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Topics in Functional Equations
Titu Andreescu, University of Texas at Dallas, Richardson, TX, Iurie Boreico, Stanford University, CA, and Oleg Mushkarov and Nikolai Nikolov, Bulgarian Academy of Sciences, Sofia, Bulgaria
A publication of XYZ Press.
XYZ Series
2012; 505 pp; hardcover
Volume: 7
ISBN-10: 0-9799269-9-8
ISBN-13: 978-0-9799269-9-0
List Price: US$59.95
Member Price: US$47.96
Order Code: XYZ/7
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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; instead, the methods and techniques utilized in solving these equations play the most important part. For this reason the book takes a highly practical path and includes lots of problems designed to teach students how to familiarize themselves with every strategy employed, as well as how to experiment in combining and manipulating different techniques.

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

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.


Middle and high school students interested in mathematics competition preparation.

Table of Contents

  • Cauchy's equations
  • Generalized Cauchy equations
  • Reducing to Cauchy
  • Substitutions
  • Symmetrization and additional variables
  • Iterations and recurrence relations
  • Constructive problems
  • The D'Alembert equation
  • The Aczél-Gołá-Schinzel equation
  • Arithmetic functional equations
  • Binary and other bases
  • Geometric functional equations
  • Approximating by linear functions
  • Extremal element method
  • Fixed points
  • Functional equations for polynomials
  • Functional inequalities
  • Miscellaneous problems
  • Hints and solutions
  • Notation and abbreviations
  • Bibliography
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