Overview
- Interesting collection of problems and topics
- Very clear and enjoyable exposition
- Nicely organized to highlight connections between various sections
Part of the book series: Problem Books in Mathematics (PBM)
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Table of contents (8 chapters)
Keywords
About this book
Over the years, a number of books have been written on the theory of functional equations. However, very little has been published which helps readers to solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. The student who encounters a functional equation on a mathematics contest will need to investigate solutions to the equation by finding all solutions, or by showing that all solutions have a particular property. The emphasis here will be on the development of those tools which are most useful in assigning a family of solutions to each functional equation in explicit form.
At the end of each chapter, readers will find a list of problems associated with the material in that chapter. The problems vary greatly, with the easiest problems being accessible to any high school student who has read the chapter carefully. The most difficult problems will be a reasonable challenge to advanced students studying for the International Mathematical Olympiad at the high school level or the William Lowell Putnam Competition for university undergraduates. The book ends with an appendix containing topics that provide a springboard for further investigation of the concepts of limits, infinite series and continuity.
Reviews
From the reviews:
"This book is devoted to functional equations of a special type, namely to those appearing in competitions … . The book contains many solved examples and problems at the end of each chapter. … The book has 130 pages, 5 chapters and an appendix, a Hints/Solutions section, a short bibliography and an index. … The book will be valuable for instructors working with young gifted students in problem solving seminars." (EMS Newsletter, June, 2008)
Editors and Affiliations
About the editor
Bibliographic Information
Book Title: Functional Equations and How to Solve Them
Editors: Christopher G. Small
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-0-387-48901-8
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2007
Hardcover ISBN: 978-0-387-34534-5Published: 14 November 2006
Softcover ISBN: 978-0-387-34539-0Published: 08 August 2007
eBook ISBN: 978-0-387-48901-8Published: 03 April 2007
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XII, 131
Topics: Difference and Functional Equations, Numerical Analysis