# Homework Assignment 2

Assigned Tuesday September 16; due Friday September 26, 2PM, at SS 1071

this document in PDF: HW02.pdf

Required reading. All of Spivak Chapter 1.

To be handed in. From Spivak Chapter 1: 11 odd parts, 12 odd parts, 14, and also

1. Show that if , then for all values of if and only if .

2. Prove the Cauchy-Schwartz inequality

in two different ways:
1. Use (why is this true?), with

2. Consider the expression

collect terms, and apply the result of Problem 1.

Recommended for extra practice. Spivak Chapter 1: 7, 15, 18, 20, 21, 22, 23.

Just for fun. Seen on the web, source unknown (though see http://www.mrc-cbu.cam.ac.uk/~matt.davis/Cmabrigde/):

Accdronig to a rscheearch at an Elingsh uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoatnt tihng is taht frist and lsat ltteer is at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae we do not raed ervey lteter by it slef but the wrod as a wlohe.

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Dror Bar-Natan 2003-10-21