The Cauchy Schwarz Master Class An Introduction to the Art of Mathematical Inequalities 1st Edition by J Michael Steele ISBN 052154677X 9780521546775

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Product details:

ISBN 10: 052154677X

ISBN 13: 9780521546775 

Author: J. Michael Steele

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 Hölder, 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.

• Well-written: lively and user-friendly
• Over 100 worked exercises with coaching and hints
• Standard and non-standard topics

Table of contents:

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

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Tags: J Michael Steele, Cauchy Schwarz Master Class, Introduction, Art, Mathematical Inequalities