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	<updated>2026-06-19T03:51:48Z</updated>
	<subtitle>User contributions</subtitle>
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	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_April_2&amp;diff=6882</id>
		<title>08-401/Class Notes for April 2</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_April_2&amp;diff=6882"/>
		<updated>2008-04-03T05:03:06Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: &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;
===Notes===&lt;br /&gt;
Here is one set of [[08-401-Apr02-Notes|notes by LeoDaVinci]]&lt;br /&gt;
&lt;br /&gt;
Lecture Notes for Apr 02 by gopsury83[http://katlas.math.toronto.edu/drorbn/images/1/15/080402.pdf]&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:080402.pdf&amp;diff=6881</id>
		<title>File:080402.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:080402.pdf&amp;diff=6881"/>
		<updated>2008-04-03T05:02:03Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: apr 02 lecture note&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;apr 02 lecture note&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_March_26&amp;diff=6801</id>
		<title>08-401/Class Notes for March 26</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_March_26&amp;diff=6801"/>
		<updated>2008-03-27T05:02:27Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;uploaded by leelorik&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-26-2008_09%3B07%3B33PM.JPG pg 1 front] [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-26-2008_09%3B06%3B29PM.JPG pg 1 back]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-26-2008_09%3B08%3B22PM.JPG pg 2 front] [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-26-2008_09%3B08%3B48PM.JPG pg 2 back]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-26-2008_09%3B09%3B33PM.JPG pg 3 front] [http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-26-2008_09%3B10%3B13PM.JPG pg 3 back]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-26-2008_09%3B10%3B58PM.JPG pg 4]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/d/d6/20080326.pdf above notes combined in pdf] by gopsury83&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:20080326.pdf&amp;diff=6800</id>
		<title>File:20080326.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:20080326.pdf&amp;diff=6800"/>
		<updated>2008-03-27T05:01:31Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: in pdf&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;in pdf&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Homework_Assignment_5&amp;diff=6799</id>
		<title>08-401/Homework Assignment 5</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Homework_Assignment_5&amp;diff=6799"/>
		<updated>2008-03-27T04:58:11Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
&lt;br /&gt;
===Reading===&lt;br /&gt;
Read chapters 16 and 17 (to page 306) of Gallian&#039;s book (&#039;&#039;&#039;6th edition&#039;&#039;&#039;) three times:&lt;br /&gt;
* First time as if you were reading a novel - quickly and without too much attention to detail, just to learn what the main keywords and concepts and goals are.&lt;br /&gt;
* Second time like you were studying for an exam on the subject - slowly and not skipping anything, verifying every little detail.&lt;br /&gt;
* And then a third time, again at a quicker pace, to remind yourself of the bigger picture all those little details are there to paint.&lt;br /&gt;
&lt;br /&gt;
===Doing===&lt;br /&gt;
Solve problems S20, 22, 24, S27, S31, 32, 38, S39, 40, S45, 49 in Chapter 16 of Gallian&#039;s book (&#039;&#039;&#039;6th edition&#039;&#039;&#039;) and problems 2, S4, 5 in Chapter 17 of the same book, but submit only the solutions of the problems marked with the letter &amp;quot;S&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
===Due Date===&lt;br /&gt;
This assignment is due in class on Wednesday February 13, 2008.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;span style=&amp;quot;color: red;&amp;quot;&amp;gt;The notes below are by the students and for the students. Hopefully they are useful, but they come with no guarantee of any kind.&amp;lt;/span&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=== Corresponding Questions for Gallian&#039;s 5th Edition ===&lt;br /&gt;
&amp;lt;B&amp;gt;Chapter 16&amp;lt;/B&amp;gt; - S20, 22, 24, S27, S31, 32, 38, S39, 40&lt;br /&gt;
&amp;lt;BR&amp;gt;&lt;br /&gt;
S45: Let F be a field. Show that there exists a,b in F with property (x^2 + x + 1) divides (x^43 + ax + b)&lt;br /&gt;
&amp;lt;BR&amp;gt;&lt;br /&gt;
49: Show that 1 is the only solution of x^25 - 1 = 0 in Z/37&lt;br /&gt;
&amp;lt;BR&amp;gt;&lt;br /&gt;
&amp;lt;B&amp;gt;Chapter 17&amp;lt;/B&amp;gt; - 2, S4, 5&lt;br /&gt;
&lt;br /&gt;
solution to selected problems [http://katlas.math.toronto.edu/drorbn/images/e/ee/Hwk5.pdf]&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:Hwk5.pdf&amp;diff=6798</id>
		<title>File:Hwk5.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:Hwk5.pdf&amp;diff=6798"/>
		<updated>2008-03-27T04:57:56Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: homework 5&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;homework 5&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_16&amp;diff=6797</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=6797"/>
		<updated>2008-03-27T04:44:33Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: &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;
by gopsury83 [http://katlas.math.toronto.edu/drorbn/images/6/66/20080116.pdf]&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:20080116.pdf&amp;diff=6796</id>
		<title>File:20080116.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:20080116.pdf&amp;diff=6796"/>
		<updated>2008-03-27T04:43:49Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: jan 16 lecture note&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;jan 16 lecture note&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_January_9&amp;diff=6795</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=6795"/>
		<updated>2008-03-27T04:21:01Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: &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;br /&gt;
&lt;br /&gt;
by gopsury83 [http://katlas.math.toronto.edu/drorbn/images/9/95/20080109.pdf]&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:20080109.pdf&amp;diff=6794</id>
		<title>File:20080109.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:20080109.pdf&amp;diff=6794"/>
		<updated>2008-03-27T04:19:49Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: jan 09 lecture notes&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;jan 09 lecture notes&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Notes_for_March_5&amp;diff=6589</id>
		<title>08-401/Class Notes for March 5</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=08-401/Class_Notes_for_March_5&amp;diff=6589"/>
		<updated>2008-03-06T05:34:15Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{08-401/Navigation}}&lt;br /&gt;
&lt;br /&gt;
Week 7 Notes uploaded by leelorik&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-05-2008_09%3B04%3B08PM.JPG page 1 front]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-05-2008_09%3B04%3B53PM.JPG page 1 back]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-05-2008_09%3B06%3B06PM.JPG page 2 front]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-05-2008_09%3B07%3B55PM.JPG page 2 back]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-05-2008_09%3B10%3B32PM.JPG page 3 front]&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/index.php?title=Image:03-05-2008_09%3B11%3B14PM.JPG page 3 back]&lt;br /&gt;
&lt;br /&gt;
March 5th lecture notes uploaded by gopsury83&lt;br /&gt;
&lt;br /&gt;
[http://katlas.math.toronto.edu/drorbn/images/8/8d/0305.pdf]&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=File:0305.pdf&amp;diff=6588</id>
		<title>File:0305.pdf</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=File:0305.pdf&amp;diff=6588"/>
		<updated>2008-03-06T05:25:40Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: March 5th Lecture notes&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;March 5th Lecture notes&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6516</id>
		<title>Talk:08-401</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6516"/>
		<updated>2008-02-20T21:05:18Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: &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;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Textbook Edition ==&lt;br /&gt;
&lt;br /&gt;
Is anyone else in the class using the &amp;lt;B&amp;gt;5th edition&amp;lt;/B&amp;gt; of the text?&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Would it be helpful to post the actual questions up? (since the numberings may be different in the two texts)&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6423</id>
		<title>Talk:08-401</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6423"/>
		<updated>2008-02-09T06:10:58Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: &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;br /&gt;
&lt;br /&gt;
== Regarding Textbook ==&lt;br /&gt;
Hello! My name is Tim.&lt;br /&gt;
As I was about to do assignment 3 which was due yesterday...&lt;br /&gt;
I realized that my textbook was missing several pages...&lt;br /&gt;
obviously I couldn&#039;t do the assignment...&lt;br /&gt;
and it looks like i am missing almost entire chapter 15...&lt;br /&gt;
I didn&#039;t buy the textbook because a friend gave me a photocopied version...&lt;br /&gt;
If I had known that there are pages missing, I would&#039;ve bought one...&lt;br /&gt;
I am wondering if anyone is willing to scan some pages for me...&lt;br /&gt;
The pages are... pages 262-265, 286-293, 302-305...&lt;br /&gt;
or, atleast please type up the questions that are due next week&lt;br /&gt;
so I can atleast try to do the assignment...&lt;br /&gt;
my email address is tim.shin@utoronto.ca&lt;br /&gt;
Thank you all!!!&lt;br /&gt;
&lt;br /&gt;
YEAH!!! I finally got the missing pages!!!&lt;br /&gt;
Thank you professor!!&lt;br /&gt;
&lt;br /&gt;
== Textbook Edition ==&lt;br /&gt;
&lt;br /&gt;
Is anyone else in the class using the &amp;lt;B&amp;gt;5th edition&amp;lt;/B&amp;gt; of the text?&lt;br /&gt;
&amp;lt;br&amp;gt;&lt;br /&gt;
Would it be helpful to post the actual questions up? (since the numberings may be different in the two texts)&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6297</id>
		<title>Talk:08-401</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6297"/>
		<updated>2008-01-31T06:34:31Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: /* Regarding Textbook */&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;br /&gt;
&lt;br /&gt;
== Regarding Textbook ==&lt;br /&gt;
Hello! My name is Tim.&lt;br /&gt;
As I was about to do assignment 3 which was due yesterday...&lt;br /&gt;
I realized that my textbook was missing several pages...&lt;br /&gt;
obviously I couldn&#039;t do the assignment...&lt;br /&gt;
and it looks like i am missing almost entire chapter 15...&lt;br /&gt;
I didn&#039;t buy the textbook because a friend gave me a photocopied version...&lt;br /&gt;
If I had known that there are pages missing, I would&#039;ve bought one...&lt;br /&gt;
I am wondering if anyone is willing to scan some pages for me...&lt;br /&gt;
The pages are... pages 262-265, 286-293, 302-305...&lt;br /&gt;
or, atleast please type up the questions that are due next week&lt;br /&gt;
so I can atleast try to do the assignment...&lt;br /&gt;
my email address is tim.shin@utoronto.ca&lt;br /&gt;
Thank you all!!!&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6296</id>
		<title>Talk:08-401</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=Talk:08-401&amp;diff=6296"/>
		<updated>2008-01-31T06:33:49Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: Regarding Textbook&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;br /&gt;
&lt;br /&gt;
== Regarding Textbook ==&lt;br /&gt;
&lt;br /&gt;
As I was about to do assignment 3 which was due yesterday...&lt;br /&gt;
I realized that my textbook was missing several pages...&lt;br /&gt;
obviously I couldn&#039;t do the assignment...&lt;br /&gt;
and it looks like i am missing almost entire chapter 15...&lt;br /&gt;
I didn&#039;t buy the textbook because a friend gave me a photocopied version...&lt;br /&gt;
If I had known that there are pages missing, I would&#039;ve bought one...&lt;br /&gt;
I am wondering if anyone is willing to scan some pages for me...&lt;br /&gt;
The pages are... pages 262-265, 286-293, 302-305...&lt;br /&gt;
or, atleast please type up the questions that are due next week&lt;br /&gt;
so I can atleast try to do the assignment...&lt;br /&gt;
Thank you all!!!&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6233</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=6233"/>
		<updated>2008-01-27T05:44:53Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: /* 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=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=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=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=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=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;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=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=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;
|}&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6232</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=6232"/>
		<updated>2008-01-27T05:44:28Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: /* 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=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=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=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=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=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;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=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=Shin|first=Tae Maen|userid=gopsury83|email= tim.shin[at]utoronto.ca|location= second from right, back row|comments= You can call me Tim}}&lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6231</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=6231"/>
		<updated>2008-01-27T05:41:07Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: /* 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=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=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=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=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=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;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=Cao|first=Ying|userid=McTea|email= y.cao[at]utoronto.ca|location= third from right, in front, blue scarf|comments= ^^}}&lt;br /&gt;
&lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=08-401/Class_Photo&amp;diff=6230</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=6230"/>
		<updated>2008-01-27T05:38:47Z</updated>

		<summary type="html">&lt;p&gt;Gopsury83: /* 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 Tae Maen&lt;br /&gt;
!Last name Shin&lt;br /&gt;
!UserID gopsury83&lt;br /&gt;
!Email tim.shin@utoronto.ca&lt;br /&gt;
!In the photo back row 2nd from right&lt;br /&gt;
!Comments you can call me Tim&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, 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=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=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=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=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;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=Cao|first=Ying|userid=McTea|email= y.cao[at]utoronto.ca|location= third from right, in front, blue scarf|comments= ^^}}&lt;br /&gt;
&lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>Gopsury83</name></author>
	</entry>
</feed>