REPRESANTATION OF INTEGERS AS SUMS OF SQUARES

This book is unique in its presentation; it makes the arithmetic theory of quadratic forms accessible to a wide audience by considering only a simple class of forms – the diagonal forms, specifically sums of squares. The study of sums of squares has a long history, and it is distinguished by the diversity of the method which have been applied to it. The first several chapters can be read easily by an undergraduate, whereas the later chapters require some analysis which should be known to a beginning graduate student. These chapters may also be of interest to mathematicians in other fields. Each chapter is supplemented by a large number of exercises, ranging from elementary to quite advanced. The book also contains an extensive bibliography.