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The Cauchy-Schwarz Master Class : An Introduction to the Art of Mathematical Inequalities - J. Michael Steele

The Cauchy-Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

Hardcover Published: 5th January 2012
ISBN: 9780521837750
Number Of Pages: 318

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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.

'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 '... pleaseant reading for everyone with a solid real analysis background at undergraduate level, even before reading Polya-Szego. In fact, even researchers working on topics close to those in this book can find much to add to their repertoire.' Tamas Erdelyi, Department of Mathematics, Texas A&M University 'The book is special ... A large mathematics department with a functional graduate program could easily consider to offer a course based on this book.' Tamas Erdelyi, Journal of Approximation Theory

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
Notes
References
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521837750
ISBN-10: 0521837758
Series: MAA Problem Books
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 318
Published: 5th January 2012
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.5 x 14.9  x 2.6
Weight (kg): 0.56