Mehr lesen
Informationen zum Autor 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. Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis 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.
