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Secrets in Inequalities - basic inequalities
99,00 RON
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.

Every topic is described through various and numerous examples taken from many sources, especially from math contests around the world, from recent contests and recent books, of from (more or less) specialized sites on the Internet, which makes the book very lively and interesting to read for those who are involved in such activities, students and teachers from all over the world.

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. Află mai mult

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Secrets in Inequalities - advanced inequalities
99,00 RON
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.

Remarkably, the method of using classical inequalities is left behind the first four methods, because we realize that you can flexibly use this method only after you have already developed a larger horizon in the field of inequalities; and this is true: a solid background in a field is usually needed to find the simplest and the most natural solution to a problem. 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. Află mai mult

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Problems for the Mathematical Olympiads
75,00 RON
This book consists of a number of math problems, all of which are meant primarily as preparation for competitions such as the International Mathematical Olympiad. They are therefore of IMO level, and require only elementary notions of math; however, since the International Mathematical Olympiad is perhaps the most difficult exam in elementary mathematics, any participant should have with him a good knowledge and grasp of what he is dealing with. This book is not meant to teach elementary math at an IMO level, but to help a prospective participant train and enhance his understanding of these concepts.

The second this that is important about this book is the solutions. Any good participant at an IMO needs to know not so much theory as tricks to be employed in elementary problems. It is far less useful as far as IMO's are concerned (and far more difficult) for a student to learn multivariable calculus and Lagrange multipliers than to know how to apply geometrical inversion. That is why I emphasize on all these methods, lemmas and propositions in my solutions, and I have often sacrificed succinctness of a proof to the educational value of presenting one of these methods. Află mai mult

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Olympiad Inequalities
311,28 RON
This book is intended for the mathematical olympiad students who want to familiarise themselves with several methods for solving inequalities, providing a collection of problems which were set at the most renown mathematical competitions in the world throughout the past five decades (from 1962 to 2012). The book is divided into two standard chapters, the first consisting of the statement of the problems and the second one presenting their solutions. The problems are ordered chronologically, and consequently the difficulty increases as we approach the more recent years. In this sense, the book highlights the evolution of the set of tools and techniques one requires to be familiarised with for solving olympiad questions and also helps the reader maintain a constant learning pace, according to their individual background. Află mai mult

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Old & New Inequalities volume II
75,00 RON
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. Află mai mult

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Old & New Inequalities
75,00 RON
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. If we have not convinced you, then please take a look at the last problems and hopefully you will agree with us. Află mai mult

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Elementary Combinatorial Geometry
44,21 RON
The aim of this book is to present some ideas, methods and topics in elementary combinatorial geometry. Even if most of the book can be understood without any mathematical background, so it is accessible for 12-14 years old children too, we recommend it to high school students and college students as an introduction to a few topics in combinatorial (or convex) geometry (counting problems, pigeonhole principle, Helly's theorem, Sperner lemma). Our approach is basically an elementary one, but it is useful to know some combinatorial techniques and some basic notions. These notions appear in the subject index, so they can be identified easily.

The main purpose was not to create an exhaustive collection, but to offer a quick and short overview, to present a few properties which have surprising applications also in higher mathematics (the Sperner lemma) and to show some interesting ways of generalizations. So this book wants to be a kind of bridge between elementary problems and university courses. Află mai mult

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Cyclic Inequalities (hardcover)
265,99 RON
This book contains 182 beautiful inequalities, original hints, solutions and methods, some of them being posted in the last ten years by the author and other inventive mathematicians on Art of Problem Solving website (Vo Quoc Ba Can, Pham Kim Hung, Michael Rozenberg, Nguyen Van Quy, Pham Huu Duc, Tran Quoc Anh, Pham Van Thuan, Bin Zhao, Ji Chen). Most inequalities and methods are old and recent own creations of the author.

This book is a great opportunity to see and know many old and new elementary methods for solving mathematical cyclic inequalities. As a rule, the inequalities are increasingly ordered by the number of variables: two, three, four, five, six and n-variables. Many problems are creations of the author himself. The problems are independent and you can open the book somewhere to solve an inequality or only read its solution. If you carefully make a thorough study of the book, then you will find that your skills in solving inequalities are considerably improved.

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Bulgarian Mathematical Competitions 2003-2006
96,00 RON
Bulgaria is a country with long traditions in mathematical competitions. There are numerous regional competitions connected with important dates in Christian calendar or in Bulgarian history. These competitions range in format and difficulty and give opportunity to all students in lower and secondary school to test their abilities in problem solving. Great many of them being fascinated by problem solving in such competitions start working hard in order to acquire new knowledge in mathematics.

The most important and prestigious national competitions in Bulgaria are Winter Mathematical Competitions, Spring Mathematical Competitions and National Olympiad. The organization of these competitions is responsibility of the Ministry of Education and Science, the Union of Bulgarian Mathematicians and the local organizers. The problems for the competitions are prepared by so called Team of extra curricula research - a specialized body of the Union of Bulgarian Mathematicians.

This book contains all problems for grades 8 to 12 from the above mentioned national competitions in the period 2003-2006. The problems from all selection tests for BMO and IMO are also included. Most of the problems are regarded as difficult IMO type problems. The book is intended for undergraduates, high school students and teachers who are interested in olympiad mathematics. Află mai mult

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Balkan Mathematical Olympiads 1984-2006
96,00 RON
The present book is a collection of all problems proposed at Balkan Mathematical Olympiads (BMO), also containing some of the problems discussed during these contests by the jury. It is not only a collection of elementary problems but a page of history - the history of BMO, one of the first reginoal mathematical competition for highschool students.

As it is already accepted, International Mathematical Olympiads (IMO), which was created in 1959, had an important contribution to development of mathematical education of young students all around the world. They extended the area of problems used in mathematical education of young people and also improved their quality. Many mathematicians realized how important is to use some parts of their research problems as elementary educational problems.

All problems are presented with complete solutions. Many problems have several alternative solutions and we also present some extensions. The reader can follow the real increasing of the quality of problems as an illustration of the improvement of mathematical preparation of students. An additional preparatory addendum, containing notions and classical useful results has been added to the end of the book. Află mai mult

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