An introduction to number theory

The book aims to take readers to a deeper understanding of the patterns of thought that have shaped the modern understanding of number theory. It begins with the fundamental theorem of arithmetic and shows how it echoes through much of number theory over the last two hundred years.

One of the main strengths of this book is the narrative. Everest and Ward present number theory as a living subject, showing how various new developments have drawn upon older traditions.

The authors concentrate on the underlying ideas instead of working out the most general and complete version of a result. They select material from both the algebraic and analytic disciplines and sometimes present several different proofs of a single result to show the differing viewpoints and also to capture the imagination of the reader and help them to discover their own tastes. They also cover important topics of significant interest, eg. elliptic functions and the new primality test, which are often omitted from other books at this level.