The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at undergraduate mathematics education, particularly in the teaching and learning of the history of mathematics and other undergraduate topics. In this monograph, the chapters cover topics such as the development of Calculus through the actuarial sciences and map making, logarithms, the people and practices behind real world mathematics, and fruitful ways in which the history of mathematics informs mathematics education. The book is meant to serve as a source of enrichment for undergraduate mathematics majors and for mathematics education courses aimed at teachers.

John Napier published his treatise on the discovery of logarithms in 1614. It was written in Latin, the scholarly language of his day, under the title Mirifici Logarithmorum Canonis Descriptio. The importance of the work was quickly perceived and an English language translation by Edward Wright followed two years later, with the title A Description of the Admirable Table of Logarithmes. A further English edition followed in 1618. It is said that this book freed the world from a logjam of calculations. John Napier spent more than twenty years working alone on his system of logarithms, during a time when the multiplication and division of large numbers, as well as the finding of square roots, was considered to be extremely difficult. Because of his discovery of logarithms, these tedious mathematical operations could be replaced by the much easier processes of simple addition, subtraction and division by two. Never again would astronomers, architects, merchants and navigators become bogged down with calculations that were simply too difficult or time consuming to carry out. Seeking a name for his discovery, Napier turned to Greek, coining the word Logarithm from logos (Greek for ratio or reckoning) and arithmos (Greek for number). Johannes Kepler, the imperial mathematician and astronomer at Prague, was one of the first to realize the enormous importance of Naperian logarithms. Initially indifferent, his attitude was quickly changed to one of great enthusiasm when he saw that tables of logarithms could considerably ease the burden of difficult astronomical calculations. The French mathematician and astronomer Pierre Simon Laplace said that logarithms, '...by shortening the labours, doubled the life of the astronomer.' At a congress held in Edinburgh to celebrate the 300th anniversary of the publication of this book, it was remarked that '...no previous work had led up to it; nothing had foreshadowed it or heralded its arrival. It stands isolated, breaking upon human thought abruptly, without borrowing from the works of other intellects or following known lines of mathematical thought.' Thus has posterity judged the worth of John Napier, Baron of Merchiston, and his logarithms.