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Cauchy-Schwarz Master Class : An Introduction to the Art of Mathematical Inequalities by J. Michael Steele (2004, Trade Paperback)
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-10052154677X
ISBN-139780521546775
eBay Product ID (ePID)18038315643
Product Key Features
Number of Pages318 Pages
LanguageEnglish
Publication NameCauchy-Schwarz Master Class : an Introduction to the Art of Mathematical Inequalities
Publication Year2004
SubjectGeneral, Mathematical Analysis
TypeTextbook
Subject AreaMathematics
AuthorJ. Michael Steele
FormatTrade Paperback
Dimensions
Item Height0.6 in
Item Weight15.2 Oz
Item Length8.9 in
Item Width5.9 in
Additional Product Features
Intended AudienceCollege Audience
LCCN2004-040402
Reviews'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, '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, "...this book is a 'must have' for a university's library, and I recommend it highly to its 'ideal audience.' Many other readers are alos bound to discover a satisfying number of attractive and less than familiar results." MAA Reviews, Leo Livshits, Colby College, "I believe George Polya would enjoy reading this book, and I recommend it to both the novice and the sophisticate. It is a nice read." Ingram Olkin, Stanford University for SIAM Review, '… 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, '... pleaseant reading for everyone with a solid real analysis background at undergraduate level, even before reading P lya-Szeg . In fact, even researchers working on topics close to those in this book can find much to add to their repertoire.' Tam s Erd lyi, 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 master course based on this book." Tamas Erdelyi, Journal of Approximation Theory, '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, "...this book is a 'must have' for a university's library, and I recommend it highly to its 'ideal audience.' Many other readers are also bound to discover a satisfying number of attractive and less than familiar results." MAA Reviews, '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, "The book is special...A large mathematics department with a functional graduate program could easily consider to offer a master 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, '… pleaseant reading for everyone with a solid real analysis background at undergraduate level, even before reading Plya-Szeg. In fact, even researchers working on topics close to those in this book can find much to add to their repertoire.' Tams Erdlyi, Department of Mathematics, Texas A&M University, "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
TitleLeadingThe
Dewey Edition22
IllustratedYes
Dewey Decimal512.9/7
Table Of Content1. 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.
SynopsisUsing 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., This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most 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 one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way 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. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics., 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.
LC Classification NumberQA295.S78 2004
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