The Cauchy-Schwarz Master Class - J. Michael Steele

The Cauchy-Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities
Buch | Hardcover
318 Seiten
2004
Cambridge University Press (Verlag)
978-0-521-83775-0 (ISBN)
139,65 inkl. MwSt
Using the Cauchy-Schwarz inequality as a guide, this 2004 book presents a fascinating collection of problems related to inequalities and coaches readers through solutions. Undergraduate and beginning graduate students in mathematics, theoretical computer science, statistics, engineering, and economics will find the book perfect for self-study or as a supplement to probability and analysis courses.
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.

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.

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.

Erscheint lt. Verlag 26.4.2004
Zusatzinfo Worked examples or Exercises; 35 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 149 x 235 mm
Gewicht 556 g
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 0-521-83775-8 / 0521837758
ISBN-13 978-0-521-83775-0 / 9780521837750
Zustand Neuware
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