科技英语课后答案.docx
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科技英语课后答案.docx
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科技英语课后答案
Unit1Mathematics
PartIESTReading
1.WhoisBertrandRussell?
BertrandArthurWilliamRussell(b.1872–d.1970)wasaBritishphilosopher,logician,essayistandsocialcriticbestknownforhisworkinmathematicallogicandanalyticphilosophy.Hismostinfluentialcontributionsincludehisdefenseoflogicism(theviewthatmathematicsisinsomeimportantsensereducibletologic),hisrefiningofthepredicatecalculusintroducedbyGottlobFrege(whichstillformsthebasisofmostcontemporarylogic),hisdefenseofneutralmonism(theviewthattheworldconsistsofjustonetypeofsubstancethatisneitherexclusivelymentalnorexclusivelyphysical),andhistheoriesofdefinitedescriptionsandlogicalatomism.Russellisgenerallyrecognizedasoneofthefoundersofmodernanalyticphilosophy,andisregularlycreditedwithbeingoneofthemostimportantlogiciansofthetwentiethcentury.
2.WhatisRussell’sParadox?
Russelldiscoveredtheparadoxthatbearshisnamein1901,whileworkingonhisPrinciplesofMathematics(1903).Theparadoxarisesinconnectionwiththesetofallsetsthatarenotmembersofthemselves.Suchaset,ifitexists,willbeamemberofitselfifandonlyifitisnotamemberofitself.Theparadoxissignificantsince,usingclassicallogic,allsentencesareentailedbyacontradiction.Russell'sdiscoverythuspromptedalargeamountofworkinlogic,settheory,andthephilosophyandfoundationsofmathematics.
SectionCPost-readingTask
ReadingComprehension
1.Directions:
Workonyourownandfillintheblankswiththemainidea.
Part1(Para.1):
BriefintroductiontoRussell’sparadox
Part2(Paras.2-5):
TheeffectofRussell’sparadoxonGottlobFrege’ssystem.
Para.2:
Russell’sparadoxdealtaheavyblowtoFrege’sattemptstodevelopafoundationforallofmathematicsusingsymboliclogic.
Para.3:
AnillustrationofRussell’sparadoxintermsofsets
Para.4:
Contradictionfoundintheset.
Para.5:
FregenoticedthedevastatingeffectofRussell’sparadoxonhissystemandinabilitytosolveit.
Part3(Paras.6-8):
SolutionsofferedbymathematicianstoRussel’sparadox
Para.6:
Russell’sownresponsetotheparadoxwithhis"theoryoftypes."
Para.7:
Zermelo'ssolutiontoRussell'sparadox
Para.8:
Whatbecameoftheefforttodevelopalogicalfoundationforallofmathematics?
Part4(Para.9):
CorrespondencebetweenRussellandFregeontheparadox
VocabularyandStructure
2.Directions:
Completethesentenceswiththewordsgiveninthebrackets.Changetheformifnecessary.
1)Thekeytounravelingsuchapparentparadoxesistocharacterizetheinitialsetofpossibilities("initial"meaningbeforeyoureceiveanyextrainformation)andthentoeliminatepossibilitiesbasedonthatextrainformation.(base)
2)Indeed,thisseparationofmeaningisreflectedbythedefinitionof"weak"intheOALD,withadistinctsensereservedforitsusewhenpertainingtothatofsolutions(definition)
3)TheresultingradicalpollutioncontrolprogrammeoutlinedbyNixon,callingfora90percentreductioninvehicleemissionsby1980,notonlyledtohimbeingcredited(albeitbriefly)aspolicyinitiatorofanenvironmentalclean-upbutalsoprovidedhimwiththechancetodealablowtooneofhismostimportantopponentsinthe1972elections,EdmundMuskie(blow)
4)Singapore'scontinuinginvestmentsineducationandtraininghasbroughtatenfoldincreaseinourpoolofInformationTechnologyprofessionalsandtheSingaporeworkerhasbeenconsistentlyratedbyBERIastheworld'sbestintermsoftechnicalskills,attitudeandproductivity.(term)
5)Inthisworkhewasledtotopology,astillnewkindofmathematicsrelatedtogeometry,andtothestudyofshapes(compactmanifolds)ofalldimensions.(lead)
6)Ifthereisnoallowablestringwhichspansthewholegraph,thenwecansearchinthesamewayasdescribedabove,butwherevertherequiredpathdoesnotexistinthetree,checkifthatpositioninthetreeisflaggedforend-of-word(way)
7)Duringthepastcentury,stepsforwardinphysicshaveoftencomeintheformofnewlyfoundparticles;inengineering,morecomplexdevices;inastronomy,fartherplanetsandstars;inbiology,rarergenes;andinchemistry,moreusefulmaterialsandmedications.(form)
8)Asecondreasonformeasurementsisthemoretheoretical,putbyLoveas"thediscoveryofnumericalrelationsbetweenthequantitiesthatcanbemeasuredtoserveasabasisfortheinductivedeterminationoftheformoftheintrinsicenergyfunction."(serve)
9)Thustheoptimumconditionsforcoastalterracedevelopmentwouldseemtobeareaswithsmalltidalranges.Finally,tidalrangeisanimportantfactorinthegenerationoftidalcurrentswhichmaylocallybecomeofgeomorphologicalimportance(become)
10)Theoriginaldoubleentrancedoorstothebookinghallhadbeenreplacedbyanutterlyincongruouspicturewindowashadadjacentbookinghallandwaitingroomwindows.(replace)
3.Directions:
Reorderthedisorderedpartsofasentencetomakeacompletesentence.
1)Asimplewaytodescribetopologyisasa'rubbersheetgeometry'—topologistsstudythosepropertiesofshapesthatremainthesamewhentheshapesarestretchedorcompressed.
2)Sincethemid-1990sscientistshavefloatedtheideathatrepresentationsofnumericquantities,whetherexpressedasdigitsoraswrittenwords,arecodifiedbytheparietalcortex,ahigher-processingregioninthebrainlocatedjustabovetheforehead.
3)Asactivitywasmonitored,locatedjustabovetheforehead,researchersnotedchangesundertheassumptionthatthebrainreducesactivityasitbecomesaccustomedtoastimulusandthenreactivateswhenanovelstimulusispresented.
4)Thathasnotstoppedphysicistsfromdevisingnewalgorithmsforthedevices,whichcancalculatealotfasterthanordinarycomputers—infact,exponentiallyfaster,inquitealiteralsense.
5)Suchadevicewouldbemadeofmetamaterial,athicketofmetalringsorothershapesthatbendslightinfunnyways.
4.Directions:
Changethefollowingsentencesintonominalizedones.
1)Thepassageofnightcouldbemarkedbytheappearanceof18ofthesestars.
2)ThefullproofofFermat'sLastTheoremiscontainedinthesetwopapers.
3)Theconceptoffixed-lengthhours,however,didnotoriginateuntiltheHellenisticperiod.
4)Thereisaprobabilitythatmyfirstsockisredbecauseonlyoneoftheremainingthreesocksisred.
5)TheimportanceofaccuratedatainquantitativemodelingiscentraltousingBayes'stheoremtocalculatetheprobabilityoftheexistenceofGod.
DiscourseUnderstanding
1.C.A"3percentmarginoferror"meansthatthereisa95percentchancethatthesurveyresultwillbewithin3percentofthepopulationvalue.
2.E.Howisitthatasurveyofonly1,000peoplecanreachthislevelofaccuracy?
3.G.Themarginoferrordependsinverselyonthesquarerootofthesamplesize.
4.A.Themarginoferrorisamathematicalabstraction,andthereareanumberofreasonswhyactualerrorsinsurveysarelarger.
5.F.Finally,the3percentmarginoferrorisanunderstatementbecauseopinionschange.
SectionAPre-readingTask
1.WhodiscoveredtheMandelbrotset?
Thisisnotatrickquestion,noteasytoanswer.ManypeopleincludingMandelbrothavelaidclaimtothediscovery.
2.WhywasthesetnamedafterBenoitB.Mandelbrot?
ThesetisnamedafterBenoitB.Mandelbrot,amathematicianattheIBMThomasJ.WatsonResearchCenterbecausehecoinedthetermfractaltodescribephenomena(suchas coastlines,snowflakes,mountainsandtrees)whosepatternsrepeatthemselvesatsmallerandsmallerscales.
3.WhyhastherebeensomuchcontroversyaboutwhodiscoveredtheMandelbrotset?
MandelbrotclaimsthatheandhealonediscoveredtheMandelbrotset,butthereareothermathematicianswhohavechallengedhisclaim.
4.WhatdidthechallengerssayaboutMandelbrot’sclaimofdiscovery?
TwomathematicianssaidthattheyindependentlydiscoveredanddescribedthesetataboutthesametimeasMandelbrotdid.AndanothermathematicianalsoassertedthathisworkonthesetnotonlypredatedMandelbrot'seffortsbutalsohelpedtoguidethem
5.WhydidsomeprofessorssupportMandelbrot’sclaim?
Mandelbrotdeservestohavethesetnamedafterhim,becausehiseffortsbroughtthesettotheattentionofboththepublicandofthepure-mathematicscommunity.
SectionCPost-readingTask
LanguageinUse
1.MatchtheChineseintheleftcolumnwiththeEnglishintherightcolumn.
迭代函数iterativefunction
优先权之争prioritybattle
分形特征fractalproperties
有意义makesense
以越来越小的规模重复同一模式patternsrepeatthemselvesatsmallerandsmallerscales
混沌理论 chaostheory
季刊aquarterlyjournal
数学界themathematicscommunity
波纹线crisplines
会议公报proceedingsofaconference
2.Jointhefollowingshortsentencesintolongerones.
e.g.a.Afractalisgenerallyaroughorfragmentedgeometricshape.
b.Theshapecanbesubdividedinparts.
c.eachpartis(atleastapproximately)areduced-sizecopyofthewhole,apropertycalledd.eachparthasapropertyofself-similarity.
e.g.Afractalisgenerally"aroughorfragmentedgeometricshapethatcanbesubdividedinparts,eachofwhichis(atleastapproximately)areduced-sizecopyofthewhole",apropertycalledself-similarity.
1)Inadditiontocoiningtheterm"fractal"todescribeobjectsandsurfaceswhichareirregularatvariousdimensionsofscale,healsointroducedsuchconceptsas"fractaldimensions"andtheparticularfractalknownastheMandelbrotset,frequentlyrepresentedwiththemathematicalformulaz→z2+c.
2)Itappearedthatthingsweresettlingintoapleasantandfruitfulroutine,withhisschoollesson
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