Steele, J. Michael

The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities - Cambridge Cambridge University Press 2004 - x, 306 pp.

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. Holder's inequality;
10. Hilbert's inequality;
11. Hardy's inequality;
12. Symmetric sums;
13. Majorization and Schur convexity;
14. Cancellation and aggregation;
Solutions to the exercises

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

9780521546775


Inequalities (Mathematics)

QA295