Bất Đẳng Thức - Hojoo Lee

Bất Đẳng Thức - Hojoo Lee

Introduction

Inequalities are useful in all fields of Mathematics. The purpose in this book is to present standard techniques in the theory of inequalities. The readers will meet classical theorems including Schur’s inequality, Muirhead’s theorem, the Cauchy-Schwartz inequality, AM-GM inequality, and Ho ̈lder’s theorem, etc. There are many problems from Mathematical olympiads and competitions. The book is available at

http://my.netian.com/∼ideahitme/eng.html

I wish to express my appreciation to Stanley Rabinowitz who kindly sent me his paper On The Computer Solution of Symmetric Homogeneous Triangle Inequalities. This is an unfinished manuscript. I would greatly appreciate hearing about any errors in the book, even minor ones. You can send all comments to the author at hojoolee@korea.com.

To Students

The given techniques in this book are just the tip of the inequalities iceberg. What young students read this book should be aware of is that they should find their own creative methods to attack problems. It’s impossible to present all techniques in a small book. I don’t even claim that the methods in this book are mathematically beautiful. For instance, although Muirhead’s theorem and Schur’s theorem which can be found at chapter 3 are extremely powerful to attack homogeneous symmetric polynomial inequalities, it’s not a good idea for beginners to learn how to apply them to problems. (Why?) However, after mastering homogenization method using Muirhead’s theorem and Schur’s theorem, you can have a more broad mind in the theory of inequalities. That’s why I include the methods in this book. Have fun!

Bất Đẳng Thức - Hojoo Lee

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