The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities

The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities

by J. Michael Steele
     
 

ISBN-10: 052154677X

ISBN-13: 9780521546775

Pub. Date: 04/28/2004

Publisher: Cambridge University Press

"This 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 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…  See more details below

Overview

"This 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 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.

Product Details

ISBN-13:
9780521546775
Publisher:
Cambridge University Press
Publication date:
04/28/2004
Edition description:
New Edition
Pages:
318
Sales rank:
684,601
Product dimensions:
5.98(w) x 8.98(h) x 0.67(d)

Related Subjects

Table of Contents

1Starting with Cauchy1
2The AM-GM inequality19
3Lagrange's identity and Minkowski's conjecture37
4On geometry and sums of squares51
5Consequences of order73
6Convexity - the third pillar87
7Integral intermezzo105
8The ladder of power means120
9Holder's inequality135
10Hilbert's inequality and compensating difficulties155
11Hardy's inequality and the flop166
12Symmetric sums178
13Majorization and Schur convexity191
14Cancellation and aggregation208

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