Inequalities : a Mathematical Olympiad approach
This book is intended for the Mathematical Olympiad students who wish to p- pare 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...
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| Médium: | Livre numérique |
| Jazyk: | Anglais |
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Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Vydání: | 1st ed. 2009. |
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Description d'après consultation du 26 mars 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Inequalities, a Mathematical Olympiad approach, Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado, Basel, Birkhäuser, 2009, 1 vol. (VIII-210 p.), 978-3-0346-0049-1 |
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| 009 | PPN149041500 | ||
| 020 | |a 9783034600507 | ||
| 020 | |a 9783034600507 | ||
| 041 | 0 | |a eng | |
| 082 | |a 510 | ||
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| 100 | 1 | |a Bulajich Manfrino, Radmila, |d 19..- | |
| 245 | 1 | 0 | |a Inequalities : |b a Mathematical Olympiad approach |c by Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado. |
| 250 | |a 1st ed. 2009. | ||
| 260 | |a Basel : |b Birkhäuser Basel. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 500 | |a Description d'après consultation du 26 mars 2012 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a Introduction 1 Numerical Inequalities 1.1 Order in the real numbers 1.2 The quadratic function ax2 + 2bx + c 1.3 A fundamental inequality, arithmetic mean-geometric mean 1.4. A wonderful inequality: the rearrangement inequality 1.5 Convex functions 1.6 A helpful inequality 1.7 The substitutions strategy 1.8 Muirhead's theorem 2 Geometric Inequalities 2.1 Two basic inequalities 2.2 Inequalities between the sides of a triangle 2.3 The use of inequalities in the geometry of the triangle 2.4 Euler's inequality and some applications 2.5 Symmetric functions of a, b and c 2.6 Inequalities with areas and perimeters. 2.7 Erdös-Mordell theorem 2.8 Optimization problems 3 Recent Inequality Problems 4 Solutions to Exercises and Problems Bibliography Index | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a This book is intended for the Mathematical Olympiad students who wish to p- pare 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 pr- lems. An important part of this book deals with geometric inequalities and this fact makes a big di?erence 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 di?erent character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. H- ever, 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- Schwarzinequality, the rearrangementinequality, the Jensen inequality, the Mu- head theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad pr- lems. We also emphasize how the substitution strategy is used to deduce several inequalities | ||
| 700 | 1 | |a Gómez Ortega, José Antonio, |d 19..- |4 aut | |
| 700 | 1 | |a Valdez Delgado, Rogelio, |d 19..- |4 aut | |
| 700 | 1 | |a Gómez Ortega, José Antonio. |4 aut | |
| 700 | 1 | |a Delgado, Rogelio Valdez. |4 aut | |
| 760 | 0 | |t Mathematics and Statistics | |
| 776 | 0 | |0 138510563 |t Inequalities |o a Mathematical Olympiad approach |f Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado |c Basel |n Birkhäuser |d 2009 |p 1 vol. (VIII-210 p.) |z 978-3-0346-0049-1 | |
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