By J Quaintance and H W Gould
World Scientific
Written by Henry Gould’s assistant Jocelyn Quaintance, this book is the result of the deep work and personal relationship between the great mathematician and the author. They met when Quaintance had recently graduated with a PhD, and was looking for a career in research and an advisor who could guide him. He had the luck to collaborate with Gould, who showed him his manuscripts: several handwritten volumes on combinatorial identities. Quaintance offered to edit a text collecting together all of that material, which led to the publication of this book.
The first eight chapters introduce readers to the special techniques that Gould used in proving his binomial identities. This first part is easily accessible to people who have taken basic courses in calculus and discrete mathematics. The second half of the book applies the techniques from the first part, and is particularly relevant for mathematics researchers. It focuses on the connection between various classes of Stirling numbers, and between them and Bernoulli numbers.
Some of the demonstrations presented in the volume represent the only systematic record of Gould’s results. As such, this book is a unique work that could appeal to a wide audience: from graduate students to specialists in enumerative combinatorics, to enthusiasts of Gould’s work.
