The Cauchy-Schwarz master class an introduction to the art of mathematical inequalities - Steele, John Michael 1949- (Cambridge University Press, 2010)
Using the Cauchy-Schwarz inequality as the initial guide, this text explains the concepts of mathematical inequalities by presenting a sequence of problems as they might have been discovered, the solutions to which can either be found with one of history's great mathematicians or by the reader themselves
Includes bibliographical references and index
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 difficulties -- 11. Hardy's inequality and the flop -- 12. Symmetric sums -- 13. Majorization and Schur convexity -- 14. Cancellation and aggregation
Keywords: Inequalities (Mathematics); Ungleichung