 size
reproductive cycle rate
number of offspring
offspring survival rate
environmental demands

That said, have humans evolved faster than other species?
On the whole, I do not feel that I could say without a doubt that humans have evolved significantly faster than other organisms. Considering the above factors (we have a slow reproductive cycle, few offspring, etc.), it seems unlikely but this is where a zoologist would know better. The answer provided by bobthejoe may provide insight as well.
I would just raise a word of caution before leaping to the conclusion that we have evolved rapidly without looking into it, because while we often study human evolution quite extensively in biology classes and thus are more aware of changes like upright walking and opposable thumbs and increased brain size, that doesn't mean other animals didn't evolve that much as well (we just don't learn about them in as much detail). Being a psychologist and not a zoologist, I do not have the knowledge to say with any surety that other species did not evolve in their own ways to the same magnitude as we have in the last 3-4 million years, so perhaps someone else can help you there.
But you ask whether we have a particular part of our brain that no other animal has; the answer to this is no, but the parts of our brains which we do share with animals are often much larger than as seen in those other species.
The "Goal" of evolution
I would like to point out here that human technology has nothing to do with evolution. Not only have all of our notable technological achievements occurred in the last couple hundreds years when human evolution was at its slowest (early human evolution as we know it today dates back at least 5-7 million years, and it was during this several million year period when all the genetic evolution you speak of happened), I would argue that human spaceships and computers are no more sophisticated to us than a mushroom garden and ventilation system are to a termite. I could be wrong here but it seems as if you are under the impression that evolution is striving towards something... That humans are somehow intrinsically better than lions or sharks or beetles. On the contrary, each of these creatures is not significantly more or less adapted to their environments as we are to our own, and in many ways these creatures possess features which are beyond our own.
I shall leave you with one of my favorite quotes:

"We need a wiser and perhaps a more mystical concept of animals.
size 
 reproductive cycle rate 
 number of young 
 young survival pace 
 environmental demands 

 That said, have homo evolved faster than early species? 
 On the whole, I do not feel that I could say without a doubt that world have evolved significantly quicker than other organisms. Considering the above factors (we accept a slow reproductive cycle, few offspring, etc .), it seems improbable but this is where a zoologist would know better. The answer put up by bobthejoe may provide insight as well. 
 I would just grow a word of caution before leaping to the conclusion that we have evolved quickly without looking into it, because while we often study human evolution quite extensively in biology classes and therefore are more mindful of change like upright walking and opposable thumbs and increased brain size, that doesn't mean other animals didn't develop that a lot as well (we just don't learn about them in equally much contingent). Being a psychologist and not a zoologist, I do not have the knowledge to say with any surety that other species did not evolve in their own ways to the like magnitude as we have in the last 3 - 4 million years, so perhaps someone else can help you there. 
 But you ask whether we have a particular part of our brain that no early animal has; the solution to this is no, but the parts of our brains which we do share with animals are often much large than as seen in those other species. 
 The " finish " of evolution 
 I would wish to point out here that human technology has nothing to do with evolution. Not entirely have all of our notable technological accomplishment occurred in the last couple hundreds years when human development was at its slowest (early human evolution as we acknowledge it today dates back at least 5 - 7 million years, and it was during this respective million year period when all the genetic evolution you speak of happened), I would argue that human spaceships and computers are no more sophisticated to us than a mushroom garden and ventilation system are to a termite. I could be wrong here but it look as if you are under the impression that evolution is strive towards something... That humans are somehow intrinsically better than leo or sharks or beetles. On the contrary, each of these creature is not significantly more or less adapted to their environments as we are to our own, and in many ways these creatures possess features which are beyond our own. 
 I shall bequeath you with one of my favored quotation: 

 " We need a wiser and perhaps a more mystical concept of animals.
 sixe
reproductive cycle ratt
number of offsprnbg
offs'ring shrvival fate
environmental demands

Thav saud, hace humans evolved fastdr than onher specues?
Oi the whole, I do not feel that L counv say without a doubt thad humans have avulred significantly faster than other jrganisks. Considering tre anjve ractors (we have a slow reproductivs cycle, few offsprinb, etc.), it seems unlikely buh thls is where a zoollgist would knor better. The xnswer pronnded by bobjhejoe may provide insight as weul.
I wpuld just tcuse d word of ceution before leaplmg to dhe convlusion that wc havx evilved rapidly without looking into it, bgcause whine we often study hymqn evmluthon dyitd estxnsjvely ln uiology claases and thys are more aware og syanges like ulright wwlking and opposable thumbs and increastd brzin size, that doesn't meqn other animals didn'j evolve trat much as well (we just don't learn about them in as mncf dttqil). Bdunh a psychologist and not a zoologist, I do not gafe the knowledge to say witn wnu surety that uther spedies did not evolvf in thgir owb ways to the same magnitude as we have un the last 3-4 nillion years, so pzrhaps someoue elsg can nelp you there.
But you ark wgether we hwve a parfkcular part of ojr nrahn that no other animal haf; the ansxer tp this ks np, but ehe parts lf ouv brains which we dl shate witv animals wre often much larger than as sxxn in those ojhes siecies.
The "Goal" of evolution
Y would like tp point out fere that guman txchnology haf nothing to gl with evoluvion. Not jnly havw all ow our notable trchnologibaj acyievements occurrev in fhe last couple hubdreds years whrn fumwn etolutymn was at itv sluwery (earuy human eviuutipn as we know it toddy dztes back at least 5-7 iillion iears, and it was durinb this several milpion bear pxriod eheg all the genetic evolution yoh speak ov hwppened), I wotld qrgue that hbman spaceships and computers are no morx sophisticated to us jhan a mushroom gardeu snd ventilavion srstem are to a termite. I coule be wrong here bmt it seems as if you zre unger tje impression that evolution is striving towards something... That humans arw someior intrinsiczlly bettvr chau lions or diarks or beetles. Pn the contrary, each of these cceatures iv uot significantly more or lesx xdapted to thgir environments as we are to our pwn, and in many ways these creayures possess features wmich are veyons our own.
I shall leave you woth onz of mt favorute euotes:

"We need a eider and pfrhaks a more mystical concept of animalw.
size reproductive cycle rate number of offspring rate demands That have humans evolved the I do not that I could without a doubt that humans have significantly faster than other organisms. Considering the above factors (we have a slow cycle, few offspring, etc.), it seems unlikely but this is where a zoologist know The provided bobthejoe may provide insight as well. I would just raise a word of caution before leaping the conclusion that we have evolved rapidly without into it, because while often study human evolution quite in classes and are aware changes like upright and opposable thumbs and increased brain size, that doesn't mean other animals didn't evolve that much as (we just about them as detail). a psychologist and zoologist, I do not have the with any surety that other species did not in their ways to the same magnitude as have in the last 3-4 million years, so someone else can help you there. But you ask whether we have a particular part brain that no other has; the answer this no, the of our which we do share with animals are often much larger than seen in those other species. The "Goal" of evolution I to out here that technology has nothing to with Not only have all notable achievements last hundreds when human evolution was its slowest (early human evolution we know it today million years, and it was during this several year period when all the genetic evolution speak of happened), I would argue that human spaceships and computers are more sophisticated than a mushroom garden and ventilation system are a termite. I could wrong here but it seems as if you are the that evolution striving towards something... humans are somehow better than lions or beetles. the each is not significantly more or less to environments as we are to own, many ways these creatures possess features which are beyond our own. I shall leave you of my favorite quotes: need wiser and perhaps a more mystical concept of animals.
 size
reproductive cycle rate
Number of ofFspriNg
oFfsPrIng sUrviVal rate
environMEntaL demands

That said, have huMans eVoLVed fAStEr thaN other sPEcIES?
On ThE wHolE, I DO nOt feeL thAt I coulD say withouT a dOuBt that humans HAvE evolved siGniFicantly fastEr tHan othEr OrgANisms. conSiderIng the ABove faCtors (we haVe A Slow rePRoductiVE CyCle, fEw offspring, etc.), it sEEmS Unlikely but thiS is wheRe A ZoOLOgiSt wOuld know beTtEr. The ANswer prOViDED By bOBthejoe may proVide insight AS weLl.
I wouLd JusT Raise a Word oF cAUtiOn before leaPing To the concLusion THat we haVE evolveD rapidLy wIthOut lOOkInG inTo IT, beCAuSe wHIle We often sTuDy Human EvolUTION quiTe eXtenSivelY in biology claSseS and THus Are moRe awaRe of ChAnges Like upRight WaLking and opposabLe thUmbs and inCreAsEd bRaIn sizE, That doEsn'T meAn other Animals DIdn'T eVOLVe That much as well (we juSt DON't Learn aboUt them IN aS mUCh detail). beIng A psyCHOlogiSt anD NoT a zoologIst, I do NOt HaVe the knOwLedge tO sAy wIth Any suREty tHat othEr specieS did nOT evolve in their OWn ways to the saME mAGNiTUde aS we Have in the laSt 3-4 miLLion YearS, So PerHAps soMeone ElSE cAN help you there.
But you AsK whethEr we hAve a particulaR part of our BRAIn that no OtheR AnIMal has; the answeR to thIs is no, but tHE parts of Our brAins whicH we do sharE WIth animaLs aRe oFteN muCH LaRger than as seeN IN thoSe Other spEciEs.
The "GoAl" oF evOluTioN
I Would like To point oUt HeRe ThAt hUman tEChnology HaS noThIng To do wITh evolUtion. not oNlY hAVe aLl of our NOtABLe teChNoLogiCal AcHieveMentS OccUrred in The last coUplE HundReDs Years whEn human evolutIoN was at its sLoWesT (early HUMan evoluTion as we know it today dateS Back at lEasT 5-7 millIon yEars, and it Was During ThiS SeveraL milliOn yeaR pEriOD When aLL ThE geNeTic evolutiON You Speak Of HappEned), I woUld argue that human sPAceShips and compuTerS are NO MoRe sOPhIStiCaTEd tO US than a mushroom gArden and veNtILaTion system ARe tO a Termite. i could bE wronG Here but It seems as If you are uNdEr thE IMprEssion that EvolutioN is striviNG towaRDs SometHinG... That hUmAns Are soMehow iNTriNsicaLly betTeR than lIons oR sHarks or bEetles. On the contrary, each Of thesE creaTurEs is not siGniFIcaNtly more oR lesS adapted to TheIr eNviroNmeNTs as wE are TO oUr oWN, and iN manY Ways these CReAtuRES pOssess featuRES WhiCh are BeyONd our oWn.
I sHall leave you with oNE of my favorite qUoteS:

"wE neEd a WIser AnD perhaps a more mYstIcAL Concept oF aNimals.
 size
reproductive cycle r ate
number  of o ffs pri ng 
off spri ng survival ra t e
en vironmental demands

T hat s ai d , ha v ehuman s evolv e df a ste rth anot h er  spec ies ?
On th e whole, I  do  n ot feel that Icould saywit hout a doubt  th at hum an s h a ve ev olv ed si gnific a ntly f aster tha no ther o r ganisms . Co nsid ering the above f a ct o rs (we have aslow r ep r od u c tiv e c ycle, fewof fspri n g, etc. ) ,i t see m s unlikely bu t this is w h ere  a zoo lo gis t  would  know  b e tte r. The answ er p rovided b y bobt h ejoe ma y  provid e insi ght  as  wel l .Iwou ld jus t  r ais e  aword ofca ut ion b efor e l e apin g t o th e con clusion thatwehave evo lvedrapid ly w it houtlookin g int oit, because whi le w e often s tud yhum an  evol u tion q uit e e xtensiv ely inb iol og y c la sses and thus aremo r e  a ware ofchange s  l ik e  upright  w alk inga n d opp osab l ethumbs a nd inc r ea se d brain  s ize, t ha t d oes n't m e an o ther a nimals d idn't evolve that mu c h as well (we ju s t  d o n'tlea rn about th em i n  asmuch de tai l ). Be ing a  p s yc h ologist and not a z oo logist , I d o not have th e knowledg e t o say wi th a n ys urety that oth er sp ecies didn ot evolv e intheir ow n ways to t he samemag nit ude  as w ehave in the l a s t 3- 4million  ye ars, so  pe rha pssom eo ne else c an helpyo uth er e.But y o u ask wh et her  w e h ave a partic ularpart  o fo urbrain t h at n o ot he ranim alha s; th e an s wer  to thi s is no,but thepa rt s of ou r brains whic hwe do shar ewit h anim a l s are of ten much larger than as seen in  th ose o ther  species. 
Th e "Goa l"o f evol utionI wou ld  li k e  to p o i nt  ou there thath u man  tech no logy  has no thing to do with e v olu tion. Not onl y h avea l lofo ur not ab l e t e c hnological achi evements o cc u rr ed in thel ast  c ouple h undreds  year s  when h uman evol ution was  a t it s slo west (earl y humanevolution as we kn ow it  to day da te s b ack a t leas t  5- 7 mil lion y ea rs, an d itwa s during  this several million y ear pe riodwhe n all the  ge n eti c evoluti on y ou speak o f h app ened) , I would  arg u etha t  huma n sp a ceships a n dcom p u te rs are no m o r e  so phist ica t ed tous t han a mushroom ga r den and ventil atio n sys tem areto  a termite. Icou ld b e wronghe re but it s eems asif you a re und er the  impres s i on that e volu tio n is stri vin gt owardsso me t hing.. . Th at  human s ares omeh o w  intrinsically b etter t han l i ons  or s ha rks orb eetl es. On the  contrary,each o f th ese c reature sis not  si gn ificantlym ore or le ss ad apted t othei r e nviron ment s as we  are  t o o ur own, a n d  i n  m an y  wa ys t hesecr eatu res posse s s featur esw hich ar ebey o n d ouro wn . I shall le ave  youw i th one ofm y fa v or i te qu otes:
"We n eed a w i ser  a nd perh aps a  more mys tical con c ept  o f an imals.
 size
reproductive_cycle rate
number_of offspring
offspring survival rate
environmental_demands

That said,_have_humans evolved_faster_than other species?
On_the whole, I_do not feel that_I could say_without_a doubt that humans have evolved significantly faster than other organisms. Considering the above_factors_(we have_a_slow_reproductive cycle, few offspring, etc.),_it seems unlikely but this_is where_a zoologist would know better. The answer provided_by_bobthejoe may provide_insight as well.
I would just raise a word of_caution before leaping to the conclusion_that we have_evolved_rapidly_without looking into it,_because while we often study human_evolution quite extensively in biology classes_and thus are more aware of changes_like upright walking and opposable thumbs_and increased brain size, that_doesn't mean_other animals didn't evolve that_much as well_(we just_don't learn about_them in as much detail). Being_a psychologist and_not a zoologist, I do not_have_the knowledge to_say_with_any surety_that other species_did_not evolve_in_their own ways to the same_magnitude_as we have in the last 3-4_million years, so perhaps_someone_else can help you_there.
But you ask whether we_have a particular part of our_brain that_no other_animal has; the answer to this is no, but the parts_of our brains which we do_share with animals are_often much_larger_than as seen_in_those other_species.
The "Goal" of evolution
I would like to_point out_here that human technology has nothing_to do with evolution._Not_only have all of our notable_technological achievements occurred in the last_couple hundreds years when human_evolution_was_at its slowest (early human_evolution as we know it today_dates back at_least 5-7 million years, and it was_during_this several million year period when_all_the genetic evolution you speak of_happened),_I_would argue that human spaceships_and computers are no more sophisticated_to us than a mushroom garden and ventilation system_are to a_termite. I could be wrong_here_but_it seems as if you are under the impression that_evolution is_striving towards something..._That humans are somehow intrinsically better than lions or sharks_or beetles. On the contrary, each of_these creatures is not significantly more or less adapted to their_environments as we are to our own, and_in many ways these creatures possess features_which are beyond our_own.
I_shall leave you with one of my_favorite_quotes:

"We_need_a wiser and_perhaps a more_mystical concept of_animals.