OVER AND
OVER AGAIN
GENGZHE CHANG and
THOMAS W. SEDERBERG
Relations of mathematical objects to each other are expressed by transformations. The repeated application of a transformation over and over again  i.e., its iteration  can lead to solutions of equations, as in Newton's methods for finding roots, or Picard's method for solving differential equations. This book studies a treasure trove of iterations, in number theory, analysis and geometry, and applies them to various problems, many of them taken from international and national Mathematical Olympiad competitions. The eminent mathematician and expositor Philip Davis has said about this book:
