UNCOMMON MATHEMATICAL EXCURSIONS

Uncommon Mathematical Excursions by Dan Kalman

This book presents an assortment of topics that extend the standard algebra-geometry-calculus curriculum of advanced secondary school and introductory college mathematics. It is intended as enrichment reading for anyone familiar with the standard curriculum, including teachers, scientists, engineers, analysts, and advanced students of mathematics. The book is divided into three parts each with a specific theme. In the first part, all of the topics are related to polynomials: properties and applications of Horner form, reverse and palindromic polynomials, identities linking roots and coefficients, among others. Topics in the second part are all connected in some way with maxima and minima. They include a new idea about an old approach to Lagrange multipliers, optimization as a method of proof, and some unusual max/min problems. In the final part calculus is the focus. Here the reader will find a limit-free development of differentiation, visually appealing treatment of envelopes and asymptotes, a rumination on the subject's surprising power and simplicity, and other topics. The book is particularly recommended for professional development and continuing education of secondary and college mathematics teachers. For more information, visit www.maa.org/ume.