数学专业英语
尸冷-钣金工是做什么的
2023年2月20日发(作者：莱茵电梯)学专业英语－HowtoWriteMathematics?
HowtoWriteMathematics?
------HonestyistheBestPolicy
Thepurposeofusinggoodmathematicallanguageis,ofcourse,tomaketheu
nderstandingofthesubjecteasyforthereader,
styleshouldbegoodnotinthesenseofflashybrilliance,butgoodinthese
poseistosmooththereader’swanted,
notpedantry;understanding,notfuss.
Theemphasisintheprecedingparagraph,whileperhapsnecessary,mightsee
mtopointinanundesirabledirection,andIhastentocorrectapossiblemisin
voidingpedantryandfuss,Idonotwanttoavoidrigoran
dprecision;meantoadvise
ayoungauthortobeverysoslightlybutveryverycleverlydishonestandto
mes,forinstance,theremaybenobetterwayt
caseitistheauthor’s
dutytocarryitout,inpublic;thehecandotoalleviateitistoextendhiss
ympathytothereaderbysomephrasesuchas“unfortunatelytheonlyknown
proofisthefollowingcumbersomecomputation.”
ta
inpoint,havingproudlyprovedapropositionP,youfeelmovedtosay:“Not
e,however,thatpdoesnotimplyq”,andthen,thinkingthatyou’vedonea
goodexpositoryjob,tivesmaybeper
fectlypure,ewallabo
utthesubject,hewouldn’tbereadingyou;forhimthenonimplicationis,qui
telikely,vious?(Sayso.)Willacounterexamplebesuppl
iedlater?(Promiseitnow.)Isitastandardpresentpurposesirrelevantpartof
theliterature?(Giveareference.)Or,horribledictum,doyoumerelymeanth
atyouhavetriedtoderiveqfromp,youfailed,andyoudon’tinfactknow
whetherpimpliesq?(Confessimmediately.)anyevent:takethereaderintoy
ourconfidence.
Thereisnothingwrongwithoftenderided“obvious”and“easytosee”,b
whenyouwrotethatso
methingwasobvious,,amonth,ortwomonths,or
sixmonthslater,youpickedupthemanuscriptandre-readit,didyoustillthi
nkthatsomethingwasobvious?(Afewmonths’ripeningalwaysimprovesma
nuscripts.)Whenyouexplainedittoafriend,ortoaseminar,wasthesometh
ingatissueacceptedasobvious?(Ordidsomeonequestionitandsubside,mu
ttering,whenyoureassuredhim?Didyourassurancedemonstrationorintimida
tion?)theobviousanswerstotheserhetoricalquestionsareamongtherulesth
atshouldcontroltheuseof“obvious”.Thereisthemostfrequentsourceo
fmathematicalerror:makethatthe“obvious”istrue.
Itshouldgowithoutsayingthatyouarenotsettingouttohidefactsfromthe
reader:msayingnowisthatyou
shouldnothidethestatusofyourstatementsandyourattitudetowardthemeit
eryoutellhimsomething,tellhimwhereitstands:thishasbeen
proved,thathasn’t,thiswillbeproved,thatwon’izetheimportan
sonsayingthattheyareobviousistoputt
yoursayingsomakesan
occasionalreaderangryatyou,agoodpurposeisservedbyyourtellinghim
,ofcourse,’tle
tthereaderdown;tiousness,bluff,andconc
ealmentmaynotgetcaughtoutimmediately,butmostreaderswillsoonsense
thatthereissomethingwrong,andtheywillblameneitherthefactsnorthem
selves,butquiteproperly,tehonestymakesforgreatestclar
ity.
---------s
vocabulary
flashy一闪的counter-example反例
unobtrusiveness谦虚dictum断言；格言
forestall阻止，先下手deride嘲弄
anticipate预见subside沉静
pedantry迂腐；卖弄学问mutter出怨言，喃喃自语
fuss小题大做intimidation威下
reconcilable使一致的rhetorical合符修辞学的
gloss掩饰pretentiousness自命不凡
alleviate减轻，缓和bluff欺骗
implication包含，含意concealment隐匿
notes
1.本课文选自美国数学学会出版的小册子Howtowritemathematics中.的文章第9节
poseissmooththereader’way,
yiswhat’swanted,notpedantry;understanding,notfuss.
意思是：目的是为读者扫清阅读上的障碍，即预先设想读者会遇到什么困难，并力求避免出现这类困难。
我们需要的是清晰明了，而不是故弄玄虚。这里fuss的意思是“小题大做”。Understanding后面省去is
what’swanted以避免重复。
meantoadviseayoungauthortobeeversoslightlybutveryverycleverlydishonestan
dtoglossoverdifficulties.
意思是：我的意思是青年的作者绝不可有哪怕只是些少，当却是掩饰得非常巧妙得虚伪，我也劝告他们不
要去掩饰困难。
4．HereisthesortofthingImeanbythancompletehonesty.
意思是：这就是我所认为的不够完全诚实的那类事情（东西）。注意：Hereis的意思是：“这里就是--
-”，然后把要说的事情在随后给出，若用Thisisthesortofthing---一般是当你把要说的事情已经说了然
后用指示代词This来概括所说的事，注意这一区分。
5．Inanyevent:takethereaderintoyourconfidence.
意思是：在任何情况，要敢于对读者讲出真相。这里take---intoone’sconfidence意思是：“对---吐露
秘密；把---当成心腹朋友”。
6．Don’tletthereaderdown..
意思是：不要使读者丧气。这里down是形容词。
7．Completehonestymakesforgreatestclarity.
意思是：彻底的诚实就是最大的明嘹。Makefor是“有助于”的意思。这样简洁而又充满哲理的句子
还有Emphasizetheimportantminimizethetrivial.
Exercise
(MiscellaneousExercises)
Ⅰ.Fillineachblankwithasuitableword.
edthe________________of.
2.p(x)=isa_________of_________n.
a___________________.
edthe________of.
phof(p>0)isa___________.
calleda_________________sequence.
_________oftwoequationswiththree_______.
ssuchasandπarecalled________numbers.
ationbetweenthecelementsofasetofrealnumbersdenoted
by<(or;>)iscalledan_________relation.
ationbetweensets,denotedbyiscalledan_________relation.
Ⅱ.tthe ntences.
continuousfunctiondefinedon[a,b].
entiatingbothsidesofwithrespecttox,theequationbecomesy’=—x/y
ederivativesofbothsidesoftheequation,wegetx+yy’=0.
mtiveofhereCisaconstant.
hathasalimitAatifapproachestoAwhenXtendsto.
Ⅲ.TranslatethefollowingsentencesintoChinese(payattentiontothephrasesunderlined):
owinapositiontoprovethemaintheorem.
ogousargumentgivesaproofofthecorrespondingtheoremfordecreasingfunctions.
diateconsequenceofBolzano’stheoremistheintermediate-valuetheoremforcontinuous
functions.
mthathasnorealsolution,Infactifisarealsolution,thenwehavewhichisimpossibl
e.
earthatthemethoddescribedabovealsoappliestothegeneralcase.
sytoshowthathasderivativesuptoordernatthepointx=0,wheren>1.
Ⅳ.TranslatethefollowingpassageintoChinese:
lpfultointroducethewords”local”and“global”tocontrasttwotypesofsituationsthatfre
econsideringagivensetD,thenwesaythatanyspecificpropertyholds“locally”
atofDifitistreatifandatallpointsnear；thustherewillbeanopenballBapoutandtheproper
therhand,apropertythatholdsatallpointsinDissaidtohold“globall
y”inD.
dyofsequencesisconcernedprimarilywiththefollowingtypeofquestion:ifeachtermof
asequencehasacertainproperty,suchascontinuity,differentiabilityorintegrability,towhatextendist
hispropertytransferredtothelimitfunction?