Functional Equations And How To Solve Them

Over the years a number of books have been written on the theory of functionalequations. However very little has been published which helps readers to solvefunc... » 

Over the years a number of books have been written on the theory of functionalequations. However very little has been published which helps readers to solvefunctional equations in mathematics competitions and mathematical problemsolving. This book fills that gap. The student who encounters a functionalequation on a mathematics contest will need to investigate solutions to theequation by finding all solutions or by showing that all solutions have aparticular property. The emphasis here will be on the development of thosetools which are most useful in assigning a family of solutions to eachfunctional equation in explicit form. At the end of each chapter readers willfind a list of problems associated with the material in that chapter. Theproblems vary greatly with the easiest problems being accessible to any highschool student who has read the chapter carefully. The most difficult problemswill be a reasonable challenge to advanced students studying for theInternational Mathematical Olympiad at the high school level or the WilliamLowell Putnam Competition for university undergraduates. The book ends with anappendix containing topics that provide a springboard for further investigationof the concepts of limits infinite series and continuity. TOCPreface. Anhistorical introduction. Functional equations with two variables. Functionalequations with one variable. Miscellaneous methods for functional equations.Some closing heuristics. Appendix Hamel bases. Hints and partial solutionsto problems. Bibliography. Index. «