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	<id>https://drorbn.net/index.php?action=history&amp;feed=atom&amp;title=14-1100%2FClassnotes_for_Thursday_November_13</id>
	<title>14-1100/Classnotes for Thursday November 13 - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://drorbn.net/index.php?action=history&amp;feed=atom&amp;title=14-1100%2FClassnotes_for_Thursday_November_13"/>
	<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;action=history"/>
	<updated>2026-06-19T02:09:01Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.39.6</generator>
	<entry>
		<id>https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;diff=14561&amp;oldid=prev</id>
		<title>Tselings at 20:44, 13 December 2014</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;diff=14561&amp;oldid=prev"/>
		<updated>2014-12-13T20:44:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 16:44, 13 December 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 27:&lt;/td&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 27:&lt;/td&gt;
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&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;For another explanation to this proof of the Fundamental Theorem: [http://math.uchicago.edu/~womp/2007/PIDmod2007.pdf Fundamental theorem of modules over a PID and applications] (See the last page)&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;For another explanation to this proof of the Fundamental Theorem: [http://math.uchicago.edu/~womp/2007/PIDmod2007.pdf Fundamental theorem of modules over a PID and applications] (See the last page)&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. &lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;It also gives another explanation to the proof given in class on the Jordan Canonical Form on pages 2-4.&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Tselings</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;diff=14548&amp;oldid=prev</id>
		<title>Tselings at 18:01, 13 December 2014</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;diff=14548&amp;oldid=prev"/>
		<updated>2014-12-13T18:01:17Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 14:01, 13 December 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 26:&lt;/td&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 26:&lt;/td&gt;
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&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|[[File:14-1100 Lec 18 page 3.JPG|200px|thumb|left|Lec 14 page 3]]&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|[[File:14-1100 Lec 18 page 3.JPG|200px|thumb|left|Lec 14 page 3]]&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;For another explanation to this proof of the Fundamental Theorem: [http://math.uchicago.edu/~womp/2007/PIDmod2007.pdf Fundamental theorem of modules over a PID and applications] (See the last page)&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Tselings</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;diff=14161&amp;oldid=prev</id>
		<title>Yvon.verberne at 03:24, 21 November 2014</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;diff=14161&amp;oldid=prev"/>
		<updated>2014-11-21T03:24:08Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 23:24, 20 November 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 18:&lt;/td&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 18:&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Here are some handwritten notes:&#039;&#039;&#039;&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Here are some handwritten notes:&#039;&#039;&#039;&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br /&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{|&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|[[File:14-1100 Lec 18 page 1.JPG|200px|thumb|left|Lec 14 page 1]]&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|[[File:14-1100 Lec 18 page 2.JPG|200px|thumb|left|Lec 14 page 2]]&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{|&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|[[File:14-1100 Lec 18 page 3.JPG|200px|thumb|left|Lec 14 page 3]]&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-empty diff-side-deleted&quot;&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yvon.verberne</name></author>
	</entry>
	<entry>
		<id>https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;diff=14111&amp;oldid=prev</id>
		<title>Anai: Created page with &quot;{{14-1100/Navigation}}  {| |Lec 18 board 1 |Lec 18 board 2 ...&quot;</title>
		<link rel="alternate" type="text/html" href="https://drorbn.net/index.php?title=14-1100/Classnotes_for_Thursday_November_13&amp;diff=14111&amp;oldid=prev"/>
		<updated>2014-11-14T04:01:58Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;{{14-1100/Navigation}}  {| |&lt;a href=&quot;/index.php?title=File:14-1100_Lec_18_board_1_flip.JPG&quot; title=&quot;File:14-1100 Lec 18 board 1 flip.JPG&quot;&gt;200px|thumb|left|Lec 18 board 1&lt;/a&gt; |&lt;a href=&quot;/index.php?title=File:14-1100_Lec_18_board_2_flip.JPG&quot; title=&quot;File:14-1100 Lec 18 board 2 flip.JPG&quot;&gt;200px|thumb|left|Lec 18 board 2&lt;/a&gt; ...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{14-1100/Navigation}}&lt;br /&gt;
&lt;br /&gt;
{|&lt;br /&gt;
|[[File:14-1100 Lec 18 board 1 flip.JPG|200px|thumb|left|Lec 18 board 1]]&lt;br /&gt;
|[[File:14-1100 Lec 18 board 2 flip.JPG|200px|thumb|left|Lec 18 board 2]]&lt;br /&gt;
|}&lt;br /&gt;
{|&lt;br /&gt;
|[[File:14-1100 Lec 18 board 3 flip.JPG|200px|thumb|left|Lec 18 board 3]]&lt;br /&gt;
|[[File:14-1100 Lec 18 board 4 flip.JPG|200px|thumb|left|Lec 18 board 4]]&lt;br /&gt;
|}&lt;br /&gt;
{|&lt;br /&gt;
|[[File:14-1100 Lec 18 board 5 flip.JPG|200px|thumb|left|Lec 18 board 5]]&lt;br /&gt;
|[[File:14-1100 Lec 18 board 6 flip.JPG|200px|thumb|left|Lec 18 board 6]]&lt;br /&gt;
|}&lt;br /&gt;
{|&lt;br /&gt;
|[[File:14-1100 Lec 18 board 7 flip.JPG|200px|thumb|left|Lec 18 board 7]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Here are some handwritten notes:&amp;#039;&amp;#039;&amp;#039;&lt;/div&gt;</summary>
		<author><name>Anai</name></author>
	</entry>
</feed>