THE CAUCHY–SCHWARZ MASTER CLASS

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 H¨older, Hilbert, and
Hardy.