What is a good way to teach children about math? Is it to have them memorize facts, say the multiplication table, and in that manner experience mathematics? Or, should one introduce mathematics in some other way so that the concepts and facts flow from the students’ experience? Y. E. O. Adrian's answer is to show children series upon series with their respective closed forms and expect that the child will appreciate them. His book is based on the premise that children, and his examples are his grandchildren aged 4 and 6, can grasp infinite sums at a young age.
This book is a compilation of various series with the aim of introducing the reader (or should I say child-reader?) to interesting sums. We see Euler's series and Wallis equations, for sums with π as a factor and then series with sums involving e, the base of the natural logarithm. After meeting π and e, we are then shown over twenty different ways to write different, albeit related, series that all sum to one.
The last part of the book is a compilation of proofs for the summations in the first part divided into "Easy Proofs," "Less Easy Proofs," and "Not-So-Easy Proofs." None of these are particularly difficult at all, but for a child, well, they would be challenging. Still, I find it hard to believe these proofs would appeal to a child at all.
Adrian's book left me empty, without any new appreciation for any of the many series he shows and certainly with little added appreciation of the mathematics. I did not see how showing series upon series would be interesting in and of itself; certainly not for me. I don't think most adults would enjoy this book. And, lest you think I'm being harsh, the book is not a reference but is intended to be read for pleasure. Unfortunately, I didn't find much pleasure in it.
David S. Mazel received his doctorate from the Georgia Institute of Technology in electrical engineering and is a practicing engineer in Washington, DC. His research interests are in the dynamics of billiards, signal processing, and cellular automata