Drorbn - User contributions [en]

Template:0708-1300/Navigation

2008-04-09T15:27:15Z

Aroesler:

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[0708-1300]]/[[Template:0708-1300/Navigation|Navigation Panel]]  </div>
<div class="NavContent">
{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|-
|colspan=3 align=center|[[Image:0708-1300-ClassPhoto.jpg|215px]]<br>[[0708-1300/Class Photo|Add your name / see who's in!]]
|- align=center
!#
!Week of...
!Links
|-
|colspan=3 align=center|'''Fall Semester'''
|- align=left
|align=center|1
|Sep 10
|[[0708-1300/About This Class|About]], [[0708-1300/Class notes for Tuesday, September 11|Tue]], [[0708-1300/Class notes for Thursday, September 13|Thu]]
|- align=left
|align=center|2
|Sep 17
|[[0708-1300/Class notes for Tuesday, September 18|Tue]], [[0708-1300/Homework Assignment 1|HW1]], [[0708-1300/Class notes for Thursday, September 20|Thu]]
|- align=left
|align=center|3
|Sep 24
|[[0708-1300/Class notes for Tuesday, September 25|Tue]], [[0708-1300/Class Photo|Photo]], [[0708-1300/Class notes for Thursday, September 27|Thu]]
|- align=left
|align=center|4
|Oct 1
|[[0708-1300/Questionnaire|Questionnaire]], [[0708-1300/Class notes for Tuesday, October 2|Tue]], [[0708-1300/Homework Assignment 2|HW2]], [[0708-1300/Class notes for Thursday, October 4|Thu]]
|- align=left
|align=center|5
|Oct 8
|Thanksgiving, [[0708-1300/Class notes for Tuesday, October_9|Tue]], [[0708-1300/Class notes for Thursday, October 11|Thu]]
|- align=left
|align=center|6
|Oct 15
|[[0708-1300/Class notes for Tuesday, October 16|Tue]], [[0708-1300/Homework Assignment 3|HW3]], [[0708-1300/Class notes for Thursday, October 18|Thu]]
|- align=left
|align=center|7
|Oct 22
|[[0708-1300/Class notes for Tuesday, October 23|Tue]], [[0708-1300/Class notes for Thursday, October 25|Thu]]
|- align=left
|align=center|8
|Oct 29
|[[0708-1300/Class notes for Tuesday, October 30|Tue]], [[0708-1300/Homework Assignment 4|HW4]], [[0708-1300/Class notes for Thursday, November 1|Thu]], [[0708-1300/the unit sphere in a Hilbert space is contractible|Hilbert sphere]]
|- align=left
|align=center|9
|Nov 5
|[[0708-1300/Class notes for Tuesday, November 6|Tue]],[[0708-1300/Class notes for Thursday, November 8|Thu]], [[0708-1300/Term Exam 1|TE1]]
|- align=left
|align=center|10
|Nov 12
|[[0708-1300/Class notes for Tuesday, November 13|Tue]], <strike>[[0708-1300/Class notes for Thursday, November 15|Thu]]</strike>
|- align=left
|align=center|11
|Nov 19
|[[0708-1300/Class notes for Tuesday, November 20|Tue]], [[0708-1300/Homework Assignment 5|HW5]]
|- align=left
|align=center|12
|Nov 26
|[[0708-1300/Class notes for Tuesday, November 27|Tue]], [[0708-1300/Class notes for Thursday, November 29|Thu]]
|- align=left
|align=center|13
|Dec 3
|[[0708-1300/Class notes for Tuesday, December 4|Tue]], [[0708-1300/Class notes for Thursday, December 6|Thu]], [[0708-1300/Homework Assignment 6|HW6]]
|-
|colspan=3 align=center|'''Spring Semester'''
|- align=left
|align=center|14
|Jan 7
|[[0708-1300/Class notes for Tuesday, January 8|Tue]], [[0708-1300/Class notes for Thursday, January 10|Thu]], [[0708-1300/Homework Assignment 7|HW7]]
|- align=left
|align=center|15
|Jan 14
|[[0708-1300/Class notes for Tuesday, January 15|Tue]], [[0708-1300/Class notes for Thursday, January 17|Thu]]
|- align=left
|align=center|16
|Jan 21
|[[0708-1300/Class notes for Tuesday, January 22|Tue]], [[0708-1300/Class notes for Thursday, January 24|Thu]], [[0708-1300/Homework Assignment 8|HW8]]
|- align=left
|align=center|17
|Jan 28
|[[0708-1300/Class notes for Tuesday, January 29|Tue]]
|- align=left
|align=center|18
|Feb 4
|[[0708-1300/Class notes for Tuesday, February 5|Tue]]
|- align=left
|align=center|19
|Feb 11
|[[0708-1300/Term Exam 2|TE2]], [[0708-1300/Homework Assignment 9|HW9]], [[0708-1300/Class notes for Thursday, February 14|Thu]], Feb 17: last chance to drop class
|- align=left
|align=center|R
|Feb 18
|Reading week
|- align=left
|align=center|20
|Feb 25
|[[0708-1300/Class notes for Tuesday, February 26|Tue]], [[0708-1300/Class notes for Thursday, February 28|Thu]], [[0708-1300/Homework Assignment 10|HW10]]
|- align=left
|align=center|21
|Mar 3
|[[0708-1300/Class notes for Tuesday, March 4|Tue]], [[0708-1300/Class notes for Thursday, March 6|Thu]]
|- align=left
|align=center|22
|Mar 10
|[[0708-1300/Class notes for Tuesday, March 11|Tue]], [[0708-1300/Class notes for Thursday, March 13|Thu]], [[0708-1300/Homework Assignment 11|HW11]]
|- align=left
|align=center|23
|Mar 17
|[[0708-1300/Class notes for Tuesday, March 18|Tue]], [[0708-1300/Class notes for Thursday, March 20|Thu]]
|- align=left
|align=center|24
|Mar 24
|[[0708-1300/Class notes for Tuesday, March 25|Tue]], [[0708-1300/Homework Assignment 12|HW12]], [[0708-1300/Class notes for Thursday, March 27|Thu]]
|- align=left
|align=center|25
|Mar 31
|[[0708-1300/Democracy At Last|Referendum]],[[0708-1300/Class notes for Tuesday, April 1|Tue]], [[0708-1300/Class notes for Thursday, April 3|Thu]]
|- align=left
|align=center|26
|Apr 7
|
|- align=left
|align=center|R
|Apr 14
|
|- align=left
|align=center|R
|Apr 21
|
|- align=left
|align=center|F
|Apr 28
|[[0708-1300/The Final Exam|Final]] (Fri, May 2)
|- align=center
|colspan=3|[[0708-1300/Register of Good Deeds|Register of Good Deeds]]
|- align=center
|colspan=3|[[0708-1300/Errata to Bredon's Book|Errata to Bredon's Book]]
|}
</div></div>
|}
<div align=center style="color: red; font-size: 150%; display: none;">Announcements go here</div>

0708-1300/Class notes for Thursday, February 28

2008-04-09T15:26:13Z

Aroesler: /* Class Notes */

File:0708-1300-Topofeb28p4.jpg

2008-04-09T15:23:25Z

Aroesler: Class notes, February 28 - page 4

Class notes, February 28 - page 4

File:0708-1300-Topofeb28p3.jpg

2008-04-09T15:22:58Z

Aroesler: Class notes, February 28 - page 3

Class notes, February 28 - page 3

File:0708-1300-Topofeb28p2.jpg

2008-04-09T15:22:32Z

Aroesler: Class notes, February 28 - page 2

Class notes, February 28 - page 2

File:0708-1300-Topofeb28p1.jpg

2008-04-09T15:22:02Z

Aroesler: Class notes, February 28 - page 1

Class notes, February 28 - page 1

Template:0708-1300/Navigation

2008-04-09T15:19:45Z

Aroesler:

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[0708-1300]]/[[Template:0708-1300/Navigation|Navigation Panel]]  </div>
<div class="NavContent">
{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|-
|colspan=3 align=center|[[Image:0708-1300-ClassPhoto.jpg|215px]]<br>[[0708-1300/Class Photo|Add your name / see who's in!]]
|- align=center
!#
!Week of...
!Links
|-
|colspan=3 align=center|'''Fall Semester'''
|- align=left
|align=center|1
|Sep 10
|[[0708-1300/About This Class|About]], [[0708-1300/Class notes for Tuesday, September 11|Tue]], [[0708-1300/Class notes for Thursday, September 13|Thu]]
|- align=left
|align=center|2
|Sep 17
|[[0708-1300/Class notes for Tuesday, September 18|Tue]], [[0708-1300/Homework Assignment 1|HW1]], [[0708-1300/Class notes for Thursday, September 20|Thu]]
|- align=left
|align=center|3
|Sep 24
|[[0708-1300/Class notes for Tuesday, September 25|Tue]], [[0708-1300/Class Photo|Photo]], [[0708-1300/Class notes for Thursday, September 27|Thu]]
|- align=left
|align=center|4
|Oct 1
|[[0708-1300/Questionnaire|Questionnaire]], [[0708-1300/Class notes for Tuesday, October 2|Tue]], [[0708-1300/Homework Assignment 2|HW2]], [[0708-1300/Class notes for Thursday, October 4|Thu]]
|- align=left
|align=center|5
|Oct 8
|Thanksgiving, [[0708-1300/Class notes for Tuesday, October_9|Tue]], [[0708-1300/Class notes for Thursday, October 11|Thu]]
|- align=left
|align=center|6
|Oct 15
|[[0708-1300/Class notes for Tuesday, October 16|Tue]], [[0708-1300/Homework Assignment 3|HW3]], [[0708-1300/Class notes for Thursday, October 18|Thu]]
|- align=left
|align=center|7
|Oct 22
|[[0708-1300/Class notes for Tuesday, October 23|Tue]], [[0708-1300/Class notes for Thursday, October 25|Thu]]
|- align=left
|align=center|8
|Oct 29
|[[0708-1300/Class notes for Tuesday, October 30|Tue]], [[0708-1300/Homework Assignment 4|HW4]], [[0708-1300/Class notes for Thursday, November 1|Thu]], [[0708-1300/the unit sphere in a Hilbert space is contractible|Hilbert sphere]]
|- align=left
|align=center|9
|Nov 5
|[[0708-1300/Class notes for Tuesday, November 6|Tue]],[[0708-1300/Class notes for Thursday, November 8|Thu]], [[0708-1300/Term Exam 1|TE1]]
|- align=left
|align=center|10
|Nov 12
|[[0708-1300/Class notes for Tuesday, November 13|Tue]], <strike>[[0708-1300/Class notes for Thursday, November 15|Thu]]</strike>
|- align=left
|align=center|11
|Nov 19
|[[0708-1300/Class notes for Tuesday, November 20|Tue]], [[0708-1300/Homework Assignment 5|HW5]]
|- align=left
|align=center|12
|Nov 26
|[[0708-1300/Class notes for Tuesday, November 27|Tue]], [[0708-1300/Class notes for Thursday, November 29|Thu]]
|- align=left
|align=center|13
|Dec 3
|[[0708-1300/Class notes for Tuesday, December 4|Tue]], [[0708-1300/Class notes for Thursday, December 6|Thu]], [[0708-1300/Homework Assignment 6|HW6]]
|-
|colspan=3 align=center|'''Spring Semester'''
|- align=left
|align=center|14
|Jan 7
|[[0708-1300/Class notes for Tuesday, January 8|Tue]], [[0708-1300/Class notes for Thursday, January 10|Thu]], [[0708-1300/Homework Assignment 7|HW7]]
|- align=left
|align=center|15
|Jan 14
|[[0708-1300/Class notes for Tuesday, January 15|Tue]], [[0708-1300/Class notes for Thursday, January 17|Thu]]
|- align=left
|align=center|16
|Jan 21
|[[0708-1300/Class notes for Tuesday, January 22|Tue]], [[0708-1300/Class notes for Thursday, January 24|Thu]], [[0708-1300/Homework Assignment 8|HW8]]
|- align=left
|align=center|17
|Jan 28
|[[0708-1300/Class notes for Tuesday, January 29|Tue]]
|- align=left
|align=center|18
|Feb 4
|[[0708-1300/Class notes for Tuesday, February 5|Tue]]
|- align=left
|align=center|19
|Feb 11
|[[0708-1300/Term Exam 2|TE2]], [[0708-1300/Homework Assignment 9|HW9]], [[0708-1300/Class notes for Thursday, February 14|Thu]], Feb 17: last chance to drop class
|- align=left
|align=center|R
|Feb 18
|Reading week
|- align=left
|align=center|20
|Feb 25
|[[0708-1300/Class notes for Tuesday, February 26|Tue]], [[0708-1300/Homework Assignment 10|HW10]]
|- align=left
|align=center|21
|Mar 3
|[[0708-1300/Class notes for Tuesday, March 4|Tue]], [[0708-1300/Class notes for Thursday, March 6|Thu]]
|- align=left
|align=center|22
|Mar 10
|[[0708-1300/Class notes for Tuesday, March 11|Tue]], [[0708-1300/Class notes for Thursday, March 13|Thu]], [[0708-1300/Homework Assignment 11|HW11]]
|- align=left
|align=center|23
|Mar 17
|[[0708-1300/Class notes for Tuesday, March 18|Tue]], [[0708-1300/Class notes for Thursday, March 20|Thu]]
|- align=left
|align=center|24
|Mar 24
|[[0708-1300/Class notes for Tuesday, March 25|Tue]], [[0708-1300/Homework Assignment 12|HW12]], [[0708-1300/Class notes for Thursday, March 27|Thu]]
|- align=left
|align=center|25
|Mar 31
|[[0708-1300/Democracy At Last|Referendum]],[[0708-1300/Class notes for Tuesday, April 1|Tue]], [[0708-1300/Class notes for Thursday, April 3|Thu]]
|- align=left
|align=center|26
|Apr 7
|
|- align=left
|align=center|R
|Apr 14
|
|- align=left
|align=center|R
|Apr 21
|
|- align=left
|align=center|F
|Apr 28
|[[0708-1300/The Final Exam|Final]] (Fri, May 2)
|- align=center
|colspan=3|[[0708-1300/Register of Good Deeds|Register of Good Deeds]]
|- align=center
|colspan=3|[[0708-1300/Errata to Bredon's Book|Errata to Bredon's Book]]
|}
</div></div>
|}
<div align=center style="color: red; font-size: 150%; display: none;">Announcements go here</div>

0708-1300/Class notes for Tuesday, March 4

2008-04-09T15:18:40Z

Aroesler: /* Class Notes */

===Class Notes===

<span style="color: red;">The notes below are by the students and for the students. Hopefully they are useful, but they come with no guarantee of any kind.</span>

[[Image:0708-1300-March4_01.jpg|400px]]
[[Image:0708-1300-March4_02.jpg|400px]]
[[Image:0708-1300-March4_03.jpg|400px]]
[[Image:0708-1300-March4_04.jpg|400px]]
[[Image:0708-1300-March4_05.jpg|400px]]
[[Image:0708-1300-March4_06.jpg|400px]]
[[Image:0708-1300-March4_07.jpg|400px]]
[[Image:0708-1300-March4_08.jpg|400px]]

File:0708-1300-March4 08.jpg

2008-04-09T15:17:33Z

Aroesler: Class notes, March 4 - page 8

Class notes, March 4 - page 8

File:0708-1300-March4 07.jpg

2008-04-09T15:17:06Z

Aroesler: Class notes, March 4 - page 7

Class notes, March 4 - page 7

File:0708-1300-March4 06.jpg

2008-04-09T15:16:37Z

Aroesler: Class notes, March 4 - page 6

Class notes, March 4 - page 6

File:0708-1300-March4 05.jpg

2008-04-09T15:16:13Z

Aroesler: Class notes, March 4 - page 5

Class notes, March 4 - page 5

File:0708-1300-March4 04.jpg

2008-04-09T15:15:46Z

Aroesler: Class notes, March 4 - page 4

Class notes, March 4 - page 4

File:0708-1300-March4 03.jpg

2008-04-09T15:15:13Z

Aroesler:

File:0708-1300-March4 02.jpg

2008-04-09T15:14:55Z

Aroesler: Class notes, March 4 - page 2

Class notes, March 4 - page 2

File:0708-1300-March4 01.jpg

2008-04-09T15:14:29Z

Aroesler: Class notes, March 4 - page 1

Class notes, March 4 - page 1

Template:0708-1300/Navigation

2008-04-09T00:26:17Z

Aroesler:

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[0708-1300]]/[[Template:0708-1300/Navigation|Navigation Panel]]  </div>
<div class="NavContent">
{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|-
|colspan=3 align=center|[[Image:0708-1300-ClassPhoto.jpg|215px]]<br>[[0708-1300/Class Photo|Add your name / see who's in!]]
|- align=center
!#
!Week of...
!Links
|-
|colspan=3 align=center|'''Fall Semester'''
|- align=left
|align=center|1
|Sep 10
|[[0708-1300/About This Class|About]], [[0708-1300/Class notes for Tuesday, September 11|Tue]], [[0708-1300/Class notes for Thursday, September 13|Thu]]
|- align=left
|align=center|2
|Sep 17
|[[0708-1300/Class notes for Tuesday, September 18|Tue]], [[0708-1300/Homework Assignment 1|HW1]], [[0708-1300/Class notes for Thursday, September 20|Thu]]
|- align=left
|align=center|3
|Sep 24
|[[0708-1300/Class notes for Tuesday, September 25|Tue]], [[0708-1300/Class Photo|Photo]], [[0708-1300/Class notes for Thursday, September 27|Thu]]
|- align=left
|align=center|4
|Oct 1
|[[0708-1300/Questionnaire|Questionnaire]], [[0708-1300/Class notes for Tuesday, October 2|Tue]], [[0708-1300/Homework Assignment 2|HW2]], [[0708-1300/Class notes for Thursday, October 4|Thu]]
|- align=left
|align=center|5
|Oct 8
|Thanksgiving, [[0708-1300/Class notes for Tuesday, October_9|Tue]], [[0708-1300/Class notes for Thursday, October 11|Thu]]
|- align=left
|align=center|6
|Oct 15
|[[0708-1300/Class notes for Tuesday, October 16|Tue]], [[0708-1300/Homework Assignment 3|HW3]], [[0708-1300/Class notes for Thursday, October 18|Thu]]
|- align=left
|align=center|7
|Oct 22
|[[0708-1300/Class notes for Tuesday, October 23|Tue]], [[0708-1300/Class notes for Thursday, October 25|Thu]]
|- align=left
|align=center|8
|Oct 29
|[[0708-1300/Class notes for Tuesday, October 30|Tue]], [[0708-1300/Homework Assignment 4|HW4]], [[0708-1300/Class notes for Thursday, November 1|Thu]], [[0708-1300/the unit sphere in a Hilbert space is contractible|Hilbert sphere]]
|- align=left
|align=center|9
|Nov 5
|[[0708-1300/Class notes for Tuesday, November 6|Tue]],[[0708-1300/Class notes for Thursday, November 8|Thu]], [[0708-1300/Term Exam 1|TE1]]
|- align=left
|align=center|10
|Nov 12
|[[0708-1300/Class notes for Tuesday, November 13|Tue]], <strike>[[0708-1300/Class notes for Thursday, November 15|Thu]]</strike>
|- align=left
|align=center|11
|Nov 19
|[[0708-1300/Class notes for Tuesday, November 20|Tue]], [[0708-1300/Homework Assignment 5|HW5]]
|- align=left
|align=center|12
|Nov 26
|[[0708-1300/Class notes for Tuesday, November 27|Tue]], [[0708-1300/Class notes for Thursday, November 29|Thu]]
|- align=left
|align=center|13
|Dec 3
|[[0708-1300/Class notes for Tuesday, December 4|Tue]], [[0708-1300/Class notes for Thursday, December 6|Thu]], [[0708-1300/Homework Assignment 6|HW6]]
|-
|colspan=3 align=center|'''Spring Semester'''
|- align=left
|align=center|14
|Jan 7
|[[0708-1300/Class notes for Tuesday, January 8|Tue]], [[0708-1300/Class notes for Thursday, January 10|Thu]], [[0708-1300/Homework Assignment 7|HW7]]
|- align=left
|align=center|15
|Jan 14
|[[0708-1300/Class notes for Tuesday, January 15|Tue]], [[0708-1300/Class notes for Thursday, January 17|Thu]]
|- align=left
|align=center|16
|Jan 21
|[[0708-1300/Class notes for Tuesday, January 22|Tue]], [[0708-1300/Class notes for Thursday, January 24|Thu]], [[0708-1300/Homework Assignment 8|HW8]]
|- align=left
|align=center|17
|Jan 28
|[[0708-1300/Class notes for Tuesday, January 29|Tue]]
|- align=left
|align=center|18
|Feb 4
|[[0708-1300/Class notes for Tuesday, February 5|Tue]]
|- align=left
|align=center|19
|Feb 11
|[[0708-1300/Term Exam 2|TE2]], [[0708-1300/Homework Assignment 9|HW9]], [[0708-1300/Class notes for Thursday, February 14|Thu]], Feb 17: last chance to drop class
|- align=left
|align=center|R
|Feb 18
|Reading week
|- align=left
|align=center|20
|Feb 25
|[[0708-1300/Class notes for Tuesday, February 26|Tue]], [[0708-1300/Homework Assignment 10|HW10]]
|- align=left
|align=center|21
|Mar 3
|[[0708-1300/Class notes for Thursday, March 6|Thu]]
|- align=left
|align=center|22
|Mar 10
|[[0708-1300/Class notes for Tuesday, March 11|Tue]], [[0708-1300/Class notes for Thursday, March 13|Thu]], [[0708-1300/Homework Assignment 11|HW11]]
|- align=left
|align=center|23
|Mar 17
|[[0708-1300/Class notes for Tuesday, March 18|Tue]], [[0708-1300/Class notes for Thursday, March 20|Thu]]
|- align=left
|align=center|24
|Mar 24
|[[0708-1300/Class notes for Tuesday, March 25|Tue]], [[0708-1300/Homework Assignment 12|HW12]], [[0708-1300/Class notes for Thursday, March 27|Thu]]
|- align=left
|align=center|25
|Mar 31
|[[0708-1300/Democracy At Last|Referendum]],[[0708-1300/Class notes for Tuesday, April 1|Tue]], [[0708-1300/Class notes for Thursday, April 3|Thu]]
|- align=left
|align=center|26
|Apr 7
|
|- align=left
|align=center|R
|Apr 14
|
|- align=left
|align=center|R
|Apr 21
|
|- align=left
|align=center|F
|Apr 28
|[[0708-1300/The Final Exam|Final]] (Fri, May 2)
|- align=center
|colspan=3|[[0708-1300/Register of Good Deeds|Register of Good Deeds]]
|- align=center
|colspan=3|[[0708-1300/Errata to Bredon's Book|Errata to Bredon's Book]]
|}
</div></div>
|}
<div align=center style="color: red; font-size: 150%; display: none;">Announcements go here</div>

0708-1300/Class notes for Thursday, March 6

2008-04-09T00:24:12Z

Aroesler: /* Class Notes */

File:0708-1300-March6 02.jpg

2008-04-09T00:23:24Z

Aroesler: Class notes, March 6 - page 2

Class notes, March 6 - page 2

File:0708-1300-March6 01.jpg

2008-04-09T00:22:53Z

Aroesler: Class notes, March 6 - page 1

Class notes, March 6 - page 1

0708-1300/Class notes for Thursday, March 13

2008-04-09T00:21:12Z

Aroesler: /* Class Notes */

File:0708-1300-March13 03.jpg

2008-04-09T00:20:29Z

Aroesler: Class notes, March 13 - page 3

Class notes, March 13 - page 3

File:0708-1300-March13 02.jpg

2008-04-09T00:20:03Z

Aroesler: Class notes, March 13 - page 2

Class notes, March 13 - page 2

File:0708-1300-March13 01.jpg

2008-04-09T00:19:35Z

Aroesler: Class notes, March 13 - page 1

Class notes, March 13 - page 1

Template:0708-1300/Navigation

2008-04-08T21:38:42Z

Aroesler:

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[0708-1300]]/[[Template:0708-1300/Navigation|Navigation Panel]]  </div>
<div class="NavContent">
{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|-
|colspan=3 align=center|[[Image:0708-1300-ClassPhoto.jpg|215px]]<br>[[0708-1300/Class Photo|Add your name / see who's in!]]
|- align=center
!#
!Week of...
!Links
|-
|colspan=3 align=center|'''Fall Semester'''
|- align=left
|align=center|1
|Sep 10
|[[0708-1300/About This Class|About]], [[0708-1300/Class notes for Tuesday, September 11|Tue]], [[0708-1300/Class notes for Thursday, September 13|Thu]]
|- align=left
|align=center|2
|Sep 17
|[[0708-1300/Class notes for Tuesday, September 18|Tue]], [[0708-1300/Homework Assignment 1|HW1]], [[0708-1300/Class notes for Thursday, September 20|Thu]]
|- align=left
|align=center|3
|Sep 24
|[[0708-1300/Class notes for Tuesday, September 25|Tue]], [[0708-1300/Class Photo|Photo]], [[0708-1300/Class notes for Thursday, September 27|Thu]]
|- align=left
|align=center|4
|Oct 1
|[[0708-1300/Questionnaire|Questionnaire]], [[0708-1300/Class notes for Tuesday, October 2|Tue]], [[0708-1300/Homework Assignment 2|HW2]], [[0708-1300/Class notes for Thursday, October 4|Thu]]
|- align=left
|align=center|5
|Oct 8
|Thanksgiving, [[0708-1300/Class notes for Tuesday, October_9|Tue]], [[0708-1300/Class notes for Thursday, October 11|Thu]]
|- align=left
|align=center|6
|Oct 15
|[[0708-1300/Class notes for Tuesday, October 16|Tue]], [[0708-1300/Homework Assignment 3|HW3]], [[0708-1300/Class notes for Thursday, October 18|Thu]]
|- align=left
|align=center|7
|Oct 22
|[[0708-1300/Class notes for Tuesday, October 23|Tue]], [[0708-1300/Class notes for Thursday, October 25|Thu]]
|- align=left
|align=center|8
|Oct 29
|[[0708-1300/Class notes for Tuesday, October 30|Tue]], [[0708-1300/Homework Assignment 4|HW4]], [[0708-1300/Class notes for Thursday, November 1|Thu]], [[0708-1300/the unit sphere in a Hilbert space is contractible|Hilbert sphere]]
|- align=left
|align=center|9
|Nov 5
|[[0708-1300/Class notes for Tuesday, November 6|Tue]],[[0708-1300/Class notes for Thursday, November 8|Thu]], [[0708-1300/Term Exam 1|TE1]]
|- align=left
|align=center|10
|Nov 12
|[[0708-1300/Class notes for Tuesday, November 13|Tue]], <strike>[[0708-1300/Class notes for Thursday, November 15|Thu]]</strike>
|- align=left
|align=center|11
|Nov 19
|[[0708-1300/Class notes for Tuesday, November 20|Tue]], [[0708-1300/Homework Assignment 5|HW5]]
|- align=left
|align=center|12
|Nov 26
|[[0708-1300/Class notes for Tuesday, November 27|Tue]], [[0708-1300/Class notes for Thursday, November 29|Thu]]
|- align=left
|align=center|13
|Dec 3
|[[0708-1300/Class notes for Tuesday, December 4|Tue]], [[0708-1300/Class notes for Thursday, December 6|Thu]], [[0708-1300/Homework Assignment 6|HW6]]
|-
|colspan=3 align=center|'''Spring Semester'''
|- align=left
|align=center|14
|Jan 7
|[[0708-1300/Class notes for Tuesday, January 8|Tue]], [[0708-1300/Class notes for Thursday, January 10|Thu]], [[0708-1300/Homework Assignment 7|HW7]]
|- align=left
|align=center|15
|Jan 14
|[[0708-1300/Class notes for Tuesday, January 15|Tue]], [[0708-1300/Class notes for Thursday, January 17|Thu]]
|- align=left
|align=center|16
|Jan 21
|[[0708-1300/Class notes for Tuesday, January 22|Tue]], [[0708-1300/Class notes for Thursday, January 24|Thu]], [[0708-1300/Homework Assignment 8|HW8]]
|- align=left
|align=center|17
|Jan 28
|[[0708-1300/Class notes for Tuesday, January 29|Tue]]
|- align=left
|align=center|18
|Feb 4
|[[0708-1300/Class notes for Tuesday, February 5|Tue]]
|- align=left
|align=center|19
|Feb 11
|[[0708-1300/Term Exam 2|TE2]], [[0708-1300/Homework Assignment 9|HW9]], [[0708-1300/Class notes for Thursday, February 14|Thu]], Feb 17: last chance to drop class
|- align=left
|align=center|R
|Feb 18
|Reading week
|- align=left
|align=center|20
|Feb 25
|[[0708-1300/Class notes for Tuesday, February 26|Tue]], [[0708-1300/Homework Assignment 10|HW10]]
|- align=left
|align=center|21
|Mar 3
|
|- align=left
|align=center|22
|Mar 10
|[[0708-1300/Class notes for Tuesday, March 11|Tue]], [[0708-1300/Homework Assignment 11|HW11]]
|- align=left
|align=center|23
|Mar 17
|[[0708-1300/Class notes for Tuesday, March 18|Tue]], [[0708-1300/Class notes for Thursday, March 20|Thu]]
|- align=left
|align=center|24
|Mar 24
|[[0708-1300/Class notes for Tuesday, March 25|Tue]], [[0708-1300/Homework Assignment 12|HW12]], [[0708-1300/Class notes for Thursday, March 27|Thu]]
|- align=left
|align=center|25
|Mar 31
|[[0708-1300/Democracy At Last|Referendum]],[[0708-1300/Class notes for Tuesday, April 1|Tue]], [[0708-1300/Class notes for Thursday, April 3|Thu]]
|- align=left
|align=center|26
|Apr 7
|
|- align=left
|align=center|R
|Apr 14
|
|- align=left
|align=center|R
|Apr 21
|
|- align=left
|align=center|F
|Apr 28
|[[0708-1300/The Final Exam|Final]] (Fri, May 2)
|- align=center
|colspan=3|[[0708-1300/Register of Good Deeds|Register of Good Deeds]]
|- align=center
|colspan=3|[[0708-1300/Errata to Bredon's Book|Errata to Bredon's Book]]
|}
</div></div>
|}
<div align=center style="color: red; font-size: 150%; display: none;">Announcements go here</div>

0708-1300/Class notes for Thursday, March 20

2008-04-08T21:37:36Z

Aroesler:

0708-1300/Class notes for Thursday, March 27

2008-04-08T21:36:33Z

Aroesler: /* Class Notes */

{{0708-1300/Navigation}}

==Handout==

{{Home Link|classes/0102/AlgTop/Pathologies/index.html|Topological Pathologies in <math>{\mathbb R}^n</math>}} (from {{Dror}}'s {{Home Link|classes/0102/AlgTop/|2001-2002 class}}).

===Class Notes===

<span style="color: red;">The notes below are by the students and for the students. Hopefully they are useful, but they come with no guarantee of any kind.</span>

[[Image:0708-1300-March27_01.jpg|400px]]
[[Image:0708-1300-March27_02.jpg|400px]]
[[Image:0708-1300-March27_03.jpg|400px]]
[[Image:0708-1300-March27_03.jpg|400px]]

0708-1300/Class notes for Thursday, March 27

2008-04-08T21:35:02Z

Aroesler: /* Class Notes */

{{0708-1300/Navigation}}

==Handout==

{{Home Link|classes/0102/AlgTop/Pathologies/index.html|Topological Pathologies in <math>{\mathbb R}^n</math>}} (from {{Dror}}'s {{Home Link|classes/0102/AlgTop/|2001-2002 class}}).

===Class Notes===

<span style="color: red;">The notes below are by the students and for the students. Hopefully they are useful, but they come with no guarantee of any kind.</span>

[[Image:0708-1300-March20_01.jpg|400px]]
[[Image:0708-1300-March20_02.jpg|400px]]
[[Image:0708-1300-March20_03.jpg|400px]]

File:0708-1300-March20 03.jpg

2008-04-08T21:34:40Z

Aroesler: Class notes, March 20 - page 3

Class notes, March 20 - page 3

File:0708-1300-March20 02.jpg

2008-04-08T21:34:11Z

Aroesler: Class notes, March 20 - page 2

Class notes, March 20 - page 2

File:0708-1300-March20 01.jpg

2008-04-08T21:33:19Z

Aroesler: Class notes, March 20 - page 1

Class notes, March 20 - page 1

0708-1300/Class notes for Thursday, March 27

2008-04-08T18:42:14Z

Aroesler: /* Handout */

File:0708-1300-March27 04.jpg

2008-04-08T18:41:18Z

Aroesler: Class notes, March 27 - page 4

Class notes, March 27 - page 4

File:0708-1300-March27 03.jpg

2008-04-08T18:40:53Z

Aroesler:

File:0708-1300-March27 02.jpg

2008-04-08T18:40:38Z

Aroesler: Class notes, March 27 - page 2

Class notes, March 27 - page 2

File:0708-1300-March27 01.jpg

2008-04-08T18:40:02Z

Aroesler: Class notes, March 27 - page 1

Class notes, March 27 - page 1

Template:0708-1300/Navigation

2008-04-08T18:33:15Z

Aroesler:

{| cellpadding="0" cellspacing="0" style="clear: right; float: right"
|- align=right
|<div class="NavFrame"><div class="NavHead">[[0708-1300]]/[[Template:0708-1300/Navigation|Navigation Panel]]  </div>
<div class="NavContent">
{| border="1px" cellpadding="1" cellspacing="0" width="220" style="margin: 0 0 1em 0.5em; font-size: small"
|-
|colspan=3 align=center|[[Image:0708-1300-ClassPhoto.jpg|215px]]<br>[[0708-1300/Class Photo|Add your name / see who's in!]]
|- align=center
!#
!Week of...
!Links
|-
|colspan=3 align=center|'''Fall Semester'''
|- align=left
|align=center|1
|Sep 10
|[[0708-1300/About This Class|About]], [[0708-1300/Class notes for Tuesday, September 11|Tue]], [[0708-1300/Class notes for Thursday, September 13|Thu]]
|- align=left
|align=center|2
|Sep 17
|[[0708-1300/Class notes for Tuesday, September 18|Tue]], [[0708-1300/Homework Assignment 1|HW1]], [[0708-1300/Class notes for Thursday, September 20|Thu]]
|- align=left
|align=center|3
|Sep 24
|[[0708-1300/Class notes for Tuesday, September 25|Tue]], [[0708-1300/Class Photo|Photo]], [[0708-1300/Class notes for Thursday, September 27|Thu]]
|- align=left
|align=center|4
|Oct 1
|[[0708-1300/Questionnaire|Questionnaire]], [[0708-1300/Class notes for Tuesday, October 2|Tue]], [[0708-1300/Homework Assignment 2|HW2]], [[0708-1300/Class notes for Thursday, October 4|Thu]]
|- align=left
|align=center|5
|Oct 8
|Thanksgiving, [[0708-1300/Class notes for Tuesday, October_9|Tue]], [[0708-1300/Class notes for Thursday, October 11|Thu]]
|- align=left
|align=center|6
|Oct 15
|[[0708-1300/Class notes for Tuesday, October 16|Tue]], [[0708-1300/Homework Assignment 3|HW3]], [[0708-1300/Class notes for Thursday, October 18|Thu]]
|- align=left
|align=center|7
|Oct 22
|[[0708-1300/Class notes for Tuesday, October 23|Tue]], [[0708-1300/Class notes for Thursday, October 25|Thu]]
|- align=left
|align=center|8
|Oct 29
|[[0708-1300/Class notes for Tuesday, October 30|Tue]], [[0708-1300/Homework Assignment 4|HW4]], [[0708-1300/Class notes for Thursday, November 1|Thu]], [[0708-1300/the unit sphere in a Hilbert space is contractible|Hilbert sphere]]
|- align=left
|align=center|9
|Nov 5
|[[0708-1300/Class notes for Tuesday, November 6|Tue]],[[0708-1300/Class notes for Thursday, November 8|Thu]], [[0708-1300/Term Exam 1|TE1]]
|- align=left
|align=center|10
|Nov 12
|[[0708-1300/Class notes for Tuesday, November 13|Tue]], <strike>[[0708-1300/Class notes for Thursday, November 15|Thu]]</strike>
|- align=left
|align=center|11
|Nov 19
|[[0708-1300/Class notes for Tuesday, November 20|Tue]], [[0708-1300/Homework Assignment 5|HW5]]
|- align=left
|align=center|12
|Nov 26
|[[0708-1300/Class notes for Tuesday, November 27|Tue]], [[0708-1300/Class notes for Thursday, November 29|Thu]]
|- align=left
|align=center|13
|Dec 3
|[[0708-1300/Class notes for Tuesday, December 4|Tue]], [[0708-1300/Class notes for Thursday, December 6|Thu]], [[0708-1300/Homework Assignment 6|HW6]]
|-
|colspan=3 align=center|'''Spring Semester'''
|- align=left
|align=center|14
|Jan 7
|[[0708-1300/Class notes for Tuesday, January 8|Tue]], [[0708-1300/Class notes for Thursday, January 10|Thu]], [[0708-1300/Homework Assignment 7|HW7]]
|- align=left
|align=center|15
|Jan 14
|[[0708-1300/Class notes for Tuesday, January 15|Tue]], [[0708-1300/Class notes for Thursday, January 17|Thu]]
|- align=left
|align=center|16
|Jan 21
|[[0708-1300/Class notes for Tuesday, January 22|Tue]], [[0708-1300/Class notes for Thursday, January 24|Thu]], [[0708-1300/Homework Assignment 8|HW8]]
|- align=left
|align=center|17
|Jan 28
|[[0708-1300/Class notes for Tuesday, January 29|Tue]]
|- align=left
|align=center|18
|Feb 4
|[[0708-1300/Class notes for Tuesday, February 5|Tue]]
|- align=left
|align=center|19
|Feb 11
|[[0708-1300/Term Exam 2|TE2]], [[0708-1300/Homework Assignment 9|HW9]], [[0708-1300/Class notes for Thursday, February 14|Thu]], Feb 17: last chance to drop class
|- align=left
|align=center|R
|Feb 18
|Reading week
|- align=left
|align=center|20
|Feb 25
|[[0708-1300/Class notes for Tuesday, February 26|Tue]], [[0708-1300/Homework Assignment 10|HW10]]
|- align=left
|align=center|21
|Mar 3
|
|- align=left
|align=center|22
|Mar 10
|[[0708-1300/Class notes for Tuesday, March 11|Tue]], [[0708-1300/Homework Assignment 11|HW11]]
|- align=left
|align=center|23
|Mar 17
|[[0708-1300/Class notes for Tuesday, March 18|Tue]]
|- align=left
|align=center|24
|Mar 24
|[[0708-1300/Class notes for Tuesday, March 25|Tue]], [[0708-1300/Homework Assignment 12|HW12]], [[0708-1300/Class notes for Thursday, March 27|Thu]]
|- align=left
|align=center|25
|Mar 31
|[[0708-1300/Democracy At Last|Referendum]],[[0708-1300/Class notes for Tuesday, April 1|Tue]], [[0708-1300/Class notes for Thursday, April 3|Thu]]
|- align=left
|align=center|26
|Apr 7
|
|- align=left
|align=center|R
|Apr 14
|
|- align=left
|align=center|R
|Apr 21
|
|- align=left
|align=center|F
|Apr 28
|[[0708-1300/The Final Exam|Final]] (Fri, May 2)
|- align=center
|colspan=3|[[0708-1300/Register of Good Deeds|Register of Good Deeds]]
|- align=center
|colspan=3|[[0708-1300/Errata to Bredon's Book|Errata to Bredon's Book]]
|}
</div></div>
|}
<div align=center style="color: red; font-size: 150%; display: none;">Announcements go here</div>

0708-1300/Class notes for Thursday, April 3

2008-04-08T18:30:41Z

Aroesler: /*Class notes*/

File:0708-1300-Apr3 03.jpg

2008-04-08T18:29:31Z

Aroesler: Class notes, April 3 - page 3

Class notes, April 3 - page 3

File:0708-1300-Apr3 02.jpg

2008-04-08T18:28:54Z

Aroesler: Class notes, April 3 - page 2

Class notes, April 3 - page 2

File:0708-1300-Apr3 01.jpg

2008-04-08T18:28:06Z

Aroesler: Class notes for Thursday, April 3 - page 1

Class notes for Thursday, April 3 - page 1

0708-1300/Class notes for Tuesday, March 11

2008-03-12T00:53:05Z

Aroesler:

{{0708-1300/Navigation}}

[[Image:0708-1300-WantedByExcision.png|center|480px]]

===Class Notes===

<span style="color: red;">The notes below are by the students and for the students. Hopefully they are useful, but they come with no guarantee of any kind.</span>

[[Image:0708-1300-TopoMarch11p1.jpg|400px]]
[[Image:0708-1300-TopoMarch11p2.jpg|400px]]
[[Image:0708-1300-TopoMarch11p3.jpg|400px]]

File:0708-1300-TopoMarch11p3.jpg

2008-03-12T00:52:15Z

Aroesler: Class notes for Tuesday, March 11, page 3

Class notes for Tuesday, March 11, page 3

File:0708-1300-TopoMarch11p2.jpg

2008-03-12T00:50:15Z

Aroesler: Class notes for Tuesday, March 11, page 2

Class notes for Tuesday, March 11, page 2

File:0708-1300-TopoMarch11p1.jpg

2008-03-12T00:48:47Z

Aroesler: Class notes for Tuesday, March 11, page 1

Class notes for Tuesday, March 11, page 1

0708-1300/Class notes for Tuesday, February 12

2008-03-10T01:47:06Z

Aroesler: /* Typed Notes */

INCOMPLETE

===Class Notes===

<span style="color: red;">The notes below are by the students and for the students. Hopefully they are useful, but they come with no guarantee of any kind.</span>

[[Image:0708-1300-Topofeb12p1.jpg|400px]]
[[Image:0708-1300-Topofeb12p2.jpg|400px]]
[[Image:0708-1300-Topofeb12p3.jpg|400px]]
[[Image:0708-1300-Topofeb12p4.jpg|400px]]
[[Image:0708-1300-Topofeb12p5.jpg|400px]]

==Typed Notes==

Informal definition of homology:

Given X (General topological spaces with no base point) then H_n(X) = {Boundaryless compact n-dim m submanifolds of X}/{Boundaries of (n+1)-dim submanifolds

because <math>\partial\partial = \empty</math>, the this makes sense.

We will need to formalize this by using vector spaces generated by sets.

We begin by computing the homology of some examples. These are correct in spirit but very wrong in the details, indeed, we havn't even defined what the right details are!

Now, 0 dimensional submanifolds are merely points. 1 dimensional submanifolds are paths. So, if two points have a path between them, then the points contribute nothing to the zeroth homology. Hence H_0(S^1) = H_0(S^2) = 0 etc...

Hence, H_0(connected) = <pts>/{all points are connected] = \mathbb{Z}

H_1(S^1) = \mathbb{Z} as boundaryless paths are generated by loops around the circle, which are vacuously not the boundary of 2 manifolds.

H_1(S^2) = <closed paths>/<boundaries of disks > = 0

<math>H_2(S^2) = <S^2></math>/ nothing = <math>\mathbb{Z}</math>

In general we have

<math>H_k(S^n) = \begin{matrix}
\mathbb{Z}&k=0\\
0&0<k<n\\
\mathbb{Z}&k=n\\
\end{matrix}</math>

Likewise, we know the zeroth and second homology of the torus is \mathbb{Z}

We now need to compute the first homology of the torus. That is, we search for closed paths with no inner disk.

We think of the torus generated by a square subset of the real plane with the usual identifications. Call one side a and the other b.
Now consider a diagonal across the square, labeled c. Clearly we have a path with, c = a + b, which is the boundary of a triangle.

Varying the diagonal into an arbitrary path which yields the same result we see that H_1(T^2)=\mathbb{Z}^2

We get functorality as for f:X\rightarrow Y we get a map f^*:H_n(X)\rightarrow H_n(Y) as f maps boundaryless manifolds to boundaryless manifolds.

''Applications''

Brouwer's theorem for D^{n+1}

I.e., there is no retract D^{n+1}\rightarrow S^n

Indeed, if there were such an retract we would get a commuting diagram and I = i :S^n\rightarrow S^n} where I is the identity on S^n and i is the natural inclusion into D^{n+1}. But after applying the functor this would get a commuting diagram where S^n goes to \mathbb{Z} and D^{n+1} goes to zero. But then have I* = 0 map, this is impossible.

'''Definition:'''

The p-simplex \Delta_p is is

\mathbb{R}^{p+1}\ni\Delta_p:=\{(\lambda_0\cdots\lambda_p)\ |\ \sum_i^p \lambda_i = 1,\ \lambda_i\geq0\} = \{\sum\lambda_i e_i\ |\ \sum_i^p \lambda_i = 1,\ \lambda_i\geq0\}

'''Example'''

p=0 is just the point 1 on the real line.

p=1 is the diagonal line between (1,0) and (0,1) in the real plane. here e_1 represents the vector from 0 to (0,1) and e_0 represents the vector from 0 to (1,0)

p=2 forms a triangle between the tips of the three unit vectors in \mathbb{R}^3.

In general, we have the convex full of p+1 points.

Likewise, if (v_0,\cdots, v_p)\in\mathbb{R}^N then have map [v_0,\cdots, v_p]:\Delta_p\rightarrow\mathbb{R}^N defined by \sum\lambda_i e_i\mapsto \sum \lambda_i v_i

Now, we want to define the boundary of a simplex. Loosely, we get a bunch of p-1 simplexes found by forgetting a vertex each time.

'''Definition'''

F_i^p:\Delta_{p-1}\rightarrow\Delta_p is the ith face of \Delta_p, namely, F_i^p = [e_0\cdots \hat{e_i}\cdots e_p]

'''Definition'''

Given X, \Delta_p(X)=C_p(X) = <p\ simplexes\ in\ X> = \{\sum a_i\sigma_i\ |\ a_i\in\mathbb{Z},\ \sigma_i:\Delta_p\rightarrow X\ is\ cont.\}

Note: \sigma is not necessarily 1:1 as was implied in the earlier naive computations. Furthermore, we note that C_p(X) has an abelian group structure)

Definition: \partial_p:C_p(X)\rightarrow Cc_{p-1}(X) a group homomorphism via \sum a_i\sigma_i\mapsto \sum a_i\partial_p(\sigma_i) where \partial_p\sigma = \sum_{i=0}^p (-1)^i\sigma\circ\F_i^p

This results in a chain \cdots C_3(X)\rightarrow^{\partial_3}C_2(X)\rightarrow^{\partial_2}C_1(X)\rightarrow^{\partial_1}C_0(X)

'''Definition'''

Z_p(X) = ker\partial_p called "p cycles in X"

B_p(X) = Im\partial_{p+1} called "p boundaries in X"

We want to define H_p(X) = Z_p(X)/B_p(X)

'''Lemma'''

B_p(X)\subset Z_p(X) \Leftrightarrow im\partial{p+1}\subset \partial_p\Leftrightarrow \partial_p\circ\partial_{p+1} =0

Notationally we simply write \partial^2 = 0

Let \sigma\in C_{p+1}

\sigma:\Delta_{p+1}\rightarrow X, \partial\sigma = \sum_{i=0}^p (-1)^i\sigma\circ F_i^{p}

\partial\partial\sigma = \partial(\sum (-1)^i\sigma\circ F_i^p) = \sum_{i=0}^{p+1}\sum_{j=0}^p\sigma\circ F_i^p\circ F_j^{p-1}(-1)^{i+j}

I.e., dropping e_m, e_n occurs twice, only with a different sign. Formally,

F_i^p\circ F_j^{p-1} = [e_o\cdots \hat{e_j},\hat{e_i}\cdots e_{p+1}] for i>j and

F_i^p\circ F_j^{p-1} = [e_o\cdots \hat{e_i},\hat{e_j+1}\cdots e_{p+1}] for i\leq j

So \partial\partial\sigma = \sum_{i=o}^{p+1}\sum_{j=0}^{p-1}(-1)^{i+j}\sigma\circ[\hat{e_j}\hat{e_i}] + \sum_{i=0}^{p+1}\sum_{j=i}^p (-1)^{i+j}\sigma\circ[\hat{e_i}\hat{e_{j+1}}]

File:0708-1300-Topofeb12p5.jpg

2008-03-10T01:46:14Z

Aroesler: Class notes for Tuesday February 12, page 5

Class notes for Tuesday February 12, page 5

File:0708-1300-Topofeb12p4.jpg

2008-03-10T01:45:35Z

Aroesler: Class notes for Tuesday February 12, page 4

Class notes for Tuesday February 12, page 4

File:0708-1300-Topofeb12p3.jpg

2008-03-10T01:44:18Z

Aroesler: Class notes for Tuesday February 12, page 3

Class notes for Tuesday February 12, page 3

File:0708-1300-Topofeb12p2.jpg

2008-03-10T01:42:56Z

Aroesler: Class notes for Tuesday February 12, page 2

Class notes for Tuesday February 12, page 2