Advanced Olympiad Inequalities: Algebraic & Geometric Olympiad Inequalities

This book contains a unique collection of new inequalities that were specifically imagined by the author to challenge the boundaries of curiosity and imagination. The inequalities are extremely beautiful and sharp, and the book covers various topics from 3 and 4 variables inequalities, symmetric and non-symmetric inequalities to geometric inequalities. Many of the exercises are presented with detailed solutions covering a variety of must-know old and new techniques in tackling Olympiad problems. The book contains also a variety of unsolved exercises which were left to the reader as additional challenges. Most importantly, the book deals with the daunting topic of asymmetric inequalities where most classical approaches fail. The book has been organised in five chapters. In the first one, we presented a collection of classical algebraic and geometric inequalities such as Cauchy-Schwarz, Cheybeshev’s, Newton’s, Bernoulli’s, Euler’s, Walker’s inequalities among others. These are the classical inequalities that any student should master if he is aiming for a medal at Mathematical Olympiad competitions. The second and third chapters deal respectively with 3 and 4 variables inequalities covering both symmetric and asymmetric inequalities. The fourth chapter is about Geometric inequalities involving triangle sides, medians, altitudes, internal bisectors, areas, perimeters, orthic triangles, angles, circumradius, inradius...The last chapter contains detailed solutions to the proposed problems with more than one solution for some of the inequalities.