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 Hoelder, 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.
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