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.
• Designed to surprise, intrigue, and delight readers by presenting unexpected aspects of the mathematics surrounding the standard curriculum • For anyone who appreciates the intrinsic fascination of mathematics beyond its applicability and utility • Further reading and the history of the topic being discussed is found at the end of every chapter
Preface; Part I. The Province of Polynomia: 1. Horner's foam; 2. Polynomial potpourri; 3. Polynomial roots and coefficients; 4. Solving polynomial equations; Part II. Maxministan: 5. Leveling with Lagrange; 6. A maxmini miscellany; 7. Envelopes and the ladder problem; 8. Deflections on an ellipse; Part III. The Calculusian Republic: 9. A generalized logarithm for exponential-linear equations; 10. Envelopes and asymptotes; 11. Derivatives without limits; 12. Two calculusian miracles.