eBook ISBN:  9780883859216 
Product Code:  NML/3.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
eBook ISBN:  9780883859216 
Product Code:  NML/3.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 

Book DetailsAnneli Lax New Mathematical LibraryVolume: 3; 1961; 133 pp
Most people when they think of mathematics think first of numbers and equations—the number \((x)=\) that number \((y)\). But professional mathematicians in dealing with quantities that can be ordered according to their size, often are more interested in unequal magnitudes that are equal. This book provides an introduction to the fascinating world of inequalities beginning with a systematic discussion of the relation “greater than” and the meaning of “absolute values” of numbers and ending with descriptions of some unusual geometries.
In the course of the book, the reader will encounter some of the more famous inequalities in mathematics. Starting with the basic order properties of real numbers, this book carries the reader through the classical inequalities of Cauchy, Minkowsky and Hörder with many variants and applications. The concluding chapter points the way to other metrics in the plane and the interrelations between geometry (convexity) and algebra (inequalities).

Table of Contents

Chapters

Chapter 1. Fundamentals

Chapter 2. Tools

Chapter 3. Absolute Value

Chapter 4. The Classical Inequalities

Chapter 5. Maximization and Minimization Problems

Chapter 6. Properties of Distance


Reviews

The book is classical, but still it has kept its freshness and still seems wellwritten and wellmotivated. This book will also be very useful for teachers, both for its content and as a model of mathematical writing.
Mehdi Hassani, MAA Reviews


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Most people when they think of mathematics think first of numbers and equations—the number \((x)=\) that number \((y)\). But professional mathematicians in dealing with quantities that can be ordered according to their size, often are more interested in unequal magnitudes that are equal. This book provides an introduction to the fascinating world of inequalities beginning with a systematic discussion of the relation “greater than” and the meaning of “absolute values” of numbers and ending with descriptions of some unusual geometries.
In the course of the book, the reader will encounter some of the more famous inequalities in mathematics. Starting with the basic order properties of real numbers, this book carries the reader through the classical inequalities of Cauchy, Minkowsky and Hörder with many variants and applications. The concluding chapter points the way to other metrics in the plane and the interrelations between geometry (convexity) and algebra (inequalities).

Chapters

Chapter 1. Fundamentals

Chapter 2. Tools

Chapter 3. Absolute Value

Chapter 4. The Classical Inequalities

Chapter 5. Maximization and Minimization Problems

Chapter 6. Properties of Distance

The book is classical, but still it has kept its freshness and still seems wellwritten and wellmotivated. This book will also be very useful for teachers, both for its content and as a model of mathematical writing.
Mehdi Hassani, MAA Reviews