Items related to Topics in Functional Equations
Synopsis
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 - rather, the methods and techniques utilized in solving these equations play the most important part. For this reason the book has taken a highly practical path, including lots of problems designed to teach students how to familiarize themselves with every strategy employed, as well as 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 they are solved. It explains the reasoning behind each method, and offers advice on how to invent meaningful solutions.
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About the Author
Dr. Titu Andreescu is an associate professor of mathematics in the Science and Mathematics Education department at the University of Texas at Dallas (UTD). Much of his career has been devoted to competition math, an efficient medium for teaching creative problem-solving for a wide-range of math topics. With over 30 years of experience teaching, coaching, and mentoring the brightest mathematical minds of our age, Dr. Andreescu's books are essential for every math enthusiast's library. Here are just a few highlights from his distinguished career: -Authored, co-authored, and edited more than 40 math books and publications -Head coach and leader of the USA International Mathematical Olympiad (IMO) for 8 years -Director of the Mathematical Association of American (MAA) American Mathematics -Competitions for 5 years -Has contributed hundreds of problems to various math competitions including up to and including the IMO -Co-founder of the Purple Comet! Math Meet, the first international team based math competition -Founder and Director of AwesomeMath, an organization that provides enriching experiences in mathematics to intellectually curious learners
Review
You come across functional equations in math contests, but it has been difficult to find a book that gives you the strategies, techniques, and approaches for solving them. To have a resource with so many problems on this important topic, full of engaging and interesting solutions has been a real find! --David Cordeiro
This book is also another amazing work of Prof. Andreescu and his colleagues. There are many very nice and original results from the authors of the book and from others. In spite of the book's title "Topics in Functional Equations", there are much more, and also one chapter on Functional Inequalities. The book's contents are: Introduction 1. Cauchy's Equations 2. Generalized Cauchy's Equations 3. Reducing to Cauchy 4. Substitutions 5. Symmetrization and Additional Variables 6. Iterations and Recurrence Relations 7. Constructive Problems 8. D'Alembert Equation 9. The Aczél-Go b-Schinzel Equation 10. Arithmetic Functional Equations 11. Binary and Other Bases 12. Geometric Functional Equations 13. Approximating by Linear Functions 14. Extremal Element Method 15. Fixed Points 16. Functional Equations for Polynomials 17. Functional Inequalities 18. Miscellaneous Problems 19. Hints and solutions 20. Notation and Abbreviations Bibliography I do highly recommend this book and all other invaluable books of Prof. Andreescu. --H. A. Shah Ali
In the recent years a few new books appeared on the subject of functional equations. This book is a unique in style - it is aimed mostly for mathematics Olympiad contestants. This book consists of 20 chapters: 1. Cauchy's equations 2. Generalized Cauchy's equations 3. Reducting to Cauchy 4. Substitutions 5. Symmetrization and Additional Variables 6. Iterations and Recurrence Relations 7. Constructive Problems 8. D'Alembert Equation 9. The Aczel-Golab-Schinzel Equation 10. Arithmetic Functional Equations 11. Binary and Other Bases 12. Geometric Functional Equations 13. Approximating by Linear Functions 14. Extermal Element Method 15. Fixed Points 16. Functional Equations for Polynomials 17. Functional inequalities 18. Miscellaneous Problems 19. Hints and Solutions 20. Notions and Abbreviations Most of these chapters are self-contained so a reader can just choose his own. The structure of each chapter is similar - 1. Short introduction to the subject, including all the new theorems that might be used in the rest of the chapter. 2. Examples - ~10 carefuly chosen solved problems on he subject. 3. Practice problem. Unsolved problems which are fully solved on chapter 19. The source of most of the problem is past mathematics Olympiads from various places in the world but not only, the text includes also classical and historically important problems. The writing style is very clear and you mostly got the feeling the writer is talking to you. Many of the topics covered in this book wasn't covered anywhere else. I would suggest anyone who's interested in functional equations to have this great book. --Yair Mulian
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- PublisherAmer Mathematical Society
- Publication date2012
- ISBN 10 0979926998
- ISBN 13 9780979926990
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages505
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