Elementary Mathematical Models: Order Aplenty and a Glimpse of Chaos (Mathematical Association of America Textbooks)

The language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. With numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences. In a book written for the intelligent and literate non-mathematician, Kalman aims at an understanding of the power and utility of quantitative methods rather than at technical mastery of mathematical operations. He shows first that mathematical models can serve a critical function in understanding the world, and he concludes with a discussion of the problems encountered by traditional algebraic assumptions in chaos theory. Though models can often approximate future events based on existing data and quantitative relationships, Kalman shows that the appearance of regularity and order can often be misleading. By beginning with quantitative models and ending with an introduction to chaos, Kalman offers a broad treatment of both the power and limitations of quantitatively-based predictions.

Dan Kalman has been writing about and teaching mathematics for 20 years. A graduate of Harvey Mudd College (BS, 1974) and the University of Wisconsin (PhD, 1975) he is currently a member of the mathematics faculty at American University, Washington, DC He previously held faculty positions at the University of Wisconsin, Green Bay, and Augustana College, Sioux Falls, among other institutions, and worked for several years as an applied mathematician at the Aerospace Corporation. Her also served for one year as an Associate Executive Director of the MAA. Kalman was recognized with a Plya Award in 1994, and a Trevor Evans Award in 1997. He is an Associate Editor for "Mathematics Magazine" and has served on the Editorial Boards for the Spectrum and Classroom Resources Materials series of publications of the Mathematical Association of America.