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 several complex variables, I have
written "Har- monic Analysis of Functions of Several Complex Variables
in the Classical Domains", * and for university students I have written
"Introduction to Higher Mathematics". The present volume had been
written for those who were beginning to engage in research at the
Chinese University of Science and Technology and at the Guangdong
Zhongshan University. Its purpose is none other than to make the
students see the crucial ideas in their simplest manifestations, so that
when they go on to the more complex parts of modem mathematics, they
will not be without guidance. For example, in the first chapter when I
point out that the Poisson kernel is just the Jacobian of some
transformation, I am merely revealing the source of one of the main
tools in my work on harmonic analysis in the classical domains.
