Description
Book SynopsisThis 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.
Trade Review“The book is a trove of original and ingenious problems, and will provide any student, teacher or prospective Olympian with a fine source of inspiration.” (Stephen Rout, The Mathematical Gazette, Vol. 104 (560), July, 2020)
Table of ContentsBasic 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.
