Softcover ISBN:  9780821853146 
Product Code:  MCL/6 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470416171 
Product Code:  MCL/6.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Softcover ISBN:  9780821853146 
eBook: ISBN:  9781470416171 
Product Code:  MCL/6.B 
List Price:  $105.00 $80.00 
MAA Member Price:  $94.50 $72.00 
AMS Member Price:  $84.00 $64.00 
Softcover ISBN:  9780821853146 
Product Code:  MCL/6 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470416171 
Product Code:  MCL/6.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Softcover ISBN:  9780821853146 
eBook ISBN:  9781470416171 
Product Code:  MCL/6.B 
List Price:  $105.00 $80.00 
MAA Member Price:  $94.50 $72.00 
AMS Member Price:  $84.00 $64.00 

Book DetailsMSRI Mathematical Circles LibraryVolume: 6; 2011; 363 ppMSC: Primary 39; 00; 26
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 problemsolving 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 copublished with the Mathematical Sciences Research Institute (MSRI).
ReadershipHigh school teachers and students, undergraduate students interested in functional equations; anyone interested in tips, tricks, and techniques for mathematical competitions and math circles.

Table of Contents

Chapters

Title page

Contents

Introduction

Acknolwedgments

Background

Functions

Basic equations

A primer on functional relations

Equations for arithmetic functions

Equations reducing to algebraic systems

Cauchy’s equations

Cauchy’s $\mathbb {NQR}$ method

Equations for trigonometric functions

Generalizations

The Pexider, Vincze and Wilson equations

Vector and matrix variables

Systems of equations

Changing the rules

Less than continuity

More than continuity

Functional equations for polynomials

Conditional functional equations

Functional inequalities

Equations with no parameters

Iterations

Solving by invariants and linearization

More on fixed points

Getting additional experience

Miscellaneous problems

Additional problems

Auxiliary material

Acronyms and abbreviations

Set conventions

Named equations

Bibliography

Index


Additional Material

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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 problemsolving 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 copublished 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.

Chapters

Title page

Contents

Introduction

Acknolwedgments

Background

Functions

Basic equations

A primer on functional relations

Equations for arithmetic functions

Equations reducing to algebraic systems

Cauchy’s equations

Cauchy’s $\mathbb {NQR}$ method

Equations for trigonometric functions

Generalizations

The Pexider, Vincze and Wilson equations

Vector and matrix variables

Systems of equations

Changing the rules

Less than continuity

More than continuity

Functional equations for polynomials

Conditional functional equations

Functional inequalities

Equations with no parameters

Iterations

Solving by invariants and linearization

More on fixed points

Getting additional experience

Miscellaneous problems

Additional problems

Auxiliary material

Acronyms and abbreviations

Set conventions

Named equations

Bibliography

Index