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OverviewThis 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. Full Product DetailsAuthor: Titu Andreescu , Mark SaulPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.253kg ISBN: 9781470434649ISBN 10: 1470434644 Pages: 124 Publication Date: 30 December 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsSome introductory problems Squares are never negative The arithmetic-geometric mean inequality, part I The arithmetic-geometric mean inequality, part II The harmonic mean Symmetry in algebra, part I Symmetry in algebra, part II Symmetry in algebra, part III The rearrangement inequality The Cauchy-Schwarz inequality.Reviews"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" 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 Author InformationTitu Andreescu, The University of Texas at Dallas, Richardson, TX. Mark Saul, Executive Director, Julia Robinson Math Festivals. Tab Content 6Author Website:Countries AvailableAll regions |
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