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THE CAUCHY–SCHWARZ MASTER CLASS
_An Introduction to the Art of Mathematical Inequalities
by J. MICHAEL STEELE
英文
Contents
Preface page ix
1 Starting with Cauchy 1
2 The AM-GM Inequality 19
3 Lagrange’s Identity and Minkowski’s Conjecture 37
4 OnGeometry and Sums of Squares 51
5 Consequences of Order 73
6 Convexity — The Third Pillar 87
7 Integral Intermezzo 105
8 The Ladder of Power Means 120
9 H¨older’s Inequality 135
10 Hilbert’s Inequality and Compensating Difficulties 155
11 Hardy’s Inequality and the Flop 166
12 Symmetric Sums 178
13 Majorization and Schur Convexity 191
14 Cancellation and Aggregation 208
Solutions to the Exercises 226
Chapter Notes 284
References 291
Index 301
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