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**ENGLISH BOOKS**

** 360 Problems for Mathematical Contests**

**Authors:** Titu Andreescu, Dorin Andrica

**Price:** 25 euro

**Disponibility**: sold out

**Format:** hardcover

**About book: ** This book is intended to help students preparing for all rounds of Mathematical Olympiads or any other significant mathematics contest. Teachers will also find this work useful in training young talented students. Our experience as contestants was a great asset in preparing this book. To this we added our vast personal experience from the other side of the “barricade”, as creators of problems and members of numerous contest committees.

The book is organized in six chapters: algebra, number theory, geometry, trigonometry, analysis and comprehensive problems. In addition, other fields of mathematics found their place in this book, for example, combinatorial problems can be found in the last chapter, and problems involving complex numbers are included in the trigonometry section. Moreover, in all chapters of this book the serious reader can find numerous challenging inequality problems. All featured problems are interesting, with an increased level of difficulty; some of them are real gems that will give great satisfaction to any math lover attempting to solve or even extend them.

** Algebraic Inequalities**

**Author:** Vasile Cîrtoaje

**Price:** 40 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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. However, one needs not to read every single page of this material; the chapters are independent and you may even open the book somewhere, arbitrarily, and try to solve an inequality or find its solution from the book. 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.

** Algebraic Inequalities**

**Author:** Vasile Cîrtoaje

**Price:** 69.95 euro

**Disponibility**: available

**Format:** hardcover

**About book: ** 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.

As a result, it is suitable for a wide variety of audiences; high school students and teachers, college and university students, mathematics educators and mathematicians will find something of interest here. 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. Some long problems and methods could be used in a classroom for advanced high school students as group projects.

The difficulty level of the problems makes the book most suitable for the bright high school or undergraduate mathematics students.

** An Introduction to Diophantine Equations**

**Authors:** Titu Andreescu, Dorin Andrica

**Price:** 25 euro

**Disponibility**: available

**Format:** hardcover

**About book: ** As one can see from the title, this book is an introduction to the study of diophantine equations. The material is organized in two parts. The first part contains three chapters. Chapter 1 introduces the reader to the main elementary methods in solving diophantine equations such as decomposition, modular arithmetic, mathematical induction, Fermat’s infinite descent. Chapter 2 presents some classical diophantine equations, including linear, pythagorean and some higher degree equations. Chapter 3 focuses on Pell’s-type equations, serving again as an introduction to this special class of quadratic diophantine equations. Throughout Part I, each of the sections contains representative examples that illustrate the theoretical part.

Part II contains the complete solutions to all exercises featured in Part I. For several problems multiple solutions are included, along with useful comments and remarks. Many of the selected exercises and problems are original or have been give original solutions.

The book is intended for undergraduates, high school students and their teachers, mathematical contest (including Olympiad and Putnam) participants, as well as any person interested in essential mathematics.

** Balkan Mathematical Olympiads 1984-2006**

**Authors:** M. Becheanu, B. Enescu

**Price:** 23 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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 regional 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.

** Bulgarian Mathematical Competitions 2003-2006**

**Authors:** Boyvalencov, Mushkarov, Kolev, Nikolov

**Price:** 23 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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.

** Cyclic Inequalities**

**Authors:** Vasile Cîrtoaje

**Price:** 59.95 euro

**Disponibility**: available

**Format:** hardcover

**About book: ** 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.

**Elementary combinatorial geometry**

**Authors:** Szilard Andras

**Price:** 10 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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.

**Inequalities with Beautiful Solutions**

**Authors:** Vo Quoc Ba Can, Tran Quoc Anh, Vasile Cîrtoaje

**Price:** 23 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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.

**Old and New Inequalities**

**Authors:** Titu Andreescu, Vasile Cîrtoaje, Gabriel Dospinescu, Mircea Lascu

**Price:** 18 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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.

**Old and New Inequalities – volume 2**

**Authors:** Vo Quoc Ba Can, Cosmin Pohoaţǎ

**Price:** 18 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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.

**Olympiad Inequalities**

**Authors:** Xiong Bin, Iurie Boreico, Aleksandar Bulj, Vo Quoc Ba Can, Mircea Lascu

**Price:** 69.95 euro

**Disponibility**: available

**Format:** hardcover

**About book: ** 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.

**Problems for the Mathematical Olympiads**

**Authors:** Andrei Neguț

**Price:** 18 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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.

**Secrets in Inequalities – basic inequalities**

**Authors:** Phan Kim Hung

**Price:** 23 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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.

**Secrets in Inequalities – advanced inequalities**

**Authors:** Phan Kim Hung

**Price:** 23 euro

**Disponibility**: available

**Format:** paperback

**About book: ** 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.

**An Introduction to Inequalities**

**Authors:** Xiong Bin, Iurie Boreico, Vo Quoc Ba Can, Vasile Cîrtoaje, Mircea Lascu

**Price:** 59.95 euro

**Disponibility**: available

**Format:** hardcover

**About book: **Xiong Bin, Iurie Boreico, Vo Quoc Ba Can, Vasile Cirtoaje, Mircea Lascu

This book gathers these methods and tricks into a compact guide. It starts from the very basics, but covers almost all elementary methods known today (aside from a few very advanced ones). At higher levels of competition, good contestants are pretty much expected to know every technique listed here – meaning that there do appear inequalities that fit every presented category. Conversely, the vast majority of inequalities that do appear may be assigned to one of the sections of the book. That being said, the present work is not meant as a textbook, or a comprehensive training material. It is very compact and fast-paced. There are a few examples for every subject, but to fully assimilate said subject, one needs to look elsewhere for more practice problems. The reader who truly starts ”from scratch” may quickly find him/herself overwhelmed by the pace and the increasing difficulty of the content; may this entirely normal impression not deter the student from pushing through! Rather, the book is meant as crash course introduction to all facets of the subject, and as a reference guide. The readerwill get acquainted with all themethods, but must practice each tool on his/her own, using other sources. The one truth about competitive math is that solving problems is the most important part of learning. This holds just as true for inequalities and fortunately there are a lot of them out there to be used for training purposes.