Friday, March 13, 2015

New MAA Textbook: Modeling Approach in Biology

by Steve Kennedy

When biology was primarily a descriptive science, biologists had little need of mathematical services (and our science). But a revolution has occurred—more precisely, is occurring—in biology, and the discipline is becoming increasingly mathematical and computational. In 2003, a report (Bio2010) from the National Academy of Sciences (NAS) set a goal of having biology undergraduates be quantitatively literate by 2010:

It is essential that biology undergraduates become quantitatively literate, studying the mathematical concepts of change, modeling, equilibria and stability, structure of a system, interactions among components, data and measurement, visualization, and algorithms. Every student should acquire the ability to analyze issues in these contexts in some depth, using analytical methods (e.g., pencil and paper) and appropriate computational tools. An appropriate course of study would include aspects of probability, statistics, discrete models, linear algebra, calculus and differential equations, modeling and programming.

Five years past 2010, the goal hasn't been met fully. The current state of affairs is well described in the draft CUPM Curriculum Guide. That report, besides enumerating biological and mathematical core competencies for biomathematics study, strongly urges foundational courses in modeling and data analysis as the beginning steps of such study.

And that brings me, finally, to my point. MAA Books has just released a book perfectly suited for that foundational modeling course, Jim Cornette and Ralph Ackerman’s Calculus for the life Sciences: A Modeling Approach. If you teach a life sciences calculus course, you may already be aware of the existence of this book, as draft versions have been on the Internet for several years. Reading this terrific and innovative book, you realize that it could have been written in reaction to the first sentence of the NAS report—it addresses, in a deep and significant way, every single mathematical concept listed in the quote above.

Chapter 1 is a primer on modeling in the biological realm, and biological modeling is the theme and frame for the entire book. The authors build models of bacterial growth, light penetration through a column of water, and dynamics of a colony of mold in the first few pages. In each case there is actual data that needs fitting. In the case of the mold colony, that data is a set of photographs of the colony growing on a ruled sheet of graph paper, and the students need to make their own approximations. Fundamental questions about the nature of mathematical modeling—trying to approximate a real-world phenomenon with an equation—are all laid out for the students to wrestle with.

Students intending to major in the life sciences now outnumber engineering and physical science majors in college and university Calculus I courses. Cornette and Ackerman’s textbook takes into account the needs of that plurality. And it does so not just by including examples and problems with a biological flavor—the authors have reimagined the entire year-long calculus course with the needs of biology students as the organizing principle. Thus, to mention just one example among many, your students using this book could get a substantial dose of discrete and continuous dynamical systems theory in their year of calculus study.

Cornette and Ackerman have produced a beautifully written introduction to the uses of mathematics in the life sciences. The exposition is crystalline, the problems are overwhelmingly from biology and interesting and rich, and the emphasis on modeling is invigorating. This book should become the standard text for this course. Please take special note of the student-friendly price—$35 for an ebook.

This article was written for MAA FOCUS as part of MAA Books Beat. It appears in the February/March 2015 issue.

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