Limit search to available items
Book Cover
Author Bulajich Manfrino, Radmila.

Title Inequalities : a Mathematical Olympiad approach / Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado
Published Basel ; Boston : Birkhäuser, ©2009


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 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
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 207-208) 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
Other Titles Mathematical Olympiad approach