Hardcover ISBN:  9780883853412 
Product Code:  DOL/35 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781470458447 
Product Code:  DOL/35.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853412 
eBook: ISBN:  9781470458447 
Product Code:  DOL/35.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 
Hardcover ISBN:  9780883853412 
Product Code:  DOL/35 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781470458447 
Product Code:  DOL/35.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853412 
eBook ISBN:  9781470458447 
Product Code:  DOL/35.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 35; 2009; 265 ppRecipient of the Mathematical Association of America's Beckenbach Book Prize in 2012!
This text serves as a tour guide to little known corners of the mathematical landscape, not far from the main byways of algebra, geometry, and calculus. It is for the seasoned mathematical traveller who has visited these subjects many times and, familiar with the main attractions, is ready to venture abroad off the beaten track. For the old hand and new devotee alike, this book will surprise, intrigue, and delight readers with unexpected aspects of old and familiar subjects. In the first part of the book all of the topics are related to polynomials: properties and applications of Horner form, reverse and palindromic polynomials and identities linking roots and coefficients, among others. Topics in the second part are all connected in some way with maxima and minima. In the final part calculus is the focus.

Table of Contents

Chapters

Part I. The Province of Polynomia

Chapter 1. Horner’s Form

Chapter 2. Polynomial Potpourri

Chapter 3. Polynomial Roots and Coefficients

Chapter 4. Solving Polynomial Equations

Part II. Maxiministan

Chapter 5. Leveling with Lagrange: Constrained Maxima and Mimima with Lagrangian Functions

Chapter 6. A Maxmini Miscellany

Chapter 7. Envelopes and the Ladder Problem

Chapter 8. Deflection on an Ellipse

Part III. The Calculusian Republic

Chapter 9. A Generalized Logarithm for ExponentialLinear Equations

Chapter 10. Envelopes and Asymptotes

Chapter 11. Derivatives Without Limits

Chapter 12. Two Calculusian Miracles


Additional Material

Reviews

Kalman takes a deep look at several classical topics with which mathematics teachers are familiar, yet all will be surprised by the beauty and depth of those familiar topics and intrigued by the results uncovered.
Dan Teague, The Mathematics Teacher


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This text serves as a tour guide to little known corners of the mathematical landscape, not far from the main byways of algebra, geometry, and calculus. It is for the seasoned mathematical traveller who has visited these subjects many times and, familiar with the main attractions, is ready to venture abroad off the beaten track. For the old hand and new devotee alike, this book will surprise, intrigue, and delight readers with unexpected aspects of old and familiar subjects. In the first part of the book all of the topics are related to polynomials: properties and applications of Horner form, reverse and palindromic polynomials and identities linking roots and coefficients, among others. Topics in the second part are all connected in some way with maxima and minima. In the final part calculus is the focus.

Chapters

Part I. The Province of Polynomia

Chapter 1. Horner’s Form

Chapter 2. Polynomial Potpourri

Chapter 3. Polynomial Roots and Coefficients

Chapter 4. Solving Polynomial Equations

Part II. Maxiministan

Chapter 5. Leveling with Lagrange: Constrained Maxima and Mimima with Lagrangian Functions

Chapter 6. A Maxmini Miscellany

Chapter 7. Envelopes and the Ladder Problem

Chapter 8. Deflection on an Ellipse

Part III. The Calculusian Republic

Chapter 9. A Generalized Logarithm for ExponentialLinear Equations

Chapter 10. Envelopes and Asymptotes

Chapter 11. Derivatives Without Limits

Chapter 12. Two Calculusian Miracles

Kalman takes a deep look at several classical topics with which mathematics teachers are familiar, yet all will be surprised by the beauty and depth of those familiar topics and intrigued by the results uncovered.
Dan Teague, The Mathematics Teacher