Radmila Bulajich Manfrino: Inequalities

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Cover: 9783034600491 | Inequalities | A Mathematical Olympiad Approach | Manfrino (u. a.)

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

Develops of the basic theory of inequalities

Gradually increases the level of difficulty

Introduces to a wide range of techniques used in Mathematical Olympiads

Quest for an equilibrium between algebraic and geometric inequalities

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2009
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Seiten:	220
Inhalt:	220 S.
ISBN-13:	9783034600491
ISBN-10:	3034600496
Sprache:	Englisch
Herstellernummer:	12591565
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Bulajich Manfrino, Radmila Valdez Delgado, Rogelio Gómez Ortega, José Antonio
Auflage:	2009
Hersteller:	Springer Basel Birkhäuser Basel
Maße:	240 x 170 x 13 mm
Von/Mit:	Radmila Bulajich Manfrino (u. a.)
Erscheinungsdatum:	18.09.2009
Gewicht:	0,382 kg

preigu-id: 101638840