The book MATHEMATICAL INEQUALITIES (5 volumes, over 2400 pages) 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 etc. 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.