Dror Bar-Natan: Classes: 2003-04: Math 157 - Analysis I: | (88) |
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Assigned Tuesday March 9; due Friday March 19, 2PM,
at SS 1071

This document in PDF: HW.pdf

**Required reading. ** All of Spivak's Chapter 22.

**To be handed in. ** From Spivak Chapter 22: 1 (odd
parts), 2 (odd parts), 5, 13.

**Recommended for extra practice. ** From Spivak
Chapter 22: 1 (even parts), 2 (even parts), 9, 27, 28, 29.

**Just for fun. ** For some constant number ,
consider the function
. Let be the set of all
pairs so that
and is a limit of a
subsequence of the sequence
,
,
, .... Write a computer program to draw the
set in the plane whose axes are and , and if your program
and picture are nice, they'll find their place on this class' web
site.

It's a hard one, but it's well worth it. The set is way more complex than you would expect, with parts that scream ``structure'' and parts that scream ``mess''. If you've ever heard the word ``chaos'' in a mathematical context before, this is it. And if you've ever seen pictures of the beautiful ``Mandelbrot Set'', our is a close relation.

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L^{A}TEX2`HTML`.

Dror Bar-Natan 2004-03-08