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Robert M. Young, "Excursions in Calculus: An Interplay of the Continuous and the Discrete"

The purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus. The book is addressed primarily to well-trained calculus students and those who teach them, but it can also serve as a supplement in a traditional calculus course for anyone who wants to see more. The problems, taken for the most part from probability, analysis, and number theory, are an integral part of the text. There are over 400 problems presented in this book.

Summary: Outstanding Supplement for any Mathematics Student or Teacher

Rating: 5

This unique book is a precious addition to anyone's bookshelf, whether student or teacher. The material within is fun and fascinating. Much of it is accessible to those with minimal knowledge of calculus, yet the book also contains some deep topics and outlines a number of unsolved problems in mathematics. Many recurring themes appear in the book, including the interplay between the finite and infinite, the discrete and continuous, and the connections between fields such as analysis and number theory.

This is one of those rare books that actually teaches people how to think "outside the box"--how to come up with different ways of looking at things, creative ways of solving problems. The author places an emphasis on simplicity and elegance.

If you want a book that will be a fun, easy read, yet that you will keep coming back to over and over again--or if you want a book to help you create some new and fun problems--or if you feel like you need a little infusion of that mathematical creativity that is so critically needed in advanced mathematical work, this book will be able to help you a great deal.

Summary: Brilliant and inspiring for students and teachers alike.

Rating: 5

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.

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Rating:
2.5 out of 5 by Book123