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

Author: J Michael Steele
Publisher: Cambridge ; New York : Cambridge University Press, 2004.
Series: MAA problem books series.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
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 themselves.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: J Michael Steele
ISBN: 0521837758 9780521837750 052154677X 9780521546775
OCLC Number: 54079548
Description: x, 306 p. : ill. ; 24 cm.
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.
Series Title: MAA problem books series.
Responsibility: J. Michael Steele.
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Abstract:

This 2004 book presents a fascinating collection of problems related to the Cauchy-Schwarz inequality and coaches readers through solutions.  Read more...

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'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.' Read more...

 
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