109 Inequalities from the AwesomeMath Summer Program

A fairly esoteric problem book on inequalities, 109 Inequalities from the AwesomeMath Summer Program lives up to its promise as “an instructive resource for students striving for success at national and international competitions.” AwesomeMath is a mathematical program for aspiring bright mathematicians at the middle and high school levels; the program is an educational supplement and is tailored specifically to competitions such as the USAMO. This problem book provides the essential theorems about inequalities, various examples, and many problems. The exposition is succinct but sufficient; the conciseness may prove challenging at times, and much is left for the reader to discover through the examples. Thus, the book is valuable to a rigorous student or competitor, but unfit for the casual mathematician or reader.

The heart of a problem book is, of course, the problems. As the title suggests, there are 109 problems relating to inequalities — 54 introductory problems and 55 advanced problems. Many problems and their presented solutions are quite subtle, and involve delicate applications of various inequalities. The advanced problems are justly named and are quite difficult. Overall, the problems form an excellent training regiment for mathematical inequalities and will help readers master the subject.

109 Inequalities from the AwesomeMath Summer Program was intended for a specific audience — students wishing to perform well in mathematical competitions — and it is that audience that will glean the most from its contents. It is an excellent resource and would be a valuable addition to a problem-solver’s library.

Readers like myself who enjoyed this book may also take interest in AwesomeMath’s other publications. The program has released problem books on a wide array of mathematical topics. Examples include 105 Algebra Problems from the AwesomeMath Summer Program and 107 Geometry Problems from the AwesomeMath Year-Round Program.

Jack Chen (jackchen5@hotmail.com) is a high school student who enjoys mathematics. He hopes to pursue mathematics in his post-secondary education. His current mathematical interests are in modular arithmetic and cryptography.