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A Festival of Mathematics: A Source Book

Alice Peters and Mark Saul
AMS/Mathematical Sciences Research Institute
Publication Date: 
Number of Pages: 
Problem Book
[Reviewed by
Steve Benson
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There are a number of books available with intriguing problems for students (and others) to puzzle over, but you will want to make room in your bookshelf for one more. This collection, the 28th volume from MSRI’s Mathematical Circles Library, provides a unique set of resources for use in mathematical circles and similar formal and informal settings. The activities, chosen from those used in Julia Robinson Mathematics Festivals (founded in 2007 by Nancy Blackman and inspired by the Saint Mary’s College contests of the 1970s) have been carefully curated to optimize involvement (low threshold/high ceiling with ample opportunities for “tweaks” motivating new investigations). 
The first section consists of 10 “activity guides” organized around a different problem/puzzle type and provide helpful suggestions and teaching notes designed to promote student engagement. Each of these guides start with an intriguing puzzle, game, or problem, easing participants into more sophisticated and involved scenarios emphasizing progress over completion, encouraging participants to follow their own conjectures and includes dives into mathematical concepts which might arise during these investigations. The activity guides each conclude with a Notes section, providing a plethora of resources promoting further investigation, historical notes, and helpful hints for organizing local mathematical festivals. 
Part 2 of the book (”Handouts”) consists of careful problem statements and extensions of the activities which were investigated in full in Part 1. They can be copied or transcribed into handouts for use in classes, study groups, and circles. 
The activities featured in this book – from well-known favorites like Magic Squares and Nim to tilings, prisoner puzzles, graphs, and expressing numbers as special sums – are presented in an incredibly engaging way. I had to keep reminding myself that my job was to review this volume rather than to work on every problem myself. My advice is to get this book then go volunteer at a Julia Robinson Mathematics Festival near you, or maybe start one yourself! 
Steve Benson is a Professor of Mathematics at Lesley University and co- Director of the Master of Science for Teachers program at the University of New Hampshire. He received his Ph.D. in Mathematics from the University of Illinois under the supervision of Dr. Leon R. McCulloh.