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Cover: 9780521546775 | The Cauchy-Schwarz Master Class | J. Michael Steele | Taschenbuch
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The Cauchy-Schwarz Master Class
An Introduction to the Art of Mathematical Inequalities
Taschenbuch von J. Michael Steele
Sprache: Englisch

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Beschreibung
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.
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.
Über den 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.
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.
Details
Erscheinungsjahr: 2004
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 318
ISBN-13: 9780521546775
ISBN-10: 052154677X
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Steele, J. Michael
Hersteller: Cambridge University Press
Maße: 229 x 152 x 18 mm
Von/Mit: J. Michael Steele
Erscheinungsdatum: 01.04.2004
Gewicht: 0,463 kg
preigu-id: 102402807
Über den 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.
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.
Details
Erscheinungsjahr: 2004
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 318
ISBN-13: 9780521546775
ISBN-10: 052154677X
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Steele, J. Michael
Hersteller: Cambridge University Press
Maße: 229 x 152 x 18 mm
Von/Mit: J. Michael Steele
Erscheinungsdatum: 01.04.2004
Gewicht: 0,463 kg
preigu-id: 102402807
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