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The Cauchy-Schwarz Master Class

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

$45.99 (P)

  • Date Published: April 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521546775

$ 45.99 (P)
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About the Authors
  • Michael Steele describes the fundamental topics in mathematical inequalities and their uses. Using the Cauchy-Schwarz inequality as a guide, Steele presents a fascinating collection of problems related to inequalities and coaches readers through solutions, in a style reminiscent of George Polya, by teaching basic concepts and sharpening problem solving skills at the same time. Undergraduate and beginning graduate students in mathematics, theoretical computer science, statistics, engineering, and economics will find the book appropriate for self-study.

    • Well-written: lively and user-friendly
    • Over 100 worked exercises with coaching and hints
    • Standard and non-standard topics
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    Reviews & endorsements

    "...this book is a 'must have' for a university's library, and I recommend it highly to its 'ideal audience.' Many other readers are also bound to discover a satisfying number of attractive and less than familiar results."
    MAA Reviews

    "This eminently readable book will be treasured not only by students and their teachers but also by all those who seek to make sense of the elusive macrocosm of twentieth-century mathematics."
    Zentralblatt MATH

    "The book is special...A large mathematics department with a functional graduate program could easily consider to offer a master course based on this book."
    Tamas Erdelyi, Journal of Approximation Theory

    "I believe George Polya would enjoy reading this book, and I recommend it to both the novice and the sophisticate. It is a nice read."
    Ingram Olkin, Stanford University for SIAM Review

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    Product details

    • Date Published: April 2004
    • format: Paperback
    • isbn: 9780521546775
    • length: 318 pages
    • copublisher: The Mathematical Association of America
    • dimensions: 227 x 150 x 16 mm
    • weight: 0.43kg
    • contains: 35 b/w illus. 161 exercises
    • availability: Available
  • 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. Hölder's inequality
    10. Hilbert's inequality and compensating difficulties
    11. Hardy's inequality and the flop
    12. Symmetric sums
    13. Majorization and Schur convexity
    14. Cancellation and aggregation
    Solutions to the exercises
    Notes
    References.

  • Author

    J. Michael Steele, University of Pennsylvania
    J. Michael Steele is C. F. Koo Professor of Statistics at 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.

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