<span>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.</span>

Algebraic Inequalities: New Vistas PDF

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