© | Dror Bar-Natan: Classes: 2004-05: Math 157 - Analysis I: | (10) |
Next: Class Notes for Tuesday September 21, 2004
Previous: Class Notes for Thursday September 16, 2004 |

Assigned Tuesday September 21; due Friday October 1, 2PM,
at SS 1071

this document in PDF: HW.pdf

**Required reading. ** Like last week, read,
reread and rereread your notes from this week's classes, and make sure
that you really, really really, really really really understand
everything in them. Do the same every week! Also, read all of Spivak's
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. ** From Spivak
Chapter 1: 7, 15, 18, 20, 21, 22, 23.

**Just for fun. ** Can you draw 3 linked circles,
with the property that if any one of them disappears, the other two are
no longer linked? Can you draw 4 linked circles, with the property that
if any one of them disappears, the other 3 are no longer linked? What
about more than 4? (In the example below, if you drop any of the
components the other two remain linked).

The generation of this document was assisted by
L^{A}TEX2`HTML`.

Dror Bar-Natan 2004-09-20