The Cauchy-Schwarz Master Class
eBook - PDF

The Cauchy-Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

The Cauchy-Schwarz Master Class

An Introduction to the Art of Mathematical Inequalities

About this book

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.

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Yes, you can access The Cauchy-Schwarz Master Class by J. Michael Steele in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Series-title
  4. Title
  5. Copyright
  6. Contents
  7. Preface
  8. 1 Starting with Cauchy
  9. 2 Cauchy’s Second Inequality: The AM-GM Bound
  10. 3 Lagrange’s Identity and Minkowski’s Conjecture
  11. 4 On Geometry and Sums of Squares
  12. 5 Consequences of Order
  13. 6 Convexity — The Third Pillar
  14. 7 Integral Intermezzo
  15. 8 The Ladder of Power Means
  16. 9 Hölder’s Inequality
  17. 10 Hilbert’s Inequality and Compensating Dificulties
  18. 11 Hardy’s Inequality and the Flop
  19. 12 Symmetric Sums
  20. 13 Majorization and Schur Convexity
  21. 14 Cancellation and Aggregation
  22. Solutions to the Exercises
  23. Chapter Notes
  24. References
  25. Index