Efthimiou Costas
Introduction to functional equations : theory and problem-solving strategies for mathematical competitions and beyond - Rhode Island: American Mathematical Society, [c2011] - 363 p - MSRI Mathematical Circles Library Vol. 6 .
I. Background
II. Basic equations
III. Generalizations
IV. Changing the rules
V. Equations with no parameters
VI. Getting additional experience
VII. Auxiliary material
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. --- summary provided by publisher
9780821853146
Mathematics
QA431
Introduction to functional equations : theory and problem-solving strategies for mathematical competitions and beyond - Rhode Island: American Mathematical Society, [c2011] - 363 p - MSRI Mathematical Circles Library Vol. 6 .
I. Background
II. Basic equations
III. Generalizations
IV. Changing the rules
V. Equations with no parameters
VI. Getting additional experience
VII. Auxiliary material
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. --- summary provided by publisher
9780821853146
Mathematics
QA431