOI: 10.5642/codee.202114.01.03.

   This paper grew out of a talk I gave at the 2020 Joint Mathematics Meetings in Denver.

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3. G. Ledder and M. Homp (2021), Using a COVID-19 Model in Various Classroom Settings to Assess Effects of Interventions, PRIMUS, DOI: 10.1080/10511970.2020.1861143.>

   Michelle Homp and I present a primer on mathematical modeling and mathematical epidemiology and discuss the teaching modules listed above.

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4. C. Diaz-Eaton et al (2019), A "Rule-of-Five" Framework for Models and Modeling to Unify Mathematicians and Biologists and Improve Student Learning, PRIMUS 29, 799-829, DOI: 10.1080/10511970.2018.1489318.

   This paper grew out of a NimBios workshop on mathematics education in biology. It provides a pedagogical framework for mathematical modeling.

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5. G. Ledder (2017), Empirical Modeling: Choosing Models and Fitting Them to Data, College Math. J. 47, 109-119, DOI: 10.4169/college.math.j.47.2.109.>

   In this paper, I discuss linear least squares, the semilinear least squares method I introduced in my 2013 book, and the Akaike Information Criterion for model selection.

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6. G.Ledder (2017), Scaling for Dynamical Systems in Biology, Bull Math Biol 79, 2747-2772.

   Asymptotic methods are ubiquitous in models for physical science, but not often used in biological science. This is unfortunate, as many biological models have features that lend themselves to asymptotic methods. The first step in asymptotic analysis is scaling, which is not easy in biology. In this paper, I present some of the basic principles I use in scaling, using my onchocerciasis model as an example.

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7. G.Ledder (2008), An Experimental Approach to Mathematical Modeling in Biology, PRIMUS 18, 119-138.

   I had the good fortune to be able to serve as guest editor for the January 2008 issue of the undergraduate mathematics pedagogy journal PRIMUS. A number of excellent papers can be found in that issue, as well as this paper of mine, which was slipped in unobtrusively by the guest editor.

Notes

1. Epidemiology Primer is a gentle chapter-length introduction to mathematical epidemiology, using the SEIR model as the primary example. Calculus I is a required prerequisite. Ordinary Differential Equations would be a helpful prerequisite, but not required. The important background can be found in the Ledder and Homp book chapter cited above.
2. Mathematical Models FAQ is an informal FAQ on mathematical models. Much of what mathematicians write about mathematical models is misleading. This document corrects these misconceptions.