Preface -- The purpose of this book is three-fold -- namely, to show: (1) how wide a variety of problems in mathematics can be computed quickly; (2) how these problems can be computed mentally with a minimum of pencil-and-paper work; and (3) how, by means of one checking method or another, the possibility of errors in computation can be virtually eliminated. The third purpose is no less important than the others for, as most people know, some errors can be very costly. And unhurried study of this book should make it possible for the average reader to acquire the ability to compute the answers to thousands of different problems without making a single mistake. As a first step, note particularly "How to Read This Book" on page xix.