tailieunhanh - 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 | AN INTRODUCTION TO THE ART OF MATHEMATICAL INEQUALITIES 77ie Cauchy-Schwarz Master Class 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 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. 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. .and. . He is also the founding editor of .