Softcover ISBN:  9781470434649 
Product Code:  MCL/19 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470435950 
Product Code:  MCL/19.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Softcover ISBN:  9781470434649 
eBook: ISBN:  9781470435950 
Product Code:  MCL/19.B 
List Price:  $105.00$80.00 
MAA Member Price:  $94.50$72.00 
AMS Member Price:  $84.00$64.00 
Softcover ISBN:  9781470434649 
Product Code:  MCL/19 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470435950 
Product Code:  MCL/19.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 
Softcover ISBN:  9781470434649 
eBook ISBN:  9781470435950 
Product Code:  MCL/19.B 
List Price:  $105.00$80.00 
MAA Member Price:  $94.50$72.00 
AMS Member Price:  $84.00$64.00 

Book DetailsMSRI Mathematical Circles LibraryVolume: 19; 2016; 124 ppMSC: Primary 97;
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 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.ReadershipUndergraduate students interested in learning and teaching high school algebra.

Table of Contents

Cover

Title page

Contents

Acknowledgments

Introduction

Chapter 0. Some Introductory Problems

How Do Inequalities Behave?

Solutions

Chapter 1. Squares Are Never Negative

Problems

Solutions

Chapter 2. The ArithmeticGeometric Mean Inequality, Part I

Problems

Solutions

Chapter 3. The ArithmeticGeometric Mean Inequality, Part II

Problems

Solutions

Chapter 4. The Harmonic Mean

Introduction

It’s more than just \boldmath{𝐷=𝑅𝑇}

Notes and Summary

Problems

The Harmonic Mean of Several Quantities

Problems

The Harmonic Mean in Geometry

Problems

Solutions

Chapter 5. Symmetry in Algebra, Part I

Problems

Symmetry in Inequalities

Problems

Solutions

Chapter 6. Symmetry in Algebra, Part II

Problems

Solutions

Chapter 7. Symmetry in Algebra, Part III

Problems

Solutions

Chapter 8. The Rearrangement Inequality

The General Rearrangement Inequality

Permutations

Problems

Chebyshev’s Inequality

Problems

Solutions

Chapter 9. The CauchySchwarz Inequality

Problems

Higher Dimensions

Problems

More Generally…

An Important Problem

The Importance of the Problem

Problems

Solutions

Back Cover


Additional Material

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


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
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 Reviews
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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 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.
Undergraduate students interested in learning and teaching high school algebra.

Cover

Title page

Contents

Acknowledgments

Introduction

Chapter 0. Some Introductory Problems

How Do Inequalities Behave?

Solutions

Chapter 1. Squares Are Never Negative

Problems

Solutions

Chapter 2. The ArithmeticGeometric Mean Inequality, Part I

Problems

Solutions

Chapter 3. The ArithmeticGeometric Mean Inequality, Part II

Problems

Solutions

Chapter 4. The Harmonic Mean

Introduction

It’s more than just \boldmath{𝐷=𝑅𝑇}

Notes and Summary

Problems

The Harmonic Mean of Several Quantities

Problems

The Harmonic Mean in Geometry

Problems

Solutions

Chapter 5. Symmetry in Algebra, Part I

Problems

Symmetry in Inequalities

Problems

Solutions

Chapter 6. Symmetry in Algebra, Part II

Problems

Solutions

Chapter 7. Symmetry in Algebra, Part III

Problems

Solutions

Chapter 8. The Rearrangement Inequality

The General Rearrangement Inequality

Permutations

Problems

Chebyshev’s Inequality

Problems

Solutions

Chapter 9. The CauchySchwarz Inequality

Problems

Higher Dimensions

Problems

More Generally…

An Important Problem

The Importance of the Problem

Problems

Solutions

Back Cover

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