J. Michael Steele

Cauchy-Schwarz Master Class (eBook, PDF)

An Introduction to the Art of Mathematical Inequalities

• Format: PDF

Produktbeschreibung

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 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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 26. April 2004
• Englisch
• ISBN-13: 9780511207761
• Artikelnr.: 38194703

Autorenporträt

J. Michael Steele is C. F. Koo Professor of Statistics at 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.

Inhaltsangabe

1. Starting with Cauchy
2. The AM-GM inequality
3. Lagrange's identity and Minkowski's conjecture
4. On geometry and sums of squares
5. Consequences of order
6. Convexity - the third pillar
7. Integral intermezzo
8. The ladder of power means
9. Hölder's inequality
10. Hilbert's inequality and compensating difficulties
11. Hardy's inequality and the flop
12. Symmetric sums
13. Majorization and Schur convexity
14. Cancellation and aggregation
Solutions to the exercises
Notes
References.

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1. Starting with Cauchy; 2. The AM-GM inequality; 3. Lagrange's identity and Minkowski's conjecture; 4. On geometry and sums of squares; 5. Consequences of order; 6. Convexity - the third pillar; 7. Integral intermezzo; 8. The ladder of power means; 9. Hölder's inequality; 10. Hilbert's inequality and compensating difficulties; 11. Hardy's inequality and the flop; 12. Symmetric sums; 13. Majorization and Schur convexity; 14. Cancellation and aggregation; Solutions to the exercises; Notes; References.

Rezensionen

'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.' Zentralblatt MATH