Inequalities A Mathematical Olympiad Approach /

• Main Authors: Manfrino, Radmila Bulajich (Author), Gómez Ortega, José Antonio (Author), Delgado, Rogelio Valdez (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2009.
• Subjects: Mathematics.; Algebra.; Mathematical analysis.; Analysis (Mathematics).; Mathematics, general.; Analysis.

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...

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.