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七本令人垂涎的不等式英文专著

(2012-07-23 16:33:06)
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七本令人垂涎的不等式英文专著
   The book is a rich source of beautiful, serious and profound mathematics, dealing with classical and new approaches and techniques which help the reader to develop its inequality-solving skills, intuition and creativity.
 Each problem has a hint, and many problems have multiple solutions, almost all of which are, not surprisingly, quite ingenious.
   Almost all inequalities presented in this book require careful thought and analysis, making the book a rich and rewarding source for anyone interested in Olympiad - type problems and in development of algebraic inequalities.
七本令人垂涎的不等式英文专著
  The name of Vasile Cirtoaje, in mathematical terms, 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.
   Also, we must add that the book is full of up to date problems, since the author is an active member of the Mathlinks Site Forum on the Internet.
   Last, but not least, one has to remark the outstanding tenacity and enthusiasm of the author in solving inequalities; definitely, he is a passionate of this realm of elementary mathematics. And this book is neither more, nor less than a work of a master.
七本令人垂涎的不等式英文专著
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.
    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.       
Book title: Inequalities with Beautiful Solutions.
Authors: Vasile Cirtoaje - Võ Quốc Bá Cẩn - Trần Quốc Anh.
Publisher: GIL publishing house.
ISBN: 9786065000148.
Foreword
"Let solutions say the method!" is the way this book is written. 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. The main weapons here are skilful technics of handling with algebraic 
expre ssions    and virtuous applicationsof classical inequalities. 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.
Reading the book, you sometimes are surprising with the way the authors solve the problems. "How simple! Why didn't I think about this?", you ask. If you read this book for fun only, it is OK. But if you want to learn something from this book? Don't be surprised only. You should ask more "Where does the solution come from? Why and how the authors think about the way?". The answer is not simple, and you may not to find it immediately in single solution. Try to gather the answer from several solutions. If you succeed, you are going on the right way, the way that the authors of the book want you to go.
Tran Nam Dung    Ho Chi Minh city University of Science
Preface
"The only way to learn Mathematics is to do Mathematics."  Paul Halmos
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.
七本令人垂涎的不等式英文专著
    This work blends together classic inequality results with brand new problems, some of which devised only a few days ago. What could be special about it when so many inequality problem books have already been written? We strongly believe that even if the topic we plunge into is so general and popular our book is very different. Of course, it is quite easy to say this, so we will give some supporting arguments. 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.
   Some of the problems we chose to present are known, but we have included them here with new solutions which show the diversity of ideas pertaining to inequalities. Anyone will find here a challenge to prove his or her skills.
七本令人垂涎的不等式英文专著
    In the pages that follow, we present a large variety of problems involving such inequalities, questions that became famous in (mathematical) competitions or journals because of their beauty. The most important prerequisite for benefiting from this book is the desire to master the craft of discovery and proof. The formal requirements are quite modest. Anyone who knows basic inequalities such as the ones of Cauchy-Schwarz, Holder, Schur, Chebyshev or Bernoulli is well prepared for almost everything to be found here. The student who is not that experienced will also be exposed in the first part to a wide combination of moderate and easy problems, ideas, techniques, and all the ingredients leading to a good preparation for mathematical contests. Some of the problems we chose to discuss are known, but we have included them here with new solutions which show the diversity of ideas pertaining to inequalities. Nevertheless, the book develops many results which are rarely seen, and even experienced readers are likely to find material that is challenging and informative.
   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.
七本令人垂涎的不等式英文专著
   As you have seen in "Secrets in Inequalities. Volume 1" and also from the title, 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 will find here good modern approaches to prove inequalities: the mixing variables method (in its general and special forms), the method of analyzing squares, the contradiction method, the method of induction (and again, the above mentioned method of using classical inequalities). As you are already used from previous parts, you have lots of beautiful and hard problems to exercise your skills in using all these methods.
七本令人垂涎的不等式英文专著
   It is true that there are very many books on inequalities and you have all the right to be bored and tired of them. But we tell you that this is not the case with this one. Just read the proof of Nesbitt's Inequality in the very beginning of the material, and you will understand exactly what we mean.
  Don't let the problems overwhelm you, though they are quite impressive problems, study applications of the first five basic inequalities mentioned above, plus the Abel formula, symmetric inequalities and the derivative method. Now relax with the AM-GM inequality - the foundational brick of inequalities.
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关于十二本不等式的书_

七本令人垂涎的不等式英文专著

七本令人垂涎的不等式英文专著

七本令人垂涎的不等式英文专著

七本令人垂涎的不等式英文专著

七本令人垂涎的不等式英文专著

七本令人垂涎的不等式英文专著


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

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