The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities
Material type: TextPublication details: Cambridge Cambridge University Press 2004Description: x, 306 ppISBN: 9780521546775Subject(s): Inequalities (Mathematics)LOC classification: QA295Item type | Current library | Collection | Shelving location | Call number | Copy number | Status | Date due | Barcode |
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Book | ICTS | Mathematics | Rack No 5 | QA295 (Browse shelf (Opens below)) | 1 | Available | 02573 |
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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