<?xml version="1.0"?>
<feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en">
	<id>https://drorbn.net/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=Sorin.c</id>
	<title>Drorbn - User contributions [en]</title>
	<link rel="self" type="application/atom+xml" href="https://drorbn.net/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=Sorin.c"/>
	<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Special:Contributions/Sorin.c"/>
	<updated>2026-05-04T17:26:46Z</updated>
	<subtitle>User contributions</subtitle>
	<generator>MediaWiki 1.39.6</generator>
	<entry>
		<id>https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=7134</id>
		<title>User talk:Drorbn</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=7134"/>
		<updated>2008-04-26T05:13:20Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Is the grammar intentional on the user page?&lt;br /&gt;
-John&lt;br /&gt;
&lt;br /&gt;
Yes, but there&#039;s nothing deep there beyond silliness. --[[User:Drorbn|Drorbn]] 06:18, 6 October 2006 (EDT)&lt;br /&gt;
&lt;br /&gt;
==TTC Strike==&lt;br /&gt;
It has just been announced that a TTC strike is in effect. In the event that the strike is still on on the date of the exam, would the exam be affected in any way ?&lt;br /&gt;
--[[User:Sorin.c|Sorin.c]] 01:13, 26 April 2008 (EDT)&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=7099</id>
		<title>08-401/Class Notes for January 9</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=7099"/>
		<updated>2008-04-24T15:16:48Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://www.wikifortio.com/857756/08-401-1.pdf Here] are the lecture 1 notes by [[User:Sorin.c|Sorin]]. Click on &amp;quot;Download&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
by gopsury83 [http://katlas.math.toronto.edu/drorbn/images/9/95/20080109.pdf]&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=7083</id>
		<title>08-401/Class Notes for January 9</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=7083"/>
		<updated>2008-04-19T05:30:09Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://www.filedropper.com/08-401-1 Here] are the lecture 1 notes by [[User:Sorin.c|Sorin]]. Click on &amp;quot;Download this file&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
by gopsury83 [http://katlas.math.toronto.edu/drorbn/images/9/95/20080109.pdf]&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=7082</id>
		<title>08-401/Class Notes for January 9</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=7082"/>
		<updated>2008-04-19T05:29:50Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://www.filedropper.com/08-401-1 Here] are the lecture 1 notes by [[User:Sorin.c|Sorin]].&lt;br /&gt;
&lt;br /&gt;
by gopsury83 [http://katlas.math.toronto.edu/drorbn/images/9/95/20080109.pdf]&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6718</id>
		<title>User talk:Drorbn</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6718"/>
		<updated>2008-03-18T23:00:26Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Is the grammar intentional on the user page?&lt;br /&gt;
-John&lt;br /&gt;
&lt;br /&gt;
Yes, but there&#039;s nothing deep there beyond silliness. --[[User:Drorbn|Drorbn]] 06:18, 6 October 2006 (EDT)&lt;br /&gt;
&lt;br /&gt;
Navigation panel added to Lecture 2 Notes. Sorin.c&lt;br /&gt;
08-401 added to lecture notes. I haven&#039;t re-uploaded the Lecture 1 notes as I&#039;m trying to figure out why in the world they are 7MB, while the other ones are 700KB. Sorin.c&lt;br /&gt;
&lt;br /&gt;
Thanks. --[[User:Drorbn|Drorbn]] 06:20, 17 January 2008 (EST)&lt;br /&gt;
== Uploads ==&lt;br /&gt;
&lt;br /&gt;
Good afternoon, professor.&lt;br /&gt;
One of our classmates asked me to demonstrate how one uploads lecture notes to the wiki, and I picked a random pdf file from my computer in order to demonstrate it.&lt;br /&gt;
My apologies for the inconvenience.&lt;br /&gt;
&lt;br /&gt;
--[[User:Sorin.c|Sorin.c]] 19:00, 18 March 2008 (EDT)&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_February_6&amp;diff=6379</id>
		<title>08-401/Class Notes for February 6</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_February_6&amp;diff=6379"/>
		<updated>2008-02-07T01:55:33Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/d/d1/08-401-5.pdf Here] are the lecture 5 notes by [[User:Sorin.c|Sorin]].&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:08-401-5.pdf&amp;diff=6378</id>
		<title>File:08-401-5.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:08-401-5.pdf&amp;diff=6378"/>
		<updated>2008-02-07T01:55:17Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_February_6&amp;diff=6377</id>
		<title>08-401/Class Notes for February 6</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_February_6&amp;diff=6377"/>
		<updated>2008-02-07T00:42:50Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/1/19/08-401-4.pdf Here] are the lecture 5 notes by [[User:Sorin.c|Sorin]].&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6327</id>
		<title>08-401/Class Photo</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6327"/>
		<updated>2008-02-04T21:01:12Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
&lt;br /&gt;
Our class on Janury 23, 2007:&lt;br /&gt;
&lt;br /&gt;
[[Image:08-401 Class Photo.jpg|thumb|centre|500px|Class Photo: click to enlarge]]&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;
If you are not in the photo, Dror can take your picture some other time and stitch you in.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Who We Are...===&lt;br /&gt;
&lt;br /&gt;
{| align=center border=1 &lt;br /&gt;
|-&lt;br /&gt;
!First name &lt;br /&gt;
!Last name &lt;br /&gt;
!UserID &lt;br /&gt;
!Email &lt;br /&gt;
!In the photo &lt;br /&gt;
!Comments &lt;br /&gt;
&lt;br /&gt;
{{Photo Entry|last=Anwar|first=Farheen|userid=Farheen|email=farheen.anwar @ utoronto.ca|location= Only girl with head scarf, 4th from the right|comments=}}&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}}&lt;br /&gt;
{{Photo Entry|last=Cao|first=Ying|userid=McTea|email= y.cao[at]utoronto.ca|location= third from right, in front, blue scarf|comments= ^^}}&lt;br /&gt;
{{Photo Entry|last=Constantinescu|first=Sorin|userid=Sorin.c|email=first_name.last_name @ utoronto.ca|location=Sixth person from the right, blue striped dress shirt.|comments=If my shirt was red, I would look like Spiderman (sorta).}}&lt;br /&gt;
{{Photo Entry|last=Gershon|first=Amir|userid=LeoDaVinci|email=amir.gershon @ utoronto.ca|location=&#039;&#039;&#039;Really&#039;&#039;&#039; tall bearded guy, back row, fourth from the right in the bright red shirt.|comments=&amp;lt;math&amp;gt;N=q^{\alpha} p_1^{2e_1} \ldots p_k^{2e_k}, &amp;lt;/math&amp;gt;&amp;lt;br&amp;gt;&amp;lt;math&amp;gt;{\alpha} \equiv 1 \pmod 4&amp;lt;/math&amp;gt;}}&lt;br /&gt;
{{Photo Entry|last=Ho|first=Shelley|userid=Mcgrill|email=shelley.ho @ utoronto.ca|location=the girl 5th from the right,front row|comments= =)}}&lt;br /&gt;
{{Photo Entry|last=Lan|first=Kemei|userid=Lankemei2002|email=lankemei2002 @ yahoo.com|location=2nd from the left with black short hair|comments= this is fun!}}&lt;br /&gt;
{{Photo Entry|last=Lee|first=Lori|userid=leelorik|email=leelorik @ gmail.com|location=6th from the left, in the front row|comments=2 + 2 = 4}}&lt;br /&gt;
{{Photo Entry|last=Memon|first=Shaun|userid=s.memon|email=s.memon @ utoronto.ca|location=back row in the centre, I have 14 people to the left and 14 people to the right of me|comments=Shaun ∈ Z(MAT401)}}&lt;br /&gt;
{{Photo Entry|last=Robertson|first=James|userid=Emailforjimmy|email=emailforjimmy NOSPAM @ gmail.com|location= I am the tall person (2nd only to the bearded fellow in red...Amir I think) near the middle in the back|comments= can you tell who just found out he handed in the wrong problems for Ass. # 1?}}&lt;br /&gt;
{{Photo Entry|last=Sansern|first=Oak|userid=Hamlet|email=oak.sansern @ utoronto.ca|location=front row, 1st from the projector in white--looking too tired for eve class|comments=seriously? maybe later =)}}&lt;br /&gt;
{{Photo Entry|last=Selariu|first=Diana|userid=Diana|email=dselariu @ gmail.com|location=5th from the left, front row}}&lt;br /&gt;
{{Photo Entry|last=Shin|first=Tae Maen|userid=gopsury83|email= tim.shin @ utoronto.ca|location= second from right, back row|comments= You can call me Tim}}&lt;br /&gt;
{{Photo Entry|last=Udasco|first=Chris|userid=Christopher|email=chris dot udasco at utoronto dot ca|location=front row grin|comments=2 + 2 = 1 (..huh?)&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;... Mod 3! (whaaaaat!!)}}&lt;br /&gt;
{{Photo Entry|last=Yiu|first=Tony|userid=Tonytastic|email=tony.yiu @ utoronto.ca|location=Asian guy, left of the middle wearing blue|comments=Chuck Norris can divide by zero}}&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6326</id>
		<title>08-401/Class Photo</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6326"/>
		<updated>2008-02-04T20:53:52Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: /* Who We Are... */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
&lt;br /&gt;
Our class on Janury 23, 2007:&lt;br /&gt;
&lt;br /&gt;
[[Image:08-401 Class Photo.jpg|thumb|centre|500px|Class Photo: click to enlarge]]&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;
If you are not in the photo, Dror can take your picture some other time and stitch you in.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Who We Are...===&lt;br /&gt;
&lt;br /&gt;
{| align=center border=1 &lt;br /&gt;
|-&lt;br /&gt;
!First name &lt;br /&gt;
!Last name &lt;br /&gt;
!UserID &lt;br /&gt;
!Email &lt;br /&gt;
!In the photo &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}}&lt;br /&gt;
{{Photo Entry|last=Anwar|first=Farheen|userid=Farheen|email=farheen.anwar @ utoronto.ca|location= Only girl with head scarf, 4th from the right|comments=}}&lt;br /&gt;
{{Photo Entry|last=Bathelt|first=Jenny|userid=|email=jenny.bathelt @ utoronto.ca|location=Third from the left, front row, in the white sweater|comments=}}&lt;br /&gt;
{{Photo Entry|last=Cao|first=Ying|userid=McTea|email= y.cao[at]utoronto.ca|location= third from right, in front, blue scarf|comments= ^^}}&lt;br /&gt;
{{Photo Entry|last=Constantinescu|first=Sorin|userid=Sorin.c|email=first_name.last_name @ utoronto.ca|location=Sixth person from the right, blue striped dress shirt.|comments=If my shirt was red, I would look like Spiderman (sorta).}}&lt;br /&gt;
{{Photo Entry|last=Gershon|first=Amir|userid=LeoDaVinci|email=amir.gershon @ utoronto.ca|location=&#039;&#039;&#039;Really&#039;&#039;&#039; tall bearded guy, back row, fourth from the right in the bright red shirt.|comments=&amp;lt;math&amp;gt;N=q^{\alpha} p_1^{2e_1} \ldots p_k^{2e_k}, &amp;lt;/math&amp;gt;&amp;lt;br&amp;gt;&amp;lt;math&amp;gt;{\alpha} \equiv 1 \pmod 4&amp;lt;/math&amp;gt;}}&lt;br /&gt;
{{Photo Entry|last=Ho|first=Shelley|userid=Mcgrill|email=shelley.ho @ utoronto.ca|location=the girl 5th from the right,front row|comments= =)}}&lt;br /&gt;
{{Photo Entry|last=Lan|first=Kemei|userid=Lankemei2002|email=lankemei2002 @ yahoo.com|location=2nd from the left with black short hair|comments= this is fun!}}&lt;br /&gt;
{{Photo Entry|last=Lee|first=Lori|userid=leelorik|email=leelorik @ gmail.com|location=6th from the left, in the front row|comments=2 + 2 = 4}}&lt;br /&gt;
{{Photo Entry|last=Memon|first=Shaun|userid=s.memon|email=s.memon @ utoronto.ca|location=back row in the centre, I have 14 people to the left and 14 people to the right of me|comments=Shaun ∈ Z(MAT401)}}&lt;br /&gt;
{{Photo Entry|last=Robertson|first=James|userid=Emailforjimmy|email=emailforjimmy NOSPAM @ gmail.com|location= I am the tall person (2nd only to the bearded fellow in red...Amir I think) near the middle in the back|comments= can you tell who just found out he handed in the wrong problems for Ass. # 1?}}&lt;br /&gt;
{{Photo Entry|last=Sansern|first=Oak|userid=Hamlet|email=oak.sansern @ utoronto.ca|location=front row, 1st from the projector in white--looking too tired for eve class|comments=seriously? maybe later =)}}&lt;br /&gt;
{{Photo Entry|last=Selariu|first=Diana|userid=Diana|email=dselariu @ gmail.com|location=5th from the left, front row}}&lt;br /&gt;
{{Photo Entry|last=Shin|first=Tae Maen|userid=gopsury83|email= tim.shin @ utoronto.ca|location= second from right, back row|comments= You can call me Tim}}&lt;br /&gt;
{{Photo Entry|last=Udasco|first=Chris|userid=Christopher|email=chris dot udasco at utoronto dot ca|location=front row grin|comments=2 + 2 = 1 (..huh?)&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;... Mod 3! (whaaaaat!!)}}&lt;br /&gt;
{{Photo Entry|last=Yiu|first=Tony|userid=Tonytastic|email=tony.yiu @ utoronto.ca|location=Asian guy, left of the middle wearing blue|comments=Chuck Norris can divide by zero}}&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_30&amp;diff=6278</id>
		<title>08-401/Class Notes for January 30</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_30&amp;diff=6278"/>
		<updated>2008-01-31T02:01:53Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/1/19/08-401-4.pdf Here] are the lecture 4 notes by [[User:Sorin.c|Sorin]].&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:08-401-4.pdf&amp;diff=6277</id>
		<title>File:08-401-4.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:08-401-4.pdf&amp;diff=6277"/>
		<updated>2008-01-31T02:01:41Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6242</id>
		<title>Talk:08-401</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6242"/>
		<updated>2008-01-27T20:28:30Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;something i still unclear on ideal test..&lt;br /&gt;
&lt;br /&gt;
since there are two conditons in ideal test&lt;br /&gt;
1. a-b in A whenever a, b in A&lt;br /&gt;
2.ra and ar are in A whenever a in A and r in A&lt;br /&gt;
&lt;br /&gt;
i just wonder when i use the ideal test,  i need to use both condtions together &lt;br /&gt;
&lt;br /&gt;
or just use one of both , then i can conclude a nonempty subset of a ring R is an ideal of R&lt;br /&gt;
&lt;br /&gt;
thx&lt;br /&gt;
&lt;br /&gt;
I would think both need to be satisfied. [[User:Sorin.c|Sorin.c]]&lt;br /&gt;
&lt;br /&gt;
thx so much&lt;br /&gt;
&lt;br /&gt;
now,   i have a tiny question,   is the Z/n equal to Z_n?  are they the same thing.  &lt;br /&gt;
&lt;br /&gt;
because the textbook give us the symbol &amp;quot; Z_n&amp;quot;,  and the lecture notes give us &amp;quot; Z/n&amp;quot;&lt;br /&gt;
&lt;br /&gt;
there is any difference? BY the way,  i just uploaded a picture , just follow the link please:&lt;br /&gt;
&lt;br /&gt;
http://katlas.math.toronto.edu/drorbn/index.php?title=Image:08-401.jpg&lt;br /&gt;
&lt;br /&gt;
There is no difference. [[User:Drorbn|Dror]] said he prefers writing &amp;lt;math&amp;gt;\mathbb Z/n&amp;lt;/math&amp;gt; instead of &amp;lt;math&amp;gt;\mathbb Z_n&amp;lt;/math&amp;gt;.&lt;br /&gt;
--[[User:Sorin.c|Sorin.c]] 15:28, 27 January 2008 (EST)&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User:Sorin.c/signature&amp;diff=6241</id>
		<title>User:Sorin.c/signature</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User:Sorin.c/signature&amp;diff=6241"/>
		<updated>2008-01-27T20:21:00Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;-- [[User:Sorin.c|Sorin.c]]&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6240</id>
		<title>Talk:08-401</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6240"/>
		<updated>2008-01-27T20:09:14Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;something i still unclear on ideal test..&lt;br /&gt;
&lt;br /&gt;
since there are two conditons in ideal test&lt;br /&gt;
1. a-b in A whenever a, b in A&lt;br /&gt;
2.ra and ar are in A whenever a in A and r in A&lt;br /&gt;
&lt;br /&gt;
i just wonder when i use the ideal test,  i need to use both condtions together &lt;br /&gt;
&lt;br /&gt;
or just use one of both , then i can conclude a nonempty subset of a ring R is an ideal of R&lt;br /&gt;
&lt;br /&gt;
thx&lt;br /&gt;
&lt;br /&gt;
I would think both need to be satisfied. [[User:Sorin.c|Sorin.c]]&lt;br /&gt;
&lt;br /&gt;
thx so much&lt;br /&gt;
&lt;br /&gt;
now,   i have a tiny question,   is the Z/n equal to Z_n?  are they the same thing.  &lt;br /&gt;
&lt;br /&gt;
because the textbook give us the symbol &amp;quot; Z_n&amp;quot;,  and the lecture notes give us &amp;quot; Z/n&amp;quot;&lt;br /&gt;
&lt;br /&gt;
there is any difference? BY the way,  i just uploaded a picture , just follow the link please:&lt;br /&gt;
&lt;br /&gt;
http://katlas.math.toronto.edu/drorbn/index.php?title=Image:08-401.jpg&lt;br /&gt;
&lt;br /&gt;
There is no difference. [[User:Drorbn|Dror]] said he prefers writing &amp;lt;math&amp;gt;\mathbb Z/n&amp;lt;/math&amp;gt; instead of &amp;lt;math&amp;gt;\mathbb Z_n&amp;lt;/math&amp;gt;. [[User:Sorin.c|Sorin.c]]&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6210</id>
		<title>User talk:Drorbn</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6210"/>
		<updated>2008-01-24T14:07:40Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Is the grammar intentional on the user page?&lt;br /&gt;
-John&lt;br /&gt;
&lt;br /&gt;
Yes, but there&#039;s nothing deep there beyond silliness. --[[User:Drorbn|Drorbn]] 06:18, 6 October 2006 (EDT)&lt;br /&gt;
&lt;br /&gt;
Navigation panel added to Lecture 2 Notes. Sorin.c&lt;br /&gt;
08-401 added to lecture notes. I haven&#039;t re-uploaded the Lecture 1 notes as I&#039;m trying to figure out why in the world they are 7MB, while the other ones are 700KB. Sorin.c&lt;br /&gt;
&lt;br /&gt;
Thanks. --[[User:Drorbn|Drorbn]] 06:20, 17 January 2008 (EST)&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6209</id>
		<title>08-401/Class Notes for January 23</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6209"/>
		<updated>2008-01-24T14:07:00Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/6/60/08-401-3.pdf Here] are the lecture 3 notes by [[User:Sorin.c|Sorin]].&lt;br /&gt;
&lt;br /&gt;
This is my notes ([[User:Ilovemath|Ilovemath]]&#039;s):&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_001.jpg Page 1], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_002.jpg 2], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_003.jpg 3], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 4], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_005.jpg 5], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_006.jpg 6], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_007.jpg 7], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_008.jpg 8], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_009.jpg 9], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_010.jpg 10]and [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_011.jpg 11].&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:08-401-3.pdf&amp;diff=6208</id>
		<title>File:08-401-3.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:08-401-3.pdf&amp;diff=6208"/>
		<updated>2008-01-24T14:06:42Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6207</id>
		<title>08-401/Class Notes for January 16</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6207"/>
		<updated>2008-01-24T14:05:33Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/9/9e/08-401-2.pdf Here] are the lecture 2 notes by [[User:Sorin.c|Sorin]].&lt;br /&gt;
&lt;br /&gt;
hello, everyone,  can someone tell me how to upload my notes to this website.&lt;br /&gt;
&lt;br /&gt;
thx so much&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:08-401-2.pdf&amp;diff=6206</id>
		<title>File:08-401-2.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:08-401-2.pdf&amp;diff=6206"/>
		<updated>2008-01-24T14:05:07Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6193</id>
		<title>08-401/Class Notes for January 23</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6193"/>
		<updated>2008-01-24T05:13:54Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/c/c0/Lecture3.pdf Here] are the lecture 3 notes by [[User:Sorin.c|Sorin]].&lt;br /&gt;
&lt;br /&gt;
This is my notes ([[User:Ilovemath|Ilovemath]]&#039;s):&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_001.jpg Page 1], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_002.jpg 2], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_003.jpg 3], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 4], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_005.jpg 5], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_006.jpg 6], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_007.jpg 7], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_008.jpg 8], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_009.jpg 9], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_010.jpg 10]and [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_011.jpg 11].&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=6192</id>
		<title>08-401/Class Notes for January 9</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=6192"/>
		<updated>2008-01-24T05:13:11Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://www.sorinc.net/lecture1.pdf Here] are the lecture 1 notes by [[User:Sorin.c|Sorin]].&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6191</id>
		<title>08-401/Class Notes for January 16</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6191"/>
		<updated>2008-01-24T05:12:56Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://www.sorinc.net/lecture2.pdf Here] are the lecture 2 notes by [[User:Sorin.c|Sorin]].&lt;br /&gt;
&lt;br /&gt;
hello, everyone,  can someone tell me how to upload my notes to this website.&lt;br /&gt;
&lt;br /&gt;
thx so much&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User_talk:Ilovemath&amp;diff=6190</id>
		<title>User talk:Ilovemath</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User_talk:Ilovemath&amp;diff=6190"/>
		<updated>2008-01-24T05:12:14Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;If you want to upload all notes at once, you should make a .rar or .zip archive. Though I don&#039;t know how many people would know how to deal with them.&lt;br /&gt;
Cheers, [[User:Sorin.c|Sorin]].&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6189</id>
		<title>08-401/Class Notes for January 23</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6189"/>
		<updated>2008-01-24T05:10:57Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/c/c0/Lecture3.pdf Here] are the lecture 3 notes by [[User:Sorin.c|Sorin]].&lt;br /&gt;
&lt;br /&gt;
This is my notes ([[User:Ilovemath|Ilovemath]]&#039;s):&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_001.jpg Page 1], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_002.jpg 2], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_003.jpg 3], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 4], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 5], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 6], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 7], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 8], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 9], [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 10]and [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:Mat401_004.jpg 11].&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User:Sorin.c&amp;diff=6188</id>
		<title>User:Sorin.c</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User:Sorin.c&amp;diff=6188"/>
		<updated>2008-01-24T05:10:32Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[http://en.wikipedia.org/wiki/User:Sorin.c About me.]&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User:Sorin.c&amp;diff=6187</id>
		<title>User:Sorin.c</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User:Sorin.c&amp;diff=6187"/>
		<updated>2008-01-24T05:07:39Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6167</id>
		<title>08-401/Class Photo</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6167"/>
		<updated>2008-01-24T03:49:05Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
&lt;br /&gt;
Our class on Janury 23, 2007:&lt;br /&gt;
&lt;br /&gt;
[[Image:08-401 Class Photo.jpg|thumb|centre|500px|Class Photo: click to enlarge]]&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;
If you are not in the photo, Dror can take your picture some other time and stitch you in.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Who We Are...===&lt;br /&gt;
&lt;br /&gt;
{| align=center border=1 &lt;br /&gt;
|-&lt;br /&gt;
!First name&lt;br /&gt;
!Last name &lt;br /&gt;
!UserID &lt;br /&gt;
!Email &lt;br /&gt;
!In the photo &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}}&lt;br /&gt;
{{Photo Entry|last=Constantinescu|first=Sorin|userid=Sorin.c|email=first_name.last_name@utoronto.ca|location=Sixth person from the right, blue striped dress shirt.|comments=If my shirt was red, I would look like Spiderman (sorta).}}&lt;br /&gt;
{{Photo Entry|last=Gershon|first=Amir|userid=LeoDaVinci|email=amir.gershon @ utoronto.ca|location=&#039;&#039;&#039;Really&#039;&#039;&#039; tall bearded guy on the right in the bright red shirt.|comments=&amp;lt;math&amp;gt;N=q^{\alpha} p_1^{2e_1} \ldots p_k^{2e_k}, &amp;lt;/math&amp;gt;}}&lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6158</id>
		<title>08-401/Class Photo</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6158"/>
		<updated>2008-01-24T03:27:22Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: /* Who We Are... */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
&lt;br /&gt;
Our class on Janury 23, 2007:&lt;br /&gt;
&lt;br /&gt;
[[Image:08-401 Class Photo.jpg|thumb|centre|500px|Class Photo: click to enlarge]]&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;
If you are not in the photo, Dror can take your picture some other time and stitch you in.&lt;br /&gt;
&lt;br /&gt;
===Who We Are...===&lt;br /&gt;
&lt;br /&gt;
{| align=center border=1 &lt;br /&gt;
|-&lt;br /&gt;
!First name&lt;br /&gt;
!Last name &lt;br /&gt;
!UserID &lt;br /&gt;
!Email &lt;br /&gt;
!In the photo &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}}&lt;br /&gt;
{{Photo Entry|last=Constantinescu|first=Sorin|userid=Sorin.c|email=first_name.last_name@utoronto.ca|location=Sixth person from the right, blue striped dress shirt.|comments=If my shirt was red, I would look like Spiderman (sorta).}}&lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6153</id>
		<title>08-401/Class Notes for January 23</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6153"/>
		<updated>2008-01-24T02:02:25Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/c/c0/Lecture3.pdf Here] are the lecture 3 notes.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:Lecture3.pdf&amp;diff=6152</id>
		<title>File:Lecture3.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:Lecture3.pdf&amp;diff=6152"/>
		<updated>2008-01-24T02:01:58Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: Lecture 3 Notes.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Lecture 3 Notes.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6151</id>
		<title>08-401/Class Notes for January 23</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_23&amp;diff=6151"/>
		<updated>2008-01-24T02:00:33Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
{{08-401/Class Notes Warning}}&lt;br /&gt;
&lt;br /&gt;
[http://www.sorinc.net/lecture3.pdf Here] are the lecture 2 notes.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User:Sorin.c&amp;diff=6145</id>
		<title>User:Sorin.c</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User:Sorin.c&amp;diff=6145"/>
		<updated>2008-01-23T02:54:16Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;math&amp;gt;\lim_{n \to \infty} \sqrt[n]{3^n + 5^n}&amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6140</id>
		<title>Talk:08-401</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6140"/>
		<updated>2008-01-21T03:00:14Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;something i still unclear on ideal test..&lt;br /&gt;
&lt;br /&gt;
since there are two conditons in ideal test&lt;br /&gt;
1. a-b in A whenever a, b in A&lt;br /&gt;
2.ra and ar are in A whenever a in A and r in A&lt;br /&gt;
&lt;br /&gt;
i just wonder when i use the ideal test,  i need to use both condtions together &lt;br /&gt;
&lt;br /&gt;
or just use one of both , then i can conclude a nonempty subset of a ring R is an ideal of R&lt;br /&gt;
&lt;br /&gt;
thx&lt;br /&gt;
&lt;br /&gt;
I would think both need to be satisfied. [[User:Sorin.c|Sorin.c]]&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6139</id>
		<title>Talk:08-401</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6139"/>
		<updated>2008-01-21T03:00:05Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;something i still unclear on ideal test..&lt;br /&gt;
&lt;br /&gt;
since there are two conditons in ideal test&lt;br /&gt;
1. a-b in A whenever a, b in A&lt;br /&gt;
2.ra and ar are in A whenever a in A and r in A&lt;br /&gt;
&lt;br /&gt;
i just wonder when i use the ideal test,  i need to use both condtions together &lt;br /&gt;
&lt;br /&gt;
or just use one of both , then i can conclude a nonempty subset of a ring R is an ideal of R&lt;br /&gt;
&lt;br /&gt;
thx&lt;br /&gt;
I would think both need to be satisfied. [[User:Sorin.c|Sorin.c]]&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6106</id>
		<title>User talk:Drorbn</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6106"/>
		<updated>2008-01-17T03:10:17Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Is the grammar intentional on the user page?&lt;br /&gt;
-John&lt;br /&gt;
&lt;br /&gt;
Yes, but there&#039;s nothing deep there beyond silliness. --[[User:Drorbn|Drorbn]] 06:18, 6 October 2006 (EDT)&lt;br /&gt;
&lt;br /&gt;
Navigation panel added to Lecture 2 Notes. sorin.c&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6105</id>
		<title>User talk:Drorbn</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6105"/>
		<updated>2008-01-17T03:10:04Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Is the grammar intentional on the user page?&lt;br /&gt;
-John&lt;br /&gt;
&lt;br /&gt;
Yes, but there&#039;s nothing deep there beyond silliness. --[[User:Drorbn|Drorbn]] 06:18, 6 October 2006 (EDT)&lt;br /&gt;
&lt;br /&gt;
Navigation panel added to Lecture 2 Notes.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6104</id>
		<title>User talk:Drorbn</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=User_talk:Drorbn&amp;diff=6104"/>
		<updated>2008-01-17T03:09:47Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: Navigation panel&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Is the grammar intentional on the user page?&lt;br /&gt;
-John&lt;br /&gt;
&lt;br /&gt;
Yes, but there&#039;s nothing deep there beyond silliness. --[[User:Drorbn|Drorbn]] 06:18, 6 October 2006 (EDT)&lt;br /&gt;
&lt;br /&gt;
== Navigation panel ==&lt;br /&gt;
&lt;br /&gt;
Added to Lecture 2 Notes.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6103</id>
		<title>08-401/Class Notes for January 16</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6103"/>
		<updated>2008-01-17T03:04:17Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
[http://www.sorinc.net/lecture2.pdf Here] are the lecture 2 notes.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6100</id>
		<title>08-401/Class Notes for January 16</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6100"/>
		<updated>2008-01-17T02:03:06Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[http://www.sorinc.net/lecture2.pdf Here] are the lecture 2 notes.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=6077</id>
		<title>08-401/Class Notes for January 9</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=6077"/>
		<updated>2008-01-10T01:53:54Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[http://www.sorinc.net/lecture1.pdf Here] are the lecture 1 notes.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/About_This_Class&amp;diff=6076</id>
		<title>08-401/About This Class</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/About_This_Class&amp;diff=6076"/>
		<updated>2008-01-09T23:33:38Z</updated>

		<summary type="html">&lt;p&gt;Sorin.c: /* The Term Test */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
===Crucial Information===&lt;br /&gt;
{{08-401/Crucial Information}}&lt;br /&gt;
&lt;br /&gt;
&#039;&#039;&#039;URL:&#039;&#039;&#039; {{SERVER}}/drorbn/index.php?title=08-401.&lt;br /&gt;
&lt;br /&gt;
===Abstract===&lt;br /&gt;
Taken from the Faculty of Arts and Science [http://www.artsandscience.utoronto.ca/ofr/calendar/crs_mat.htm Calendar]:&lt;br /&gt;
:Commutative rings; quotient rings. Construction of the rationals. Polynomial algebra. Fields and Galois theory: Field extensions, adjunction of roots of a polynomial. Constructibility, trisection of angles, construction of regular polygons. Galois groups of polynomials, in particular cubics, quartics. Insolvability of quintics by radicals.&lt;br /&gt;
&lt;br /&gt;
*Prerequisite: MAT224H1 (Linear Algebra II), MAT235Y1/MAT237Y1 (Calculus II/Multivariable Calculus), MAT246H1/MAT257Y1 (Concepts in Abstract Mathematics/Analysis II).&lt;br /&gt;
*Exclusion: MAT347Y1 (Groups, Rings and Fields).&lt;br /&gt;
&lt;br /&gt;
===Text Book(s)===&lt;br /&gt;
* (Required) J. A. Gallian, &amp;quot;Contemporary Abstract Algebra&amp;quot;, chapters 12-17, 20-23 and 31-33 (approx.).&lt;br /&gt;
* (Recommended) D. S. Dummit and R. M. Foote, &amp;quot;Abstract Algebra&amp;quot;, chapters 7, 8, 9, 13, 14.&lt;br /&gt;
* (Suggested) T. Hungerford, &amp;quot;Abstract Algebra, an Introduction&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
===Plan===&lt;br /&gt;
I will aim to cover the above-mentioned 13 chapters of Gallian&#039;s book at a bit faster than one per week, so as to leave us some time for extras at the end, but we may fall back to a rate of just one chapter a week or even less. If so, chapters 23 and 31 will be the first candidates for skipping.&lt;br /&gt;
&lt;br /&gt;
===Wiki===&lt;br /&gt;
The class web site is a wiki, as in [http://www.wikipedia.org Wikipedia] - meaning that anyone can and is welcome to edit almost anything and in particular, students can post notes, comments, pictures, whatever. Some rules, though -&lt;br /&gt;
* This wiki is a part of my ({{Dror}}&#039;s) academic web page. All postings on it must be class-related (or related to one of the other projects I&#039;m involved with).&lt;br /&gt;
* I ({{Dror}}) will allow myself to exercise editorial control, when necessary.&lt;br /&gt;
* The titles of all pages related to this class should begin with &amp;quot;08-401/&amp;quot; or with &amp;quot;08-401-&amp;quot;, just like the title of this page.&lt;br /&gt;
&lt;br /&gt;
To edit, you must have a wiki account. To get one email a request to {{Dror}} at drorbn@math.toronto.edu, and include:&lt;br /&gt;
* Your first and last name.&lt;br /&gt;
* Your preferred user id.&lt;br /&gt;
* Your email address, if different from the address you&#039;ve used for this email.&lt;br /&gt;
Some further editing help is available at [[Help:Contents]].&lt;br /&gt;
&lt;br /&gt;
===Marking Scheme===&lt;br /&gt;
There will be one term test (25% of the total grade) and a final exam (50%), as well as about 10 homework assignments (25%).&lt;br /&gt;
&lt;br /&gt;
====The Term Test====&lt;br /&gt;
The term test will take place in class on February 27. A student who misses the term test without providing a valid reason (for example, a doctor’s note) within one week of the test will receive a mark of 0 on the term test. There will be no make-up term test. If a student misses the term test for a valid reason, the weight of the problem sets will increase to 35% and the weight of the final exam to 65%.&lt;br /&gt;
&lt;br /&gt;
====Homework====&lt;br /&gt;
Assignments will be posted on the course web page approximately on the weeks shown in the class timeline. Typically an &amp;quot;in preparation&amp;quot; version of any assignment will be posted a bit before class and the &amp;quot;in preparation&amp;quot; tag will be removed shortly after class, once our progress in class is precisely measured. Assignments will be due in class a week after they are assigned and they will be marked by the TA, usually within another week. All students (including those who join the course late) will receive a mark of 0 on each assignment not handed in; though to allow you some leeway, in computing the homework grade your worst two assignments will not count. I encourage you to discuss the assignments with other students or even browse the web, so long as you do at least some of the thinking on your own and you write up your own solutions. Remember that cheating is always possible and may increase your homework grade a bit. But it will hurt your exam grades a lot more.&lt;br /&gt;
&lt;br /&gt;
===Good Deeds===&lt;br /&gt;
Students will be able to earn up to 25 &amp;quot;good deeds&amp;quot; points throughout the year for doing services to the class as a whole. There is no pre-set system for awarding these points, but the following will definitely count:&lt;br /&gt;
* Drawing a beautiful picture to illustrate a point discussed in class and posting it on this site.&lt;br /&gt;
* Taking class notes in nice handwriting, scanning them and posting them here.&lt;br /&gt;
* Typing up or formatting somebody else&#039;s class notes, correcting them or expanding them in any way.&lt;br /&gt;
* Writing an essay expanding on anything mentioned in class and posting it here; correcting or expanding somebody else&#039;s article.&lt;br /&gt;
* Doing anything on our [[08-401/To do]] list.&lt;br /&gt;
* Any other service to the class as a whole.&lt;br /&gt;
&lt;br /&gt;
Good deed points will count towards your final grade! If you got &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt; of those, they are solidly your and the formula for the final grade below will only be applied to the remaining &amp;lt;math&amp;gt;100-n&amp;lt;/math&amp;gt; points. So if you got 25 good deed points (say) and your final grade is 80, I will report your grade as &amp;lt;math&amp;gt;25+80(100-25)/100=85&amp;lt;/math&amp;gt;. Yet you can get an overall 100 even without doing a single good deed.&lt;br /&gt;
&lt;br /&gt;
[[Image:08-401-Galois.jpeg|thumb|right|Galois at the age of fifteen from the pencil of a classmate. He was young-looking for his age and had black hair.]]&lt;br /&gt;
===Class Photo===&lt;br /&gt;
To help me learn your names, I will take a class photo on the third week of classes. I will post the picture on the class&#039; web site and you will be &#039;&#039;required&#039;&#039;  to identify yourself on the [[08-401/Class Photo|Class Photo]] page of this wiki.&lt;br /&gt;
&lt;br /&gt;
===On Galois===&lt;br /&gt;
The first paragraph of the [http://en.wikipedia.org/wiki/Galois Wikipedia entry] on Galois:&lt;br /&gt;
&lt;br /&gt;
:&#039;&#039;&#039;Évariste Galois&#039;&#039;&#039; (IPA: [evaʁist gaˈlwa]; October 25, 1811 – May 31, 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem. His work laid the foundations for Galois theory, a major branch of abstract algebra, and the subfield of Galois connections. He was the first to use the word &amp;quot;group&amp;quot; (French: groupe) as a technical term in mathematics to represent a group of permutations. A radical Republican during the monarchy of Louis Philippe in France, he died from wounds suffered in a duel under murky circumstances at the age of twenty.&lt;/div&gt;</summary>
		<author><name>Sorin.c</name></author>
	</entry>
</feed>