Hojoo Lee - Topics in Inequalities, Theorems and Techniques

Inequalities are useful in all fields of Mathematics. The aim of this problem-oriented book is to present elementary techniques in the theory of inequalities. The readers will meet classical theorems including Schur’s inequality, Muirhead’s theorem, the Cauchy-Schwarz inequality, the Power Mean inequality, the AM-GM inequality, and Holder’s theorem. I would greatly appreciate hearing about comments and corrections from my readers.

My target readers are challenging high schools students and undergraduate students. The given techniques in this book are just the tip of the inequalities iceberg. Young students should find their own methods to attack various problems. A great Hungarian Mathematician Paul Erdos was fond of saying that God has a transfinite book with all the theorems and their best proofs. I strongly encourage readers to send me their own creative solutions of the problems in this book. Have fun!