Algebraic Inequalities

This unique collection of new and classical problems provides full coverage of algebraic inequalities. Many of the exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. Algebraic Inequalities can be considered a continuation of the book Geometric Inequalities: Methods of Proving by the authors.This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving algebraic inequalities.

Basic Inequalities and their Applications.- Strums Method.- The HM-GM-AM-QM Inequalities.- Cauchy-Bunyakovsky-Schwarz Inequality.- Change of Variable(s) Method.- Symmetry and Homogeneity.- The Principle of Mathematical Introduction.- One Useful Inequality.- Using Derivatives and Integrals.- Using Functions.- Jensens Inequality.- Inequalities of Sequences.- Algebraic Inequalities in Number Theory.- Miscellaneous Inequalities.