This book is a unique work which provides an in-depth exploration
into the mathematical expertise, philosophy, and knowledge of H W
Gould. It is written in a style that is accessible to the reader
with basic mathematical knowledge, and yet contains material that
will be of interest to the specialist in enumerative combinatorics.
This book begins with exposition on the combinatorial and algebraic
techniques that Professor Gould uses for proving binomial
identities. These techniques are then applied to develop formulas
which relate Stirling numbers of the second kind to Stirling
numbers of the first kind. Professor Gould's techniques also
provide connections between both types of Stirling numbers and
Bernoulli numbers. Professor Gould believes his research success
comes from his intuition on how to discover combinatorial
identities.This book will appeal to a wide audience and may be used
either as lecture notes for a beginning graduate level
combinatorics class, or as a research supplement for the specialist
in enumerative combinatorics.
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