Inequalities A Mathematical Olympiad Approach

Inequalities A Mathematical Olympiad Approach / by Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado.

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...

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Bibliographic Details
Main Authors: Bulajich Manfrino, Radmila (Author), Gómez Ortega, José Antonio (Author), Valdez Delgado, Rogelio (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2009.
Edition:1st ed. 2009.
Series:Springer eBook Collection.
Subjects:
Algebra.
Mathematics.
Mathematical analysis.
Analysis (Mathematics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

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