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	<updated>2026-09-19T13:32:11Z</updated>
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	<entry>
		<id>https://drorbn.net/index.php?title=12-240/Class_Photo&amp;diff=12902</id>
		<title>12-240/Class Photo</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=12-240/Class_Photo&amp;diff=12902"/>
		<updated>2013-02-21T06:03:50Z</updated>

		<summary type="html">&lt;p&gt;Leighwinnitoy: /* Who We Are... */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Our class on September 25, 2012:&lt;br /&gt;
&lt;br /&gt;
[[Image:12-240-ClassPhoto.jpg|thumb|centre|800px|Class Photo: click to enlarge]]&lt;br /&gt;
{{12-240/Navigation}}&lt;br /&gt;
&lt;br /&gt;
Please identify yourself in this photo! There are two ways to do that:&lt;br /&gt;
&lt;br /&gt;
* [[Special:Userlogin|Log in]] to this Wiki and edit this page. Put your name, userid, email address and location in the picture in the alphabetical list below.&lt;br /&gt;
* Send [[User:Drorbn|Dror]] an email message with this information.&lt;br /&gt;
&lt;br /&gt;
The first option is more fun but less private.&lt;br /&gt;
&lt;br /&gt;
===Who We Are...===&lt;br /&gt;
&lt;br /&gt;
{| align=center border=1 cellspacing=0&lt;br /&gt;
|-&lt;br /&gt;
!First Name &lt;br /&gt;
!Last Name &lt;br /&gt;
!ID wcashore&lt;br /&gt;
!e-mail &lt;br /&gt;
!Location &lt;br /&gt;
!Comments &lt;br /&gt;
&lt;br /&gt;
{{Photo Entry|last=Bar-Natan|first=Dror|userid=Drorbn|email=drorbn@ math. toronto. edu|location=facing everybody, as the photographer|comments=Take this entry as a model and leave it first. Otherwise alphabetize by last name. Feel free to leave some fields blank. For better line-breaking, leave a space next to the &amp;quot;@&amp;quot; in email addresses.}}&lt;br /&gt;
{{Photo Entry|last=Wu|first=Lin-Liang|userid=okmijn22|email=wlinliang@ gmail. com|location= U of T Shirt standing on the left. |comments=}}&lt;br /&gt;
{{Photo Entry|last=Bartnicki|first=Piotr|userid=Peter|email=piotr.bartnicki@ mail.utoronto.ca|location=Left part of the last row sitting directly between two standing guys, *left* of the one in orange (from the camera&#039;s perspective) and to the right of one in a black striped shirt |comments=}}&lt;br /&gt;
{{Photo Entry|last=Can|first=Oguzhan|userid=Oguzhancan|email=oguzhan.can @ mail. utoronto .ca|location=seventh row from front, fifth from the right, blue tshirt|comments=}}&lt;br /&gt;
{{Photo Entry|last=Cashore|first=Walter|userid=wcashore|email=wcashore 12 @ hotmail .com|location=third row back, in the green star wars shirt|comments=great pic guys}}&lt;br /&gt;
{{Photo Entry|last=Frailich|first=Rebecca|userid=Rebecca.frailich|email=rebecca. frailich@ mail. utoronto. ca|location=Last row, in between two guys standing at the back (one in red, one in black) |comments=}}&lt;br /&gt;
{{Photo Entry|last=Hoover|first=Ken|userid=Khoover|email=ken.hoover@ mail.utoronto.ca|location=First row, fourth from the right.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Kennedy|first=Christopher|userid=ckennedy|email=christopherpa. kennedy@ mail. utoronto. ca|location=Third row; third from the right in white |comments=}}&lt;br /&gt;
{{Photo Entry|last=Klingspor|first=Josefine|userid=Josefine|email=josefine. klingspor@ mail. utoronto. ca|location=First row, second from left.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Le|first=Quan|userid=Quanle|email=quan. le@ mail. utoronto. ca|location=Start bottom right corner, third from right. Go three steps north-west. Directly north-east from there, in blue collar shirt|comments=}}&lt;br /&gt;
{{Photo Entry|last=Liu|first=Zhaowei|userid=tod|email=tod. liu@ mail. utoronto .ca|location=First row, third from the right|comments=}}&lt;br /&gt;
{{Photo Entry|last=Lue|first=Peter|userid=Peterlue|email=peter. lue@ mail. utoronto. ca|location=On the left edge 3rd from the back in the reddish shirt|comments=}}&lt;br /&gt;
{{Photo Entry|last=Millson|first=Richard|userid=Richardm|email=r.millson@ mail. utoronto. ca|location=Seventh row from the front, fourth from the right, blue sweater|comments=}}&lt;br /&gt;
{{Photo Entry|last=McGrath|first=Celton|userid=CeltonMcGrath|email=celton. mcgrath@ mail. utoronto. ca|location=4th row front from, centre right, brown sweater|comments=}}&lt;br /&gt;
{{Photo Entry|last=Morenz|first=Karen|userid=KJMorenz|email=kjmorenz@ gmail.com|location=3rd-ish row from the back, centre right, purple shirt|comments=}}&lt;br /&gt;
{{Photo Entry|last=Pan|first=Li|userid=panli19|email=panli19@ gmail. com|location=fourth row, the guy in grey fleece sweater.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Ratz|first=Derek|userid=Derek.ratz|email=ratz. derek@ gmail. com|location=2nd from the back, 2 in from the far left, yellow shirt|comments=}}&lt;br /&gt;
{{Photo Entry|last=Sarkar|first=Pratyush|userid=Pratyush|email=pratyush. sarkar@ mail. utoronto. ca|location=Somewhere at the back. I think I was in the &amp;lt;math&amp;gt;8^{th}&amp;lt;/math&amp;gt; row, &amp;lt;math&amp;gt;3^{rd}&amp;lt;/math&amp;gt; from the right. There were some empty seats so I am closer to the middle along the row.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Tong|first=Cheng Yu|userid=Chengyu.tong|email=chengyu. tong@ mail. utoronto. ca|location=fourth row from the front on the left side of the picture wearing green sweater and black rimmed glasses |comments=}}&lt;br /&gt;
{{Photo Entry|last=Vicencio-Heap|first=Felipe|userid=Heapfeli|email=felipe. vicencio. heap@ mail. utoronto. ca|location=Second row from the front, furthest to the right.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Wamer|first=Kyle|userid=kylewamer|email=kyle. wamer @ mail. utoronto. ca|location=Second row, fifth from the left in the red shirt.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Yang|first=Chen|userid=chen|email=neochen. yang@ mail. utoronto. ca|location=sixth row, first from the right in the black pull-over.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Yang|first=Tianlin|userid=Tianlin.yang|email=Tianin.Yang@ mail. utoronto. ca|location=4th row, first from left in blue wind coat.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Zhang|first=BingZhen|userid=Zetalda|email=bingzhen. zhang@ mail. utoronto. ca|location=Second last row, third from left.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Zhao|first=TianChen|userid=Ericolony|email=zhao_ tianchen@ hotmail. com|location=fourth row, the guy in green shirt.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Zibert|first=Vincent|userid=vincezibert|email=vincent. zibert@ mail. utoronto. ca|location=Directly beneath the white notice posted on the door on the right-hand side.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Zoghi|first=Sina|userid=sina.zoghi|email=sina.zoghi@ utoronto .ca|location=First row, leftest left.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Léger|first=Zacharie|userid=zach.leger8|email=zacharie. leger@ mail. utronto. ca|location= 5th row in a black T-shirt.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Wang|first=Minqi|userid=Michael.Wang|email=wangminqi@ yahoo.cn|location=First row, fourth from the left in black oufit) |comments=}}&lt;br /&gt;
{{Photo Entry|last=Zhu|first=Grace|userid=gracez|email=grace. zhu@ mail. utoronto. ca|location=Third row, second from right |comments=}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--PLEASE KEEP IN ALPHABETICAL ORDER, BY LAST NAME--&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--PLEASE KEEP IN ALPHABETICAL ORDER, BY LAST NAME--&amp;gt;&lt;/div&gt;</summary>
		<author><name>Leighwinnitoy</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=12-240/The_Final_Exam&amp;diff=12808</id>
		<title>12-240/The Final Exam</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=12-240/The_Final_Exam&amp;diff=12808"/>
		<updated>2012-12-12T07:44:27Z</updated>

		<summary type="html">&lt;p&gt;Leighwinnitoy: /* Cheat Sheets made by Students */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{12-240/Navigation}}&lt;br /&gt;
&lt;br /&gt;
Our final exam is coming up. It will take place on Thursday December 13th, from 9AM until noon, at NF003 - Northrop Frye Hall, Victoria College, 73 Queen&#039;s Park Crescent. &lt;br /&gt;
&lt;br /&gt;
===Content and Style===&lt;br /&gt;
It will consist of 5-6 questions (each may have several parts) on everything that we have covered in class this semester:&lt;br /&gt;
*Fields and vector spaces.&lt;br /&gt;
*Spans, independence, replacement and bases.&lt;br /&gt;
*Linear transformation, rank, nullity, matrices.&lt;br /&gt;
*Row and column reduction and elementary matrices, systems of linear equations.&lt;br /&gt;
*Determinants.&lt;br /&gt;
*A bit on diagonalization.&lt;br /&gt;
*Several other &amp;quot;smaller&amp;quot; topics.&lt;br /&gt;
&lt;br /&gt;
As for the style -&lt;br /&gt;
&lt;br /&gt;
*You can expect to be asked to reproduce some proofs that were given in class.&lt;br /&gt;
*You can expect some fresh things to prove, though generally not as hard as the previous type of proofs.&lt;br /&gt;
*You can expect questions (or parts of questions) that will be identical or nearly identical to questions that were assigned for homework.&lt;br /&gt;
*You can expect some calculations (but nothing that will require a calculator).&lt;br /&gt;
&lt;br /&gt;
It is likely that the exam will be close in spirit to the exams of six and three years ago. See [[06-240/The_Final_Exam]] and [[09-240/The Final Exam]].&lt;br /&gt;
&lt;br /&gt;
Basic calculators (not capable of displaying text or sounding speech) will be allowed but will not be necessary. You may wish to bring one nevertheless, as under pressure &amp;lt;math&amp;gt;5+7&amp;lt;/math&amp;gt; often comes out to be &amp;lt;math&amp;gt;13&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;Remember.&#039;&#039;&#039; Neatness counts! Organization counts! Language counts! Proofs are best given as short and readable essays; without the English between the formulas one never knows how to interpret those formulas. When you write, say, &amp;quot;&amp;lt;math&amp;gt;v\in V&amp;lt;/math&amp;gt;&amp;quot;, does it mean &amp;quot;choose &amp;lt;math&amp;gt;v\in V&amp;lt;/math&amp;gt;&amp;quot;, or &amp;quot;we&#039;ve just proven that &amp;lt;math&amp;gt;v\in V&amp;lt;/math&amp;gt;&amp;quot;, or &amp;quot;assume by contradiction that &amp;lt;math&amp;gt;v\in V&amp;lt;/math&amp;gt;&amp;quot;, or &amp;quot;for every &amp;lt;math&amp;gt;v\in V&amp;lt;/math&amp;gt;&amp;quot; or &amp;quot;there exists &amp;lt;math&amp;gt;v\in V&amp;lt;/math&amp;gt;&amp;quot;? If you don&#039;t say, your reader has no way of knowing. Also remember that long and roundabout solutions of simple problems, full of detours and irrelevant facts, are often an indication that their author didn&#039;t quite get the point, even if they are entirely correct. Avoid those!&lt;br /&gt;
&lt;br /&gt;
==Office Hours==&lt;br /&gt;
Brandon and Peter and I will hold pre-exam office hours as follows:&lt;br /&gt;
* Friday December 7, 10AM-11AM, with Peter at 215 Huron, 10th floor.&lt;br /&gt;
* Monday December 10, 10:30AM-11:30AM, with Dror at Bahen 6178.&lt;br /&gt;
* Monday December 10, 2PM-4PM, with Peter at 215 Huron, 10th floor.&lt;br /&gt;
* Tuesday December 11, 1PM-3:30PM, with Brandon at 215 Huron, 10th floor.&lt;br /&gt;
* Wednesday December 12, 11AM-1PM, with Peter at 215 Huron, 10th floor.&lt;br /&gt;
* Wednesday December 12, 1PM-3:30PM, with Brandon at 215 Huron, 10th floor.&lt;br /&gt;
* Wednesday December 12, 4PM at least until 6PM, with Dror at Bahen 6178.&lt;br /&gt;
&lt;br /&gt;
{{12-240:Dror/Students Divider}}&lt;br /&gt;
&lt;br /&gt;
==Cheat Sheets made by Students==&lt;br /&gt;
Caveat emptor! These notes should not be used in anyway that violates the Code of Academic Integrity. Furthermore, to use these notes effectively, you should be able to prove every bullet points stated.&lt;br /&gt;
&lt;br /&gt;
Materials covered before the midterm: [http://drorbn.net/images/1/12/Midterm1.JPG Part 1] [http://drorbn.net/images/2/23/Midterm2.JPG Part 2] [http://drorbn.net/images/6/62/Midterm3.JPG Part 3]&lt;br /&gt;
&lt;br /&gt;
[http://drorbn.net/images/1/17/DeterminantsforDummies.JPG Determinants for Determined Dummies] (this would especially helps if you are lost in the topic of determinants) (or if you like bad puns)&lt;br /&gt;
&lt;br /&gt;
Errata:&lt;br /&gt;
Part 1, 1L says &amp;quot;the characteristic of a finite field is either prime or zero.&amp;quot; This is incorrect. The characteristic of a finite field must be nonzero and prime. On an unrelated notes, I believe there exists infinite fields of prime characteristics. Yet, a field with characteristic 0 has to be infinite.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
I don&#039;t know where to post this, but if you are doing some last minute study questions like me and you want to check the even answers (as the odd can be checked in the back of the book), here&#039;s a good link:&lt;br /&gt;
http://www.scribd.com/doc/64217240/Linear-Algebra-Friedberg-4th-Ed-Solutions-Manual&lt;/div&gt;</summary>
		<author><name>Leighwinnitoy</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=12-240/Class_Photo&amp;diff=12105</id>
		<title>12-240/Class Photo</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=12-240/Class_Photo&amp;diff=12105"/>
		<updated>2012-10-09T02:35:21Z</updated>

		<summary type="html">&lt;p&gt;Leighwinnitoy: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Our class on September 25, 2012:&lt;br /&gt;
&lt;br /&gt;
[[Image:12-240-ClassPhoto.jpg|thumb|centre|800px|Class Photo: click to enlarge]]&lt;br /&gt;
{{12-240/Navigation}}&lt;br /&gt;
&lt;br /&gt;
Please identify yourself in this photo! There are two ways to do that:&lt;br /&gt;
&lt;br /&gt;
* [[Special:Userlogin|Log in]] to this Wiki and edit this page. Put your name, userid, email address and location in the picture in the alphabetical list below.&lt;br /&gt;
* Send [[User:Drorbn|Dror]] an email message with this information.&lt;br /&gt;
&lt;br /&gt;
The first option is more fun but less private.&lt;br /&gt;
&lt;br /&gt;
===Who We Are...===&lt;br /&gt;
&lt;br /&gt;
{| align=center border=1 cellspacing=0&lt;br /&gt;
|-&lt;br /&gt;
!First Name &lt;br /&gt;
!Last Name &lt;br /&gt;
!ID wcashore&lt;br /&gt;
!e-mail &lt;br /&gt;
!Location &lt;br /&gt;
!Comments &lt;br /&gt;
&lt;br /&gt;
{{Photo Entry|last=Bar-Natan|first=Dror|userid=Drorbn|email=drorbn@ math. toronto. edu|location=facing everybody, as the photographer|comments=Take this entry as a model and leave it first. Otherwise alphabetize by last name. Feel free to leave some fields blank. For better line-breaking, leave a space next to the &amp;quot;@&amp;quot; in email addresses.}}&lt;br /&gt;
{{Photo Entry|last=Bartnicki|first=Piotr|userid=Peter|email=piotr.bartnicki@ mail.utoronto.ca|location=Left part of the last row sitting directly between two standing guys, *left* of the one in orange (from the camera&#039;s perspective) and to the right of one in a black striped shirt |comments=}}&lt;br /&gt;
{{Photo Entry|last=Cashore|first=Walter|userid=wcashore|email=wcashore 12 @ hotmail .com|location=third row back, in the green star wars shirt|comments=great pic guys}}&lt;br /&gt;
{{Photo Entry|last=Frailich|first=Rebecca|userid=Rebecca.frailich|email=rebecca. frailich@ mail. utoronto. ca|location=Last row, in between two guys standing at the back (one in red, one in black) |comments=}}&lt;br /&gt;
{{Photo Entry|last=Hoover|first=Ken|userid=Khoover|email=ken.hoover@ mail.utoronto.ca|location=First row, fourth from the right.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Kennedy|first=Christopher|userid=ckennedy|email=christopherpa. kennedy@ mail. utoronto. ca|location=Third row; third from the right in white |comments=}}&lt;br /&gt;
{{Photo Entry|last=Klingspor|first=Josefine|userid=Josefine|email=josefine. klingspor@ mail. utoronto. ca|location=First row, second from left.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Le|first=Quan|userid=Quanle|email=quan. le@ mail. utoronto. ca|location=Start bottom right corner, third from right. Go three steps north-west. Directly north-east from there, in blue collar shirt|comments=}}&lt;br /&gt;
{{Photo Entry|last=Liu|first=Zhaowei|userid=tod|email=tod. liu@ mail. utoronto .ca|location=First row, third from the right|comments=}}&lt;br /&gt;
{{Photo Entry|last=Millson|first=Richard|userid=Richardm|email=r.millson@ mail. utoronto. ca|location=Seventh row from the front, fourth from the right, blue sweater|comments=}}&lt;br /&gt;
{{Photo Entry|last=McGrath|first=Celton|userid=CeltonMcGrath|email=celton. mcgrath@ mail. utoronto. ca|location=4th row front from, centre right, brown sweater|comments=}}&lt;br /&gt;
{{Photo Entry|last=Morenz|first=Karen|userid=KJMorenz|email=kjmorenz@ gmail.com|location=3rd-ish row from the back, centre right, purple shirt|comments=}}&lt;br /&gt;
{{Photo Entry|last=Pan|first=Li|userid=panli19|email=panli19@gmail.com|location=fourth row, the guy in grey fleece sweater.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Ratz|first=Derek|userid=Derek.ratz|email=ratz.derek@gmail.com|location=2nd from the back, 2 in from the far left, yellow shirt|comments=}}&lt;br /&gt;
{{Photo Entry|last=Tong|first=Cheng Yu|userid=Chengyu.tong|email=chengyu. tong@ mail. utoronto. ca|location=fourth row from the front on the left side of the picture wearing green sweater and black rimmed glasses |comments=}}&lt;br /&gt;
{{Photo Entry|last=Vicencio-Heap|first=Felipe|userid=Heapfeli|email=felipe. vicencio. heap@ mail. utoronto. ca|location=Second row from the front, furthest to the right.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Wamer|first=Kyle|userid=kylewamer|email=kyle. wamer @ mail. utoronto. ca|location=Second row, fifth from the left in the red shirt.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Winnitoy|first=Leigh|userid=Leighwinnitoy|email=leigh.winnitoy@ mail. utoronto. ca|location=sixth row, near the middle of the picture|comments=}}&lt;br /&gt;
{{Photo Entry|last=Yang|first=Chen|userid=chen|email=neochen. yang@ mail. utoronto. ca|location=sixth row, first from the right in the black pull-over.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Yang|first=Tianlin|userid=Tianlin.yang|email=Tianin.Yang@ mail. utoronto. ca|location=4th row, first from left in blue wind coat.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Zhang|first=BingZhen|userid=Zetalda|email=bingzhen. zhang@ mail. utoronto. ca|location=Second last row, third from left.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Zhao|first=TianChen|userid=Ericolony|email=zhao_ tianchen@ hotmail. com|location=fourth row, the guy in green shirt.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Zibert|first=Vincent|userid=vincezibert|email=vincent. zibert@ mail. utoronto. ca|location=Directly beneath the white notice posted on the door on the right-hand side.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Zoghi|first=Sina|userid=sina.zoghi|email=sina.zoghi@ utoronto .ca|location=First row, leftest left.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Léger|first=Zacharie|userid=zach.leger8|email=zacharie. leger@ mail. utronto. ca|location= 5th row in a black T-shirt.|comments=}}&lt;br /&gt;
{{Photo Entry|last=Wang|first=Minqi|userid=Michael.Wang|email=wangminqi@ yahoo.cn|location=First row, fourth from the left in black oufit) |comments=}}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--PLEASE KEEP IN ALPHABETICAL ORDER, BY LAST NAME--&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!--PLEASE KEEP IN ALPHABETICAL ORDER, BY LAST NAME--&amp;gt;&lt;/div&gt;</summary>
		<author><name>Leighwinnitoy</name></author>
	</entry>
</feed>