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The Cauchy - Schwarz Master Class

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The Cauchy - Schwarz Master Class

The Cauchy - Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

- Collection Mathematical Association of America

306 pages, parution le 03/12/2004

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
Voir tout
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Caractéristiques techniques du livre "The Cauchy - Schwarz Master Class"

  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

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