Algebraic inequalities : new vistas
 Responsibility
 Titu Andreescu, Mark Saul.
 Publication
 Berkeley, California : Mathematical Sciences Research Institute ; Providence, Rhode Island : American Mathematical Society, [2016]
 Copyright notice
 ©2016
 Physical description
 x, 124 pages : illustrations ; 26 cm.
 Series
 MSRI mathematical circles library ; 19.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA295 .A6244 2016  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Andreescu, Titu, 1956 author.
 Contributor
 Saul, Mark E., author.
Contents/Summary
 Contents

 * Some introductory problems* Squares are never negative* The arithmeticgeometric mean inequality, part I* The arithmeticgeometric 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 CauchySchwarz inequality.
 (source: Nielsen Book Data)
 Summary

This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the CauchySchwarz 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 CauchySchwarz inequality provides an introduction to vectors as mathematical objects. And there are many other secret pathways that the authors hope the reader will discoverand 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)
Subjects
Bibliographic information
 Publication date
 2016
 Copyright date
 2016
 Series
 MSRI mathematical circles library ; 19
 ISBN
 9781470434649 (paperback alkaline paper)
 1470434644 (paperback alkaline paper)