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Inequalities: A Mathematical Olympiad Approach
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Inequalities: A Mathematical Olympiad Approach

Inequalities: A Mathematical Olympiad Approach

Radmila / Gomez Ortega Bulajich Manfrino

220 pages, parution le 17/09/2009

Résumé

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 originate from Mathematical Olympiad contests around the world.

This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.Numerical Inequalities.- Geometric Inequalities.- Recent Inequality Problems.- Solutions to Exercises and Problems.

Caractéristiques techniques

  PAPIER
Éditeur(s) Springer
Auteur(s) Radmila / Gomez Ortega Bulajich Manfrino
Parution 17/09/2009
Nb. de pages 220
EAN13 9783034600491

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