## Titu Andreescu and Mark SaulThis book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not “linear”. The central topic of inequalities is linked to others in mathematics. Often these topics relate to much more than algebraic inequalities. |

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### Contents

Chapter 0 Some Introductory Problems | 1 |

Chapter 1 Squares Are Never Negative | 7 |

Chapter 2 The ArithmeticGeometric Mean Inequality Part I | 21 |

Chapter 3 The ArithmeticGeometric Mean Inequality Part II | 33 |

Chapter 4 The Harmonic Mean | 43 |

Chapter 5 Symmetry in Algebra Part I | 57 |

Chapter 6 Symmetry in Algebra Part II | 69 |

Chapter 7 Symmetry in Algebra Part III | 85 |

Chapter 8 The Rearrangement Inequality | 91 |

Chapter 9 The CauchySchwarz Inequality | 107 |

Back Cover | 126 |