The Cauchy-Schwarz Master Class
The Cauchy-Schwarz Master Class
Michael Steele describes the fundamental topics in mathematical inequalities and their uses. Using the Cauchy-Schwarz inequality as a guide, Steele presents a fascinating collection of problems related to inequalities and coaches readers through solutions, in a style reminiscent of George Polya, by teaching basic concepts and sharpening problem solving skills at the same time. Undergraduate and beginning graduate students in mathematics, theoretical computer science, statistics, engineering, and economics will find the book appropriate for self-study.
- Well-written: lively and user-friendly
- Over 100 worked exercises with coaching and hints
- Standard and non-standard topics
Reviews & endorsements
"...this book is a 'must have' for a university's library, and I recommend it highly to its 'ideal audience.' Many other readers are also bound to discover a satisfying number of attractive and less than familiar results."
MAA Reviews
"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
"The book is special...A large mathematics department with a functional graduate program could easily consider to offer a master course based on this book."
Tamas Erdelyi, Journal of Approximation Theory
"I believe George Polya would enjoy reading this book, and I recommend it to both the novice and the sophisticate. It is a nice read."
Ingram Olkin, Stanford University for SIAM Review
Product details
April 2004Paperback
9780521546775
318 pages
227 × 150 × 16 mm
0.43kg
35 b/w illus. 161 exercises
Available
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
- Solutions to the exercises
- Notes
- References.
