Over the years, a number of books have been written on the theory
of functional equations. However, very little has been published
which helps readers to solve functional equations in mathematics
competitions and mathematical problem solving. This book fills that
gap. The student who encounters a functional equation on a
mathematics contest will need to investigate solutions to the
equation by finding all solutions, or by showing that all solutions
have a particular property. The emphasis here will be on the
development of those tools which are most useful in assigning a
family of solutions to each functional equation in explicit form.
At the end of each chapter, readers will find a list of problems
associated with the material in that chapter. The problems vary
greatly, with the easiest problems being accessible to any high
school student who has read the chapter carefully. The most
difficult problems will be a reasonable challenge to advanced
students studying for the International Mathematical Olympiad at
the high school level or the William Lowell Putnam Competition for
university undergraduates. The book ends with an appendix
containing topics that provide a springboard for further
investigation of the concepts of limits, infinite series and
continuity.
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