The “Handbook of mathematical induction” presents a short history of induction, and then discusses an almost endless string of exercises (actually there are 750 of them) in which statements are to be proved using various forms of induction: identities involving binomial coefficients, Fibonacci numbers, inequalities, elementary divisibility properties, results from graph theory and Ramsey theory. Solutions to these problems take up more than half of the almost 900 pages.
It is a great pity that the author did not dare to include a couple of nontrivial induction proofs: if there is a result showing that induction proofs can be beautiful, then it is van der Waerden’s Theorem; this result is mentioned, but its proof (like that of Schur’s Theorem) is not given. In a similar vein, Gauss’s proof of the quadratic reciprocity law by induction is not even mentioned.
I also find myself unable to accept the author’s way of writing the historical parts: author X says this, author Y says that, and Internet sources suggest that something else is true. It is not the task of the reader to sort these things out. Similarly outraging is a comment such as the following, which refers to Fermat’s Last Theorem: “I forget the reference, but I recall reading that it was proved that the method of descent would not work for \(n > 17\).”
In the preface, the author states that “This book is intended for anyone who enjoys a good proof, and for those who would like to master the technique of mathematical induction”. The reviewer agrees with the second part of this sentence, but would refer readers enjoying a good proof by induction to some of the sources listed in Sect. 1.9. of this book.