Review of "Number Treasury^3: Investigations, Facts and Conjectures about More than 100 Number Families," by Margaret J. Kenney and Stanley J. Bezuszka

Review of

Number Treasury³: Investigations, Facts and Conjectures about More than 100 Number Families, by Margaret J. Kenney and Stanley J. Bezuszka, World Scientific Publishing, Singapore, 2015. 324 pages, $75.00 (hardbound). ISBN 978-9814603683. 

Five out of five stars

This is a book that can serve as a resource for math classes from the later elementary grades all the way through college. It contains a set of descriptions and exercises involving over 100 number families. Some, such as the Fibonacci numbers, are well known. Yet, others are very obscure. For example, the last two are the “tautonymic” and “Lagado” numbers. Great fodder for people that are on the lookout for new number categories to explore.

 With few exceptions, all of the numbers are integers and the exercises require only arithmetic operations on them. If the size of the numbers is kept low, then students in elementary grades can perform the investigations on their own. Many of the exercises involve looking for the presence and absence of patterns in the numbers. Solutions to all of the exercises are given in one of the last sections. Yet, instructors of college classes in number theory can also find material for use in exercises where proofs are expected.

 It is a indeed an extremely rare occasion when a book can be used as a reference through such a broad level of math classes, this one is an existence proof that it can happen. 

This review was originally published on the Mathematical Association of America reviews site. 

http://www.maa.org/press/maa-reviews/number-treasury-3-investigations-facts-and-conjectures-about-more-than-100-number-families