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.

Autorentext

Hayk Sedrakyan is an IMO medal winner, Professor of Mathematics in Paris, France and a professional Math Olympiad Coach in Greater Boston area, Massachusetts, USA. He has defended his PhD thesis in mathematics at UPMC-Sorbonne University, Paris, France. Hayk is a Doctor of Mathematical Sciences in the United States, France and Armenia. He has received three Master's degrees in mathematics from Germany, Austria, Armenia and has spent a small part of his PhD studies in Italy. Hayk has authored several books on the topic of problem solving and Olympiad style mathematics published globally.

Nairi Sedrakyan is involved in national and international Olympiads of mathematics, having been the President of Armenian Mathematics Olympiads and an IMO problem selection committee member. He is the author of one of the hardest problems ever proposed in the history of International Mathematical Olympiad (5th problem of 37th IMO). He has been the Leader of Armenian IMO Team, a jury member of IMO, a jury member and problem selection committee member of Zhautykov International Mathematical Olympiad (ZIMO), a jury member and problem selection committee member of the International Olympiad of Metropolises and the President of International Mathematical Olympiad Tournament of the Towns. He is also the author of a large number of problems proposed in these Olympiads and has authored several books on the topic of problem solving and Olympiad style mathematics published globally. Students of Nairi Sedrakyan have obtained 20 medals in International Mathematical Olympiad (1 Gold Medal, 4 Silver Medals, 15 Bronze Medals, one of which his son had gotten). For his outstanding teaching, Nairi Sedrakyan received the title of the best teacher of the Republic of Armenia and was awarded a special gift from the Prime Minister

Inhalt

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.