**develop its inequality-solving skills**,

**intuition and creativity.**

**in mathematical terms,** The name of Vasile
Cirtoaje ,

**actually equals with inequalities**. Many problems from the book, their majority I would say, are obtained by the author himself.

**If you will carefully read the book, you may find that your skills in solving inequalities were considerably improved.**

**an active member of the Mathlinks**Site Forum on the Internet.

The inequalities appeared in Mathematics a long time ago, have developed and evolved sably in course of time, and even more in our days. As stated by Richard Bellman in 1978, "...

**there are at least three reasons for the study of inequalities: practical, theoretical, and aesthetic;**...

**beauty is in the eyes of the inequality beholder;**...it is generally agreed that certain pieces of music,

**art of mathematics are beautiful; there is an elegance to inequalities that makes them very attractive".**We add two new reasons to the three ones already formulated by Bellman:

**fascination to create a new strong and beautiful inequality,**and happiness to prove such an inequality by an original and nice way. For all these reasons, the inequalities became very popular in advanced and elementary Mathematics, being very useful in level-transfer tests, in university entrance tests, and especially in national and international contests for excellent students. This explains why a large number of people are so concerned with mathematical inequalities.

**form a general overview on the inequality field**, as well as learn the secret of "

**finding way**" to deal with inequalities and other mathematical problems. We look forward to receiving heart-felt comments from the readers to improve the book in the next republication.

**Book title:**Inequalities with Beautiful Solutions.

**Authors:**Vasile Cirtoaje - Võ Quốc Bá Cẩn - Trần Quốc Anh.

**Publisher:**GIL publishing house.

**ISBN:**9786065000148.

**Foreword**

" Readers
don't find here the entire theory, strong theorems as well as
detailed explanation of the methods.
But you
can find here a lot of beautiful problems with beautiful
solutions.Most
of these solutions are simple and elementary, the authors try to
avoid as much as possible of using advanced methods of proving
inequalities.

**Let solutions say the method!**" is the way this book is written.**The main weapons**here
are **skilful technics****of****handling**with
algebraic **expre ssions**

**and**

**virtuous**

**applications**

**of**

**classical**

**It makes the book more romantic rather than academic. And even a student of 8th, 9th grade can read most of the content of this book.**inequalities.

**Reading the book, you sometimes are surprising with the way the authors solve the problems.**

Tran Nam Dung
Ho
Chi Minh city University of Science

"The only way to learn Mathematics is to do Mathematics." Paul
Halmos

...

Nowadays, many clever people find out a lot of new ideas and methods to deal with inequalities, and a lot of "modern style" reference books are published. In our viewpoint, the methods for solving inequalities are very important, but above all,

With more than 200 problems, which are carefully and logically arranged, the book will help the readers form a general overview on the inequality field, as well as learn the secret of "finding way" to deal with inequalities and other mathematical problems. We look forward to receiving heart-felt comments from the readers to improve the book in the next republication.

**Preface**"The only way to learn Mathematics is to do Mathematics."

**The inequalities appeared in Mathematics a long time ago, have developed and evolved stably in course of time, and even more in our days.**As stated by Richard Bellman in 1978, "...**there are at least three reasons for the study of inequalities: practical, theoretical, and aesthetic;****beauty is in the eyes of the inequality beholder**; ...it is generally agreed that certain pieces of music, art or mathematics are beautiful; there is an elegance to inequalities that makes them very attractive". We add two new reasons to the three ones already formulated by Bellman: fascination to create a new strong and beautiful inequality, and happiness to prove such an inequality by an original and nice way. For all these reasons, the inequalities became very popular in advanced and elementary Mathematics, being very useful in level-transfer tests, in university entrance tests, and especially in national and international contests for excellent students. This explains why**a large number of people are so concerned with mathematical inequalities.**

Nowadays, many clever people find out a lot of new ideas and methods to deal with inequalities, and a lot of "modern style" reference books are published. In our viewpoint, the methods for solving inequalities are very important, but above all,

**learning how to think for creating or solving an inequality is even more important.**We wrote the book "Inequalities with beautiful solutions" having in view these things, as well as our desire to make known to the inequality lovers some new inequalities of the authors.With more than 200 problems, which are carefully and logically arranged, the book will help the readers form a general overview on the inequality field, as well as learn the secret of "finding way" to deal with inequalities and other mathematical problems. We look forward to receiving heart-felt comments from the readers to improve the book in the next republication.

**This book contains a large variety of problems involving inequalities, most of them difficult, questions that became famous in competitions because of their beauty and difficulty.**

**Anyone will find here a challenge to prove his or her skills.**

**To solve a problem is a very human undertaking,**and more than a little mystery remains about how we best guide ourselves to the discovery of original solutions. Still, as George Polya and the others have taught us, there are principles of problem solving.

**With practice and good coaching we can all improve our skills.**

**Just like singers, actors, or pianists, we have a path toward a deeper mastery of our craft.**

**this volume is about advanced inequalities.**The main idea which let us start this project was a book about inequalities. There are many, we have known but we want them organized in a different way. This book will be very well understood by those who have already read Volume 1, and more than this it will be the continuation of the nominated book just like the second part of a trip,

**a trip in the world of inequalities.**

**you have lots of beautiful and hard problems to exercise your skills in using all these methods.**

http://gil.ro/publicatii-in-limba-engleza.html?p=1

### 关于十二本不等式的书_

https://leonguyenduy.wordpress.com/2011/06/14/inequality-books/