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Power Play (Spectrum) Paperback – January, 1997

by Edward J. Barbeau (Author)

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This book is a country walk through the magical world of numbers. Most people will have recognised some of the fascinating patterns exhibited by many numbers; some of these indicate a deep and complex structure which is revealed in this book in a way that is accessible to all, from amateur to expert. The author focusses on powers of numbers, which have been studied from the time of Pythagoras until the present day, with the proof of Fermat's Last Theorem. Indeed some of the results described by the author were only established quite recently, giving the book a very contemporary flavour. In sum, this will make a stimulating resource for teachers of mathematics, and will be as well a fund of knowledge for amateurs.

Power Play (Spectrum)

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Product Details

Series: Spectrum
Paperback: 250 pages
Publisher: The Mathematical Association of America (January 1997)
Language: English
ISBN-10: 0883855232
ISBN-13: 978-0883855232
Product Dimensions: 6 x 0.5 x 9 inches
Shipping Weight: 8.8 ounces
Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
Amazon Best Sellers Rank: #1,779,765 in Books (See Top 100 in Books)
- #1193 in Books > Science & Math > Mathematics > Pure Mathematics > Algebra > Elementary
- #12024 in Books > Medical Books > Psychology > General
- #52919 in Books > Health, Fitness & Dieting > Psychology & Counseling

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1 of 1 people found the following review helpful

Fodder for integer lovers

By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on February 22, 2000

Format: Paperback

Integers are the most adorable of all mathematical objects. Simple in concept, yet boundless in mystery. In this volume, the author explores some of the territory marked out by integers taken to integral powers. While most of this territory has been thoroughly explored, like trips to your favorite places, each time yields new joy and insight.
The specific topics of the chapters are:

1) Odd integers and squares.
2) Pythagorean triples and their relations.
3) Sequences.
4) Pell's equation.
5) Equal sums of equal powers.
6) Digits and sums of powers.
7) Interesting sets.

The level of the motivating text is deliberately kept low. Most talented high school math students will be able to follow it with a bit of guidance. Higher order material is reserved for the problems and each section terminates with a large problem set. There are two parts to each set and solutions to all are included, although some are simply a pointer to the proper reference. The level of difficulty is quite broad. Skill sets needed to solve the problems ranges from basic high school algebra up to that of experienced undergraduate math majors.
Since they can be used in so many different contexts, material about the integers tends to be scattered throughout the literature. The extensive bibliography included in this book is a welcome road map that can be used to track down the desired specifics.
If you are teaching mathematics at any level and looking for problem sets to motivate and challenge the better students, then this book is for you. It is also fun to read if you are an integer aficionado.

Published in Smarandache Notions Journal, reprinted with permission.

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