Preface
Acknowledgements
Abbreviations and Notations
I The basic Inequalities
1 AM-GM nequality
1.1 AM-GM Inequality and Applications
1.2 The Cauchy Reverse Technique
2 Cauchy-Schwarz and Holder inequalities
2.1 Cauchy-Schwarz inequality and Applications
2.2 Holder Inequality
3 Chebyshev Inequality
3.1 Chebyshev Inequality and Applications
3.2 The Chebyshev Associate Technique
4 Inequalities with Convex Functions
4.1 Convex functions and Jensen inequality
4.2 Convex Functions and Inequalities with Variables Restricted to an Interval
5 Abel Formula and Rearrangement Inequality
5.1 Abel formula
5.2 Rearrangement Inequality
6 The Method of Balanced Coefficients
6.1 Balancing coefficients by AM-GM inequality
6.2 Balancing coefficients by Cauchy-Schwarz and Holder inequalities
7 Derivative and Applications
7.1 Derivative of one-variable functions
7.2 Derivative of n-Variable Functions
8 A note on symmetric inequalities
8.1 Getting started
8.2 Primary symmetric polynomials
8.3 Normalization skill
8.4 Symmetric separation
9 Problems and Solutions
Glossary
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