The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities
Autor J. Michael Steeleen Limba Engleză Paperback – 25 apr 2004
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Specificații
ISBN-13: 9780521546775
ISBN-10: 052154677X
Pagini: 318
Ilustrații: 35 b/w illus. 161 exercises
Dimensiuni: 150 x 227 x 16 mm
Greutate: 0.43 kg
Ediția:New.
Editura: Cambridge University Press
Colecția The Mathematical Association of America
Locul publicării:Washington DC, United States
ISBN-10: 052154677X
Pagini: 318
Ilustrații: 35 b/w illus. 161 exercises
Dimensiuni: 150 x 227 x 16 mm
Greutate: 0.43 kg
Ediția:New.
Editura: Cambridge University Press
Colecția The Mathematical Association of America
Locul publicării:Washington DC, United States
Cuprins
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.
Recenzii
'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 Pólya-Szegö. In fact, even researchers working on topics close to those in this book can find much to add to their repertoire.' Tamás Erdélyi, 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
'… pleaseant reading for everyone with a solid real analysis background at undergraduate level, even before reading Pólya-Szegö. In fact, even researchers working on topics close to those in this book can find much to add to their repertoire.' Tamás Erdélyi, 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
Notă biografică
Descriere
This 2004 book presents a fascinating collection of problems related to the Cauchy-Schwarz inequality and coaches readers through solutions.