The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities

By: Steele, J. MichaelMaterial type: TextTextPublication details: Cambridge Cambridge University Press 2004Description: x, 306 ppISBN: 9780521546775Subject(s): Inequalities (Mathematics)LOC classification: QA295
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. 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
Summary: 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
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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

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