The Cauchy-Schwarz Master Class

This 2004 book presents a fascinating collection of problems related to the Cauchy-Schwarz inequality and coaches readers through solutions.

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 This lively! problem-oriented text! accessible to anyone who knows calculus! helps readers master the 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 a famous mathematician or by the reader. Alongside these beautiful and surprising results! 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. 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....

Klappentext
This lively, problem-oriented text, accessible to anyone who knows calculus, helps readers master the 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 a famous mathematician or by the reader. Alongside these beautiful and surprising results, 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.


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.

Inhalt
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.

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