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Uncommon Mathematical Excursions: Polynomia and Related Realms

Uncommon Mathematical Excursions: Polynomia and Related Realms

By Dan Kalman

Beckenbach Book Prize Winner
Catalog Code: DOL-35
Print ISBN: 978-0-88385-341-2
296 pp., Hardbound, 2009
List Price: $61.95
MAA Member: $49.95
Series: Dolciani Mathematical Expositions

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Uncommon Mathematical Excursions is for anyone who knows and appreciates the basics of algebra, geometry, and calculus, and would like to learn more. It offers teachers an opportunity to deepen their knowledge of mathematics, not by exploring the far reaches of the subject, but by returning to the core. More generally, for the old hand and new devotee alike, this book will surprise, intrigue, and delight readers with unexpected aspects of old and familiar subjects. The book is particularly recommended for professional development and continuing education of secondary and college mathematics teachers.

Table of Contents

I. The Province of Polynomia
Horners Form
Polynomial Potpourri
Polynomial Roots and Coefficients
Solving Polynomial Equations
II. Maxiministan
Leveling with Lagrange: Constrained Maxima and Minima with Lagrangian Functions
A Maxmini Miscellany
Envelopes and the Ladder Problem
Deflection on an Ellipse
III. The Calculusian Republic
A Generalized Logarithm for Exponential-Linear Equations
Envelopes and Asymptotes
Derivatives Without Limits
Two Calculusian Miracles
About the Author

About the Author

Dan Kalman has been writing about and teaching mathematics for 30 years. A graduate of Harvey Mudd College (BS, 1974) and the University of Wisconsin (PhD, 1980) he is a Professor of Mathematics 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. He also served for one year as an Associate Executive Director of the MAA. Kalman’s mathematical writing has been recognized with multiple MAA awards: Allendoerfer Awards in 1998 and 2002, Pólya Awards in 1994 and 2002, and an Evans Award in 1997. He is the author of one previous book, Elementary Mathematical Models, published by the MAA in 1997. Kalman has served on the Editorial Boards for several MAA publications, including Mathematics Magazine, MAA FOCUS, Math Horizons, and the Spectrum and Classroom Resource Materials book series.


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