Owing to the developments and applications of computer science, ma thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point. It'or example, from the seventeenth century till now, a great deal of effort was made in developing methods for approximating single integrals and there were only a few works on multiple quadrature until the 1950's. But in the past twenty years, a number of new methods have been devised...

to Number Theory Translated from the Chinese by Peter Shiu With 14 Figures Springer-Verlag Berlin Heidelberg New York 1982 HuaLooKeng Institute of Mathematics Academia Sinica Beijing The People's Republic of China PeterShlu Department of Mathematics University of Technology Loughborough Leicestershire LE 11 3 TU United Kingdom ISBN -13 : 978-3-642-68132-5 e-ISBN -13 : 978-3-642-68130-1 DOl: 10.1007/978-3-642-68130-1 Library of Congress Cataloging in Publication Data. Hua, Loo-Keng, 1910 -. Introduc- tion to number theory. Translation of: Shu lun tao yin. Bibliography: p. Includes index. 1....

It is with great pleasure that I am writing the preface for my little book, "Starting with the Unit Circle," in the office of Springer Verlag in Heidel berg. This is symbolic of the fact that I have once again joined in the main stream of scientific exchange between East and West. Since the establishment of the People's Republic of China, I have written "An Introduction to Number Theory" for the young people studying Number Theory: for the young people studying algebra, Prof. Wan Zhe-xian (Wan Che-hsien) and I have written "Classical Groups"; for those studying the theory of functions of...