Mathematical Inequalities Volume 1

This is Volume 1 of the five-volume book Mathematical Inequalities that introduces and develops the main types of elementary inequalities. The first three volumes are a great opportunity to look into many old and new inequalities as well as elementary procedures for solving them: Volume 1 - Symmetric Polynomial Inequalities Volume 2 - Symmetric Rational and Nonrational Inequalities Volume 3 - Cyclic and Noncyclic Inequalities. As a rule the inequalities in these volumes are increasingly ordered according to the number of variables: two three four ... n-variables. The last two volumes (Volume 4 - Extensions and Refinements of Jensen's Inequality Volume 5 - Other Recent Methods for Creating and Solving Inequalities) present beautiful and original methods for solving inequalities such as Half/Partial convex function method Equal variables method Arithmetic compensation method Highest coefficient cancellation method pqr method etc. The book is intended for a wide audience: advanced middle school students high school students college and university students and teachers. Many problems and methods can be used as group projects for advanced high school students.