<?xml version="1.0" encoding="UTF-16"?>਀㰀倀爀攀猀攀渀琀愀琀椀漀渀㸀 
<pptaddin>Articulate Presenter version 6 Pro,build10</pptaddin>਀㰀䘀椀氀攀渀愀洀攀㸀䌀㨀尀䐀漀挀甀洀攀渀琀猀 愀渀搀 匀攀琀琀椀渀最猀尀栀愀爀最椀猀爀尀䴀礀 䐀漀挀甀洀攀渀琀猀尀䴀䄀吀㄀㈀　尀瀀瀀琀尀甀渀椀琀㐀尀洀漀搀椀昀椀攀搀尀　　㌀开倀爀漀瀀攀爀琀椀攀猀ⴀ䤀渀昀椀渀椀琀攀匀礀猀琀攀洀猀琀漀䘀椀渀椀琀攀匀礀猀琀攀洀猀㌀⸀瀀瀀琀砀㰀⼀䘀椀氀攀渀愀洀攀㸀 
<LmsProperties>਀㰀瀀爀漀琀漀挀漀氀㸀 
<method/>਀㰀瘀攀爀猀椀漀渀⼀㸀 
</protocol>਀㰀挀漀洀瀀氀攀琀椀漀渀㸀 
<method/>਀㰀琀栀爀攀猀栀漀氀搀⼀㸀 
<target/>਀㰀⼀挀漀洀瀀氀攀琀椀漀渀㸀 
</LmsProperties>਀㰀䈀甀椀氀琀椀渀倀爀漀瀀攀爀琀椀攀猀㸀 
<Title><![CDATA[Lesson 3: Infinite Systems to Finite Systems]]></Title>਀㰀䈀愀猀攀倀愀琀栀㸀　　㌀开倀爀漀瀀攀爀琀椀攀猀ⴀ䤀渀昀椀渀椀琀攀匀礀猀琀攀洀猀琀漀䘀椀渀椀琀攀匀礀猀琀攀洀猀㌀㰀⼀䈀愀猀攀倀愀琀栀㸀 
<PresenterName><![CDATA[]]></PresenterName>਀㰀倀爀攀猀攀渀琀攀爀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀崀崀㸀㰀⼀倀爀攀猀攀渀琀攀爀吀椀琀氀攀㸀 
<PresenterCompany><![CDATA[]]></PresenterCompany>਀㰀倀爀攀猀攀渀琀攀爀䔀洀愀椀氀㸀㰀℀嬀䌀䐀䄀吀䄀嬀崀崀㸀㰀⼀倀爀攀猀攀渀琀攀爀䔀洀愀椀氀㸀 
<PresenterBio><![CDATA[]]></PresenterBio>਀㰀倀爀攀猀攀渀琀攀爀倀栀漀琀漀⼀㸀 
</BuiltinProperties>਀㰀刀攀昀攀爀攀渀挀攀猀㸀 
<Doc>਀㰀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀倀爀椀渀琀攀爀ⴀ䘀爀椀攀渀搀氀礀 嘀攀爀猀椀漀渀 漀昀 琀栀椀猀 倀爀攀猀攀渀琀愀琀椀漀渀崀崀㸀㰀⼀吀椀琀氀攀㸀 
<Type>file</Type>਀㰀䐀愀琀愀㸀㰀℀嬀䌀䐀䄀吀䄀嬀　　㌀开瀀爀漀瀀攀爀琀椀攀猀ⴀ椀渀昀椀渀椀琀攀猀礀猀琀攀洀猀琀漀昀椀渀椀琀攀猀礀猀琀攀洀猀㌀⸀瀀搀昀崀崀㸀㰀⼀䐀愀琀愀㸀 
</Doc>਀㰀⼀刀攀昀攀爀攀渀挀攀猀㸀 
<Slides>਀㰀匀氀椀搀攀 椀搀㴀∀戀㌀㤀㌀㌀㠀　愀ⴀ搀昀戀搀ⴀ㐀㔀㘀㈀ⴀ愀搀㠀㄀ⴀ搀　昀㤀㘀㄀愀戀　㄀挀搀∀㸀 
<Filename>slide1.swf</Filename>਀㰀䈀愀挀欀最爀漀甀渀搀䘀椀氀攀㸀戀最搀㄀氀㄀⸀猀眀昀㰀⼀䈀愀挀欀最爀漀甀渀搀䘀椀氀攀㸀 
<Title><![CDATA[Infinite Systems to Finite Systems]]></Title>਀㰀一漀琀攀猀㸀㰀℀嬀䌀䐀䄀吀䄀嬀吀攀砀琀 ጀ†䌀栀愀瀀琀攀爀 ㄀　 ጀ†匀攀挀琀椀漀渀猀 ㈀Ⰰ ㌀崀崀㸀㰀⼀一漀琀攀猀㸀 
<notesswfbig>notes/notesbig1.swf</notesswfbig>਀㰀一漀琀攀猀䠀攀椀最栀琀䈀椀最㸀㈀㈀㰀⼀一漀琀攀猀䠀攀椀最栀琀䈀椀最㸀 
<notesswfsmall>notes/notessmall1.swf</notesswfsmall>਀㰀一漀琀攀猀䠀攀椀最栀琀匀洀愀氀氀㸀㈀㈀㰀⼀一漀琀攀猀䠀攀椀最栀琀匀洀愀氀氀㸀 
<SlideTime>90</SlideTime>਀㰀眀愀椀琀昀漀爀甀猀攀爀㸀昀愀氀猀攀㰀⼀眀愀椀琀昀漀爀甀猀攀爀㸀 
<Hidden>false</Hidden>਀㰀渀愀瘀氀漀挀欀攀搀㸀昀愀氀猀攀㰀⼀渀愀瘀氀漀挀欀攀搀㸀 
<branch>਀㰀瀀爀攀瘀㸀搀攀昀愀甀氀琀㰀⼀瀀爀攀瘀㸀 
<next>default</next>਀㰀⼀戀爀愀渀挀栀㸀 
<DisplayMode></DisplayMode>਀㰀氀攀瘀攀氀㸀　㰀⼀氀攀瘀攀氀㸀 
<PlayListId>-1</PlayListId>਀㰀愀渀渀漀琀愀琀椀漀渀猀㸀 
</annotations>਀㰀匀氀椀搀攀吀攀砀琀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䤀渀昀椀渀椀琀攀 匀礀猀琀攀洀猀 琀漀 䘀椀渀椀琀攀 匀礀猀琀攀洀猀 䴀漀搀甀氀愀爀 䄀爀椀琀栀洀攀琀椀挀 吀攀砀琀 ጀ†䌀栀愀瀀琀攀爀 ㄀　 ጀ†匀攀挀琀椀漀渀猀 ㈀Ⰰ ㌀ 崀崀㸀㰀⼀匀氀椀搀攀吀攀砀琀㸀 
<framerate>30</framerate>਀㰀⼀匀氀椀搀攀㸀 
<Slide id="aef77588-225b-4e0b-8f69-8bace3b12162">਀㰀䘀椀氀攀渀愀洀攀㸀猀氀椀搀攀㈀⸀猀眀昀㰀⼀䘀椀氀攀渀愀洀攀㸀 
<BackgroundFile>bgd1l4.swf</BackgroundFile>਀㰀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䴀漀搀甀氀愀爀 䄀搀搀椀琀椀漀渀崀崀㸀㰀⼀吀椀琀氀攀㸀 
<Notes><![CDATA[]]></Notes>਀㰀渀漀琀攀猀猀眀昀戀椀最㸀渀漀琀攀猀⼀渀漀琀攀猀戀椀最㈀⸀猀眀昀㰀⼀渀漀琀攀猀猀眀昀戀椀最㸀 
<NotesHeightBig>22</NotesHeightBig>਀㰀渀漀琀攀猀猀眀昀猀洀愀氀氀㸀渀漀琀攀猀⼀渀漀琀攀猀猀洀愀氀氀㈀⸀猀眀昀㰀⼀渀漀琀攀猀猀眀昀猀洀愀氀氀㸀 
<NotesHeightSmall>22</NotesHeightSmall>਀㰀匀氀椀搀攀吀椀洀攀㸀㤀　㰀⼀匀氀椀搀攀吀椀洀攀㸀 
<waitforuser>false</waitforuser>਀㰀䠀椀搀搀攀渀㸀昀愀氀猀攀㰀⼀䠀椀搀搀攀渀㸀 
<navlocked>false</navlocked>਀㰀戀爀愀渀挀栀㸀 
<prev>default</prev>਀㰀渀攀砀琀㸀搀攀昀愀甀氀琀㰀⼀渀攀砀琀㸀 
</branch>਀㰀䐀椀猀瀀氀愀礀䴀漀搀攀㸀㰀⼀䐀椀猀瀀氀愀礀䴀漀搀攀㸀 
<level>0</level>਀㰀倀氀愀礀䰀椀猀琀䤀搀㸀ⴀ㄀㰀⼀倀氀愀礀䰀椀猀琀䤀搀㸀 
<annotations>਀㰀⼀愀渀渀漀琀愀琀椀漀渀猀㸀 
<SlideText><![CDATA[Modular Addition The algorithm is the same as in the set of whole numbers. The sum must be expressed as the remainder when the sum is divided by the mod of the system. 5+4=9=3 (mod 6)                          ]]></SlideText>਀㰀昀爀愀洀攀爀愀琀攀㸀㌀　㰀⼀昀爀愀洀攀爀愀琀攀㸀 
</Slide>਀㰀匀氀椀搀攀 椀搀㴀∀昀搀昀愀昀㌀㔀㌀ⴀ攀攀搀㤀ⴀ㐀㘀㘀㐀ⴀ㠀㔀㈀攀ⴀ攀㘀㘀挀㈀搀㠀愀戀昀戀㔀∀㸀 
<Filename>slide3.swf</Filename>਀㰀䈀愀挀欀最爀漀甀渀搀䘀椀氀攀㸀戀最搀㄀氀㐀⸀猀眀昀㰀⼀䈀愀挀欀最爀漀甀渀搀䘀椀氀攀㸀 
<Title><![CDATA[Is Mod 6 Under Addition A Group?]]></Title>਀㰀一漀琀攀猀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㐀 ⴀ ㄀崀崀㸀㰀⼀一漀琀攀猀㸀 
<notesswfbig>notes/notesbig3.swf</notesswfbig>਀㰀一漀琀攀猀䠀攀椀最栀琀䈀椀最㸀㈀㈀㰀⼀一漀琀攀猀䠀攀椀最栀琀䈀椀最㸀 
<notesswfsmall>notes/notessmall3.swf</notesswfsmall>਀㰀一漀琀攀猀䠀攀椀最栀琀匀洀愀氀氀㸀㈀㈀㰀⼀一漀琀攀猀䠀攀椀最栀琀匀洀愀氀氀㸀 
<SlideTime>90</SlideTime>਀㰀眀愀椀琀昀漀爀甀猀攀爀㸀昀愀氀猀攀㰀⼀眀愀椀琀昀漀爀甀猀攀爀㸀 
<Hidden>false</Hidden>਀㰀渀愀瘀氀漀挀欀攀搀㸀昀愀氀猀攀㰀⼀渀愀瘀氀漀挀欀攀搀㸀 
<branch>਀㰀瀀爀攀瘀㸀搀攀昀愀甀氀琀㰀⼀瀀爀攀瘀㸀 
<next>default</next>਀㰀⼀戀爀愀渀挀栀㸀 
<DisplayMode></DisplayMode>਀㰀氀攀瘀攀氀㸀　㰀⼀氀攀瘀攀氀㸀 
<PlayListId>-1</PlayListId>਀㰀愀渀渀漀琀愀琀椀漀渀猀㸀 
</annotations>਀㰀匀氀椀搀攀吀攀砀琀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䤀猀 䴀漀搀 㘀 唀渀搀攀爀 䄀搀搀椀琀椀漀渀 䄀 䜀爀漀甀瀀㼀 䌀氀漀猀攀搀㼀 ጀ†夀攀猀Ⰰ 渀漀 猀琀爀愀渀最攀爀猀⸀ 䄀猀猀漀挀椀愀琀椀瘀攀㼀    ⠀㈀⬀㌀⤀⬀㐀 㴀㔀⬀㐀 㴀㤀㴀㌀⠀洀漀搀㘀⤀      ㈀⬀⠀㌀⬀㐀⤀㴀㈀⬀㜀㴀  ㈀⬀㄀⠀洀漀搀 㘀⤀㴀㌀⠀洀漀搀 㘀⤀                        䤀搀攀渀琀椀琀礀㼀 ጀ†夀攀猀Ⰰ 琀栀攀 　 爀漀眀 愀渀搀 挀漀氀甀洀渀    栀愀瘀攀 琀栀攀 攀氀攀洀攀渀琀猀 椀渀 漀爀搀攀爀⸀   䤀渀瘀攀爀猀攀猀㼀 　 椀渀 攀愀挀栀 爀漀眀 愀渀搀 挀漀氀甀洀渀     漀渀挀攀 愀渀搀 漀渀氀礀 漀渀挀攀⸀  ㈀ 愀渀搀 㐀 愀爀攀     椀渀瘀攀爀猀攀猀⸀ 䄀氀氀 攀氀攀洀攀渀琀猀 栀愀瘀攀 椀渀瘀攀爀猀攀猀⸀  䌀漀洀洀甀琀愀琀椀瘀攀㼀 夀攀猀Ⰰ 猀礀洀洀攀琀爀礀 愀戀漀甀琀 搀椀愀最漀渀愀氀⸀  䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㐀 ⴀ ㄀  崀崀㸀㰀⼀匀氀椀搀攀吀攀砀琀㸀 
<framerate>30</framerate>਀㰀⼀匀氀椀搀攀㸀 
<Slide id="e8521c89-8f99-4e15-acba-b90a9b756c49">਀㰀䘀椀氀攀渀愀洀攀㸀猀氀椀搀攀㐀⸀猀眀昀㰀⼀䘀椀氀攀渀愀洀攀㸀 
<BackgroundFile>bgd1l4.swf</BackgroundFile>਀㰀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䴀漀搀甀氀愀爀 䴀甀氀琀椀瀀氀椀挀愀琀椀漀渀崀崀㸀㰀⼀吀椀琀氀攀㸀 
<Notes><![CDATA[In-class Assignment 24 – 2, 3, 4]]></Notes>਀㰀渀漀琀攀猀猀眀昀戀椀最㸀渀漀琀攀猀⼀渀漀琀攀猀戀椀最㐀⸀猀眀昀㰀⼀渀漀琀攀猀猀眀昀戀椀最㸀 
<NotesHeightBig>22</NotesHeightBig>਀㰀渀漀琀攀猀猀眀昀猀洀愀氀氀㸀渀漀琀攀猀⼀渀漀琀攀猀猀洀愀氀氀㐀⸀猀眀昀㰀⼀渀漀琀攀猀猀眀昀猀洀愀氀氀㸀 
<NotesHeightSmall>22</NotesHeightSmall>਀㰀匀氀椀搀攀吀椀洀攀㸀㤀　㰀⼀匀氀椀搀攀吀椀洀攀㸀 
<waitforuser>false</waitforuser>਀㰀䠀椀搀搀攀渀㸀昀愀氀猀攀㰀⼀䠀椀搀搀攀渀㸀 
<navlocked>false</navlocked>਀㰀戀爀愀渀挀栀㸀 
<prev>default</prev>਀㰀渀攀砀琀㸀搀攀昀愀甀氀琀㰀⼀渀攀砀琀㸀 
</branch>਀㰀䐀椀猀瀀氀愀礀䴀漀搀攀㸀㰀⼀䐀椀猀瀀氀愀礀䴀漀搀攀㸀 
<level>0</level>਀㰀倀氀愀礀䰀椀猀琀䤀搀㸀ⴀ㄀㰀⼀倀氀愀礀䰀椀猀琀䤀搀㸀 
<annotations>਀㰀⼀愀渀渀漀琀愀琀椀漀渀猀㸀 
<SlideText><![CDATA[Modular Multiplication The algorithm for multiplication in a mod system is the same as in multiplication with whole numbers. The product must be expressed as the remainder when the product is divided by the mod. 4 x 3 = 12 = 2 (mod 5)                           In-class Assignment 24 – 2, 3, 4  ]]></SlideText>਀㰀昀爀愀洀攀爀愀琀攀㸀㌀　㰀⼀昀爀愀洀攀爀愀琀攀㸀 
</Slide>਀㰀匀氀椀搀攀 椀搀㴀∀攀㄀㄀攀昀㌀㄀戀ⴀ戀㈀戀㐀ⴀ㐀愀㌀戀ⴀ㤀挀戀㄀ⴀ㤀㘀昀㌀昀戀昀挀㄀戀戀攀∀㸀 
<Filename>slide5.swf</Filename>਀㰀䈀愀挀欀最爀漀甀渀搀䘀椀氀攀㸀戀最搀㄀氀㈀⸀猀眀昀㰀⼀䈀愀挀欀最爀漀甀渀搀䘀椀氀攀㸀 
<Title><![CDATA[Is Mod 5 Under Multiplication a Group (Abelian)?]]></Title>਀㰀一漀琀攀猀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㐀 ጀ†㈀Ⰰ ㌀Ⰰ 㐀崀崀㸀㰀⼀一漀琀攀猀㸀 
<notesswfbig>notes/notesbig5.swf</notesswfbig>਀㰀一漀琀攀猀䠀攀椀最栀琀䈀椀最㸀㈀㈀㰀⼀一漀琀攀猀䠀攀椀最栀琀䈀椀最㸀 
<notesswfsmall>notes/notessmall5.swf</notesswfsmall>਀㰀一漀琀攀猀䠀攀椀最栀琀匀洀愀氀氀㸀㈀㈀㰀⼀一漀琀攀猀䠀攀椀最栀琀匀洀愀氀氀㸀 
<SlideTime>90</SlideTime>਀㰀眀愀椀琀昀漀爀甀猀攀爀㸀昀愀氀猀攀㰀⼀眀愀椀琀昀漀爀甀猀攀爀㸀 
<Hidden>false</Hidden>਀㰀渀愀瘀氀漀挀欀攀搀㸀昀愀氀猀攀㰀⼀渀愀瘀氀漀挀欀攀搀㸀 
<branch>਀㰀瀀爀攀瘀㸀搀攀昀愀甀氀琀㰀⼀瀀爀攀瘀㸀 
<next>default</next>਀㰀⼀戀爀愀渀挀栀㸀 
<DisplayMode></DisplayMode>਀㰀氀攀瘀攀氀㸀　㰀⼀氀攀瘀攀氀㸀 
<PlayListId>-1</PlayListId>਀㰀愀渀渀漀琀愀琀椀漀渀猀㸀 
</annotations>਀㰀匀氀椀搀攀吀攀砀琀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䤀猀 䴀漀搀 㔀 唀渀搀攀爀 䴀甀氀琀椀瀀氀椀挀愀琀椀漀渀 愀 䜀爀漀甀瀀 ⠀䄀戀攀氀椀愀渀⤀㼀 䌀氀漀猀攀㼀 ጀ夠攀猀Ⰰ 渀漀 猀琀爀愀渀最攀爀猀⸀ 䄀猀猀漀挀椀愀琀椀瘀攀㼀   ㈀砀⠀㌀砀㐀⤀㴀㐀⠀洀漀搀 㔀⤀    ⠀㈀砀㌀⤀砀㐀㴀㐀⠀洀漀搀 㔀⤀ 洀愀礀戀攀  䤀搀攀渀琀椀琀礀㼀 ጀ†夀攀猀Ⰰ 琀栀攀 爀漀眀 愀渀搀 挀漀氀甀洀渀 栀攀愀搀 ㄀    栀愀瘀攀 琀栀攀 攀氀攀洀攀渀琀猀 椀渀 漀爀搀攀爀⸀  䤀渀瘀攀爀猀攀猀㼀 夀攀猀Ⰰ 琀栀攀 椀搀攀渀琀椀琀礀 ㄀ 椀猀 椀渀 攀愀挀栀 爀漀眀     愀渀搀 挀漀氀甀洀渀 漀渀挀攀 愀渀搀 漀渀氀礀 漀渀挀攀⸀    ㌀ 愀渀搀 ㈀ 愀爀攀 椀渀瘀攀爀猀攀猀 漀昀 攀愀挀栀 漀琀栀攀爀⸀  䴀漀搀 㔀 甀渀搀攀爀 洀甀氀琀椀瀀氀椀挀愀琀椀漀渀 昀漀爀洀猀 愀 最爀漀甀瀀⸀  䌀漀洀洀甀琀愀琀椀瘀攀㼀 ጀ†夀攀猀Ⰰ 猀礀洀洀攀琀爀礀 愀戀漀甀琀 搀椀愀最漀渀愀氀⸀ 䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㐀 ጀ†㈀Ⰰ ㌀Ⰰ 㐀  崀崀㸀㰀⼀匀氀椀搀攀吀攀砀琀㸀 
<framerate>30</framerate>਀㰀⼀匀氀椀搀攀㸀 
<Slide id="916f93c0-573a-4f6e-afee-836259976163">਀㰀䘀椀氀攀渀愀洀攀㸀猀氀椀搀攀㘀⸀猀眀昀㰀⼀䘀椀氀攀渀愀洀攀㸀 
<BackgroundFile>bgd1l4.swf</BackgroundFile>਀㰀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀吀栀攀 䄀搀樀甀猀琀攀搀 匀攀琀Ⰰ 䄀崀崀㸀㰀⼀吀椀琀氀攀㸀 
<Notes><![CDATA[In-class Assignment 24 - 5]]></Notes>਀㰀渀漀琀攀猀猀眀昀戀椀最㸀渀漀琀攀猀⼀渀漀琀攀猀戀椀最㘀⸀猀眀昀㰀⼀渀漀琀攀猀猀眀昀戀椀最㸀 
<NotesHeightBig>22</NotesHeightBig>਀㰀渀漀琀攀猀猀眀昀猀洀愀氀氀㸀渀漀琀攀猀⼀渀漀琀攀猀猀洀愀氀氀㘀⸀猀眀昀㰀⼀渀漀琀攀猀猀眀昀猀洀愀氀氀㸀 
<NotesHeightSmall>22</NotesHeightSmall>਀㰀匀氀椀搀攀吀椀洀攀㸀㤀　㰀⼀匀氀椀搀攀吀椀洀攀㸀 
<waitforuser>false</waitforuser>਀㰀䠀椀搀搀攀渀㸀昀愀氀猀攀㰀⼀䠀椀搀搀攀渀㸀 
<navlocked>false</navlocked>਀㰀戀爀愀渀挀栀㸀 
<prev>default</prev>਀㰀渀攀砀琀㸀搀攀昀愀甀氀琀㰀⼀渀攀砀琀㸀 
</branch>਀㰀䐀椀猀瀀氀愀礀䴀漀搀攀㸀㰀⼀䐀椀猀瀀氀愀礀䴀漀搀攀㸀 
<level>0</level>਀㰀倀氀愀礀䰀椀猀琀䤀搀㸀ⴀ㄀㰀⼀倀氀愀礀䰀椀猀琀䤀搀㸀 
<annotations>਀㰀⼀愀渀渀漀琀愀琀椀漀渀猀㸀 
<SlideText><![CDATA[The Adjusted Set, A Mod 5 with multiplication and the base set is not a group because 0 does not have an inverse.  If 0 is deleted from the base set the resulting set is the adjusted set, A. A = {1, 2, 3, 4}  A = {1, 2, 3, …, m−1}  Then, the adjusted set, A, with mod 5 multiplication forms an  Abelian group. In-class Assignment 24 – 5  ]]></SlideText>਀㰀昀爀愀洀攀爀愀琀攀㸀㌀　㰀⼀昀爀愀洀攀爀愀琀攀㸀 
</Slide>਀㰀匀氀椀搀攀 椀搀㴀∀搀攀昀㤀搀㈀㈀戀ⴀ㈀　㜀昀ⴀ㐀㜀戀㈀ⴀ㤀愀㌀㠀ⴀ㘀搀㘀㈀搀挀昀　㈀㐀㜀搀∀㸀 
<Filename>slide7.swf</Filename>਀㰀䈀愀挀欀最爀漀甀渀搀䘀椀氀攀㸀戀最搀㄀氀㈀⸀猀眀昀㰀⼀䈀愀挀欀最爀漀甀渀搀䘀椀氀攀㸀 
<Title><![CDATA[Recognizing Groups Without Tables]]></Title>਀㰀一漀琀攀猀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㐀 ⴀ 㘀崀崀㸀㰀⼀一漀琀攀猀㸀 
<notesswfbig>notes/notesbig7.swf</notesswfbig>਀㰀一漀琀攀猀䠀攀椀最栀琀䈀椀最㸀㈀㈀㰀⼀一漀琀攀猀䠀攀椀最栀琀䈀椀最㸀 
<notesswfsmall>notes/notessmall7.swf</notesswfsmall>਀㰀一漀琀攀猀䠀攀椀最栀琀匀洀愀氀氀㸀㈀㈀㰀⼀一漀琀攀猀䠀攀椀最栀琀匀洀愀氀氀㸀 
<SlideTime>90</SlideTime>਀㰀眀愀椀琀昀漀爀甀猀攀爀㸀昀愀氀猀攀㰀⼀眀愀椀琀昀漀爀甀猀攀爀㸀 
<Hidden>false</Hidden>਀㰀渀愀瘀氀漀挀欀攀搀㸀昀愀氀猀攀㰀⼀渀愀瘀氀漀挀欀攀搀㸀 
<branch>਀㰀瀀爀攀瘀㸀搀攀昀愀甀氀琀㰀⼀瀀爀攀瘀㸀 
<next>default</next>਀㰀⼀戀爀愀渀挀栀㸀 
<DisplayMode></DisplayMode>਀㰀氀攀瘀攀氀㸀　㰀⼀氀攀瘀攀氀㸀 
<PlayListId>-1</PlayListId>਀㰀愀渀渀漀琀愀琀椀漀渀猀㸀 
</annotations>਀㰀匀氀椀搀攀吀攀砀琀㸀㰀℀嬀䌀䐀䄀吀䄀嬀刀攀挀漀最渀椀稀椀渀最 䜀爀漀甀瀀猀 圀椀琀栀漀甀琀 吀愀戀氀攀猀 䄀 洀漀搀甀氀愀爀 猀礀猀琀攀洀 眀椀琀栀 愀搀搀椀琀椀漀渀 甀猀椀渀最 琀栀攀 戀愀猀攀 猀攀琀Ⰰ 䈀 昀漀爀洀猀 愀 最爀漀甀瀀⸀ 䈀 㴀笀　Ⰰ ㄀Ⰰ ㈀Ⰰ ☀Ⱐ 洀ሀㄢ紀 ⠀䈀Ⰰ ⬀⤀ 昀漀爀洀猀 愀 最爀漀甀瀀⸀  䄀 洀漀搀甀氀愀爀 猀礀猀琀攀洀 眀椀琀栀 愀 瀀爀椀洀攀 洀漀搀Ⰰ 琀栀攀 愀搀樀甀猀琀攀搀 猀攀琀Ⰰ 愀渀搀  洀甀氀琀椀瀀氀椀挀愀琀椀漀渀 昀漀爀洀猀 愀 最爀漀甀瀀⸀ ⠀䄀Ⰰ 砀Ⰰ 瀀爀椀洀攀 洀漀搀⤀ 昀漀爀洀猀 愀 最爀漀甀瀀⸀  䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㐀 ጀ†㘀  崀崀㸀㰀⼀匀氀椀搀攀吀攀砀琀㸀 
<framerate>30</framerate>਀㰀⼀匀氀椀搀攀㸀 
</Slides>਀㰀⼀倀爀攀猀攀渀琀愀琀椀漀渀㸀 
