Dror Bar-Natan: Classes: 2003-04: Math 157 - Analysis I: | (8) |
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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

- Show that if , then
for all values
of if and only if
.
- Prove the Cauchy-Schwartz inequality
- Use
(why is this true?), with
- Consider the expression

- Use
(why is this true?), with

**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