数学专业英语

第二章精读课文----入门必修2.1数学方程与比例（Mathematics，EquationandRatio）一、词汇及短语：1.changethetermsabout变形2.fullof：有许多的充满的例Thestreetsarefullofpeopleasonaholiday(像假日一样，街上行人川流不息)3.ingroupsoften…4.matchsomethingagainstsb.“匹配”例Longago,whenpeoplehadtocountmanythings,theymatchedthemagainsttheirfingers.古时候，当人们必须数东西时，在那些东西和自己的手指之间配对。5.growoutof源于由…引起例Manyclosefriendshipsgrewoutofcommonacquaintance6.arriveat得出（到达抵达达到达成）例webotharrivedatthesameconclusion(我们俩个得出了相同的结论)7.standfor“表示，代表”8.inturn“反过来，依次”9.bringabout发生导致造成10.ariseoutof引起起源于11.expressby“用…表示”12.occur发生，产生13.comefrom来源于，起源于14.resultingmethod推论法15.beequalto等于的相等的例Twicetwoisequaltofour(2乘以2等于4)16.nomatter无论不管17.mathematicalanalysis数学分析18.differentialequation微分方程19.highermathematics高等数学higheralgebra高等代数20.equationofcondition条件等式二句型及典型翻译1.Foralongperiodofthehistoryofmathematics,thecentricplaceofmathematicalmethodswasoccupiedbythelogicaldeductions“在数学史的很长的时期内，是逻辑推理一直占据数学方法的中心地位”2.Anequationisastatementoftheequalitybetweentwoequalnumbersornumbersymbols.equation：“方程”“等式”等式是关于两个数或数的符号相等的一种陈述3.Insuchanequationeitherthetwomembersarealike,orbecomealikeonperformanceoftheindicatedoperation.这种等式的两端要么一样，要么经过执行指定的运算后变成一样。注“twomembers”表等号的两端alike相同的一样的Ontheperformanceof…中的“on”引导一个介词短语做状语Either…or…4.istrue“成立”5.tomoreandchangetheterms移次和变形withoutmakingtheequationuntrue保持方程同解2.2几何与三角（GeometryandTrigondogy）一、词汇cube立方体、cylinder柱体、geometrical几何的、surface曲面、plane平面、breadth宽度、segment线段弓形（面积）、abound大量存在、prerequisite先决条件、sphere球cone圆锥、triangle三角形、solid立体的立体、straightline直线、linesegment直线段、infinitely无限地、brokenline折线、diameter直径、angle角、prerequisite先决条件、chord弦、blindacceptanceof盲目接受二、典型句子翻译1.Manyleadinginstitutionsofhigherlearninghaverecognizedthatpositivebenefitscanbegainedbyallwhostudythisbranchofmathematics.其中“higherlearning”表示“高学识”“博学”Positive“确实的”“肯定的”全句许多居领导地位的学术机构承认，所有学习这个数学分支的人都将得到确实的收获。2….wefindthelandsurveyorsofthesepeoplere-establishingvanishinglandmarksandboundariesbyutilizingthetruthsofgeometry我们发现这些民族的土地测量者利用几何只是重新确定消失了的土地标志和边界。3.Acircleisaclosedcurvelyinginoneplane,allpointofwhichareequidistantfromafinedpointcalledthecenter.平面上到定点的距离等于定长的所有点组成的图形叫做圆。2.3BasicConceptsoftheTheoryofSetsSectionA1.setsareameansbywhichmathematicianstalkofcollectionsofthingsinanabstractway注bywhich引起一个定语从句talkof“表达译为集合是数学家们用抽象的方式来表达一些事物的集体的工具2.belongto…“属于”3.evenintegers偶数lessthan小于morethan大于4.bedenotedby被记作…5.bereferredtoas被称为…6.exactlythesame完全相同7.therefore,thedefinitionrequiresthatwecallthesesetsequal.因此，根据定义我们认为这两个集合相等8.divisibleby…被…整除SectionB1.Forexample,thesetconsistingofthosepositiveintegerslessthan10.whicharedivisibleby4isasubsetofthesetofallevenintegerslessthan.由小于10且能被4整除的正整数组成的集合是所有小于10的偶数集的子集2.“AB”读作AiscontainedinBorBcontainsA3.A=BABandBAAisequaltoBifandonlyifAiscontainedinB，andBisalsocontainedinA4.referenceto提到涉及关于5.真子集propersubset6.“”emptyset或voidset7.单元集one–elementset2.4整数有理数与实数(Integers,RationalNumbersandRealNumbers)一、专业词语1rationalnumber有理数irrationalnumber无理数2.difference差quotient商3realaxis实轴4.fraction分数denominator分母numerator分子5.数学归纳法：proofbyinduction二、Section-AIntegersandrationalnumbers1.1+1=2Thenumber1plus1isdenotedby22.Strictlyspeaking严格地说3.repeatedadditionof1“反复加1”4.Convenientmethod简便方法5.orderedfield有序域6.Thesum,difference,orproductoftwointegersisaninteger,butthequotientoftwointegersneednotbeaninteger.(两个整数的和、差或积是一个整数，但是两个整数的商未必是一个整数)思考Whatisaninductiveset?Asetofrealnumbersiscalledaninductivesetifithasthefollowingtwoproperties:(a)Thenumber1isintheset(b)Foreveryxintheset,thenumberx+1isalsointheset.三、Section-BGeometricinterpretationofrealnumberaspointsonaline1.befamiliarwith熟悉…befamiliarto被某人熟悉2.Ifxy,thepointxliestotheleftofthepointy“liesto”位于如果xy,byx点位于y点的左侧3.Thisdeviceforrepresentingrealnumbersgeometricallyisaveryworthwhileaidthathelpsustodiscoverandunderstandbettercertainpropertiesofrealnumbers这种用几何来表示实数的办法对于帮助我们更好地发现与理解实数的性质是非常有价值的。§2.5笛卡儿几何学的基本概念（BasicConceptsofCartesianGeometry）一、词组与词汇1.integral积分的、整数的、积分2.calculation计算3.theorigin坐标原点4.coordinatesystem坐标系5anorderedpair一个有序对6.horizontal水平的Perpendicular垂直的7.解析几何：analyticgeometry二、SectionA-ThecoordinatesystemofCartesiangeometry1.Asmentionedearlier,oneoftheapplicationsoftheintegralisthecalculationofarea.译：计算图形的面积是积分的一种重要应用。2.Ifwehopetoarriveatatreatmentofareathatwillenableustodealwithmanydifferentkindsofobjects,wemustfirstfindaneffectivewaytodescribetheseobjects.译：如果我们希望获得面积的计算方法以便能用它来处理多种不同类型的图形，我们就必须首先找出描述这些图形的有效办法。3.Onthex-axisaconvenientpointischosentotherightofOanditsdistancefromOiscalledtheunitdistance.译：在x-轴上O点右边选定一个适当的点，并把它到O点的距离称为单位长度。4.Itisclearthattwoorderedpairs(a,b)and(c,d)representthesamepointifandonlyifwehavea=candb=d.译：易知当(a,b)与(c,d)表示同一点时当且仅当a=cb=dSectionBGeometricfigures1.Bytranslatingtheseconditionsintoexpressions,involvingthecoordinatesxandy,weobtainoneormoreequationswhichcharacterizethefigureinquestion.译：“thefigureinquestion”在谈论中的图形，“该图形”通过把这些条件转化成含有坐标x和y的表达式，我们就得到了一个或多个刻画该图形特征的方程。2.Throughouttheirhistoricaldevelopment,calculusandanalyticgeometryhavebeenintimatelyintertwined.译：微积分与解析几何在它们的发展史上已经互相融合在一起了。3.Adeeperstudyofanalyt