This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not "linear". The central topic of inequalities is linked to others in mathematics. Often these topics relate to much more than algebraic inequalities. There are also "secret" pathways through the book. Each chapter has a subtext, a theme which prepares the student for learning other mathematical topics, concepts, or habits of mind. For example, the early chapters on the arithmetic mean/geometric mean inequality show how very simple observations can be leveraged to yield useful and interesting results. Later chapters give examples of how one can generalize a mathematical statement. The chapter on the Cauchy-Schwarz inequality provides an introduction to vectors as mathematical objects. And there are many other secret pathways that the authors hope the reader will discover--and follow. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Titu Andreescu (born 1956) is an associate professor of mathematics at the University of Texas at Dallas. He is also firmly involved in mathematics contests and olympiads, having been 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.
Mark Saul is the Director of the Center for Mathematical Talent at Courant Institute (NYU). He spent 35 years in and around New York, teaching mathematics in classrooms from grades 3 through 12. More recently, he directs the Center for Mathematical Talent at the Courant Institute of Mathematical Sciences at New York University.