The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities /
Steele, J. Michael,
The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities / J. Michael Steele, University of Pennsylvania. - 1 online resource (x, 306 pages) : illustrations. - MAA problem books series . - MAA problem books series. .
Includes bibliographical references (pages 292-301) and index.
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. Holder's inequality -- 10. Hilbert's inequality -- 11. Hardy's inequality -- 12. Symmetric sums -- 13. Majorization and Schur convexity -- 14. Cancellation and aggregation -- Solutions to the exercises -- Chapter notes -- References -- Index.
Using the Cauchy-Schwarz inequality as the initial guide, this text explains the concepts of mathematical inequalities by presenting a sequence of problems as they might have been discovered, the solutions to which can either be found with one of history's great mathematicians or by the reader themselves.
9780511211348 0511211341 9780511207761 051120776X 9780511213113 0511213115 9780511216718 0511216718 9780511817106 051181710X
OverDrive, Inc. http://www.overdrive.com F4F2B00F-E910-4C7D-AB6B-189D62A246C5 OverDrive, Inc. http://www.overdrive.com
Inequalities (Mathematics)
Processes, Infinite.
Inégalités (Mathématiques)
MATHEMATICS--Algebra--Elementary.
Processes, Infinite
Inequalities (Mathematics)
Ungleichung.
Electronic books.
QA295 / .S78 2004eb
512.9/7
The Cauchy-Schwarz master class : an introduction to the art of mathematical inequalities / J. Michael Steele, University of Pennsylvania. - 1 online resource (x, 306 pages) : illustrations. - MAA problem books series . - MAA problem books series. .
Includes bibliographical references (pages 292-301) and index.
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. Holder's inequality -- 10. Hilbert's inequality -- 11. Hardy's inequality -- 12. Symmetric sums -- 13. Majorization and Schur convexity -- 14. Cancellation and aggregation -- Solutions to the exercises -- Chapter notes -- References -- Index.
Using the Cauchy-Schwarz inequality as the initial guide, this text explains the concepts of mathematical inequalities by presenting a sequence of problems as they might have been discovered, the solutions to which can either be found with one of history's great mathematicians or by the reader themselves.
9780511211348 0511211341 9780511207761 051120776X 9780511213113 0511213115 9780511216718 0511216718 9780511817106 051181710X
OverDrive, Inc. http://www.overdrive.com F4F2B00F-E910-4C7D-AB6B-189D62A246C5 OverDrive, Inc. http://www.overdrive.com
Inequalities (Mathematics)
Processes, Infinite.
Inégalités (Mathématiques)
MATHEMATICS--Algebra--Elementary.
Processes, Infinite
Inequalities (Mathematics)
Ungleichung.
Electronic books.
QA295 / .S78 2004eb
512.9/7