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The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities

Table of Contents

1. Starting with Cauchy; 2. The AM-GM Inequality; 3. Lagrange's Identity and Minkowski's Conjecture; 4. On Geometry and Sums of Squares; 5. Consequences of Order; 6. Convexity — The Third Pillar; 7. Integral Intermezzo; 8. The Ladder of Power Means; 9. Hölder's Inequality; 10. Hilbert's Inequality and Compensating Diffculties; 11. Hardy's Inequality and the Flop; 12. Symmetric Sums; 13. Majorization and Schur Convexity; 14. Cancellation and Aggregation; Solutions to the Exercises; Chapter Notes; References

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