The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities
QA295 .S78 2004
- Unknown QA295 .S78 2004
- 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. Holder'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-- Solutions to the exercises-- Notes-- References.
- (source: Nielsen Book Data)
- Publisher's Summary
- This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Holder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.
(source: Nielsen Book Data)
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Table of contents
Contributor biographical information
- Publication date
- J. Michael Steele.
- MAA problem books