{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2007a - 2007 Am 25:mmzm'p'mn an 119113-13 nowumu wmv 199W...

Info icon This preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2007 Am 25 :mmzm 'p'mn an: 119113-13 nowumu wmv 199W: 1'"! zmmn ow 31,91va np’mnsm -: mm mm: arm 201 -— 1 — 9661 :o‘npn 190m mm mm» mmn :fimbnb ‘mm ’2 wvmv t”va mm ’3 Win mm: 3 :mvnzm 1w: tam-1mm mm»: m : 1w 1mm 9mm awn: many A4 m 2 man:- um‘nwn mum»: w .mzun mm)?! 5 11m 4 by mm m 511'an 25 mm n‘mw '2: .namuwn mt pm‘: \m m'npm mm: mm‘: 313 gamma av 13 aha”... =m-run ‘Jw m-n nub mums no»: 1mm .14 .1 a = 3an-1+10an—2 1 n > 2 113$“ 01 =1, a2 = *1, 1m 11w 2 ,1 ,0 mum-m mnnn n Tum m‘vrvn won I)" an» ,3 .mw 111211212 mm: .b1, b2, b3 nmzwn (1) 35‘): 19m: b, '11:» mm): no»: ms»: (ii) um um a,wa mun 6 v: arm: 20 p‘nnb mn‘waun 19cm 17m .2 5 mm '33: pawn mun ,ov'n'r: 8 1mm ‘JD‘; mm‘: 0551:» nmhn 2131111: U I} :4 d E5 _.| '3 '5 u '21 \.l' e ‘3 “J T] \.r 3 :1 2 5 "i \r U ‘3 3 <2] '3 2 "U 2 t u u-I I3 d U U.) f (A) = A u B mayors amp A ax mmy-1n-1nfnm 2P(N ) by f mm .mqu nsup 'nzw f2 (A) = f o f(A) m: 13% .mmomA mm: '11:)! flu) = f o f(A) nu awn z f2(A) = A u»an A c; N msnp Tm 1:113! 99112 '2! k" :pwsn 11:13! Warn» (19 —> r) -+ —{(p —> r :1: 1mm (0 751:) a WWIIOH omonn rump by on? mn Tb <=> (a=b 7N3asb) nvmopavm-r n‘ns 1mm )—> (q —~> HID] T 3n? .unvzm mva a, I) max: .vp‘an “110 um um :nmn nn'bn m‘mpwfi T—w Imn TIN “$3111 3x(P(x) V Q00) <=> (3PM) V (3xQ(x)) amt-1mm = {(—p) —-> q, .q0 = p a) r v (q —+ p)} mpwsn nsup mm 1171: (q A r) mean mt nm‘: rm 1: napwsn (mxnuu v.1) I'IWU‘W mm m £3377! I'l'fi-‘n n"m~: A=B mm 3—1 A mmp : A W WIN n: m B "WEB 1113: ‘7: m: A 7:31:17: #7312: B 3:13;: :rban B c; A an A c_: B lP(A)|= 2” E : AUB 1 3. (AUB)UC=AU(BUC) 5. (AuB)nC:(AnC)U(BmC) 7 _ _ _____—— AUB m: |A|=N mt .P(A) = {B 1 B c; A} am A .131an W: P(A) 37111.3 3133') U \ B Wm 35. 7 ,"n‘mz" mama 5:: mt n‘ran U awe-aw .1331? m7. 1-33 WWI-mun =BUA 2. AnBzBmA 4. (AmB)nC=An(BnC) a MmmuC=MuanUQ =AnB 3 AnB=ZuE AxB={(a,b)|aeAAbeB} xvanmpnAnmp 5w mm» m: n1w~u1~m(a,b)eR DR ,RchA nxA‘m onimpflRnxup: gm .R1:Rn(BxB)mnB-‘7R‘7w 1211:1373:wa BcA mnAnmp‘mRom :nw‘mnm Va 5 A, R(a,a) mm: 3373;: Va,b e A, (R(a, b) a R(b,a)) n"m~: W‘O Vagb e A, ((R(a, b) A R(b,a)) ——> (a z: 19)) Max firms: W Va,b,c e A, ((R(a, b) /\ R(b,c)) a R(a,c)) 73"mi um .nmm ,mfio m nmn mum m ‘75:: am A ‘79 R m‘m arr Va,b e A (R(a,b) v R(b,a)) .A ‘73: m‘rpw ow R 571* %= {b e A|R(b,a)} wnRon’n a e A W a/R n-hwln am. %={“R‘aeA}x°nRon°aA‘7WA/R mum-[:97 :mmnn by: m s 110 ow fin, '11:: arr .nap‘m Tm ow 111m nfism A map am <A,R> nw‘m, m 333,. 7 mm nx 13",?an A ‘79 110 or:1 run A ‘73: R m 171: err (R(a,b)),R(b,a)W 1: bata , b e A um m7 8'? nu <A,R>:1[~‘m~uma) 47mm 1:»: a e A 3:1 “mm (R(b,a)),R(a,b) :2”an b e A “73‘? m: <A,R>3 (m) awn: '12»: a e A =3 17381 B ‘79 $an 110 on, m mn B ‘7 R on, ‘71:; RI I:er am 5m B c A -1 A ‘71: 3.7511 110 on, R nx mm:.afb. (3 ° f X“) = 30(0)) 4171:) gaf2A—+Brntpmx"n g:B-—>C 4H 13 W (rummb e B 13%;? (11.77:) a e A 53513 13 B-1 A 71313.? '73: on, rm f : A a B mm. .f(a)=bnrnx rm, 11.77: a”? .111an ‘73‘7 DR (37"rn1) nw-m—m f '. A —+ B m. “11.77: 11w B—: 1:18 ‘73"; m: '73: f : A «—> B m. VbeBUog)(b)=b 1:71: g:B——)A_TP!PJWDHJW’DNMH f:A——>B m. f mpznnb mu 1131.71 g : B —> A mpm Va 6 A, (g o f )(a) = a -1 | A u B | = fiAl + [Bl ’13 mm nvmo 11131317 B, A as :amn m l A xB |= |A|- |B| "m nvmo 111312;; B, A ax :rr‘mra m .‘_,__’ (nmnou r11) nun-paw mum-m m :21 "mm max» k '72) mm: 110‘? nun-nun w- 110‘? nln'wn 1-H k l Zqi = ————n'—#— ::‘nlm (no '31) qi ) D'JM u'alo k—n an!» n ‘II‘I'O i=4 ‘11!"12!‘ "It! k+ n -— 1 k + n -- 1 D(n, k) = k = ""1 :nnm mu 110 167'? H 1mm 1: JTWIZI'? '11» mm ;n-R:n 11-: an!» I: 'u'I-o (35 W)“ ='- ifchin IIIDI'J 'w uu'nn i=0 1 I W 1- [:J=L:J 2- [:)=[:J=I 3- [:]=(";‘)+[:::) 4. n n _ Fl n n _ n—l 5. z[k]—2 6. §k[k]_2 n m qx mm mm: A map: No D‘TJ’R'H wanna mt 813297 mm mm .(|A|=N) mam N mm A :mnpn fin awn: m: 215m A amprm um»: wean Mail. ....... Hair) 1m: . a, ....... “a, numnrm No =N——ZN(ai)+ ZN(aiaj)—- ...... ..+(—1)‘N(az1 .... ..a,) ‘Ix.a&...........a,._ Isis: 15km .n=1‘7m‘7.~n‘7nnn1wwmmmrumm mm :WJW 1mmmmm)n+1 wusrmm mm: 13mm 1! 1m mmruymunwmmmm (n'me‘D .n=1 ‘wn‘; .mWn11wwmmmmnnumn :WJW .n+l wusmmmnonmnnn w'n‘rrmnwmmmmmmnwmmmm n -M DWI ) mm: D?! .‘I‘D'HP'D 11111172 D‘WJ‘R‘H 11213;? :M (mo-11171 “m nw'mn amp) 11mm nrnm mum mm ‘71:? mm mm .1 .111»: um nm’xn mum: mum ampn ‘m mnun mam .2 man mow-n om :m-m": .m w 3 1mm Mn) = c,¢(n — 1) + 61¢(n - 2) + ....... .. + ck¢(n —— k) (*) magma mum nnma Mn) '11:!) am mun numb .1131”! we“: m1 arm mp: m: m C“) mum-WW 2,, .... J, warm on. (*) amwn‘m it" -c‘;LH — ...... "—95.1" :0 m: m1 15‘? mm? um mt .¢(n) '11:}: W m an 49(11): 431" + ...... "+42," P'I 1mm .‘tnx pm: mm ‘m 131mm mt warn 118 mam nwrnw nmfip (*) :‘PDTIP'I um ‘71:? wmxn nufimb DR 2.1x: mm: .‘PD'flP'Ifi own 1139 .m .n = 2 mph: 61,62 6 R ,,¢(n) = clan—l)+cz¢(n— 2) (mm-Ion :11) am“! :mm m m: m aw 11:1 nxnmn ‘m 21,12 aw m: .12 — c111 — c2 = 0 av: ‘7"171 own ‘71:: nwmn ma ' mm 11‘? mm: n”an n’mnn .1wa mom-1.1 own be; 111119 am gp(n) : A1111" + AM; A2, A1 ‘71:? 1,1,..,1,.. .1110: W? mm’n rpxpmn .Zanx" *‘pxmwn '11:: am (an):=o .11on W mxm mxpns mm” mm n=0 1 mvn’ n .71 n‘mm 1,1,...,1 mm!) mm: 1mm .(0(x) :— 1+ x + x2... + x" + = T—- m — x m1 '7":n 71111:: W mxvn n33.71er 5m (moan an mmun mam .x .I) 1 __ xn+l .g(x)=l+x+x2...+x" = 1 — x nmwwn ‘m wan D‘190D3 mmnan 190m nu mm? *1: tl+t2+...+tn:k (**) mama: x" W 131.772.": mt numb up ,(1 si s n) 0 5 t,. s bl. M71237: nx nmfipnw ¢(x) = (1+ x+...+ xb')...(1+ x+...+ xb") mama ‘m man ufiaom) 111311119?! 150?: mn ak "was ,ao,a1,..,ak,.. raw-ton ‘71:; mam-I mpm m ¢9(x) 1x: map: (**) mum 5w Inn-man 190an m: mm mm m: as .mnmn m‘vmn m: nwpnn (‘wun ram-ma mt wean w(x) = (1 + x + x2 + ...) N'TST’TI rr'xpmn rm mm: 11:: n»:va ‘75: mm: m‘vm any *5: NO I: -1 .D(n, k) = [n +1; ] J: mm m mam“) .y/(x)—: x" w awn .179. 31': .nnuw 8'? 1x mpw 1:: war: man: :39er ‘73 mn p105 am. :1 :mn m1 aw mm 315:1: .Val(<1>, g) 1mm g nnwn: (1) 7mm: ’32:? gm amp" (I) anon .Val(d>, g)=1 uwpnn (DJ? gnaw '3‘; m: mam mp: (I) nnou nu 11%: am ‘11-1 c1) marrow: az: 1nx1.VaI(<D,g): 0 :1”an (1)37 gmer ‘72") as (mm m) .mm‘nmnu mm (1) 4—) LI’ rmoun (D‘P‘IDDH 2112mm 1.1mm munou 1n A,B,C 1x31 :1er mm: 11%.: AvBo-(fiAA—LB) .4 —.(Asz)<:>-Av—B .3 —:(AVB)<:>—uAA—13 .2 —mA¢:A .1 (AVB)VC<:>AV(BVC) .8 AABQBAA .7 AvB<=>BvA.6 AAB<=>—u(—.Av—13) .5 A-)B<:>—IAVB.11 (AVB)AC<Z>(AAC)V(BAC) .10 (AAB)AC<:>AA(BAC) .9 A—->B<:>—lB—>—.A .14 AVB<:>—.A—>B .13 (AAB)VC<:>(AVC)A(BVC).12 .A<—>B<:>(A—>B)A(B—>A) .15 m'm 1.3.1.3] Mara-m nay-pm»: rm: rump: 11’ mm: .m-mfiu .m mum nrvm‘wbw 13 pl. '71:: nvxpmwp . p1,...pn numzm: 7mm: (1) mn . p, p" numan rm: nmxumbx nwpnmp '71:; .15prva um ‘P -1 (D -‘7 nbwpw m DR (1) .111me 1.1.: .d) arm: w 3.1.: nm ans-mm .m'r'n‘ m'mv TIJW'HKTI #1173313 Til: I'I'I'I'IWTI 1'13 0’13"“: (1) 21110113 5W mun 11531321?) .1 13271 "[918: 3‘7“?! 111711175 mmznmv m‘WRUJDbRTI I'IT’EPJW'IPTI 2‘31] .2 3 (nmnou m) rum-paw W735 man .—p,. -mna pi qnnwn nmmn‘m n~xpn~npn ’18 1 mm T15: 53pm pf runum :11me mm: as ' m m ‘P 1m .‘P “'57 v nnoun mo: .2 25:22:: 1mm nv-mumbxn nvxpmwn W n’xpavov-m mi mm: .3 .(D '71:: mam-u mam .Q-n nnwpn .71 mm: mW'I‘? 1m mmoan rum: marrow: ‘7: on rm'm mm: 9 D‘fiWi? Imam m. :1 nm’m :mzun nw‘wwnn 9:111 .11 DR .111an 1:1 {—.,—>} ,{—«, v} ,{—., A} D’WWPH mmsmn :{—., A} rowan 11:13: AeBc—(AA—IB)A—.(BA—LA) .3 A—->B<:>——.(AA—.B) .2 AVB<3_1(—1AA_IB).1 {—.,v}::1:a-13mn'1m A <—-) B <:> -r(-1(-1AVB)V —-1(—13vA)). 3 A -—>B <:> fiAvB .2 AABC>—(—Av——B) .1 —.,—>}n::'15mn 11:5: AHBai-(fiAvBW—(flBx/A». 3 A—)B<:>fiAvB .2 AAB<:>—(—Av—B). .49 :M” -—+ {0,1} 793.7115 mm M rump ‘25: (9 mafia W. awn awn wan f nmnnn .f nnxnrn M 71.7“! 8'7 rump 5w mm: mm mupmnn mme (I) nnou‘va = (M, f) nun .nnmn ammo? mum-mp mmwn npwn‘; mm M mum <D-n n‘nwsmn Damn:an nmp nmnnw wupnan anM = (M, f) .113an anon ‘21:; g .173er .g nnwnnd) 5w mam T132 ValM (<1), g) “'31 mo: .nwwmnn nvznwn 5w amp mm mva mxnou T -1 (1) WIN 13"me 11312.7 ‘73: g .173er 535 ValM (‘1’,g)=VaIM (G), g) m: M = (M, f) mum-Iqu (I) mxnou .nwwamn .M map ‘73: rum: '73: mm: 1.1 m: M M‘IM <1) munou 51313.? ’73: m‘npw 1:1 as (T <=> d) “'51 1731:») mm aw? -1 (D mzmm: figflfl :mrm: raw-s N19377:"! nm’mn -((3y)U(X,y)) <=> (Vy)fiU(x,y) (Vx)(P(x) A 4200) O (Vx)P(x) A (Vx)Q(x) (330(1) (36) V Q00) <3 (3301300 V (3x)Q(x) (Vx)(Vy)U(x,y) <=> (Vy)(Vx)U(x, y) (Vx)Wy)U(x, y) <=> (Vy)(Vx)U(x, y) 11181101111 I18 mafiapnn ID ’9 '79 ’18 .115?“ H‘EPI'I‘DPZI H’KPD’D"? 'I’IW'ITI‘? “"1758 ’N WWW .THWTID WRI'ID'IDW 3‘? WC} mum (VI)P(X) V (Vx)Q(x) => (Vx)(P(x) V 906)) (3x)(3y)U(x,y) <=> (3y)6x)U(x, y) (3x)(P(x) A 906)) => (3x)P(x) A (3x)Q(x) (3x)(Vy)U(x,y) => (Vy)(3x)U(x,y) (HyXVxW(x,y) => (Vx)(3y)U(x, y) :munn 1115+:er m: nmfipnn m: x runwnn m: n‘ma x‘; B mm: m: (Vx)P(x) v B c» (Vx)(P(x) v B) (3x)P(x) A B c> (3x)(P(x) A B) ~735an .7‘7nn1 nnoun 519'? mm}: mm: ‘7: .121 A 3? n‘mpww nnoun mm A nnou “w: G 314779-11: am. :1 m: .nn'lm‘w‘m 1x (m‘mm) nmp’me ’11?!) m mnnum A w Q4: 02:"4. 11>?— On 7 301m, 4~ 100/”..2 4 (go mm 8%,, 7. km: 9mg)? ‘35. XL h-'l kn? yniafifi Em A X: éo+xi+fz+ . , X§)(x:—XI+ (Xx-X“ X249. )11 /’”X9 1.. 6 4 by T7 Y”??? ) TI; 7 f g” * p 34/ p04) Jc 5'9»! 63¢ N'nf {’0’ A r % @:K*$s> (0,95 '- 8 6 2A1 \' _ u _ ' “2’5 W”: i.“ L /< (new- bw (- ¢ 2A1 ' > 9115 h 5+ k H ‘ < (4M auwbav Q50) (fir) (ZN FOO) V (a)! (200) “1033909 " “300$ @QGWA fl mm " ( Vx-‘gob A Walch (“I m) A a am) “‘7 1 RV & xv. U T,‘ F T Ue m. flaw mg m: 0 r nflaflflafl fr .. . u.\ x) Egan T .er m . f.‘ p, . [email protected] 0 I: ‘1 ON. smug‘) jiaAC-afi‘fi 7M9) I? "lob .‘D Opt J‘Vb’ak‘a) fik MOD} 4 0.3014 ichi-D (gym?) ‘8'}; ’2 .0 o 2 ‘1 : (>63><‘+vv~+x9(x;g:;2<j)‘(wxi+x+-—~ )= 2 flaw (w mm 5-4: m w " In 1*” "¢n-'“/“""’¢v?"r 91M ,. I : 4 W New 1 rlqAU 3 ‘35)” {CAD 9'0)??? ON '- _ PX", I‘Xb (4,)“. - a - s “.11 ‘ 3” bx r-xWI’x "(4X)Gx) (1") I 7 ’0 SHL ' K nut—4 { 5 " ” ” ” "X5 : (1’ thuyw). K)>( Hg K) Lu: :n 491‘) AM Me mm} Mia?) 20 YRX/hneoua 3% ,4; 7,9693»! 91c! WU»: . U 19' __ +IL| __ 5+|D 5+5 . I?) lira-‘39 X £8 5310 (SM ) C H .L( S) / X” 4??“ XLJP'RN Yq—(w'éu x"?!me 7.. Sane-"613 "1368435??— 370536 Ame K W AW A'JIQ/ 113m" ‘2. Obffiz )HC"[}]"JI {bin 9).” P.3PBD® A2: 05 6 1000 Ar F5 6 PCN) female» 5}) mu (MIG) (Jg’yk) ’ =7 ¥ (m 40%) / MAD=I5\A,,=&\¢=E> gmflgf‘ weNA no euc,{4.4kep(~) :9fina*'i>n13u.f’(r0 56 “xxx A? w m I “JO” ‘ .JmIOP L Y: {4,1} 33w? J a J‘fl MW!” 33—: £338; (fin Iva?) {4.4} mmxmfah‘fifalwm [91" Engflfio 2') 13,5. «maven; A $11»).ch 'Fgfio’): "'3 191°ij :JJQIO/Aépab ® $1L®= H (5WD = (mmvrs HEM, AWN“ ‘ am Mam -» A W @ V -; 1: U B -' Q’g‘ffi (Q gguufi)u (5 Man?“ ’/ 3" '“Efi’fl’G NUE 3N $ED¢NUED=N Jr" Ni FNAQWVY) filfirfi Q r :M =0; anus ear—is"? I . '2) ® S: £53k [g 1 ,Seyq'lx.M‘WWEJMWHWW P?A):A® 3 on Aka/j 3,1 “as 56 me My m‘nmf «up 1?...ch mm'mca N05 my!!!» .nuuai 1m» ;® *3on 7323. my) {4,1} Mia? filfifilmwfb‘b RN89? WWI 45 ’MB ,nmc. \‘s’o LN: was?) um ,bim Jum- Acac Info 1' ',j\p\LTb(m{4 wow 9w rwww b ‘32; amwc " cum: A'Rm} AWOwa w (pm/WW (enqmflflmwwflvfi'FAQ/\Bvfilmn‘fl H ,% . g fin)» 3 Nam: K." "\“11 . J'Qrcuspo 7%04-0- ‘0)‘[email protected] ,—\r’,3*0"\\§a’[email protected] V0 I m=0~ "-7 t/ ‘3 ,er-oqgfl‘) MM aha-LN by} 2,3th we 11.0 05‘ km on’?/ warps mm‘i'é .‘ OVA: " ,OLT}; ’ ,5"er N a! saw a; aqua e W ‘-’: J 3 9‘ “:C 3mg 6, at = c 3195c m 3451:. Z‘IQn‘o) 3asb sagab ‘ A"G~HCI M) E aft 9" M p' h 39? M \’ f‘ “’Y‘ M“ 40R "" «‘33 ‘3‘ 9W3)” 3) Ah \Jm‘m ' ‘ V ’) ‘ \L") \ . _ \fi 630 0% h I \ ' la {9 . 1);} ‘ 1}“? Iqfl‘é [\f @ Cox—(Cc: 3155:; PM u o -. @® 3% (P(X)VG(X))¢%=>EX‘P(XDV (axaoo) T '6 AER/33 may . (x) A “@003 fig’fi‘j’igw op “(wapw A Vme)) 62:) jam: . a?) (a X 90‘» V (EXQCX))/ ' x = A vs '1 warm!) 4 Amie); gnaw» 6;: ‘w’ (ZIJ my» ‘ \ Ci . ‘ \ _/ Pm £5ng magm —" \2/ . 3 JHJS.”‘D.J “ \ L‘wfiflc )- ® ‘mbf Q» mm film Jug 1mm quOmMM 9L1an 1er 15 (9319‘? TbJW(fi‘1IOD 3:: 19¢er ngxm \13 pan 3:: MPH me. fibo .‘\\\0£)"D Ac m'vk‘: ‘oK 7am} LL T \wb W 129)?“ may» p2 pk ) -_”7“’ ‘- ”" 'M "2?? Ar ->m 'm 4m ‘ "” int- i “Hi-“II ’7— T 3) "-— I'i-‘E- 5' Kim‘- 6 I.“ 7} fiI-I-nfl_ <5 F’qxom x13me #110333 '53? (111% m.) mm "mm, 1‘“! Tao" A?!“wa HQ W'fihr ‘90 F Nib [Xvi Nagy} V033“ 'Tyb p'f'h’yd {'43-'— mam A’gln'y‘l 9-1105» Tupi) 1 6)»! M39, A p0] .Jvzlf 333'36 r Art)! ’3’)qu A“W\N \cf W76 - 5W *2“ {MW : C [S g Aajojfi 78);)? A <3 $(mgcurs) dehummg —.-. $05 H, w“ 1/) _/ _ J a” fl 0 — \ . fl (is 87/ 920-0:- ¥ (We, ms) =(A wow» —. J, RUB \ <3 / )% View T Tm P'BY’ ‘P’Moa’h A313“ “yeah 3e, ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern