von Sedrakyan, Hayk;Sedrakyan, Nairi
XIII, 243 Seiten; 23.5 cm x 15.5 cm
2018 Springer International Publishing
lagernd: Filiale Wiedner Hauptstr. 6
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.- 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.
Biografische Anmerkung zu den Verfassern
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