Uncommon Mathematical Excursions: Polynomia and Related Realms
265 pp., hardcover, 2009. Series: Dolciani Mathematical Expositions #35
Designed to surprise, intrigue, and delight readers, Uncommon Mathematical Excursions presents unexpected aspects of the mathematics surrounding the standard curriculum, guiding readers to little-known corners of the mathematical landscape not far from the main byways of algebra, geometry, and calculus. It is for seasoned mathematical travelers who have already visited these subjects and, familiar with the main attractions, are ready to step off the beaten track. For old hands and new devotees alike, this book brings to light thought-provoking aspects of apparently familiar topics.
The first part of the book guides readers into the Province of Polynomia for illuminating encounters with polynomials in a wide variety of guises. The journey into Maxministan offers visits to Lagrangian functions and various optimization problems The final trek ventures into the Calculusian Republic for insights into solving exponential-linear equations, envelopes and asymptotes, and other wonders.
This book is for anyone who appreciates the intrinsic fascination of mathematics, beyond its applicability and utility. Each chapter includes historical notes and recommendations for further reading.
Preface. I. The Province of Polynomia: 1. Horner's Form; 2. Polynomial Potpourri; 3. Polynomial Roots and Coefficients; 4. Solving Polynomial Equations. II. Maxministan: 5. Leveling with Lagrange; 6. A Maxmini Miscellany; 7. Envelopes and the Ladder Problem; 8. Deflections on an Ellipse. III. The Calculusian Republic: 9. A Generalized Logarithm for Exponential-Linear Equations; 10. Envelopes and Asymptotes; 11. Derivatives Without Limits; 12. Two Calculusian Miracles. References. Index.
About the Author:
Dan Kalman received his Ph.D. from the University of Wisconsin in 1980. Now a professor of mathematics at American University, in Washington, D.C., he has longstanding ties to the Mathematical Association of America. Kalman has served on the editorial boards of Mathematics Magazine, MAA FOCUS, Math Horizons, and the MAA's Spectrum and Classroom Resource Materials book series. The author of Elementary Mathematical Models (1997), published by the MAA, Kalman received the Association's Carl B. Allendoerfer Award in 1998 (with Robert Mena and Shahriar Shahriari) for the article "Variations on an Irrational Theme—Geometry, Dynamics, Algebra" and in 2003 for "Doubly Recursive Multivariate Automatic Differentiation." He also received the MAA's George Pólya Award in 1994 for "Six Ways to Sum a Series" and in 2003 for "An Undetermined Linear System for GPS."
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