Anyone involved in math Olympiads, either in the U.S. or across the world, needs to have a firm grounding in functional equations as they begin to appear more frequently in these contests. This book is a systematic and comprehensive approach to functional equations as a whole. Unlike in other branches of competitive mathematics, there is very little theory: The methods and techniques utilized in solving these equations play the most important part. For this reason, the book has taken a highly practical path, including lots of problems designed to teach students how to familiarize themselves with every strategy employed, as well as to experiment in combining and manipulating different techniques.

This book contains all the important functional equations given at contests in recent years, classified by the way they are solved. It explains the reasoning behind each method and offers advice on how to invent meaningful solutions.