Preface
Acknowledgements
Abbreviations and Notations
1 Analyzing Squares Method
1.1 Getting Started
1.2 The Standard Representation
1.3 Symmetric Inequalities and SOS Method
1.4 Cyclic Inequalities and SOS Method
1.5 The Exercises
2 Mixing Variable Method
2.1 Getting Started
2.2 Typical Applications
2.3 Stronger Mixing Variable Method
2.4 Mixing All Variables Method
2.5 Reference: The Global Derivative
2.6 The Exercises
3 Contradiction Method
3.1 Getting Started
3.2 Step by Step
3.3 Typical Applications
3.4 The Exercises
4 General Induction Method
4.1 Getting Started
4.2 Step by Step
4.3 Typical Applications
4.4 The Exercises
5 Method of using Classical Inequalities
5.1 Problem series A. Ingenious Applications
5.2 Problem series B. Clever Separations
5.3 Problem series C. Incredible Identities
5.4 Problem series D. The Non-homogeneous
6 Collected Articles on Inequalities
7 The Readers' Contributions
Contributions 1. Undefined Mixing Variable Method
7.1 Introduction
7.2 Starting with a simple idea
7.3 The Undefined Mixing Variable method
7.4 Applications for Inequalities of Degree 3
Contributions 2. SOS-Schur Method
7.5 Introduction
7.6 The SOS-Schur Representation
7.7 Applications of SOS-Schur Method
7.8 A special technique
7.9 Another Examples
Glossary
Bibliography
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