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Inequalities

A Mathematical Olympiad Approach

  • Textbook
  • © 2009

Overview

Authors:
  1. Radmila Bulajich Manfrino

    1. Facultad de Ciencias, Universidad Autónoma Estado de Morelos, Cuernavaca, México

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  2. José Antonio Gómez Ortega

    1. Departamento de Matemàticas Facultad de Ciencias, UNAM, Universidad Nacional Autónoma de México, México, D.F., México

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  3. Rogelio Valdez Delgado

    1. Facultad de Ciencias, Universidad Autónoma Estado de Morelos, Cuernavaca, México

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  • 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

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-viii
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  2. Numerical Inequalities

    • Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado
    Pages 1-49

  3. Geometric Inequalities

    • Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado
    Pages 51-99

  4. Recent Inequality Problems

    • Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado
    Pages 101-115

  5. Solutions to Exercises and Problems

    • Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado
    Pages 117-206

  6. Back Matter

    Pages 205-210
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Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

  • Facultad de Ciencias, Universidad Autónoma Estado de Morelos, Cuernavaca, México

    Radmila Bulajich Manfrino, Rogelio Valdez Delgado

  • Departamento de Matemàticas Facultad de Ciencias, UNAM, Universidad Nacional Autónoma de México, México, D.F., México

    José Antonio Gómez Ortega

Bibliographic Information

  • Book Title: Inequalities

  • Book Subtitle: A Mathematical Olympiad Approach

  • Authors: Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado

  • DOI: https://doi.org/10.1007/978-3-0346-0050-7

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Basel 2009

  • Softcover ISBN: 978-3-0346-0049-1Published: 18 September 2009

  • eBook ISBN: 978-3-0346-0050-7Published: 01 January 2010

  • Edition Number: 1

  • Number of Pages: 220

  • Topics: Algebra, Mathematics, general, Analysis

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