Elementary Mathematical Models: An Accessible Development Without Calculus, Second Edition

by Dan Kalman, Sacha Forgoston, Albert Goetz

Elementary Mathematical Models offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. Presuming only a background of exposure to high school algebra, the text introduces students to the methodology of mathematical modeling, which plays a role in nearly all real applications of mathematics. A course based on this text would have as its primary goal preparing students to be competent consumers of mathematical modeling in their future studies. Such a course would also provide students with an understanding of the modeling process and a facility with much of the standard, non-trigonometric, content of college algebra and precalculus. This book builds, successively, a series of growth models defined in terms of simple recursive patterns of change corresponding to arithmetic, quadratic, geometric, and logistic growth. Students discover and come to understand linear, polynomial, exponential, and logarithmic functions in the context of analyzing these models of intrinsically and scientifically interesting phenomena including polar ice extent, antibiotic resistance, and viral internet videos. Students gain a deep appreciation for the power and limitations of mathematical modeling in the physical, life, and social sciences as questions of modeling methodology are carefully and constantly addressed. Realistic examples are used consistently throughout the text, and every topic is illustrated with models that are constructed from and compared to real data. The text is extremely attractive and the exposition is extraordinarily clear. The lead author of this text is the recipient of nine MAA awards for expository writing including the Ford, Evans, Pólya, and Allendoerfer awards and the Beckenbach Book prize. Great care has been taken by accomplished expositors to make the book readable by students. Those students will also benefit from more than 1,000 carefully crafted exercises.

509 pages, Hardcover

Published August 2, 2019

Reviews

[Tom Schulte · Rating 4 out of 5]

...Presuming only a background of exposure to high school algebra, the text introduces students to a cogent methodology of mathematical modeling building up from raw, sequential data and employing difference and ratio equations. Sequences lead off in an effective and engaging manner. The reader is drawn easily into a working knowledge ramping up through number patterns in visual and instructive puzzles. Real-world examples abound with multiple contemporary environmental and life science topics: sea ice extent, atmospheric carbon dioxide, infectious disease spread, repeated medication doses, and more. These emphasize the power and utility of quantitative methods which is the aim here, rather than a rigorous, technical mastery. Encompassing a wide spectrum of quantitative models and touching on chaos theory, this is a broad and coherent introduction to basic, predictive data modelling....

[Look for my entire review at MAA Reviews]