,ab/ract ,algebra ,!ory & ,applica;ns ,?omas ;,w4 ,judson ,de"p;t ( ,ma!matics & ,/ati/ics ,/eph5 ;,f4 ,au/9 ,/ate ,univ}s;y ,july #bh1 #bjbb #a ,3t5ts  ,colophon ''''''''''''''''''''''''' #a ,ac"kl$ge;ts '''''''''''''''''''''' #b ,preface '''''''''''''''''''''''''' #d ,*apt} #a ,prelim9>ies '''''''''''' #i ,sec;n #a4a ,a ,%ort ,note on ,pro(s ''''''''''''''''''' #i ,subsec;n ,"s ,cau;ns & ,su7es;ns '''''''''''''''' #ad ,sec;n #a4b ,sets & ,equival;e ,rela;ns '''''''' #af ,subsec;n ,set ,!ory ''''''' #af ,subsec;n ,c>tesian ,products & ,mapp+s '''''' #be ,subsec;n ,equival;e ,rela;ns & ,"pi;ns ''''''' #dd ,*apt} #b ,! ,9teg}s ''''''''''''' #ff ,sec;n #b4a ,ma!matical ,9duc;n '''''''''''''''''''' #ff ,sec;n #b4b ,! ,divi.n ,algori?m '''''''''''''''''' #ge ,subsec;n ,! ,euclid1n ,algori?m '''''''''''''''' #hj ,subsec;n ,prime ,numb}s #hd #b ,subsec;n ,hi/orical ,note #hh ,*apt} #c ,gr|ps '''''''''''''''' #aja ,sec;n #c4a ,9teg} ,equival;e ,classes & ,symmetries ''''''''''''''' #aja ,subsec;n ,! ,9teg}s mod .2;n '''''''''''''''''''' #ajb ,subsec;n ,symmetries ''''' #aji ,sec;n #c4b ,def9i;ns & ,examples ''''''''''''''''' #aah ,subsec;n ,basic ,prop}ties ( ,gr|ps ''''' #abh ,subsec;n ,hi/orical ,note #ace ,sec;n #c4c ,subgr|ps ''''''' #acf ,subsec;n ,def9i;ns & ,examples ''''''''''''''' #acf ,subsec;n ,"s ,subgr|p ,!orems ''''''''''''''''' #adb ,*apt} #d ,cyclic ,gr|ps '''''''' #afg ,sec;n #d4a ,cyclic ,subgr|ps #afg ,subsec;n ,subgr|ps ( ,cyclic ,gr|ps '''''''''' #agd ,sec;n #d4b ,multiplicative ,gr|p ( ,complex ,numb}s '' #ahj ,subsec;n ,! ,circle #c ,gr|p & ! ,roots ( ,un;y #aij ,sec;n #d4c ,! ,me?od ( ,rep1t$ ,squ>es ''''''''''' #aie ,*apt} #e ,p}muta;n ,gr|ps '''''' #bac ,sec;n #e4a ,def9i;ns & ,nota;n ''''''''''''''''''' #bad ,subsec;n ,cycle ,nota;n '' #bah ,subsec;n ,transposi;ns ''' #bbf ,subsec;n ,! ,alt}nat+ ,gr|ps '''''''''''''''''' #bcb ,subsec;n ,hi/orical ,note #bce ,sec;n #e4b ,dih$ral ,gr|ps #bcf ,subsec;n ,! ,mo;n ,gr|p ( a ,cube ''''''''''''''''' #bdh ,*apt} #f ,cosets & ,lagrange's ,!orem '''''''''''''''''''''''' #bfe ,sec;n #f4a ,cosets ''''''''' #bfe ,sec;n #f4b ,lagrange's ,!orem '''''''''''''''''''' #bgb ,sec;n #f4c ,f}mat's & ,eul}'s ,!orems ''''''''''' #bhj ,subsec;n ,hi/orical ,note #bhb ,*apt} #g ,9troduc;n to ,cryptography ''''''''''''''''' #bij ,sec;n #g4a ,private #d ,key ,cryptography '''''''' #bib ,sec;n #g4b ,public ,key ,cryptography ''''''''''''' #bii ,subsec;n ,! ,,rsa ,cryptosy/em '''''''''''' #bii ,subsec;n ,message ,v}ifica;n '''''''''''''' #cjd ,subsec;n ,hi/orical ,note #cje ,*apt} #h ,algebraic ,cod+ ,!ory #cba ,sec;n #h4a ,}ror-,detect+ & ,correct+ ,codes '''''''''' #cba ,subsec;n ,maximum-,likelihood ,decod+ ''''''''''''''''' #ccj ,subsec;n ,block ,codes ''' #ccg ,subsec;n ,hi/orical ,note #cde ,sec;n #h4b ,l9e> ,codes '''' #cdf ,subsec;n ,l9e> ,codes '''' #cea ,sec;n #h4c ,p>;y-,*eck & ,g5}ator ,matrices '''''''' #cef ,sec;n #h4d ,e6ici5t ,decod+ #cgd ,subsec;n ,coset ,decod+ '' #cgi ,*apt} #i ,isomorphisms ''''''''' #djc ,sec;n #i4a ,def9i;n & ,examples ''''''''''''' #djc #e ,subsec;n ,cayley's ,!orem #dab ,subsec;n ,hi/orical ,note #daf ,sec;n #i4b ,direct ,products #dag ,subsec;n ,ext}nal ,direct ,products ''''''''''''''' #dag ,subsec;n ,9t}nal ,direct ,products ''''''''''''''' #dbf ,*apt} #aj ,normal ,subgr|ps & ,factor ,gr|ps '''''''''''''''' #ddf ,sec;n #aj4a ,factor ,gr|ps & ,normal ,subgr|ps ''''''' #ddf ,subsec;n ,normal ,subgr|ps #ddf ,subsec;n ,factor ,gr|ps '' #dej ,sec;n #aj4b ,! ,simplic;y ( ! ,alt}nat+ ,gr|p ''''''''' #dee ,subsec;n ,hi/orical ,note #dfd ,*apt} #aa ,homomorphisms ''''''' #dgb ,sec;n #aa4a ,gr|p ,homomorphisms '''''''''''' #dgb ,sec;n #aa4b ,! ,isomorphism ,!orems ''''''''''''''''''' #dha ,*apt} #ab ,matrix ,gr|ps & ,symmetry ''''''''''''''''''''' #ejb ,sec;n #ab4a ,matrix ,gr|ps #ejb ,subsec;n ,"s ,facts f #f ,l9e> ,algebra '''''''''' #ejb ,subsec;n ,! ,g5}al & ,special ,l9e> ,gr|ps ''' #eji ,subsec;n ,! ,or?ogonal ,gr|p _% ,o(n) _: ''''''' #eab ,sec;n #ab4b ,symmetry '''''' #ebe ,subsec;n ,! ,wallpap} ,gr|ps '''''''''''''''''' #ecc ,subsec;n ,hi/orical ,note #edh ,*apt} #ac ,! ,/ructure ( ,gr|ps #eei ,sec;n #ac4a ,f9ite ,abelian ,gr|ps '''''''''''''''''''' #efj ,sec;n #ac4b ,solvable ,gr|ps #egf ,*apt} #ad ,gr|p ,ac;ns ''''''''' #eif ,sec;n #ad4a ,gr|ps ,act+ on ,sets ''''''''''''''''''''' #eif ,sec;n #ad4b ,! ,class ,equa;n ''''''''''''''''''' #fjg ,sec;n #ad4c ,burnside's ,c.t+ ,!orem '''''''''''''' #fac ,subsec;n ,a ,geometric ,example '''''''''''''''' #fai ,subsec;n ,swit*+ ,func;ns #fbf ,subsec;n ,hi/orical ,note #fce ,*apt} #ae ,! ,syl{ ,!orems #fdh #g ,sec;n #ae4a ,! ,syl{ ,!orems #fdh ,subsec;n ,hi/orical ,note #ffj ,sec;n #ae4b ,examples & ,applica;ns ''''''''''''''' #ffa ,subsec;n ,f9ite ,simple ,gr|ps '''''''''''''''''' #ffg ,*apt} #af ,r+s ''''''''''''''''' #fhc ,sec;n #af4a ,r+s ''''''''''' #fhc ,sec;n #af4b ,9tegral ,doma9s & ,fields ''''''''' #fig ,sec;n #af4c ,r+ ,homomorphisms & ,id1ls ''' #gjd ,sec;n #af4d ,maximal & ,prime ,id1ls ''''''''''''' #gah ,subsec;n ,hi/orical ,note #gbd ,sec;n #af4e ,an ,applica;n to ,s(tw>e ,design '''''''' #gbg ,*apt} #ag ,polynomials ''''''''' #ged ,sec;n #ag4a ,polynomial ,r+s #gee ,sec;n #ag4b ,! ,divi.n ,algori?m ''''''''''''''''' #gfe ,sec;n #ag4c ,irr$ucible ,polynomials '''''''''''''' #ggg ,subsec;n ,id1ls 9 _% ,f`(x`) _: ''''''' #ghh #h ,subsec;n ,hi/orical ,note #gib ,*apt} #ah ,9tegral ,doma9s ''''' #haj ,sec;n #ah4a ,fields ( ,frac;ns '''''''''''''''''' #haj ,sec;n #ah4b ,factoriza;n 9 ,9tegral ,doma9s '''''''''' #hbb ,subsec;n ,pr9cipal ,id1l ,doma9s ''''''''''''''''' #hbf ,subsec;n ,euclid1n ,doma9s #hcg ,subsec;n ,factoriza;n 9 _% ,d`(x`) _: ''''''''''' #hdc ,subsec;n ,hi/orical ,note #hec ,*apt} #ai ,lattices & ,bool1n ,algebras ''''''''''''''''''''' #hff ,sec;n #ai4a ,lattices '''''' #hff ,subsec;n ,"pially ,ord}$ ,sets ''''''''''''''''''' #hff ,sec;n #ai4b ,bool1n ,algebras ''''''''''''''''' #hhb ,subsec;n ,f9ite ,bool1n ,algebras ''''''''''''''' #hij ,sec;n #ai4c ,! ,algebra ( ,electrical ,circuits ''''' #hii ,subsec;n ,hi/orical ,note #iae ,*apt} #bj ,vector ,spaces '' #ibg #i ,sec;n #bj4a ,def9i;ns & ,examples ''''''''''''''''' #ibg ,sec;n #bj4b ,subspaces ''''' #icb ,sec;n #bj4c ,l9e> ,9dep5d;e #icf ,*apt} #ba ,fields '''''''''''''' #iee ,sec;n #ba4a ,ext5.n ,fields #ief ,subsec;n ,algebraic ,ele;ts ''''''''''''''''' #ifc ,subsec;n ,algebraic ,closure '''''''''''''''' #ihd ,sec;n #ba4b ,splitt+ ,fields #ihi ,sec;n #ba4c ,geometric ,3/ruc;ns ''''''''''''''''' #iih ,subsec;n ,3/ructible ,numb}s '''''''''''''''' #ajjj ,subsec;n ,d|bl+ ! ,cube & ,squ>+ ! ,circle ''''''' #ajab ,subsec;n ,trisect+ an ,angle ''''''''''''''''' #ajac ,subsec;n ,hi/orical ,note #ajae ,*apt} #bb ,f9ite ,fields '''''' #ajbg ,sec;n #bb4a ,/ructure ( a ,f9ite ,field '''''''''''' #ajbg ,sec;n #bb4b ,polynomial ,codes '''''''''''''' #ajdd #aj ,subsec;n ,polynomial ,codes ''''''''''''''''' #ajdh ,subsec;n ,,b* ,codes '''' #ajfe ,*apt} #bc ,galois ,!ory ''''''' #ajhc ,sec;n #bc4a ,field ,automorphisms ''''''''''' #ajhd ,subsec;n ,sep>able ,ext5.ns ''''''''''''''' #ajig ,sec;n #bc4b ,! ,funda;tal ,!orem ''''''''''''''''''' #aajb ,subsec;n ,hi/orical ,note #aabf ,sec;n #bc4c ,applica;ns ''' #aabg ,subsec;n ,solvabil;y by ,radicals '''''''''''''' #aabg ,subsec;n ,9solvabil;y ( ! ,qu9tic '''''''''''''''' #aacg ,subsec;n ,! ,funda;tal ,!orem ( ,algebra '''''' #aadc ,h9ts & ,answ}s to ,select$ ,ex}cises '''''''''''''''''''' #aagi ,colophon '''''''''''''''''''''' #abcf #aa ,colophon ~1,$i;n ,annual ,$i;n #bjbb ~1,website ab/ract4pugets.d4$u ~c#aiig,-#bjbb ,?omas ;,w4 ,judson1 ,rob}t ,a4 ,beez} ,p}mis.n is grant$ to copy1 4tribute &_/or modify ? docu;t "u ! t}ms ( ! ,,gnu ,free ,docu;ta;n ,lic5se1 ,v}.n #a4b or any lat} v}.n publi%$ by ! ,free ,s(tw>e ,f.da;n2 ) no ,9v>iant ,sec;ns1 no ,front-,cov} ,texts1 & no ,back-,cov} ,texts4 ,a copy ( ! lic5se is 9clud$ 9 ! app5dix 5titl$ 8,,gnu ,free ,docu;ta;n ,lic5se40 #a ,ac"kl$ge;ts ,i wd l to ac"kl$ge ! foll{+ review}s = _! help;l com;ts & su7es;ns4 _4 ,david ,&}son1 ,univ}s;y ( ,t5;see1 ,knoxville _4 ,rob}t ,beez}1 ,univ}s;y ( ,puget ,s.d _4 ,myron ,hood1 ,cali=nia ,polyte*nic ,/ate ,univ}s;y _4 ,h}b}t ,kasube1 ,bradley ,univ}s;y _4 ,john ,kurtzke1 ,univ}s;y ( ,portl& _4 ,9essa ,levi1 ,univ}s;y ( ,l|isville _4 ,ge(frey ,mason1 ,univ}s;y ( ,cali=nia1 ,santa ,cruz _4 ,bruce ,m}icle1 ,mankato ,/ate ,univ}s;y _4 ,kimmo ,ros5?al1 ,union ,college _4 ,m>k ,teply1 ,univ}s;y ( ,wiscons9 ,i wd al l to ?ank ,/eve ,quigley1 ,m>nie ,pommett1 ,ca?ie ,gri691 ,kelle ,k>%ick1 & ! 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