The prerequisites for this book are the "standard" first-semester course
in number theory (with incidental elementary algebra) and elementary
calculus. There is no lack of suitable texts for these prerequisites (for
example, An Introduction to the Theory of Numbers, by I. Niven and H. S.
Zuckerman, John Wiley and Sons, 1960, can be cited as a book that intro-
duces the necessary algebra as part of number theory). Usually, very little
else can be managed in that first semester beyond the transition from
improvised combinatorial amusements of antiquity to the coherently
organized background for quadratic reciprocity, which was achieved in
the eighteenth century.
The present text constitutes slightly more than enough for a second-
semester course, carrying the student on to the twentieth century by
motivating some heroic nineteenth-century developments in algebra and
analysis. The relation of this textbook to the great treatises will necessarily
be like that of a historical novel to chronicles. We hope that once the
student knows what to seek he will find "chronicles" to be as exciting as a
"historical novel."