MATHEMATICALENGLISHMathematicalEnglish，SchoolofAppl.Math.AimoftheCourse:Expectedprogressinthefollowingaspects:.Readingskillsoftheoriginalmathematicalarticlesandbooks.Writingskillsofmathematicalandotherscientificarticles.Translatingskillsofmathematicalarticles:bothtranslationfromChinesetoEnglishandEnglishtoChinese*Reading,writingandtranslationofmathematicalmaterialsshouldbebrife,simple,exactandeasytobeunderstood2SomeEnglishexpressionsofnumbers:ThesetofnumbersconsistsofrealnumbersandpureimaginarynumbersshownasfollowsComplexnumbers(C)Pureimaginarynumbers(I)Realnumbers(R)Rationalnumbers(Q)Irrationalnumbers(Q′)Integers(Z)

Fractions(F)Naturalnumbers(N),Zero,NegativesofNaturalNumbersNotice:ReadingofIntegersone,ten,hundred,thousand,tenthousand,hundredthousand,million.Tenmillion,hundredmillion,billion···3Expressions

ofsomebasicmathematicalsigns:1.Generalsignsofoperation+Plus,positive-Minus,negativeExample:2+3readastwoplusthree

Example:6-2readassixminustwo±Plusorminus,PositiveornegativeExample:readas

equalsplusorminus3Multipliedby,timesExample:

readas5times6or5multipliedby6OveroristoordividedbyExample:readas3over4,threequarters,3dividedby44Proportion

Example:readastheratioof1to2Percent,PercentExample:readas2PercentPermille,permilleExample:readas5permille2.BasicsignsofrelationshipsBeequalto,equalsBeidenticalwith/to,beequivalenttoExample:readascisidenticalwith(to)5,cisequivalentto55BenotequaltoExample:cplusdtimesaisnotequalsto0Beapproximatelyequalto3dividedby7isapproximatelyEqualtozeropointfourtwonineExample:Belessthan,begreaterthanExample:

aislessthanb,cisgreaterthandBelessthanorequalto,begreaterthanorequaltoExample:xisgreaterthanorequaltominus3andlessthanorequalto8Befarlessthan,befargreaterthanExample:cisfargreaterthanminus66xbelongstoAxisanelement(oramember)ofAxdoesnotbelongtoAxisnotanelement(oramember)ofAAiscontainedinBorAisasubsetofBAcontainsBorBisasubsetofAAcapBorAmeetBorAintersectionBAcupBorAjoinBorAunionBAminusBorthedifferencebetweenAandB6SignsofelementaryalgebraAbsolutevalue

Example:

Theabsolutevalueof2timesxplus1equals7FactorialnExample:

Factorial5equals5times4times3times2times1Thesumofthetermsindicated,summationofExample:

Thesumofsnfromnequals1to5TheproductofthetermsindicatedExample:Productofallanfromnequals1toinfinity7max,minmaximumvalue,minimumvalueEample:

Maximumvalueoff(x)Maximumvalueoftheseriesa1toanPowersandrootsExample:

xsquaredxcubedxtothefourth,orxtothepowerfourxtothenth,orxtothepowernxtothepowerminusnxinverseExample:

(square)rootx,thesquarerootofxcuberoot(of)x8Imaginarynumberandtwocommonirrationalnumbers

ratioofthecircumferenceofacircletoitsdiameter,approximatevalue3.14159269Example:

Twotothefourthpowerissixteenfourthroot(of)xnthroot(of)xxplusyallsquaredxoveryallsquaredSomesignsinelemetaryanalysisIntervalsOpenintervalTheopeninterval

referstothesetofallrealnumbersxbetweenleftendpointatotherightendpointb(excludingaandb)witha<x<b.ClosedintervalTheclosedinterval

referstothesetofallrealnumbersxbetweenleftendpointatotherightendpointb(includingaandb)withHalfopen(closed)intervalThehalfopeninterval

refersrealnumbersxbetweenleftendpointatotherightendpointb(includingabutnotb)withtothesetofall10Function

Example:Thefunctionofx

equalsatimesthesquareofx

plusbtimesxplusc,whereaisnotequaltozero.Approach,tendtoExample:approaches(tendsto)infinitylimitExample:Thelimitoff(x)asxtendstox0

isA11infinityExample:Thelimitofxn

asnapproachesinfinityisa.Example:ThelimitasxapproacheszeroThelimitasxapproacheszerofromaboveThelimitasxapproacheszerofrombelowtheintegralfromzerotoinfinityExample:integralfromatoboff(x)dxdoubleintegraloverthedomainDtripleintegraloverthedomainD12fprimex,fdashedxEx