109 Inequalities from the AwesomeMath Summer Program

by Titu Andreescu, Adithya Ganesh

This book aims to convey the theory and techniques involved in proving algebraic inequalities. Each chapter begins with a theoretical part, in which several classical theorems are stated and proven. These include the fundamental Arithmetic-Geometric Mean and Cauchy-Schwarz inequalities, as well as the Nesbitt, Schur, Hölder, Rearrangement, and Chebyshev inequalities. Numerous examples are provided to illustrate the subtleties involved in applying these inequalities. Problems range from relatively easy to extremely challenging, benefiting both beginners and veteran problem solvers alike. To help the reader hone their skills, 109 inequality problems are provided, of which 54 are introductory and 55 are advanced. Detailed solutions to all of these problems are given, in which an eclectic medley of ideas are employed.

203 pages, Hardcover

Published January 1, 2015

About the author

Titu Andreescu is an associate professor of mathematics at the University of Texas at Dallas. He is also firmly involved in mathematics contests and Olympiads, being the Director of AMC (as appointed by the Mathematical Association of America), Director of MOP, Head Coach of the USA IMO Team and Chairman of the USAMO. He has also authored a large number of books on the topic of problem solving and Olympiad-style mathematics.