Description: The Cauchy-Schwarz Master Class An Introduction to the Art of Mathematical Inequalities This 2004 book presents a fascinating collection of problems related to the Cauchy-Schwarz inequality and coaches readers through solutions. J. Michael Steele (Author) 9780521837750, Cambridge University Press Hardback, published 26 April 2004 318 pages 23.5 x 14.9 x 2.6 cm, 0.556 kg 'The book is special … A large mathematics department with a functional graduate program could easily consider to offer a course based on this book.' Tamas Erdelyi, Journal of Approximation Theory 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. 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. Subject Areas: Combinatorics & graph theory [PBV], Probability & statistics [PBT], Calculus & mathematical analysis [PBK], Mathematical foundations [PBC]
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BIC Subject Area 1: Combinatorics & graph theory [PBV]
BIC Subject Area 2: Probability & statistics [PBT]
BIC Subject Area 3: Calculus & mathematical analysis [PBK]
BIC Subject Area 4: Mathematical foundations [PBC]
Number of Pages: 318 Pages
Language: English
Publication Name: The Cauchy-Schwarz Master Class: an Introduction to the Art of Mathematical Inequalities
Publisher: Cambridge University Press
Publication Year: 2004
Subject: Mathematics
Item Height: 235 mm
Item Weight: 556 g
Type: Textbook
Author: J. Michael Steele
Item Width: 149 mm
Format: Hardcover
