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The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities Hardcover - 2004
by Steele, J. Michael
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- Hardcover
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Details
- Title The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities
- Author Steele, J. Michael
- Binding Hardcover
- Edition First Edition
- Condition New
- Pages 318
- Volumes 1
- Language ENG
- Publisher The Mathematical Association of America
- Date 2004-04-01
- Illustrated Yes
- Features Bibliography, Illustrated, Index
- Bookseller's Inventory # Q-0521837758
- ISBN 9780521837750 / 0521837758
- Weight 1.21 lbs (0.55 kg)
- Dimensions 9.2 x 6.52 x 0.78 in (23.37 x 16.56 x 1.98 cm)
- Library of Congress subjects Inequalities (Mathematics)
- Library of Congress Catalog Number 2004040402
- Dewey Decimal Code 512.97
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Summary
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 line
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.