Drorbn - User contributions [en]

File:12-240 Dec4 page 4.jpg

2012-12-04T17:55:44Z

Yaaleni.vijay:

File:12-240 Dec4 page 3.jpg

2012-12-04T17:55:06Z

Yaaleni.vijay:

File:12-240 Dec4 page 2.jpg

2012-12-04T17:54:54Z

Yaaleni.vijay:

12-240/Classnotes for Tuesday December 4

2012-12-04T17:54:44Z

Yaaleni.vijay:

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==
{{12-240/Navigation}}

<gallery>
Image:12-240 Dec4 page 1.jpg|'''Page 1'''
Image:12-240 Dec4 page 2.jpg|'''Page 2'''
Image:12-240 Dec4 page 3.jpg|'''Page 3'''
Image:12-240 Dec4 page 4.jpg|'''Page 4'''

</gallery>

File:12-240 Dec4 page 1.jpg

2012-12-04T17:52:36Z

Yaaleni.vijay:

12-240/Navigation

2012-12-04T17:48:58Z

Yaaleni.vijay:

<noinclude>Back to [[12-240]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 10
|[[12-240/About This Class|About This Class]], [[12-240/Classnotes for Tuesday September 11|Tuesday]], [[12-240/Classnotes for Thursday September 13|Thursday]]
|- align=left
|align=center|2
|Sep 17
|[[12-240/Homework Assignment 1|HW1]], [[12-240/Classnotes for Tuesday September 18|Tuesday]], [[12-240/Classnotes for Thursday September 20|Thursday]]
|- align=left
|align=center|3
|Sep 24
|[[12-240/Homework Assignment 2|HW2]], [[12-240/Classnotes for Tuesday September 25|Tuesday]], [[12-240/Class Photo|Class Photo]], [[12-240/Classnotes for Thursday September 27|Thursday]]
|- align=left
|align=center|4
|Oct 1
|[[12-240/Homework Assignment 3|HW3]], [[12-240/Classnotes for Tuesday October 2|Tuesday]], [[12-240/Classnotes for Thursday October 4|Thursday]]
|- align=left
|align=center|5
|Oct 8
|[[12-240/Homework Assignment 4|HW4]], [[12-240/Classnotes for Tuesday October 09|Tuesday]], [[12-240/Classnotes for Thursday October 11|Thursday]]
|- align=left
|align=center|6
|Oct 15
|[[12-240/Classnotes for Tuesday October 16|Tuesday]], [[12-240/Classnotes for Thursday October 18|Thursday]]
|- align=left
|align=center|7
|Oct 22
|[[12-240/Homework Assignment 5|HW5]], [[12-240/Classnotes for Tuesday October 23|Tuesday]], [[12-240/Term Test|Term Test]] was on Thursday.
|- align=left
|align=center|8
|Oct 29
|[[12-240/Linear Algebra - Why We Care|Why LinAlg?]], [[12-240/Homework Assignment 6|HW6]], [[12-240/Classnotes for Tuesday October 30|Tuesday]], [[12-240/Classnotes for Thursday November 1|Thursday]], Nov 4 is the last day to drop this class
|- align=left
|align=center|9
|Nov 5
|[[12-240/Classnotes for Tuesday November 6|Tuesday]], [[12-240/Classnotes for Thursday November 8|Thursday]]
|- align=left
|align=center|10
|Nov 12
|Monday-Tuesday is UofT November break, [[12-240/Homework Assignment 7|HW7]], [[12-240/Classnotes for Tuesday November 15|Thursday]]
|- align=left
|align=center|11
|Nov 19
|[[12-240/Homework Assignment 8|HW8]], [[12-240/Classnotes for Tuesday November 20|Tuesday]],[[12-240/Classnotes for Thursday October 22|Thursday]]
|- align=left
|align=center|12
|Nov 26
|[[12-240/Homework Assignment 9|HW9]], [[12-240/Classnotes for Tuesday November 27|Tuesday]] , [[12-240/Classnotes for Thursday November 29|Thursday]]
|- align=left
|align=center|13
|Dec 3
|[[12-240/Classnotes for Tuesday December 4|Tuesday]] UofT Fall Semester ends Wednesday
|- align=left
|align=center|F
|Dec 10
|[[12-240/The Final Exam|The Final Exam]] (time, place, style, office hours times)
|- align=left
|colspan=3 align=center|[[12-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:12-240-ClassPhoto.jpg|310px]] [[12-240/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|[[Image:12-240-Splash.png|310px]]
|}

12-240/Navigation

2012-12-04T17:47:48Z

Yaaleni.vijay:

<noinclude>Back to [[12-240]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 10
|[[12-240/About This Class|About This Class]], [[12-240/Classnotes for Tuesday September 11|Tuesday]], [[12-240/Classnotes for Thursday September 13|Thursday]]
|- align=left
|align=center|2
|Sep 17
|[[12-240/Homework Assignment 1|HW1]], [[12-240/Classnotes for Tuesday September 18|Tuesday]], [[12-240/Classnotes for Thursday September 20|Thursday]]
|- align=left
|align=center|3
|Sep 24
|[[12-240/Homework Assignment 2|HW2]], [[12-240/Classnotes for Tuesday September 25|Tuesday]], [[12-240/Class Photo|Class Photo]], [[12-240/Classnotes for Thursday September 27|Thursday]]
|- align=left
|align=center|4
|Oct 1
|[[12-240/Homework Assignment 3|HW3]], [[12-240/Classnotes for Tuesday October 2|Tuesday]], [[12-240/Classnotes for Thursday October 4|Thursday]]
|- align=left
|align=center|5
|Oct 8
|[[12-240/Homework Assignment 4|HW4]], [[12-240/Classnotes for Tuesday October 09|Tuesday]], [[12-240/Classnotes for Thursday October 11|Thursday]]
|- align=left
|align=center|6
|Oct 15
|[[12-240/Classnotes for Tuesday October 16|Tuesday]], [[12-240/Classnotes for Thursday October 18|Thursday]]
|- align=left
|align=center|7
|Oct 22
|[[12-240/Homework Assignment 5|HW5]], [[12-240/Classnotes for Tuesday October 23|Tuesday]], [[12-240/Term Test|Term Test]] was on Thursday.
|- align=left
|align=center|8
|Oct 29
|[[12-240/Linear Algebra - Why We Care|Why LinAlg?]], [[12-240/Homework Assignment 6|HW6]], [[12-240/Classnotes for Tuesday October 30|Tuesday]], [[12-240/Classnotes for Thursday November 1|Thursday]], Nov 4 is the last day to drop this class
|- align=left
|align=center|9
|Nov 5
|[[12-240/Classnotes for Tuesday November 6|Tuesday]], [[12-240/Classnotes for Thursday November 8|Thursday]]
|- align=left
|align=center|10
|Nov 12
|Monday-Tuesday is UofT November break, [[12-240/Homework Assignment 7|HW7]], [[12-240/Classnotes for Tuesday November 15|Thursday]]
|- align=left
|align=center|11
|Nov 19
|[[12-240/Homework Assignment 8|HW8]], [[12-240/Classnotes for Tuesday November 20|Tuesday]],[[12-240/Classnotes for Thursday October 22|Thursday]]
|- align=left
|align=center|12
|Nov 26
|[[12-240/Homework Assignment 9|HW9]], [[12-240/Classnotes for Tuesday November 27|Tuesday]] , [[12-240/Classnotes for Thursday November 29|Thursday]]
|- align=left
|align=center|13
|Dec 3
[[12-240/Classnotes for Tuesday December 4|Tuesday]]
|UofT Fall Semester ends Wednesday
|- align=left
|align=center|F
|Dec 10
|[[12-240/The Final Exam|The Final Exam]] (time, place, style, office hours times)
|- align=left
|colspan=3 align=center|[[12-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:12-240-ClassPhoto.jpg|310px]] [[12-240/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|[[Image:12-240-Splash.png|310px]]
|}

12-240/Classnotes for Tuesday November 27

2012-11-28T18:38:25Z

Yaaleni.vijay:

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==
{{12-240/Navigation}}

<gallery>
Image:12-240 Nov27 page 1.jpg|'''Page 1'''
Image:12-240 Nov27 page 2.jpg|'''Page 2'''
Image:12-240 Nov27 page 3.jpg|'''Page 3'''
Image:12-240 Nov27 page 4.jpg|'''Page 4'''
Image:12-240 Nov27 page 5.jpg|'''Page 5'''
Image:12-240 Nov27 page 6.jpg|'''Page 6'''

</gallery>

File:12-240 Nov27 page 4.jpg

2012-11-28T18:36:13Z

Yaaleni.vijay:

File:12-240 Nov27 page 6.jpg

2012-11-28T18:32:29Z

Yaaleni.vijay:

File:12-240 Nov27 page 3.jpg

2012-11-28T18:31:58Z

Yaaleni.vijay:

File:12-240 Nov27 page 5.jpg

2012-11-28T18:31:44Z

Yaaleni.vijay:

File:12-240 Nov27 page 2.jpg

2012-11-28T18:31:04Z

Yaaleni.vijay:

File:12-240 Nov27 page 1.jpg

2012-11-28T18:29:53Z

Yaaleni.vijay:

12-240/Navigation

2012-11-28T18:18:33Z

Yaaleni.vijay:

<noinclude>Back to [[12-240]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 10
|[[12-240/About This Class|About This Class]], [[12-240/Classnotes for Tuesday September 11|Tuesday]], [[12-240/Classnotes for Thursday September 13|Thursday]]
|- align=left
|align=center|2
|Sep 17
|[[12-240/Homework Assignment 1|HW1]], [[12-240/Classnotes for Tuesday September 18|Tuesday]], [[12-240/Classnotes for Thursday September 20|Thursday]]
|- align=left
|align=center|3
|Sep 24
|[[12-240/Homework Assignment 2|HW2]], [[12-240/Classnotes for Tuesday September 25|Tuesday]], [[12-240/Class Photo|Class Photo]], [[12-240/Classnotes for Thursday September 27|Thursday]]
|- align=left
|align=center|4
|Oct 1
|[[12-240/Homework Assignment 3|HW3]], [[12-240/Classnotes for Tuesday October 2|Tuesday]], [[12-240/Classnotes for Thursday October 4|Thursday]]
|- align=left
|align=center|5
|Oct 8
|[[12-240/Homework Assignment 4|HW4]], [[12-240/Classnotes for Tuesday October 09|Tuesday]], [[12-240/Classnotes for Thursday October 11|Thursday]]
|- align=left
|align=center|6
|Oct 15
|[[12-240/Classnotes for Tuesday October 16|Tuesday]], [[12-240/Classnotes for Thursday October 18|Thursday]]
|- align=left
|align=center|7
|Oct 22
|[[12-240/Homework Assignment 5|HW5]], [[12-240/Classnotes for Tuesday October 23|Tuesday]], [[12-240/Term Test|Term Test]] was on Thursday.
|- align=left
|align=center|8
|Oct 29
|[[12-240/Linear Algebra - Why We Care|Why LinAlg?]], [[12-240/Homework Assignment 6|HW6]], [[12-240/Classnotes for Tuesday October 30|Tuesday]], [[12-240/Classnotes for Thursday November 1|Thursday]], Nov 4 is the last day to drop this class
|- align=left
|align=center|9
|Nov 5
|[[12-240/Classnotes for Tuesday November 6|Tuesday]], [[12-240/Classnotes for Thursday November 8|Thursday]]
|- align=left
|align=center|10
|Nov 12
|Monday-Tuesday is UofT November break, [[12-240/Homework Assignment 7|HW7]], [[12-240/Classnotes for Tuesday November 15|Thursday]]
|- align=left
|align=center|11
|Nov 19
|[[12-240/Homework Assignment 8|HW8]], [[12-240/Classnotes for Tuesday November 20|Tuesday]],[[12-240/Classnotes for Thursday October 22|Thursday]]
|- align=left
|align=center|12
|Nov 26
|[[12-240/Homework Assignment 9|HW9]],[[12-240/Classnotes for Tuesday November 27|Tuesday]]
|- align=left
|align=center|13
|Dec 3
|UofT Fall Semester ends Wednesday
|- align=left
|align=center|F1
|Dec 10
|Finals
|- align=left
|align=center|F2
|Dec 17
|Finals
|- align=left
|colspan=3 align=center|[[12-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:12-240-ClassPhoto.jpg|310px]] [[12-240/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|[[Image:12-240-Splash.png|310px]]
|}

12-240/Classnotes for Thursday November 8

2012-11-23T03:31:32Z

Yaaleni.vijay: /* Lecture notes upload by yaaleni.vijay */

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==
{{12-240/Navigation}}

<gallery>
Image:12-240 Nov 8 Page 1.jpg|Page 1
Image:12-240 Nov 8 Page 2.jpg|Page 2

</gallery>

12-240/Classnotes for Thursday November 8

2012-11-22T22:55:15Z

Yaaleni.vijay:

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==
{{12-240/Navigation}}

<gallery>
Image:12-240 Nov 8 Page 2.jpg|Page 1
Image:12-240 Nov 8 Page 2.jpg|Page 2

</gallery>

File:12-240 Nov 8 Page 2.jpg

2012-11-22T22:54:18Z

Yaaleni.vijay: November 8 Lecture Notes Page 2

November 8 Lecture Notes Page 2

12-240/Navigation

2012-11-22T22:53:15Z

Yaaleni.vijay:

<noinclude>Back to [[12-240]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 10
|[[12-240/About This Class|About This Class]], [[12-240/Classnotes for Tuesday September 11|Tuesday]], [[12-240/Classnotes for Thursday September 13|Thursday]]
|- align=left
|align=center|2
|Sep 17
|[[12-240/Homework Assignment 1|HW1]], [[12-240/Classnotes for Tuesday September 18|Tuesday]], [[12-240/Classnotes for Thursday September 20|Thursday]]
|- align=left
|align=center|3
|Sep 24
|[[12-240/Homework Assignment 2|HW2]], [[12-240/Classnotes for Tuesday September 25|Tuesday]], [[12-240/Class Photo|Class Photo]], [[12-240/Classnotes for Thursday September 27|Thursday]]
|- align=left
|align=center|4
|Oct 1
|[[12-240/Homework Assignment 3|HW3]], [[12-240/Classnotes for Tuesday October 2|Tuesday]], [[12-240/Classnotes for Thursday October 4|Thursday]]
|- align=left
|align=center|5
|Oct 8
|[[12-240/Homework Assignment 4|HW4]], [[12-240/Classnotes for Tuesday October 09|Tuesday]], [[12-240/Classnotes for Thursday October 11|Thursday]]
|- align=left
|align=center|6
|Oct 15
|[[12-240/Classnotes for Tuesday October 16|Tuesday]], [[12-240/Classnotes for Thursday October 18|Thursday]]
|- align=left
|align=center|7
|Oct 22
|[[12-240/Homework Assignment 5|HW5]], [[12-240/Classnotes for Tuesday October 23|Tuesday]], [[12-240/Term Test|Term Test]] was on Thursday.
|- align=left
|align=center|8
|Oct 29
|[[12-240/Linear Algebra - Why We Care|Why LinAlg?]], [[12-240/Homework Assignment 6|HW6]], [[12-240/Classnotes for Tuesday October 30|Tuesday]], [[12-240/Classnotes for Thursday November 1|Thursday]], Nov 4 is the last day to drop this class
|- align=left
|align=center|9
|Nov 5
|[[12-240/Classnotes for Tuesday November 6|Tuesday]], [[12-240/Classnotes for Thursday November 8|Thursday]]
|- align=left
|align=center|10
|Nov 12
|Monday-Tuesday is UofT November break, [[12-240/Homework Assignment 7|HW7]], [[12-240/Classnotes for Tuesday November 15|Thursday]]
|- align=left
|align=center|11
|Nov 19
|[[12-240/Homework Assignment 8|HW8]], [[12-240/Classnotes for Tuesday November 20|Tuesday]],[[12-240/Classnotes for Thursday October 22|Thursday]]
|- align=left
|align=center|12
|Nov 26
|HW9
|- align=left
|align=center|13
|Dec 3
|UofT Fall Semester ends Wednesday
|- align=left
|align=center|F1
|Dec 10
|Finals
|- align=left
|align=center|F2
|Dec 17
|Finals
|- align=left
|colspan=3 align=center|[[12-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:12-240-ClassPhoto.jpg|310px]] [[12-240/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|[[Image:12-240-Splash.png|310px]]
|}

12-240/Navigation

2012-11-22T22:52:19Z

Yaaleni.vijay:

<noinclude>Back to [[12-240]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 10
|[[12-240/About This Class|About This Class]], [[12-240/Classnotes for Tuesday September 11|Tuesday]], [[12-240/Classnotes for Thursday September 13|Thursday]]
|- align=left
|align=center|2
|Sep 17
|[[12-240/Homework Assignment 1|HW1]], [[12-240/Classnotes for Tuesday September 18|Tuesday]], [[12-240/Classnotes for Thursday September 20|Thursday]]
|- align=left
|align=center|3
|Sep 24
|[[12-240/Homework Assignment 2|HW2]], [[12-240/Classnotes for Tuesday September 25|Tuesday]], [[12-240/Class Photo|Class Photo]], [[12-240/Classnotes for Thursday September 27|Thursday]]
|- align=left
|align=center|4
|Oct 1
|[[12-240/Homework Assignment 3|HW3]], [[12-240/Classnotes for Tuesday October 2|Tuesday]], [[12-240/Classnotes for Thursday October 4|Thursday]]
|- align=left
|align=center|5
|Oct 8
|[[12-240/Homework Assignment 4|HW4]], [[12-240/Classnotes for Tuesday October 09|Tuesday]], [[12-240/Classnotes for Thursday October 11|Thursday]]
|- align=left
|align=center|6
|Oct 15
|[[12-240/Classnotes for Tuesday October 16|Tuesday]], [[12-240/Classnotes for Thursday October 18|Thursday]]
|- align=left
|align=center|7
|Oct 22
|[[12-240/Homework Assignment 5|HW5]], [[12-240/Classnotes for Tuesday October 23|Tuesday]], [[12-240/Term Test|Term Test]] was on Thursday.
|- align=left
|align=center|8
|Oct 29
|[[12-240/Linear Algebra - Why We Care|Why LinAlg?]], [[12-240/Homework Assignment 6|HW6]], [[12-240/Classnotes for Tuesday October 30|Tuesday]], [[12-240/Classnotes for Thursday November 1|Thursday]], Nov 4 is the last day to drop this class
|- align=left
|align=center|9
|Nov 5
|[[12-240/Classnotes for Tuesday November 6|Tuesday]], [[12-240/Classnotes for Tuesday November 8|Thursday]]
|- align=left
|align=center|10
|Nov 12
|Monday-Tuesday is UofT November break, [[12-240/Homework Assignment 7|HW7]], [[12-240/Classnotes for Tuesday November 15|Thursday]]
|- align=left
|align=center|11
|Nov 19
|[[12-240/Homework Assignment 8|HW8]], [[12-240/Classnotes for Tuesday November 20|Tuesday]],[[12-240/Classnotes for Thursday October 22|Thursday]]
|- align=left
|align=center|12
|Nov 26
|HW9
|- align=left
|align=center|13
|Dec 3
|UofT Fall Semester ends Wednesday
|- align=left
|align=center|F1
|Dec 10
|Finals
|- align=left
|align=center|F2
|Dec 17
|Finals
|- align=left
|colspan=3 align=center|[[12-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:12-240-ClassPhoto.jpg|310px]] [[12-240/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|[[Image:12-240-Splash.png|310px]]
|}

12-240/Classnotes for Thursday October 22

2012-11-22T22:48:09Z

Yaaleni.vijay: /* Lecture notes upload by yaaleni.vijay */

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==
{{12-240/Navigation}}
[[12-240/Classnotes for Thursday October 22|Thursday]]
<gallery>
Image:12-240 Page 1.jpg|Page 1
Image:12-240 Page 2.jpg|Page 2
Image:12-240 Page 3.jpg|Page 3
</gallery>

12-240/Navigation

2012-11-22T22:45:39Z

Yaaleni.vijay:

<noinclude>Back to [[12-240]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 10
|[[12-240/About This Class|About This Class]], [[12-240/Classnotes for Tuesday September 11|Tuesday]], [[12-240/Classnotes for Thursday September 13|Thursday]]
|- align=left
|align=center|2
|Sep 17
|[[12-240/Homework Assignment 1|HW1]], [[12-240/Classnotes for Tuesday September 18|Tuesday]], [[12-240/Classnotes for Thursday September 20|Thursday]]
|- align=left
|align=center|3
|Sep 24
|[[12-240/Homework Assignment 2|HW2]], [[12-240/Classnotes for Tuesday September 25|Tuesday]], [[12-240/Class Photo|Class Photo]], [[12-240/Classnotes for Thursday September 27|Thursday]]
|- align=left
|align=center|4
|Oct 1
|[[12-240/Homework Assignment 3|HW3]], [[12-240/Classnotes for Tuesday October 2|Tuesday]], [[12-240/Classnotes for Thursday October 4|Thursday]]
|- align=left
|align=center|5
|Oct 8
|[[12-240/Homework Assignment 4|HW4]], [[12-240/Classnotes for Tuesday October 09|Tuesday]], [[12-240/Classnotes for Thursday October 11|Thursday]]
|- align=left
|align=center|6
|Oct 15
|[[12-240/Classnotes for Tuesday October 16|Tuesday]], [[12-240/Classnotes for Thursday October 18|Thursday]]
|- align=left
|align=center|7
|Oct 22
|[[12-240/Homework Assignment 5|HW5]], [[12-240/Classnotes for Tuesday October 23|Tuesday]], [[12-240/Term Test|Term Test]] was on Thursday.
|- align=left
|align=center|8
|Oct 29
|[[12-240/Linear Algebra - Why We Care|Why LinAlg?]], [[12-240/Homework Assignment 6|HW6]], [[12-240/Classnotes for Tuesday October 30|Tuesday]], [[12-240/Classnotes for Thursday November 1|Thursday]], Nov 4 is the last day to drop this class
|- align=left
|align=center|9
|Nov 5
|[[12-240/Classnotes for Tuesday November 6|Tuesday]],[[12-240/Classnotes for Tuesday November 8|Thursday]]
|- align=left
|align=center|10
|Nov 12
|Monday-Tuesday is UofT November break, [[12-240/Homework Assignment 7|HW7]], [[12-240/Classnotes for Tuesday November 15|Thursday]]
|- align=left
|align=center|11
|Nov 19
|[[12-240/Homework Assignment 8|HW8]], [[12-240/Classnotes for Tuesday November 20|Tuesday]],[[12-240/Classnotes for Thursday October 22|Thursday]]
|- align=left
|align=center|12
|Nov 26
|HW9
|- align=left
|align=center|13
|Dec 3
|UofT Fall Semester ends Wednesday
|- align=left
|align=center|F1
|Dec 10
|Finals
|- align=left
|align=center|F2
|Dec 17
|Finals
|- align=left
|colspan=3 align=center|[[12-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:12-240-ClassPhoto.jpg|310px]] [[12-240/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|[[Image:12-240-Splash.png|310px]]
|}

File:12-240 Nov 8 Page 1.jpg

2012-11-22T22:44:50Z

Yaaleni.vijay:

12-240/Navigation

2012-11-22T22:42:27Z

Yaaleni.vijay:

<noinclude>Back to [[12-240]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 10
|[[12-240/About This Class|About This Class]], [[12-240/Classnotes for Tuesday September 11|Tuesday]], [[12-240/Classnotes for Thursday September 13|Thursday]]
|- align=left
|align=center|2
|Sep 17
|[[12-240/Homework Assignment 1|HW1]], [[12-240/Classnotes for Tuesday September 18|Tuesday]], [[12-240/Classnotes for Thursday September 20|Thursday]]
|- align=left
|align=center|3
|Sep 24
|[[12-240/Homework Assignment 2|HW2]], [[12-240/Classnotes for Tuesday September 25|Tuesday]], [[12-240/Class Photo|Class Photo]], [[12-240/Classnotes for Thursday September 27|Thursday]]
|- align=left
|align=center|4
|Oct 1
|[[12-240/Homework Assignment 3|HW3]], [[12-240/Classnotes for Tuesday October 2|Tuesday]], [[12-240/Classnotes for Thursday October 4|Thursday]]
|- align=left
|align=center|5
|Oct 8
|[[12-240/Homework Assignment 4|HW4]], [[12-240/Classnotes for Tuesday October 09|Tuesday]], [[12-240/Classnotes for Thursday October 11|Thursday]]
|- align=left
|align=center|6
|Oct 15
|[[12-240/Classnotes for Tuesday October 16|Tuesday]], [[12-240/Classnotes for Thursday October 18|Thursday]]
|- align=left
|align=center|7
|Oct 22
|[[12-240/Homework Assignment 5|HW5]], [[12-240/Classnotes for Tuesday October 23|Tuesday]], [[12-240/Term Test|Term Test]] was on Thursday.
|- align=left
|align=center|8
|Oct 29
|[[12-240/Linear Algebra - Why We Care|Why LinAlg?]], [[12-240/Homework Assignment 6|HW6]], [[12-240/Classnotes for Tuesday October 30|Tuesday]], [[12-240/Classnotes for Thursday November 1|Thursday]], Nov 4 is the last day to drop this class
|- align=left
|align=center|9
|Nov 5
|[[12-240/Classnotes for Tuesday November 6|Tuesday]], [[12-240/Classnotes for Tuesday November 8|Thursday]]
|- align=left
|align=center|10
|Nov 12
|Monday-Tuesday is UofT November break, [[12-240/Homework Assignment 7|HW7]], [[12-240/Classnotes for Tuesday November 15|Thursday]]
|- align=left
|align=center|11
|Nov 19
|[[12-240/Homework Assignment 8|HW8]], [[12-240/Classnotes for Tuesday November 20|Tuesday]], [[12-240/Classnotes for Thursday October 22|Thursday]]
|- align=left
|align=center|12
|Nov 26
|HW9
|- align=left
|align=center|13
|Dec 3
|UofT Fall Semester ends Wednesday
|- align=left
|align=center|F1
|Dec 10
|Finals
|- align=left
|align=center|F2
|Dec 17
|Finals
|- align=left
|colspan=3 align=center|[[12-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:12-240-ClassPhoto.jpg|310px]] [[12-240/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|[[Image:12-240-Splash.png|310px]]
|}

12-240/Classnotes for Thursday October 22

2012-11-22T22:39:36Z

Yaaleni.vijay: /* Lecture notes upload by yaaleni.vijay */

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==
{{12-240/Navigation}}

<gallery>
Image:12-240 Page 1.jpg|Page 1
Image:12-240 Page 2.jpg|Page 2
Image:12-240 Page 3.jpg|Page 3
</gallery>

12-240/Classnotes for Thursday October 22

2012-11-22T22:36:15Z

Yaaleni.vijay:

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==
{{12-240/Navigation}}

<gallery>
[[Image:12-240 Page 1.jpg]]
[[Image:12-240 Page 2.jpg]]
[[Image:12-240 Page 3.jpg|thumb|Description]]
</gallery>

12-240/Classnotes for Thursday October 22

2012-11-22T22:35:01Z

Yaaleni.vijay: /* Lecture notes upload by yaaleni.vijay */

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==

<gallery>
[[Image:12-240 Page 1.jpg]]
[[Image:12-240 Page 2.jpg]]
[[Image:12-240 Page 3.jpg|thumb|Description]]
</gallery>

12-240/Classnotes for Thursday October 22

2012-11-22T22:32:27Z

Yaaleni.vijay:

== Lecture notes upload by [[User:yaaleni.vijay|yaaleni.vijay]] ==

<gallery>
[[Image:12-240 Page 1.jpg]]
[[Image:12-240 Page 2.jpg]]
[[Image:12-240 Page 3.jpg]]
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File:12-240 Page 3.jpg

2012-11-22T22:31:36Z

Yaaleni.vijay: Lecture Notes Page 3 November 22, 2012

Lecture Notes Page 3 November 22, 2012

File:12-240 Page 2.jpg

2012-11-22T22:28:22Z

Yaaleni.vijay: Page 2 Lecture Notes November 22, 2012

Page 2 Lecture Notes November 22, 2012

12-240/Navigation

2012-11-22T22:25:06Z

Yaaleni.vijay:

<noinclude>Back to [[12-240]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 10
|[[12-240/About This Class|About This Class]], [[12-240/Classnotes for Tuesday September 11|Tuesday]], [[12-240/Classnotes for Thursday September 13|Thursday]]
|- align=left
|align=center|2
|Sep 17
|[[12-240/Homework Assignment 1|HW1]], [[12-240/Classnotes for Tuesday September 18|Tuesday]], [[12-240/Classnotes for Thursday September 20|Thursday]]
|- align=left
|align=center|3
|Sep 24
|[[12-240/Homework Assignment 2|HW2]], [[12-240/Classnotes for Tuesday September 25|Tuesday]], [[12-240/Class Photo|Class Photo]], [[12-240/Classnotes for Thursday September 27|Thursday]]
|- align=left
|align=center|4
|Oct 1
|[[12-240/Homework Assignment 3|HW3]], [[12-240/Classnotes for Tuesday October 2|Tuesday]], [[12-240/Classnotes for Thursday October 4|Thursday]]
|- align=left
|align=center|5
|Oct 8
|[[12-240/Homework Assignment 4|HW4]], [[12-240/Classnotes for Tuesday October 09|Tuesday]], [[12-240/Classnotes for Thursday October 11|Thursday]]
|- align=left
|align=center|6
|Oct 15
|[[12-240/Classnotes for Tuesday October 16|Tuesday]], [[12-240/Classnotes for Thursday October 18|Thursday]]
|- align=left
|align=center|7
|Oct 22
|[[12-240/Homework Assignment 5|HW5]], [[12-240/Classnotes for Tuesday October 23|Tuesday]], [[12-240/Term Test|Term Test]] was on Thursday.
|- align=left
|align=center|8
|Oct 29
|[[12-240/Linear Algebra - Why We Care|Why LinAlg?]], [[12-240/Homework Assignment 6|HW6]], [[12-240/Classnotes for Tuesday October 30|Tuesday]], [[12-240/Classnotes for Thursday November 1|Thursday]], Nov 4 is the last day to drop this class
|- align=left
|align=center|9
|Nov 5
|[[12-240/Classnotes for Tuesday November 6|Tuesday]]
|- align=left
|align=center|10
|Nov 12
|Monday-Tuesday is UofT November break, [[12-240/Homework Assignment 7|HW7]], [[12-240/Classnotes for Tuesday November 15|Thursday]]
|- align=left
|align=center|11
|Nov 19
|[[12-240/Homework Assignment 8|HW8]], [[12-240/Classnotes for Tuesday November 20|Tuesday]], [[12-240/Classnotes for Thursday October 22|Thursday]]
|- align=left
|align=center|12
|Nov 26
|HW9
|- align=left
|align=center|13
|Dec 3
|UofT Fall Semester ends Wednesday
|- align=left
|align=center|F1
|Dec 10
|Finals
|- align=left
|align=center|F2
|Dec 17
|Finals
|- align=left
|colspan=3 align=center|[[12-240/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[Image:12-240-ClassPhoto.jpg|310px]] [[12-240/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|[[Image:12-240-Splash.png|310px]]
|}

File:12-240 Page 1.jpg

2012-11-22T22:13:01Z

Yaaleni.vijay: Nov 22 Page 1

Nov 22 Page 1

12-240/Classnotes for Thursday October 18

2012-11-08T19:29:01Z

Yaaleni.vijay:

{{12-240/Navigation}}
'''== Linear transformation =='''

'''Definition:'''

A function L: V-> W is called a linear transformation if it preserve following structures:

1) L(x + y)= L(x) + L(y)

2) L(cx)= c.L(x)

3) L(0 of V) = 0 of W

'''Proposition:'''

1) property 2 => property 3

2) L: V -> W is a linear transformation iff <math>\forall\,\!</math> c <math>\in\,\!</math> F, <math>\forall\,\!</math> x, y <math>\in\,\!</math> V: L(cx + y)= cL(x) + L(y)

'''Proof:'''

1) take c= 0 in F and x=0 in V. Then L(cx)=cL(x) -> L(0 of F * 0 of V)=(0 of F)*L(0 of V)=0 of W

2)(=>)Assume L is linear transformation

L(cx + y)= L(cx) + L(y)= c*L(x) + L(y)

(<=) 1. Follows from L(c*x+y) = c*L(x)+L(y) by taking c=1

2. Follows by taking y=0

'''Examples'''

1. L: '''R'''^2 -> '''R'''^2 by

2. P,Q: P(F)

== lecture note on oct 18, uploaded by [[User:starash|starash]]==

<gallery>
Image:12-240-1018-1.jpg |page1
Image:12-240-1018-2.jpg |page2
</gallery>

== Lecture notes uploaded by [[User:Grace.zhu|gracez]] ==
<gallery>
Image:12-240-O18-1.jpg|Page 1
Image:12-240-O18-2.jpg|Page 2
</gallery>

12-240/Classnotes for Tuesday October 30

2012-11-08T19:22:14Z

Yaaleni.vijay:

{{12-240/Navigation}}

==Lecture Notes==
Fix a linear transformation T:V->W

'''Definition:'''

N(T)= ker T = {v ∈ V: Tv=O} ⊂ V
"null space" "kernal"

R(T)= img T = {Tv: v ∈ V} ⊂ W
"range" "image"

'''Proposition/Definition'''

1. N(T) is a subspace of V nullity(T)= dim N(T)
2. R(T) is a subspace of W rank (T) = dim R(T)

'''Example 1'''

T= 0 of linear transformation Tv=0

ker T = N(T)= V nullity(T) = dim V

img T = R(T)={0} rank (T)= dim{0}=0

'''Example 2'''

V=W; T=I Tv=V

ker T = N(T)= {0} nullity(T) = 0

img T = R(T)= V rank (T)= dim V

'''Example 3'''

V=Pn('''R''')= W; T=d/dx T(x^3)=3(x^2)

ker T = N(T)= {c(x^0): c∈'''R'''} nullity(T) = 1

img T = R(T)= Pn-1('''R''') rank (T) = n

sum=n+1=dim V

'''Theorem: Dimension Theorem/Rank-Nullity Theorem'''

Given T:V->W, (V is finite dimensional)

dim V = rank(T) + nullity (T)

'''Corollary of Theorem'''

If dim V = dim W then TFAE (the following are equivalent)

1. T is 1-1

2. T is onto

3. rank (T) = dimV (maximal)

4. T is invertible

T is 1-1 <=> nullity (T) = 0 as n+r = dim V

<=> rank(T) = dim V

<=> T is onto

1<=> 3

invertible => 1-1 and onto

1-1 => onto => invertible

onto => 1-1 => invertible

== Lecture notes scanned by [[User:KJMorenz|KJMorenz]] ==
<gallery>
Image:12-240-Oct30.jpg|Oct 30 Page 1
Image:12-240-Oct30-2.jpg|Oct 30 Page 2
</gallery>

== Lecture notes uploaded by [[User:Grace.zhu|gracez]] ==
<gallery>
Image:12-240-O30.jpg|Page 1
</gallery>

12-240/Classnotes for Tuesday September 25

2012-11-02T18:49:36Z

Yaaleni.vijay:

{{12-240/Navigation}}

Today's class dealt with the properties of vector spaces.

== Definition ==
Let F is a field, a vector space V over F is a set V of vectors with special element O ( of V) and tow operations: (+): VxV->V, (.): FxV->V

VxV={(v,w): v,w <math>\in\!\,</math> V}

FxV={(c,v): c <math>\in\!\,</math> F, v <math>\in\!\,</math> V}

Then, (+): VxV->V is (v,w)= v+w; (.): FxV->V is (c,v)=cv

Such that

VS1 <math>\forall\!\,</math> x, y <math>\in\!\,</math> V: x+y = y+x

VS2 <math>\forall\!\,</math> x, y, z <math>\in\!\,</math> V: x+(y+z) = (x+y)+z

VS3 <math>\forall\!\,</math> x <math>\in\!\,</math> V: 0 ( of V) +x = x

VS4 <math>\forall\!\,</math> x <math>\in\!\,</math> V, <math>\exists \!\,</math> V <math>\in\!\,</math> V: v + x= 0 ( of V)

VS5 <math>\forall\!\,</math> x <math>\in\!\,</math> V, 1 (of F) .x = x

VS6 <math>\forall\!\,</math> a, b <math>\in\!\,</math> F, <math>\forall\!\,</math> x <math>\in\!\,</math> V: (ab)x = a(bx)

VS7 <math>\forall\!\,</math> a <math>\in\!\,</math> F, <math>\forall\!\,</math> x, y <math>\in\!\,</math> V: a(x + y)= ax + ay

VS8 <math>\forall\!\,</math> a, b <math>\in\!\,</math> F, <math>\forall\!\,</math> x <math>\in\!\,</math> V: (a + b)x = ax + bx

== Examples ==

==Properties ==

==Polynomials==
'''Definition''' : Pn(F) = {all polynomials of degree less than or equal n with coefficients in F}
= {anx^n + an-1x^n-1 + ... + a1x^1 + a1x^1}

0 = 0x^n + 0x^n-1 +...+ 0x^0

addition and multiplication: as you imagine

P(f) = {all polynomials with coefficients in F}

Take F= '''Z'''/2 |F| = 2

|P(F)| = infinite

in Pn('''Z'''/2) x^3≠x^2
x^3 = 1*x^3+0x^2+0x+O = f
x^2 = 1*x^2+0x+0 = g
yet f(0)= g(0) and f(1)=g(1)

==Theorem==
1. Cancellation Laws
(a) x+z=y+z ==> x=y
(b) ax+ay,a≠0 ==> x=y
(c) x≠0 of V, ax=bx ==> a=b

2. 0 of V is unique

3. Negatives are unique (so subtraction makes sense

4.(0 of F)x = 0 of V

5. a*0=0

6. (-a)x= - (ax) = a(-x)

7. a*v=0 <==> a=0 or v=0

==Proof==
1. (a) x+z=y+z
Find a w s.t. z+w=0 (V.S. 4)
(x+z)+w = (y+z)+w
Use VS2
x+(z+w) = y +(z+w)
x + 0 = y + o
Use VS3 x=y

==Scanned Notes by [[User:Richardm|Richardm]]==
<gallery>
Image:12-240-0925-1vectorspaces.jpg
Image:12-240-0925-2vectorspaces.jpg
Image:12-240-0925-3vectorspaces.jpg
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12-240/Classnotes for Thursday October 18

2012-11-02T18:31:48Z

Yaaleni.vijay: /* Linear transformation */

{{12-240/Navigation}}
'''== Linear transformation =='''
'''Definition:''' A function L: V-> W is called a linear transformation if it preserve following structures:

1) L(x + y)= L(x) + L(y)

2) L(cx)= c.L(x)

3) L(0 of V) = 0 of W

'''Proposition:'''

1) property 2 => property 3

2) L: V -> W is a linear transformation iff <math>\forall\,\!</math> c <math>\in\,\!</math> F, <math>\forall\,\!</math> x, y <math>\in\,\!</math> V: L(cx + y)= cL(x) + L(y)

'''Proof:
'''
1) take c= 0 in F and x=0 in V. Then L(cx)=cL(x) -> L(0 of F * 0 of V)=(0 of F)*L(0 of V)=0 of W

2)(=>)Assume L is linear transformation

L(cx + y)= L(cx) + L(y)= c*L(x) + L(y)

(<=) 1. Follows from L(c*x+y) = c*L(x)+L(y) by taking c=1
2. Follows by taking y=0

'''Examples'''

1. L: '''R'''^2 -> '''R'''^2 by

2. P,Q: P(F)

== lecture note on oct 18, uploaded by [[User:starash|starash]]==

<gallery>
Image:12-240-1018-1.jpg |page1
Image:12-240-1018-2.jpg |page2
</gallery>