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Introduction to Functional Equations: Theory and problem-solving strategies for mathematical competitions and beyond
Costas Efthimiou, University of Central Florida, Orlando, FL
A co-publication of the AMS and the Mathematical Sciences Research Institute.

MSRI Mathematical Circles Library
2011; 363 pp; softcover
Volume: 6
ISBN-10: 0-8218-5314-7
ISBN-13: 978-0-8218-5314-6
List Price: US$52
Member Price: US$41.60
Order Code: MCL/6
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See also:

A Decade of the Berkeley Math Circle: The American Experience, Volume I - Zvezdelina Stankova and Tom Rike

Moscow Mathematical Olympiads, 1993-1999 - Roman Fedorov, Alexei Belov, Alexander Kovaldzhi and Ivan Yashchenko

Mathematical Circles - Dmitri Fomin, Sergey Genkin and Ilia V Itenberg

Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity.

The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material.

The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques.

In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).


High school teachers and students, undergraduate students interested in functional equations; anyone interested in tips, tricks, and techniques for mathematical competitions and math circles.

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