Description
Book SynopsisThis 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 ReviewThis 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 ReviewsTable 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.
