for instance in chemistry, engineering, biology, and the arts. This book will
introduce the reader to many of the above fields, giving some idea of the
riches that exist. Many riches remain unmentioned, but the subject is too
large to encompass in a single volume.
The title of the Short Course and of this book are a salute to the famous
phrase of Wigner, who marveled at "the unreasonable effectiveness of mathe-
matics" in the real world. Until recently, few people would have applied this
phrase to number theory, but the authors and I hope that this volume will
help to further the ferment that exists in the applications of number theory.
Stefan A. Burr