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UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011 Problem Set 3 Problems 1-4 You are studying galactose metabolism in a new species of yeast. You have purified a novel protein important for galactose metabolism and have called it Gal400p. You have raised antibodies (Ab) against this p
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011 Problem Set 3 Problems 1-4 You are studying galactose metabolism in a new species of yeast. You have purified a novel protein important for galactose metabolism and have called it Gal400p. You have raised antibodies (Ab) against this p
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Study Problem Set 4 Here is the genetic code to use for this problem set:11. Before the triplet nature of the genetic code was established, it was proposed that message RNA might be read in overlapping triplets. For example, the seq
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Study Problem Set 4 Here is the genetic code to use for this problem set:11. Before the triplet nature of the genetic code was established, it was proposed that message RNA might be read in overlapping triplets. For example, the seq
UC Davis - BIO SCI - mcb 121
MCB 121 2011 Dr. Ted Powers Supplement to Problem Set 4Puromycin and the Classical Model for Translational elongation1Classical Model for Translational ElongationKey features:transfer of P site amino acid to A site translocation of tRNAs on both subu
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 5 1. Over the years, a comprehensive set of temperature sensitive mutants involved in DNA replication in E. coli has been isolated and studied, defining the dna genes. These mutants can be divided into two classes, based o
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 5 Solutions 1. Over the years, a comprehensive set of temperature sensitive mutants involved in DNA replication in E. coli has been isolated and studied, defining the dna genes. These mutants can be divided into two classe
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 6 Solutions 1a. Consider the topology of a 10 kb (10,000 base pairs) circular plasmid, named pBR600, that resides inside of a bacterial cell. This plasmid normally displays 5 negative superhelical turns (i.e., supercoiling
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 7 Solutions 1. What evidence can you point to that suggests a common origin for the evolution of transcription between prokaryotes and eukaryotes? Answer: Some of the subunits in RNA polymerase II from eukaryotes are homol
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Problem Set 8 Solutions 1. Which of the following describes a complete nucleosome as it exists in a mammalian cell nucleus? a. 2(H2A), 2(H2B), 1(H3), 1(H4), ~146 base pairs of DNA b. 2(H2A), 2(H2B), 2(H3), 2(H4), ~200 base pairs of DN
UC Davis - BIO SCI - mcb 121
MCB 121 2011 Sample Quiz I Questions Refer to the Genetic Code when necessary:1I) (Questions 1-4) Consider the following (simplified) pathways for head and tail formation for bacteriophage T4:One new temperature sensitive mutant (Gene X) of T4 has been
UC Davis - BIO SCI - mcb 121
George Mason - MATH - 214
/'(ofta/qLeeaiue /XX_x92+2v-Oq&Lcc;c"*rfif =eY.X',xW4O+r'taaA 2/'ltz'"vaJivzx^+2ft+)%=QA Sr,zr?Xont?4hWr,ite DPD2-Taazt'a-ob&*rlaZryG?G)- ,;ze 4rutcL)D+qvfa;tertEgn ^rf/'bn4)poplahbn a*9oUto9oL'*aPa4'^.2.I&o*.Ae-# Kf
UC Davis - BIO SCI - mcb 121
MCB 121 2011 Sample Quiz II QuestionsWobble Pairing: 5' Base of tRNA anticodon U G I 3' Base of codon G U C, U, A11) Below is a schematic drawing of a human mRNA, showing potential for base-pairing interactions in the 5' UTR between three sequence elem
George Mason - MATH - 214
a./l 2 tv.Se?a+a.ttoa o/ vna *lt-c .'k= acfw_+8 ,#:a0*);o,(.1 uot'tta*t/0 - sat'Xil,t s eLofian7bcF(dxlar=5k+J-t xG) =Xo#- s(x*i)f&=frae =>.-/ \XIAi=-zrrtx&) =1L)+C=Ko-+("*3)"tb t#= r-xlxb)=Ex,2-Sofu"lhis IVP|t#-3Y+tlrh)
UC Davis - BIO SCI - mcb 121
George Mason - MATH - 214
14otA z t4,Lert-,-, zalLlasr;fi'rz-lton "P- oDEt'.r) Rott cts \ DEspatn*pt/;P,'%ao.t,#,8? eft( \tr' f xt= f (*,/,*).r) flsreza-f('v9. gi^VLA)2roLe+-o(DEf,t'a,1 )? erp(ta,ff(x,+) 4Qr f(*,x',t)=o ia,pa'e;tDEk'==uLdl,t 4/w'/.4t
UC Davis - BIO SCI - mcb 121
MCB 121 Spring 2011: Sample Quiz 3 I) (Problems 1-4) 1) Tetrahymena telomerase RNA (TER) provides a template that produces the following sequence for the G-rich strand of the telomere: 5'-TTGGGG-3'. The template portion of TER that encodes this sequence i
George Mason - MATH - 214
l,lrn2/tl.t-, /, J^@.aratna-A,rra9?*P@/ft/r)F,'d ratqra-ri'y !"^*(tl = e- J Ptt)o(tft'* 2?=tlFex ,l/u H),=e#Pzrtr",uAtt(+D(2I,e*-e(bdeg'n *gLz3=/ao6.? ctar"4ddH:al"tLp/t) = eJoH = z &, t (,:rf FH r'r ft.rr,4 q r%.,u
UC Davis - BIO SCI - mcb 121
George Mason - MATH - 214
f/f ofit,+,Leafu-oEx.I (at= xJ(/ - l+2A(cfw_,Lt(n =oGlt,*(*+Llrt-= t.lt)=o=Iir _ (cfw__/) =o,U,Ji fr.i,;o,l:h*?bard,ta-h'L(orr-t /+I:o('*At f c =o^lx,lHr, h c/'u<e do=cfw_t,)9 F,'na/=2N'-l2&a^"1 gah's fu,n-/*,fThTl2,-lx-,f
George Mason - MATH - 214
ffiia,*l*) qnA t/'h d k'Ln;tale iaa= /^'-/l,A/r q* = 2 /&h/a,oeoo/U"=in;t,'a/4^:Or?a4a/ "g&r-rfia,o Cls ( o,att d,rEobcl dt *'=o)nftaotlry haau*ta,4bn = ek/Va-tl'in*L,'lo-f;3;Art* lftVonr V/9 = uwqful./rl#tdQT+Q'k)=otae*at-rhrr
George Mason - MATH - 214
,lAtult2,Lechte 7*-;M,nl)nntt/s, Cuz*9'j?H/-= Vft) 6)IuyltolLV=gvm2 cor-r5'r*'|% )a eo)j'2/tf PH, 3/+)it'tawal f ol <*</A c'l'ldatng t=6r\nrr-'.,A"At &lle ,"S a cuu'?ttt r&.*rq /ry v/o,tf* v h f^t:ry tI^|a/"r' k)i'gX(il = fu,fJ"rtst
George Mason - MATH - 214
t4o*tt,'a,Leofru- 3Lu+ h'n^o:burla.t*V A' t' ar, dtdfL* Lb7/t) ,Vft) ilae. ual,a*-arwa!-ftuoal ls* al^obl .re,t^ c,l tt /t \-ro'u,'a'd-lfrc,il *^*( #rc,/Ell- Jtg,0u'r@.,uL A (e)=oFirc( i^qimaLuze- cetrtrutocrA,-1'=clntetuouul'*gsL<1t2-
George Mason - MATH - 214
!4"n atfC/orr, ('coh'o^ ,lLq*A &u'oIacfw_s'=|Q\(.*h *etrB-q?k-tr*girre.a4Lfu/^ i scfw_alL1E= ecfw_z-"t)il'ldaoee41-.;h'6+"t'"-e ur'nto+u t= LL?gh^a&t-4-exa* &&t' (A -")&'=Cb*t;rt, 141-,'4naTz)il:;+t4o4ttu^'nla?-q 0-4r oLc
George Mason - MATH - 214
l'la;t 2/(.Leocfw_u.e' I aaa+.c\ead orrattl9a raiin gurtte9\ocfw_"*6a'*'ts-oqftr) >o'l" = f (t,fia')YaY-r.f| ?' fbl=orqaI-aPus=o.tfte*e is gtt (aa.*a - 2)th*o ts-+ hL fe44.,fru qtaitctt ,J Ct-tt*"l e*nltfiLas-)2 tn; hal4=+ lfu
George Mason - MATH - 214
kl ,ra e tq.li"r,* tt,La'l+h'u-.Q-:?- sla*e-/ tt"* tf il' , t'W(f"X) G'l +o* P@t'+ q(t)V = oA"-t/tto,fttl^t U2 boqfa,c"Ja Cr, Cz d ac4 ftra*+ (r/, s&tq A^2 / t/f=0sa&'a71.*/ ^"//, .lft)V- ,ttt r. ' ' ^ tt l,-.nr0"+Plt)Y'+ ?tt)A =O)
George Mason - MATH - 214
llon p tq.*-*'-ILe or\^-. /e6r'*r/ = O e Zad a4dr4 L'r,to,t ar",lt coe+/s6+ar"+t^t2 tr2-; c =Q * oAana&o>ish'c ghOil" +, PaAISt)h*rz tea!=)I =('ent *Czerzt4 rr=?z74 ?= 2- if - c^ t^. r hd"?' E =?*',' ut+tev)aatTar'+?r+c=oGrrq&^ ra$.
George Mason - MATH - 214
ItMa-r%Le2/+.r*r*e a 3ad" +'00'* ,? = o :)I@=-Ft)h,*h)u,u?,/,".^*2e4ae1d14,t=r?,%:': '/rea[ 4fi'eh'nct-n -tac*I = sr't acz"tJ) ' ! f/) ,-';, = Fa real r7n.t/C:'1n='tr, ert + co.i"r,ur,": r if ca'*/i42Cte'r nft + C'e?'s'e7tl4
George Mason - MATH - 214
Ltrn 2t(ffi,+plt\, * ?ut= Vft) +o0"nan/uot+, /t) =/ A*, l,an /t) + cfw_ut/*,txlu -J/'-zV = g7 ",- 4v'-3a = o-rt-1,-i-QPort'crrlat s&z-rlbe' /v aaarlaa, 1ia,- ho4luta.* Aont,a@Ur/4 = -/n oAlrn-r,-(t) = C,3=4t/' -3Vh h4. ,!e = hrttt
George Mason - MATH - 214
t-kcfu+eIrlfrd la-ffir.od'"B/'* V =Aft).Lt/atet*;@|r't= Cr e + C, e4t/Aor,t h * tzrea( tubats;nvf= C/(*vt +(>e4, ab*,, t=itt/r Uu<y'e+3)Cu,-, = c,eht + Gterr=4- - rea.l tTeddtr tH = f,/*) +/1"&l :) 4&) = ,!p'Gt + 42,?)If fft),r'qP'fu"
George Mason - MATH - 214
lvloru ttttI.bct*elbftled all;car+ f[ecrt*,'caQ l/r't-ot\ou.alnu, I futq Ku>F;V - rvlcsc Vlur:I trrd =4oLutH=c(o/Free taadat rae/ Ui&-a*aa:Cwr.f=o=o(Inu" +Ku = oFLUh)= eo, ut/o)=4o 'u(t) = C, c* tFt +Eq* raau,t fnn,ktl'r' + K= okr
George Mason - MATH - 214
tti /,VIrbra:h'4:larf a.cfw_?Ie*rn t+lhu" +hl+ kLL:F(qC/'CL(f+o dattpe-lt=o-,lvfrez ,F*o 4*a,*o4sa.l+)-'-=rcLGrrfil'ont f* g*n ,t(Ar'4 t-'(u%aA'o't d/4,to T^t;V)r)I ,Ft =ta;ne' A (eel)ny-'<e unih fftL-l /tuOl rLlLejt;c rt*'-t.r " lt
George Mason - MATH - 214
ftloll.ek,DelLuX"-e, lE .acfw_TqHT = ,-ttf(t)at,\fd*rt,a.3.f"/ f,/ t+',? h/"* fu*+pn(* /rp),b?/"* rror&n 4 /-e rrLffif g4.,'t;/*,>ta)/orrroo@S/*-'>/f".'oen*,v-v. 16) = ttAJ v/,t*c Vftt a^+-n/#t leLr*la.7V/4 ,tna,AJ cfw_oa*"o rl
George Mason - MATH - 214
lvtotl 2/qeertl,r-*cfw_ t.t_.f,(q *J:*'-*fu"r+att4,_(t<cuc ft) =cfw_-.-llr43\/Iu'(t) =cfw_?, t<3cfw_ 7229 4lil - Qsft) =Ql= oua7: *>cc>.o&')n,ba9 &4Qt= /S(o, F3,t<3#f<cfw_l-o, 3 s b<5hzcfw_l-t t>sus*th /t) + 2 us /*) -
George Mason - MATH - 214
zt't ,Lect*e eaI'lAG'ronfk) ,ilt;lo,nY',Fe.Vetu,t4-rt,taho4sfrp loh;\riu'&'Ps aa* a*=cfw_0, tl<t 2'| 2t ) |t<*i' c *=3-! , t2-L.\ J'24 fft) =( o ) +(at-|uirn -+- (r-t)urft)Ln-Br. -rt+1 =f l,olt< +4-t-I o?'tt,qll;nt-,-< +<6
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 1Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1): Let f : A B and g : B C be functions. Prove the followingimplications:f and g injective g f injec
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 2Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1): Let G be a group and S G a subset. Show thatC (S ) = cfw_g G : gs = sg for every s S is a subgroup
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 3Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Show that a subgroup of index two of a group is a normal subgroup.(2):Show that the automorphisms
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 4Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):A group G is called solvable if there is a normal chain, or sequenceG = G0G1Gn = cfw_e,with each
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 5Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Show that a group G on four elements, |G| = 4 is abelian. Let N4 be thesubset of the symmetric grou
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 6Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let G be an abelian group with |G| = pn for some n N where p is a primenumber. Show that G has a co
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 7Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let G be a group with |G| = pn m where p is a prime, gcd(p, m) = 1 andp > m 1. Show that G has a un
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 8Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let G and H be nite groups of relatively prime orders. Show thatAut(G H ) Aut(G) Aut(H ).=Here Au
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 9Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let R = cfw_m + n 2 : m, n Z show that R is a subring of R. Showfurther that R (Z2 , +, ) where Z2
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 10Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):Let R be an integral domain. If a R is a unit and b R, show there isa unique automorphism of R[X ]
George Mason - MATH - 621
MATH 621, Algebra IAssignment sheet 11Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)Homework to be handed in:(1):For a ring R, the least n N such that n = 1 + + 1 (n times) = 0 iscalled the characteristic of R a
George Mason - MATH - 621
MATH 621 Algebra I Lecture NotesGeir AgnarssonApril 19, 201211.1GroupsSome preliminariesThese lecture notes will follow the class text [1] fairly closely. They are, inpart, based on lectures of the graduate algebra class MATH 250A given bythe lat
George Mason - MATH - 621
/F\/"(,-ttf t'f-PG'-cr$qt\eG;[o,r etcoaret]\Mfrhrrq cfw_tt) i t-r'e G. , @tch Etracha,r Cnra be vieuved aswhere g;eGe fuv eotth t[Cec)ier , GsG. rdz"|'$ ol G."or,r ' i-+u yU-" ( ff bouq, A:Gtu,^p opentl'oq:i)iercfw_(qJ,*r' (t)rqr._(
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 1Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let f : A B and g : B C be functions.(i) Assume that both f and g are injective, we show that g f is also
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 2Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1): Let G be a group and S G a subset. Clearly C (S ) G, so to showthat C (S ) = cfw_g G : gs = sg for every
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 3Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1): Assume that G is a group with a subgroup H of index two in G, so[G : H ] = 2. Let g G. If g H then clearl
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 4Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Assume G is a solvable group, so G has a normal chainG = G0G1Gn = cfw_e,(1)where the quotient Gi /Gi1
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 5Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let G be a group on four elements. For each element a G the cyclicsubgroup a is a subgroup of G, and henc
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 6Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let G be an abelian group with |G| = pn for some n N where p is a primenumber. If n = 1 there is nothing
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 7Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let G be a group with |G| = pn m where p is a prime, gcd(p, m) = 1 andp > m 1. If G has N p-Sylow subgrou
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 8Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Let G and H be nite groups of relatively prime orders. We want to showthat Aut(G H ) Aut(G) Aut(H ), wher
George Mason - MATH - 621
MATH 621, Algebra ISelected solutions for HW assignment 9Spring 2012 - George Mason University.Professor: Geir Agnarsson (geir@math.gmu.edu)(1):Using our more recent notation from class we haveR = cfw_m + n 2 : m, n Z = Z[ 2],all polynomial express
George Mason - MATH - 108
)qNA0r-S",L4.-+-rj q (oll eth'one \gu'lpF-obJ-4tt'tacfw_rA:f1,3,s,1,?1Hgq A t> lh s-i o$ o Jcfw_ I^nuru/w\Arnabtn frorvsO ,1" 404,3, .1-V\!. lnuu,tbfhq e\ Q,n r e.ul'r o llntT\orF 3\Its eucfw_-q\^ebscfw_ V,1,qc^rQ-Srr\ Aslpu,tartt
George Mason - MATH - 108
lr^.12.,tc'(l/r2 /tvg\tIItt.l+-- A Iqqlergg -k,t \t^4!:t$ytsrprt) o[ [cor4>niY-?u"lcfw_r,uo\\l\e,Rse* erpill cfw_'r cur'tu"rL1P- TW Vorizou['L'\- flnq vurlcfw_Lct,\cupl r ic9pcfw_ l\fJso*lVtr*VAol-\^cfw_+l^cfw_y-D\xt14-AY5
George Mason - MATH - 108
3lchnncFs fr*ed qrr'int\A lax,itrfrun[.0- ou d cfw_htra q ct f x,u'r 'ka- 'n urhr,rni\qs1' IF ccfw_ Lo vrait't; d'vrr^e- tosls[-,e6al l-|'ftp* u^uth ,'ttrrrilqs^t':o"3x+L[Wl$q'et cfw_'Yi"q 3k\f")Iowrtb-7 ? -1l+vrb :4'l 5 '[tx)12 vat