This book presents classical inequalities and specific inequalities which are particularly useful for attacking and solving optimization problems. Most of the examples, exercises and problems that appear in the book originate from Mathematical Olympiad contests around the world. The material is divided into four chapters. In Chapter 1 algebraic inequalities are presented, starting with the basic ones and ending with more sophisticated techniques; Chapter 2 deals with geometric inequalities and Chapter 3 comprises a comprehensive list of recent problems that appeared in those contests during the last 14 years. Finally, hints and solutions to all exercises and problems are given in Chapter 4.
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From the reviews: “The book is devoted to the proofs of inequalities. As sources for considered inequalities the authors choose mathematical Olympiad of different level. … The book is really interesting and instructive for those students which suppose to develop their research skills and to increase their intuition.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1176, 2010) “This book presents a calculus-free introduction to inequalities and optimization problems with many interesting examples and exercises. … the authors present solutions or hints to all exercises and problems appearing in the book. … Most books on Olympiad-level competitions have sections on inequalities, but the book under review focuses on this genre of problems in a particularly attractive and effective way, providing good practice material. I recommend this softcover volume to anyone interested in mathematical competition preparation.” (Henry Ricardo, The Mathematical Association of America, October, 2010)
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4 of 4 people found the following review helpful:
5.0 out of 5 stars
Beautiful,
This review is from: Inequalities: A Mathematical Olympiad Approach (Paperback)
This is one of the best books I've come across.I think every math teacher should take a look at this book. There's something about the way that the authors explore these inequalities that makes you as a student want to explore it too. Each section is very well explained, with example problems and solutions. After each section, the authors give a few easy exercises which follow within two or three steps from the inequality just explained in that section. Some of these are very pretty and aesthetically beautiful since they are simple and symmetric. Middle school and high school students would benefit from seeing and working on the problems in this book because it introduces them to the essence of math, proofs. I'm not sure, but there might be a fundamentally different feeling upon being able to prove some claim or theorem as opposed to being able to solve for a quantity in question (as you would be asked to do in high school), especially a claim that starts with something as general as "For any a, b, c which are positive real numbers, we have that ...". Some of these inequalities make you think, "Really? Is this really true for any numbers I choose?" Or, "Wow. I did not know that." (And asking "Really? Is this really true for any numbers I choose?" helps you find typos perhaps or claims that aren't true. I've found only one claim so far, in section 1.4, that's slightly too strong. One of the necessary conditions for the claim to be be true is that all the numbers be of the same sign, but the authors omitted that.) Anyways, this book can be used to introduce proofs in a way that's beautiful (symmetry is aesthetically pleasing to most people) and simple (there are a lot of easy two or three line proofs which proves something non-obvious and yet still pretty). I also think that inequalities are more on the "practical"/applied side of math (optimizing anything is all about finding bounds and inequalities), just in case anyone thinks that this type of math is too non-practical for a student to care about. But honestly, I think that beauty and simplicity will attract students to math more than practicality, and the problems in this book are organized in a way that allows students to explore inequalities, starting from very basic claims to progressively more challenging problems (even ones coming from math competitions). No doubt, it's a fun book.
9 of 12 people found the following review helpful:
5.0 out of 5 stars
An excellent introduction to the Inequalities world,
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This review is from: Inequalities: A Mathematical Olympiad Approach (Paperback)
It is possible to writing a new and good book on inequalities? The answer is yes, and this work of three mexican mathematicians is an evident proof. The problems are very well selected, solutions clearly explained and, for example, it is in my opinion one of the very rare books where the Muirhead's theorem is proved in an understandable way. This powerful tool has been often used, but the proofs of it in the literature are usually obscure and very complicated. Here the difficulty of the matter can not be avoided, of course, but one can reach the end. My best congratulations to the three authors.
2 of 4 people found the following review helpful:
5.0 out of 5 stars
fun,
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This review is from: Inequalities: A Mathematical Olympiad Approach (Paperback)
This book is fun to read and solve the problems in the exercise.It also has solution to every exercise.
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