The Cauchy–Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities is a graded problem book that will teach them the principles and practice of mathematical proofs like no other book. Here is its MAA review: [0]. A pirate PDF is a Google search away. Take a look and see if you like it. [0] https://www.maa.org/press/maa-reviews/the-cauchy-schwarz-mas... (https://www.maa.org/press/maa-reviews/the-cauchy-schwarz-master-class-an-introduction-to-the-art-of-mathematical-inequalities)
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The Cauchy–Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities
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