Excursions in Calculus : An Interplay of the Continuous and the Discrete (Dolciani Mathematical Expositions)

Rating:
Summary: Brilliant and inspiring for students and teachers alike.
Review: I know of very few people who can make mathematics come alive the way Prof. Robert Young (Oberlin College) does. I have been a student of his for the past year-and-a-half. With him my mathematical maturity, integrity, and knowledge have soared. The acquisition of Excursions In Calculus has added tremendously to my growth. Prof. Young's book is a collection of some of his favourite topics in teaching elementary calculus and analysis. Intended for both teachers and motivated students of the calculus, he takes the reader through several beautiful realms of mathematical inquiry and discovery. His topics are diverse: infinite sums and products (including a brilliant presentation of some of the work of Euler, one of his favourite mathematicians), exponential spirals, Wallis's formula for pi, chaos and fractals, Cantor functions, the Weierstrass approximation theorem, and many more with an ambitious appendix on modular arithmetic and related topics such as the celebrated Chinese Remainder Theorem.Prof. Young treats each of his subjects with not only the highest responsibility and technical acuity of a trained professional mathematician, but also with the greatest reverence and passion for the glorious field to which he has devoted his life. The book reads not like a sterile mathematical text but as an intricately woven epic of centuries of mathematical inquiry and the rich personalities responsible. Complete with hundreds of very challenging and non-trivial exercises, this book has something for everyone, whether a motivated student of freshman calculus or a sophisticated mathematician. None will be bored, all will be mystified.