Algebraic Inequalities: New Vistas (MSRI Mathematical Circles Library) by Titu Andreescu (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review This slim book moves economically, effectively, and elegantly from basic arithmetic to sophisticated inequality topics…Part of what makes the presentation effective, despite requiring no more than high school algebra, are the detailed solutions for the problem sets…This compact and concentrated work will be a useful service to students and teachers in fundamental mathematics. –Tom Schulte, MAA Reviews About the Author Titu Andreescu, The University of Texas at Dallas, Richardson, TX. Mark Saul, Executive Director, Julia Robinson Math Festivals.

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