Algebraic Inequalities
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1st ed. 2018 Series: Problem Books in Mathematics Author: Sedrakyan, Hayk / Sedrakyan, Nairi Publisher: Springer ISBN: 9783319778358 Cover: HARDCOVER Date: 2018年07月 DESCRIPTION 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. TABLE OF CONTENTS Basic Inequalities and their Applications.- Strum's 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.- Jensen's Inequality.- Inequalities of Sequences.- Algebraic Inequalities in Number Theory.- Miscellaneous Inequalities.
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