116 Algebraic Inequalities from the AwesomeMath Year-Round Program

Andreescu, Titu/ Stanean, Marius

XYZ Press（2018/04発売）

• 製本 Hardcover:ハードカバー版／ページ数 216 p.
• 言語 ENG
• 商品コード 9780996874588
• DDC分類 512.97

Full Description

This book would certainly help Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various competitive levels. The inequalities from each section are ordered increasingly by the number of variables: one, two, three, four, and multi-variables. Each problem has at least one complete solution and many problems have multiple solutions, useful in developing the necessary array of mathematical machinery for competitions.

Contents

1 Some Classical and Some New Inequalities
1.1 Squares Are Nonnegative
1.2 Inequalities Between Means
1.3 The Cauchy-Schwarz Inequality
1.4 Acz ?el's Inequality
1.5 Jensen's Inequality
1.6 General Weighted Power Mean Inequalities
1.7 H ?older's Inequality
1.8 Minkowski's Inequality
1.9 Schur's Inequality
1.10 Chebyshev's Inequality
1.11 The Rearrangement Inequality
1.12 Bernoulli's Inequality
1.13 Karamata's Inequality
1.14 Popoviciu's Inequality
Problems
Inequalities
2.1 Introductory Problems
2.2 Advanced Problems
2.3 Solutions to Introductory Problems
2.4 Solutions to Advanced Problems
Index