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  1. Home
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  3. The Cauchy-Schwarz Master Class
  • Cited by 357
Publisher:
Cambridge University Press
Online publication date:
April 2013
Print publication year:
2004
Online ISBN:
9780511817106
DOI:
https://doi.org/10.1017/CBO9780511817106
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Information

Book description

This lively, problem-oriented text, first published in 2004, 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 Hölder, 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.

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.'

Source: Zentralblatt MATH

'… pleaseant reading for everyone with a solid real analysis background at undergraduate level, even before reading Pólya-Szegö. In fact, even researchers working on topics close to those in this book can find much to add to their repertoire.'

Tamás Erdélyi - 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 Source: Journal of Approximation Theory

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