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Algebraic Inequalities: New Vistas
 
Titu Andreescu The University of Texas at Dallas, Richardson, TX
Mark Saul Executive Director, Julia Robinson Math Festivals
A co-publication of the AMS and Mathematical Sciences Research Institute
Algebraic Inequalities: New Vistas
Softcover ISBN:  978-1-4704-3464-9
Product Code:  MCL/19
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Sale Price: $33.00
eBook ISBN:  978-1-4704-3595-0
Product Code:  MCL/19.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $40.00
Sale Price: $30.00
Softcover ISBN:  978-1-4704-3464-9
eBook: ISBN:  978-1-4704-3595-0
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
Sale Price: $63.00 $48.00
Algebraic Inequalities: New Vistas
Click above image for expanded view
Algebraic Inequalities: New Vistas
Titu Andreescu The University of Texas at Dallas, Richardson, TX
Mark Saul Executive Director, Julia Robinson Math Festivals
A co-publication of the AMS and Mathematical Sciences Research Institute
Softcover ISBN:  978-1-4704-3464-9
Product Code:  MCL/19
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Sale Price: $33.00
eBook ISBN:  978-1-4704-3595-0
Product Code:  MCL/19.E
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $40.00
Sale Price: $30.00
Softcover ISBN:  978-1-4704-3464-9
eBook ISBN:  978-1-4704-3595-0
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
Sale Price: $63.00 $48.00
  • Book Details
     
     
    MSRI Mathematical Circles Library
    Volume: 192016; 124 pp
    MSC: Primary 97

    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.

    Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

    Readership

    Undergraduate 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 Arithmetic-Geometric Mean Inequality, Part I
    • Problems
    • Solutions
    • Chapter 3. The Arithmetic-Geometric 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 Cauchy-Schwarz Inequality
    • Problems
    • Higher Dimensions
    • Problems
    • More Generally…
    • An Important Problem
    • The Importance of the Problem
    • Problems
    • Solutions
    • Back Cover
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 192016; 124 pp
MSC: Primary 97

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.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Readership

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 Arithmetic-Geometric Mean Inequality, Part I
  • Problems
  • Solutions
  • Chapter 3. The Arithmetic-Geometric 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 Cauchy-Schwarz 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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