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# HM-Brow

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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

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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