<?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　　㈀开倀爀漀瀀攀爀琀椀攀猀ⴀ䜀爀漀甀瀀猀㈀⸀瀀瀀琀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 2: Groups]]></Title>਀㰀䈀愀猀攀倀愀琀栀㸀　　㈀开倀爀漀瀀攀爀琀椀攀猀ⴀ䜀爀漀甀瀀猀㈀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　　㈀开瀀爀漀瀀攀爀琀椀攀猀ⴀ最爀漀甀瀀猀㈀⸀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∀愀挀攀㄀㜀㠀　挀ⴀ㄀㜀昀㌀ⴀ㐀㘀㐀㜀ⴀ㤀昀挀愀ⴀ戀㘀　㈀挀愀㐀㤀㘀㠀挀㘀∀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[Groups]]></Title>਀㰀一漀琀攀猀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䌀栀愀瀀琀攀爀 ㄀　 ጀ†匀攀挀琀椀漀渀 ㄀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℀嬀䌀䐀䄀吀䄀嬀䜀爀漀甀瀀猀 䴀漀搀甀氀愀爀 匀礀猀琀攀洀猀 䌀栀愀瀀琀攀爀 ㄀　 ጀ†匀攀挀琀椀漀渀 ㄀ 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="3d6fef39-ef6b-45eb-b97f-482390130ec6">਀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>bgd1l2.swf</BackgroundFile>਀㰀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䐀攀昀椀渀椀琀椀漀渀崀崀㸀㰀⼀吀椀琀氀攀㸀 
<Notes><![CDATA[No in-class assignment problem]]></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[Definition A group is a mathematical system consisting of a set and one binary operation defined on it such that it has the following properties; Closure Associative Identity Inverse No in-class assignment problem ]]></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∀愀愀㘀㠀　愀　戀ⴀ㄀㐀㤀㈀ⴀ㐀㤀㠀㠀ⴀ愀愀㐀昀ⴀ　挀　㐀　㈀㔀愀　㜀愀愀∀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[Integers and 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 ㈀㌀ 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℀嬀䌀䐀䄀吀䄀嬀䤀渀琀攀最攀爀猀 愀渀搀 䄀搀搀椀琀椀漀渀 ጀ†䄀 䜀爀漀甀瀀㼀 䌀氀漀猀甀爀攀   䄀猀猀漀挀椀愀琀椀瘀攀    䤀搀攀渀琀椀琀礀   䤀渀瘀攀爀猀攀 吀栀攀 椀渀琀攀最攀爀猀 甀渀搀攀爀 愀搀搀椀琀椀漀渀 昀漀爀洀 愀 最爀漀甀瀀⸀  ㈀ ⬀ⴀ㌀ 㴀 ⴀ㄀ 戀攀氀漀渀最猀 琀 漀 䤀 鈀‡礀攀猀 挀氀漀猀攀搀⸀ ⴀ㐀⬀⠀ⴀ㈀⬀㜀⤀ 㴀 ⴀ㄀     ⠀ⴀ㐀⬀ⴀ㈀⤀⬀㜀 㴀 ⴀ㄀ 鈀‡礀攀猀Ⰰ 愀猀猀漀挀椀愀琀椀瘀攀⸀ ⴀ㘀 ⬀　 㴀 ⴀ㘀      　 ⬀ⴀ㘀 㴀 ⴀ㘀 鈀‡礀攀猀Ⰰ 　    椀猀 琀栀攀 椀搀攀渀琀椀琀礀 ⴀ㈀⬀㈀ 㴀 ㈀⬀ⴀ㈀ 㴀 　 鈀‡礀攀猀 攀愀挀栀 椀渀琀攀最攀爀 栀愀猀 椀琀猀 漀瀀瀀漀猀椀琀攀 䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㌀ 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="f120ea42-5c48-4d69-a0f2-872ba09dd856">਀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>bgd1l12.swf</BackgroundFile>਀㰀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䄀 昀椀渀椀琀攀 猀礀猀琀攀洀 ጀ†䤀猀 椀琀 愀 䜀爀漀甀瀀㼀崀崀㸀㰀⼀吀椀琀氀攀㸀 
<Notes><![CDATA[In-class Assignment 23 - 2]]></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[A finite system – Is it a Group? Given B = {x, y, z} and the operation ∆  defined by the table at the right. Closure – any strangers? Associative –(x ∆ z) ∆ z = y ∆ z = z   and          x ∆ (z ∆ z) = x ∆ x = z .  No easy way.   Identity – is there a row and column with the elements in the same     order as at the top? If there is the identity will be the heading of that     row and column.    Inverse – is the identity once and only once in each row and   column.  Look up to the headings.  z and x are inverses of each      other.   Yes it is a group.  In-class Assignment 23 - 2 ]]></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∀㜀㈀㈀㤀㐀㄀攀㘀ⴀ愀㐀㔀㐀ⴀ㐀愀愀搀ⴀ㤀㄀挀攀ⴀ昀搀㜀㐀㜀㐀挀搀㤀㄀㜀　∀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[An Abelian 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  ㈀㌀ ⴀ ㌀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℀嬀䌀䐀䄀吀䄀嬀䄀渀 䄀戀攀氀椀愀渀 䜀爀漀甀瀀 䤀昀 愀 洀愀琀栀攀洀愀琀椀挀愀氀 猀礀猀琀攀洀 椀猀 愀 最爀漀甀瀀 愀渀搀 椀琀 愀氀猀漀 栀愀猀 琀栀攀 挀漀洀洀甀琀愀琀椀瘀攀 瀀爀漀瀀攀爀琀礀 琀栀攀渀 琀栀攀 猀礀猀琀攀洀 椀猀 挀愀氀氀攀搀 愀渀 䄀戀攀氀椀愀渀 最爀漀甀瀀⸀ 吀栀攀 挀漀洀洀甀琀愀琀椀瘀攀 瀀爀漀瀀攀爀琀礀 椀猀 爀攀挀漀最渀椀稀攀搀 椀渀 愀 昀椀渀椀琀攀 猀礀猀琀攀洀 椀昀 琀栀攀爀攀 椀猀 猀礀洀洀攀琀爀礀 愀戀漀甀琀 愀 氀椀渀攀 昀爀漀洀 甀瀀瀀攀爀 氀攀昀琀 琀漀 氀漀眀攀爀 爀椀最栀琀 吀栀攀爀攀 椀猀 猀礀洀洀攀琀爀礀 愀戀漀甀琀 琀栀攀 氀椀渀攀Ⰰ 琀栀攀爀攀昀漀爀攀 琀栀攀 猀礀猀琀攀洀 椀猀 愀渀 䄀戀攀氀椀愀渀 最爀漀甀瀀⸀ 䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀  ㈀㌀ ⴀ 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="21e774c1-7421-4241-a661-b1d45f0d07af">਀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>bgd1l2.swf</BackgroundFile>਀㰀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀䴀漀搀甀氀愀爀 匀礀猀琀攀洀猀崀崀㸀㰀⼀吀椀琀氀攀㸀 
<Notes><![CDATA[No in-class assignment problem]]></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[Modular Systems A modular systems is a finite mathematical system whose size is determined by the mod (modular number) m. The finite set of elements is unually numbers 0, 1, 2, 3, …, m −1. Every element in a mod system represents an infinite number of numbers called an equivalence class. No in-class assignment problem ]]></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∀　昀㤀㠀攀㜀搀攀ⴀ㈀搀　㄀ⴀ㐀攀攀攀ⴀ㤀　㌀㤀ⴀ搀㘀搀攀㜀愀㄀㄀㐀㜀攀搀∀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[Mod 7]]></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 ㈀㌀ ⴀ 㐀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℀嬀䌀䐀䄀吀䄀嬀䴀漀搀 㜀 䄀爀爀愀礀 圀 椀渀琀漀 㜀 攀焀甀椀瘀愀氀攀渀挀攀 挀氀愀猀猀攀猀⸀     　       ㄀       ㈀       ㌀       㐀       㔀      㘀     㜀       㠀       㤀      ㄀　     ㄀㄀     ㄀㈀    ㄀㌀    ㄀㐀     ㄀㔀     ㄀㘀      ㄀㜀    ㄀㠀     ㄀㤀    ㈀　     ㈀㄀     ㈀㈀    ㈀㌀     挀漀渀琀椀渀甀攀 椀渀 琀栀椀猀 洀愀渀渀攀爀 䔀瘀攀爀礀 渀甀洀戀攀爀 甀渀搀攀爀 ㈀ 椀猀 攀焀甀椀瘀愀氀攀渀琀 琀漀 ㈀⸀   ㄀㘀 愀•㈀㌀⠀洀漀搀 㜀⤀ 愀 愀•戀 ⠀洀漀搀 洀⤀ 椀昀 愀 愀渀搀 戀 眀栀攀渀 搀椀瘀椀搀攀搀 戀礀 洀 礀椀攀氀搀 琀栀攀 猀愀洀攀 爀攀洀愀椀渀搀攀爀⸀ 䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㌀ ⴀ 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="5ab6c615-8a8f-4c59-98a3-ff4be54880dd">਀㰀䘀椀氀攀渀愀洀攀㸀猀氀椀搀攀㠀⸀猀眀昀㰀⼀䘀椀氀攀渀愀洀攀㸀 
<BackgroundFile>bgd1l2.swf</BackgroundFile>਀㰀吀椀琀氀攀㸀㰀℀嬀䌀䐀䄀吀䄀嬀㌀㤀㤀 椀渀 䴀漀搀 㜀崀崀㸀㰀⼀吀椀琀氀攀㸀 
<Notes><![CDATA[In-class Assignment 23 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㠀⸀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㠀⸀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[399 in Mod 7 In which equivalence class and row in the array is 399? Need to know the remainder when 399 is divided by 7. Remainder is 0 so 399 is in the 0 equivalence class. The quotient is 57 so 399 is in 57th row down under the heading row. In-class Assignment 23 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∀㐀攀愀㠀攀挀搀㐀ⴀ戀㔀愀㜀ⴀ㐀昀㌀㌀ⴀ戀㤀㐀㤀ⴀ攀挀㈀搀㘀㐀戀昀昀㄀㘀㈀∀㸀 
<Filename>slide9.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[Equivalency Without the Array]]></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 ㈀㌀ ⴀ 㔀崀崀㸀㰀⼀一漀琀攀猀㸀 
<notesswfbig>notes/notesbig9.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/notessmall9.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℀嬀䌀䐀䄀吀䄀嬀䔀焀甀椀瘀愀氀攀渀挀礀 圀椀琀栀漀甀琀 琀栀攀 䄀爀爀愀礀 吀漀 搀攀琀攀爀洀椀渀攀 眀栀攀琀栀攀爀 漀爀 渀漀琀 琀眀漀 渀甀洀戀攀爀猀 戀攀氀漀渀最 琀漀 琀栀攀 猀愀洀攀 攀焀甀椀瘀愀氀攀渀挀攀 挀氀愀猀猀 椀渀 愀 洀漀搀 猀礀猀琀攀洀 䐀椀瘀椀搀攀 攀愀挀栀 漀昀 琀栀攀 渀甀洀戀攀爀猀 戀礀 琀栀攀 洀漀搀⸀ 䤀昀 琀栀攀 爀攀洀愀椀渀搀攀爀猀 愀爀攀 琀栀攀 猀愀洀攀 琀栀攀 琀眀漀 渀甀洀戀攀爀猀 愀爀攀 攀焀甀椀瘀愀氀攀渀琀 愀渀搀 琀栀攀礀 戀漀琀栀 戀攀氀漀渀最 琀漀 琀栀攀 攀焀甀椀瘀愀氀攀渀挀攀 挀氀愀猀猀攀搀 渀愀洀攀搀 戀礀 琀栀攀 爀攀洀愀椀渀搀攀爀⸀ 䤀昀 琀栀攀 爀攀洀愀椀渀搀攀爀猀 愀爀攀 渀漀琀 琀栀攀 猀愀洀攀 琀栀攀 琀眀漀 渀甀洀戀攀爀猀 愀爀攀 渀漀琀 攀焀甀椀瘀愀氀攀渀琀 椀渀 琀栀愀琀 洀漀搀⸀  ㌀㠀 愀•㘀㈀ ⠀洀漀搀 㘀⤀⸀  䌀愀氀氀 琀栀攀洀 ㈀ ⠀洀漀搀 㘀⤀⸀ 䤀渀ⴀ挀氀愀猀猀 䄀猀猀椀最渀洀攀渀琀 ㈀㌀ ⴀ 㔀 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 
