科技英语课后答案.docx

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