The Cauchy - Schwartz 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 mathe- maticians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geome-try of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of H ̈older, 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. J. Michael Steele is C. F. Koo Professor of Statistics at the Wharton School, University of Pennsylvania. He is the author of more than 100 mathematical publications, including the books Probability Theory and Combinatorial Optimization and Stochastic Calculus and Financial Applications. He is also the founding editor of the Annals of Applied Probability.

The Cauchy-Schwartz Master Class

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