Inequalities: a mathematical olympiad approach

This book presents classical inequalities and specific inequalities which areparticularly 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. 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 INDICE: 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.- 2.1Two 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.

• ISBN: 978-3-0346-0049-1
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 250
• Fecha Publicación: 01/08/2009
• Nº Volúmenes: 1
• Idioma: Inglés