The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities /

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Using the Cauchy-Schwarz inequality as the initial guide, this text explains the concepts of mathematical inequalities by presenting a sequence of problems as they might have been discovered, the solutions to which can either be found with one of history's great mathematicians or by the reader...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Steele, J. Michael (Author)
Format: Electronic eBook
Language:Inglés
Published: Cambridge, UK ; New York : Cambridge University Press, 2004.
Series:MAA problem books series.
Subjects:
Inequalities (Mathematics)
Processes, Infinite.
Inégalités (Mathématiques)
Processus infinis.
MATHEMATICS > Algebra > Elementary.
Processes, Infinite
Ungleichung
Online Access:Texto completo
Table of Contents:
  • 1. Starting with Cauchy
  • 2. The AM-GM inequality
  • 3. Lagrange's identity and Minkowski's conjecture
  • 4. On geometry and sums of squares
  • 5. Consequences of order
  • 6. Convexity
  • the third pillar
  • 7. Integral intermezzo
  • 8. The ladder of power means
  • 9. Holder's inequality
  • 10. Hilbert's inequality
  • 11. Hardy's inequality
  • 12. Symmetric sums
  • 13. Majorization and Schur convexity
  • 14. Cancellation and aggregation
  • Solutions to the exercises
  • Chapter notes
  • References
  • Index.

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