Methods And Techniques For Proving Inequalities: In Mathematical Olympiad And Competitions

by Yong Su, Bin Xiong

Overview

In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year.The authors are coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book explains many basic techniques for proving inequalities such as direct comparison, method of magnifying and reducing, substitution method, construction method, and so on.

Product Details

ISBN-13:	9789814696456
Publisher:	World Scientific / East China Normal Univ Press, China
Publication date:	12/03/2015
Series:	Mathematical Olympiad Series , #11
Pages:	228
Product dimensions:	5.90(w) x 8.90(h) x 0.60(d)

Table of Contents

Chapter 1 Basic Techniques for Proving Inequalities 1

Chapter 2 Identical Transformation of the Sum 25

Chapter 3 Substitution Method 41

Chapter 4 Proof by Contradiction 55

Chapter 5 Construction Method 69

Chapter 6 Local Inequality 87

Chapter 7 Mathematical Induction and Inequality 98

Chapter 8 Inequality and Extremum for Multi-Variable Function 116

Chapter 9 Special Techniques for Proving Inequalities 130

Detailed Solutions to Exercises 146