The Cauchy - Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

J.Michael Steele - Collection Mathematical Association of America

306 pages, parution le 03/12/2004

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Résumé

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 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.

L'auteur - J.Michael Steele

J. Michael Steele is C. F. Koo Professor of Statistics at the Wharton School, University of Pennsylvania. He is the author of more than 100 mathematical publications, including the books Probability Theory and Combinatorial Optimization and Stochastic Calculus and Financial Applications. He is also the founding editor of the Annals of Applied Probability.

Sommaire

Preface
Starting with Cauchy
The AM-GM Inequality
Lagrange's Identity and Minkowski's Conjecture
On Geometry and Sums of Squares
Consequences of Order
Convexity - The Third Pillar
Integral Intermezzo
The Ladder of Power Means
Holder's Inequality
Hilbert's Inequality and Compensating Difficulties
Hardy's Inequality and the Flop
Symmetric Sums
Majorization and Schur Convexity
Cancellation and Aggregation
Solutions to the Exercises
Chapter Notes
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	J.Michael Steele
Collection	Mathematical Association of America
Parution	03/12/2004
Nb. de pages	306
Format	15 x 22,5
Couverture	Broché
Poids	432g
Intérieur	Noir et Blanc
EAN13	9780521546775
ISBN13	978-0-521-54677-5