The Cauchy-Schwarz Master Class

This lively, problem-oriented text 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 Hˆlder, 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.

First sentence: Cauchy's inequality for real numbers tells us that and there is no doubt that this is one of the most widely used and most important inequalities in all of mathematics.

Year

2004

Language

English

Publisher

Cambridge University Press

Editions

8

Pages

316

ISBN

9780521546775

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