Cauchy-Schwarz proof sample

Posted on August 22, 2012 by abouzaid
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This proof of the Cauchy-Schwarz Inequality is used to start a discussion about proof elegance. The class compares this proof with the proof of the Cauchy-Schwarz inequality given in Proofs from the Book by Aigner and Ziegler. The class discusses which proof one would discover first and how it’s a good idea, after having proved something, to think about rewriting it. This writing sample was developed by Mohammed Abouzaid and Peter Speh.

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MAA Mathematical Communication ( is a developing collection of resources for engaging students in writing and speaking about mathematics. The site originated in the MIT Department of Mathematics and was expanded through support from an NSF grant.