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Elementary Mathematical Models: Order Aplenty and a Glimpse of Chaos

Elementary Mathematical Models

By Dan Kalman

Catalog Code: EMM
Print ISBN: 978-0-88385-707-6
Electronic ISBN: 978-1-61444-601-9
360 pp., Paperbound, 1997
List Price: $49.95
Member Price: $39.95
Series: MAA Textbooks

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Elementary Mathematical Models claims a middle ground between college algebra and liberal arts mathematics. Like the college algebra course, EMM emphasizes the elementary functions of analysis: linear, quadratic, polynomial, and rational functions; square roots; exponentials; and logarithms.

Table of Contents

Preface
Overview
Sequences and Difference Equations
Arithmetic Growth
Linear Graphs, Functions, and Equations
Quadratic Growth Models
Quadratic Graphs, Functions, and Equations
Polynomial and Rational Functions
Fitting a Line to Data
Geometric Growth
Exponential Functions
More on Logarithms
Geometric Sums and Mixed Models
Logistic Growth
Chaos in Logistic Models
Index

About the Author

Dan Kalman has been writing about and teaching mathematics for over 20 years. A graduate of Harvey Mudd College (BS, 1974) and the University of Wisconsin (MA, 1975; PhD 1980), 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 as an applied mathematician at the Aerospace Corporation for several years. He also served for one year as an Associate Executive Director for MAA.

Kalman was recognized with a Pólya Award in 1994, and a Trevor Evans Award in 1997. He served as an Associate Editor for Mathematics Magazine, and has served on the Editorial Boards for the Spectrum and Classroom Resource Materials series of publications.

MAA Review

Elementary Mathematical Models offers a gentle introduction into the ideas of discrete mathematical modeling with some basic extensions to continuous functions. The book is well balanced and succeeds in introducing the use of discrete models to students who might view a mathematics class with a weary eye.

The first chapter of the book is written for both teachers and students. It offers a broad overview of how the material is presented and certain expectations of the students. Moreover, an explicit discussion on the use of numerical, theoretical, and graphical approaches is given in the first chapter. This is a nice touch that sets the stage for the following chapters. Continued...

 

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