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Consider te *ro#lem o. o/ to arrange a grou* o. n *eo*le so ea! *erson !an sake
ands /it ever0 oter *erson Ho/ migt 0ou organie tis *ro!ess3 Ho/ man0
times /ill ea! *erson sake ands /it someone else3 Ho/ man0 andsakes
/ill o!!ur3 Ho/ must 0our metod var0 a!!ording to /eter or not n is even or
odd3
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Week 1 ,-2
Tere is an old 4oke tat goes someting like tis5 6I. 7od is love8 love is #lind8 and
a0 Carles is #lind8 ten a0 Carles is 7od9 E"*lain8 in te terms o. .irst:
order logi! and *redi!ate !al!ulus8 /0 tis reasoning is in!orre!t* ; 7od is love
< ; 'ove is #lind
r ; a0 Carles is #lind
s ; a0 Carles is 7od
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elate one o. te to*i!s .rom tis /eek=s material to a situation in 0our *ro.essional or
*ersonal li.e and dis!uss o/ 0ou /ould solve te issue /it te re!entl0
a!
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Com*lete 12 C 1 o. ,is!rete and Com#inatorial Matemati!s
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Com*lete te si" C 1 o. ,is!rete and Com#inatorial Matemati!s
o u**lementar0 E"er!ise 2
> C 2 o. ,is!rete and Com#inatorial Matemati!so E"er!ise 218 *ro#lem 1B * &%
o E"er!ise 228 *ro#lem % * DD
o E"er!ise 2$8 *ro#lem % * @%
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Week 2 ,-1
,es!ri#e a situation in 0our *ro.essional or *ersonal li.e /en re!ursion8 or at least
te *rin!i*le o. re!ursion8 *la0ed a role in a!!om*lising a task8 su! as a large
!ore tat !ould #e de!om*osed into smaller !unks tat /ere easier to andle
se*aratel08 #ut still ad te sem#lan!e o. te overall task ,id 0ou tra!k te!om*letion o. tis task in an0 /a0 to ensure tat no *ie!es /ere le.t undone8
mu! like an algoritm kee*s *la!eolders to tra!e a /a0 #a!k .rom a re!ursive
tra4e!tor03 I. so8 o/ did 0ou do it3 I. not8 /0 did 0ou not3
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Week 2 ,-2
,es!ri#e a .avorite re!reational a!tivit0 in terms o. its iterative !om*onents8 su! as
solving a !ross/ord or udoku *ule or *la0ing a game o. !ess or
#a!kgammon Also8 mention an0 re!ursive elements tat o!!ur
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Using a sear! engine o. 0our !oi!e8 look u* te term one:/a0 .un!tion Tis
!on!e*t arises in !r0*togra*0 E"*lain tis !on!e*t in 0our o/n /ords8 using te
terms learned in C & regarding .un!tions and teir inverses
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A !ommon result in te anal0sis o. sorting algoritms is tat .or nelements8
te #est average:!ase #eavior o. an0 sort algoritm#ased solel0 on
!om*arisonsis O(n log n) Ho/ migt a sort algoritm #eat tis average:
!ase #eavior #ased on additional *rior kno/ledge o. te data elements3
Wat sort o. s*eed:u* migt 0ou anti!i*ate .or su! an algoritm3 In oter
/ords8 does it suddenl0 #e!ome O(n)8 O(n log n) or someting similar3
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Com*lete 12 C % o. ,is!rete and Com#inatorial Matemati!s
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o E"er!ise %28 *ro#lems 11 + 1D
> C % o. ,is!rete and Com#inatorial Matemati!s
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o E"er!ise %18 *ro#lems % * 2B@
o E"er!ise %$8 *ro#lems % * 2$B
> C & o. ,is!rete and Com#inatorial Matemati!s
o E"er!ise &18 *ro#lem @ * 2&2
E"er!ise &?8 *ro#lem D * 2$
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o E"er!ise %18 *ro#lem 1@ * 2B
o E"er!ise %&8 *ro#lems 2 * 2%1
> C & o. :,is!rete and Com#inatorial Matemati!s
o E"er!ise &28 *ro#lems 2?(a + #) * 2&
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In /eek 2 /e revie/ed relations #et/een sets We /ill !ontinue tat to*i! tis /eek
too Wit de.initions and e"am*les dis!uss at least $ di..erent t0*es o. relations
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ead troug se!tions ?2 and ?$ .or to*i!s on B:1 matri!es8 dire!ted gra*s and
*artial orders Pi!k an0 o. te to*i!s (de.initions and teorems) tat /as not
alread0 !overed #0 0our .ello/ students and *resent 0our understanding Please*rovide e"am*les as 0ou dis!uss
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ead troug se!tion @1:@2 and dis!uss 0our .indings
e!tions @1 and @2 illustrate te *rin!i*le o. in!lusion and e"!lusion #ased on
!onditions .or in!lusion
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,isu!ss o/ te *rin!i*le o. in!lusion and e"!lusion is related to te rules o.
mani*ulation and sim*li.i!ation o. logi! *redi!ates .rom !a*ter 2
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Com*lete 12 C ?
o E"er!ise ?18 *ro#lems &8 D8 8 + 1%
o E"er!ise ?28 *ro#lems 28 8 +1% (,evelo* te algoritm onl08 not te !om*uter
!ode)
o E"er!ise ?$8 *ro#lems 18 D8 + 1
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Com*lete % C ?
o E"er!ise ?18 *ro#lems D8 ** $%$:$%%
o E"er!ise ?$8 *ro#lems D * $D%
o E"er!ise ?%8 *ro#lems 2 * $?B
> C @
E"er!ise @18 *ro#lems 12 * $D
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Com*lete te % C ?
o E"er!ise ?28 *ro#lems 2 +1% (,evelo* te algoritm onl08 not te!om*uter !ode) ** $&%
> C @
o E"er!ise @18 *ro#lem 2B * $?
E"er!ise @28 *ro#les % * %B1
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evie/ se!tion 111 o. te te"t and dis!uss ere at least 2 to*i!s .rom te se!tion
along /it one e"er!ise *ro#lem
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evie/ se!tions 112:11% o. te te"t and dis!uss to*i!s (tat /ere not alread0
!overed #0 0our !olleagues) .rom te se!tion ,on=t .orget te e"am*les
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Com*lete 12 C 11 o. ,is!rete and Com#inatorial Matemati!s
o E"er!ise 1118 *ro#lems $8 D8 @8 118 1&8 + 1D
> C 11 o. ,is!rete and Com#inatorial Matemati!s
o E"er!ise 1128 *ro#lems 18 D8 128 + 1$8
o E"er!ise 11$8 *ro#lems &8 2B8 218 + 22
o E"er!ise 11%8 *ro#lems 1%8 1?8 + 2%
o E"er!ise 11&8 *ro#lems % + ?
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o u**lementar0 E"er!ises8 *ro#lems 18 &8 + D
> C 1& o. ,is!rete and Com#inatorial Matemati!s
o E"er!ise 1&18 *ro#lems 18 28 118 128 1%8 + 1&
> C 1& o. ,is!rete and Com#inatorial Matemati!s
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MTH 221 Week & 'earning Team Assignment esear! Pa*er + Presentation (UOP)
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MTH 221 Week & 'earning Team Assignment esear! Pa*er + Presentation
Matemati!s : ,is!rete Matemati!s
u#mit te .inal esear! Presentation
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