Description

Book Synopsis
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”.

Trade Review
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

Table of Contents
  • 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.

Algebraic Inequalities New Vistas

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    A Paperback by Titu Andreescu, Mark Saul

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      Book details

      Publisher American Mathematical Society
      Published 12/30/2016 12:00:00 AM
      ISBN-13 9781470434649
      978-1470434649
      ISBN-10 1470434644
      Also in:
      Not Just Books Stationery

      Description

      Book Synopsis
      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”.

      Trade Review
      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

      Table of Contents
      • 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.

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