Algebraic inequalities : new vistas
- Titu Andreescu, Mark Saul.
- Berkeley, California : Mathematical Sciences Research Institute ; Providence, Rhode Island : American Mathematical Society, 
- Copyright notice
- Physical description
- x, 124 pages : illustrations ; 26 cm.
- MSRI mathematical circles library ; 19.
At the library
Science Library (Li and Ma)
|QA295 .A6244 2016||Unknown|
- * Some 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.
- (source: Nielsen Book Data)
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.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- MSRI mathematical circles library ; 19
- 9781470434649 (paperback alkaline paper)
- 1470434644 (paperback alkaline paper)
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