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.
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.
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.
Inhaltsangabe
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.
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.
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.
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.
Rezensionen
'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
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