Description 
1 online resource (viii, 210 pages) : illustrations 
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 meangeometric 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 ErdösMordell theorem  2.8 Optimization problems.3 Recent Inequality Problems  4 Solutions to Exercises and Problems  Bibliography  Index 
Summary 
This book presents classical inequalities and specific inequalities which are particularly useful for attacking and solving optimization problems. Most of the examples, exercises and problems that appear in the book originate from Mathematical Olympiad contests around the world. The material is divided into four chapters. In Chapter 1 algebraic inequalities are presented, starting with the basic ones and ending with more sophisticated techniques; Chapter 2 deals with geometric inequalities and Chapter 3 comprises a comprehensive list of recent problems that appeared in those contests during the last 14 years. Finally, hints and solutions to all exercises and problems are given in Chapter 4 
Bibliography 
Includes bibliographical references (pages 207208) and index 
Notes 
English 

Print version record 
Subject 
Inequalities (Mathematics)


Inequalities (Mathematics)


Inequalities (Mathematics)

Form 
Electronic book

Author 
Gómez Ortega, José Antonio.


Valdez Delgado, Rogelio.

ISBN 
9783034600507 

303460050X 
