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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.
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.
Produktdetails
Erscheinungsdatum
05. Januar 2012
Sprache
englisch
Seitenanzahl
318
Autor/Autorin
J. Michael Steele
Verlag/Hersteller
Produktart
gebunden
Gewicht
613 g
Größe (L/B/H)
235/157/22 mm
ISBN
9780521837750
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Pressestimmen
'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 '... pleaseant reading for everyone with a solid real analysis background at undergraduate level, even before reading Polya-Szego. In fact, even researchers working on topics close to those in this book can find much to add to their repertoire.' Tamas Erdelyi, Department of Mathematics, Texas A&M University 'The book is special ... A large mathematics department with a functional graduate program could easily consider to offer a course based on this book.' Tamas Erdelyi, Journal of Approximation Theory
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