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.
Summary: An excellent introduction to the Inequalities world Rating: 5
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.