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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 Mathematical Sciences Research Institute
Introduction to Functional Equations
Softcover ISBN:  978-0-8218-5314-6
Product Code:  MCL/6
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Sale Price: $33.00
eBook ISBN:  978-1-4704-1617-1
Product Code:  MCL/6.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $40.00
Sale Price: $30.00
Softcover ISBN:  978-0-8218-5314-6
eBook: ISBN:  978-1-4704-1617-1
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
Sale Price: $63.00 $48.00
Introduction to Functional Equations
Click above image for expanded view
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 Mathematical Sciences Research Institute
Softcover ISBN:  978-0-8218-5314-6
Product Code:  MCL/6
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Sale Price: $33.00
eBook ISBN:  978-1-4704-1617-1
Product Code:  MCL/6.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $40.00
Sale Price: $30.00
Softcover ISBN:  978-0-8218-5314-6
eBook ISBN:  978-1-4704-1617-1
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
Sale Price: $63.00 $48.00
  • Book Details
     
     
    MSRI Mathematical Circles Library
    Volume: 62011; 363 pp
    MSC: 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 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).

    Readership

    High 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 62011; 363 pp
MSC: 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 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).

Readership

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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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