数学专业英语

数学专业英语

Lesson1

MathematicsasaLanguageofScience

assertvt.断言；坚持主张；维护表明

qualitativeadj.性质的；定性的

quantitativeadj.量的；数量的；定量的；与数量有关的

astronomyn.天文学

postulate

n.假定,基本条件,基本原理vt.要求,假定vi.要求

hypothetical

adj.假设的,假定的,爱猜想的

Lesson2

deduction

n.减除,扣除,减除额,推论,演绎

inductionn.归纳；归纳法；归纳所得之结论

verificationn.验证；证实

correlate

vt.使相互关联vi.和...相关

discardvt.丢弃,抛弃v.放弃

discreditn.不信任；失信

consistentadj.一致的,调和的,坚固的,[数、统]相容的

inadequacy

n.不充分,不适当,不适合,不足额

conic,conical

adj圆锥的；圆锥形的

ellipsen.椭圆,椭圆形ellipt(n.)

hyperbolicadj.双曲线的hyperbola(n.)

parabolicadj.用寓言表达的:抛物线的，像抛物线的parabola(n.)

algebraicadj.代数的,关于代数学的

mineralogyn.矿物学

refraction

n.折光,折射

stimulus

n.刺激物,促进因素,刺激,刺激

impetus

n.冲力推动力；刺激

Lesson3

Axioms,definitionsandTheorems

axiom

n.[数]公理

definition

n.阐明；确定定义；界说

extravagant

adj.奢侈的,浪费的,过分的,放纵的

collinear

adj.在同一直线上的,同线的

convex

adj.凸出的；凸面的

segment

n.部分；片段；节,弓形；圆缺；弧形,线段

conswquently

adv.从而,因此

intermsof

adv.根据,按照,用...的话,在...方面

pretense

n.主张,要求,伪称,借口,自称

Lesson4

GeometryandGeometricalterms

term

n.学期,期限,期间,条款,条件,术语

triangle

n.[数]三角形,三人一组,三角关系

parallelogram

n.平行四边形

straightangle

n.[数]平角

rightangle

n.直角

acuteangle

n.锐角

obtuseangle

n.

钝角

reflexangle

n.优角

rectilinear

adj直线的；由直线组成的；循直线进行的

isoscelestriangle

n.

等腰三角形

equilateraltriangle

n.

等边三角形

righttriangle

n.直角三角形

obtusetriangle

n.钝角三角形

acutetriangle

n.锐角三角形

equiangulartriangle

n.

正三角形,等角三角形

hypotenuse

n.（直角三角形的）斜边

circle

圆

center

中心；中央；圆心

diameter

n.直径

radius

n.

半径,范围,辐射光线,有效航程,范围,界限

circumference

n.

圆周,周围

Lesson5

TheMethodofLimits

limit

n.限度,极限,极点

infinite

adj.无限的；无穷的

infinitesimal

adj.无穷小的,极小的,无限小的

calculus

n.微积分学,结石

exemplify

vt.例证,例示,作为...例子

inscribe

v.记下

polygon

n.[数]多角形,多边形

diminish

v.(使)减少,(使)变小

curvilinear

adj曲线的,由曲线组成的

intuition

n.直觉,直觉的知识

integral

n.[数学]积分,完整,部分

defective

adj.有缺陷的,(智商或行为有)欠缺的

differentialcoefficient

微分系数

arithmetical

adj.算术的,算术上的

convergence

n.集中,收敛

criterion

n.(批评判断的)标准,准据,规范

sequence

n.次序,顺序,序列

irrationalnumbers

n.[数]无理数

domain

，定义域

contradiction

矛盾

reversal

n.颠倒,反转,反向,逆转,撤销

Lesson6

Function

continuousvariable

连续变量;［连续变数］

variation

变分,变化

interval

区间

independentvariable

自变量

dependentvariable

应变量

rectangularcoordinate

直角坐标

abscissa

n.〈数〉横坐标

ordinate

n.[数]纵线,纵座标

gradient

adj.倾斜的

n.梯度,倾斜度,坡度

slope

n.斜坡,斜面,倾斜v.(使)顺斜

Lesson7

DifferentialandIntegralcalculus

differential

adj.微分的

n.微分(differentiation)

Integral

n.[数学]积分,完整,部分(integration)

calculus

n.微积分学,结石

interrelation

n.

相互关系

trigonometry

n.三角法

exponential

adj.指数的,幂数的

logarithm

n.[数]对数

derivative

n.导数；微商

tangent

n.切线,[数]正切

counterclockwise

adj.反时针方向的

adv.反时针方向(clockwise)

definiteintegral

定积分

approximation

n.接近,走近,[数]近似值

culminate

v.达到顶点

mean

n.平均数,中间,中庸

differential

equation

微分方程

extremevalue

n.极值

multipleintegral

多重积分

doubleintegral

lineintegral

functionalanalysis

泛函分析

Lesson8TheConceptofCardinalNumber(I)

cardinalnumber

n.基数（如：1,2,3,...有别于序数）

denumerable

adj.可数的

aggregate

n.合计,总计,集合体

adj.合计的,集合的,聚合的

v.聚集,集合,合计

purport

n.主旨v.声称

fancier

n.空想家,培育动物(或植物)的行家,爱好者

sniff

v.用力吸,嗅,闻到,发觉,轻视,用力吸气

n.吸,闻,吸气声,嗤之以鼻

scheme

n.安排,配置,计划,阴谋,方案,图解,摘要

v.计划,设计,图谋,策划,*n.（计算数学）方法，格式

superior

n.长者,高手,上级

adj.较高的,上级的,上好的,出众的,高傲的

cumbersome

adj.讨厌的,麻烦的,笨重的

instruction

n.指示,用法说明(书),教育,指导,指令

drastically

adv.激烈地,彻底地

conservation

守衡律

quadrature

n.求积,求积分

interpolation

n.插值

extrapolation

n.[数]外推法,推断

internalpoint

内点

identical

adj.同一的,同样的

generalizedsolution

广义解

functional

泛函

hydrodynamics

流体力学，水动力学

divergence

发散（性），梯度，发散量

playanimportant(fundamental...)role

起着重要的（...）作用

integro-interpolationmethod

积分插值法

Variationalmethod

变分方法

comparatively

adv.比较地,相当地

deficiency

n.缺乏,不足

fictive

adj.虚构的,想象上的,虚伪的

self-adjoint(nonself-adjoint)

自治的，自伴的，自共轭的

finiteelementmethod

有限元法

splineapproximation

样条逼近

Particles-in-the-Cell

网格质点法

herald

n.使者,传令官,通报者,先驱,预兆

vt.预报,宣布,传达,欢呼

advection

n.水平对流

phenomenological

adj.现象学的,现象的

fluctuation

n.波动,起伏

optimism

n.乐观,乐观主义

pessimism

n.悲观,悲观主义

unjustified

adj未被证明其正确的

mean-square

均方

dispersion

n.[数]离差,差量

Polynomial

nadj.[数]多项式的

interpolation

插值

arithmetic

n.算术,算法

roundingerrors

舍入误差

multiple

n.倍数,若干

subjective

adj.主观的,个人的

objective

adj.客观的,

outcome

n.结果,成果

pattern

n.样品

toss

v.投,掷

exhaust

vt.用尽,耗尽,抽完,使精疲力尽

divisible

adj.可分的

dice,die

n.骰子

assign

vt.分配,指派

attach

vt.缚上,系上,贴上

v.配属,隶属于

pitfall

n.缺陷

chairperson

主席

mechanics

n.(用作单数)机械学、力学,(用作复数)技巧,结构

statics

n.[物]静力学

dynamics

n.动力学

adequately

adv.充分地

celestial

adj.天上的

macroscopic

adj.肉眼可见的,巨观的

classicalfieldtheory

经典场理论

rigit

adj.刚硬的,刚性的,严格的

elastic

adj.弹性的

plastic

n.可塑的,塑性的,塑料的

quantum

n.量,额,[物]量子,量子论

inception

n.起初,获得学位

pertain

v.适合,属于

gravitation

n.地心吸力,引力作用

tide

n.潮,潮汐,潮流,趋势

monumental

adj.纪念碑的,纪念物的,不朽的,非常的

encompass

v.包围,环绕,包含或包括某事物

ingredient

n.成分,因素

acquainted

adj.有知识的,知晓的

synonymous

adj.同义的

configuration

n.构造,结构,配置,外形

reference

n.提及,涉及,参考,参考书目

inertia

n.惯性,惯量

attribute

特性

momentum

n.动量

proportional

adj.比例的,成比例的,相称的,均衡的

designate

指明

negligible

adj.可以忽略的,不予重视的

projectile

n.射弹adj.发射的

ballistics

n.弹道学,发射学

intractable

adj.难处理的

{MechanicsofaParticle

inconsequenceof

adv.由于的...缘故

exert

vt.尽(力),施加(压力等),努力

v.发挥,竭尽全力,尽

galaxy

n.星系,银河,一群显赫的人,一系列光彩夺目的东

furnish

vt.供应,提供,装备,布置

v.供给

torque

n.扭矩,转矩

moment

力矩的

friction

摩擦

dissipation

n.消散,分散,挥霍,浪费,消遣,放荡,狂饮

infer

v.推断

HookesLawandItsConsequences

elasticity

n.弹力,弹性

constitutive

adj.构成的,制定的

atomistic

adj.原子论的

crack

n.裂缝,噼啪声

v.(使)破裂,裂纹,(使)爆裂

continuummechanics

n.连续介质力学

superposition

n.重叠,重合,叠合

strain

n.过度的疲劳,紧张,张力,应变

vt.扭伤,损伤

v.拉紧,扯紧,(使)紧张,尽力

thermodynamics

n.[物]热力学

reckon

vt.计算,总计,估计,猜想

vi.数,计算,估计,依赖,料想

lesson20

strength强度

load载荷

empirical以经验为依据的

member构件

isolated孤立的

segment部分、段、节

stress应力

strain应变

tension拉伸

shear剪切

bend弯曲

torsion扭转、扭力

insofar在……范围

cohesive内聚性的

tensile拉力、张力

stiffness硬度

furnish供给

Lesson23FluidMechanics

eruption喷发、爆发

turbulent湍流

laminar层流

isothermal等温

isotropic各向同性

prevalent普遍的、流行的

tornado旋风、飓风

eddy旋涡

viscosity粘性、粘度

nonviscous无粘性的

rotation旋转

adiabatic

绝热的

reversible可逆的

isentropic等熵的

instant

瞬时的

streamline流线

streamtube流管

tangential切线的

incompressible不可压缩的

resultant合成的,组合的

downstream下游的,顺流的

elbow弯管,肘

similitude相似性

hydraulic水力的,水力学的

predominante占主导地位

spillway(河或水坝的)放水道,泄洪道

prototype原型,样板

Lesson24MechanicalVibration

repetitive重复的,反复的

periodic周期的,定期的

tidal潮的,像潮的

stationary固定的,不动的

vibratory振动的,摆动的

propagation传播

couple

v.连接,连合

acoustic听觉的,声学的

annoyance烦恼,困惑

adjacent接近的,邻近的

damp阻尼,衰减

restore复职,归还

neutral平衡

excitingforce激励力

resonantadj.共振的,谐振的

stiffness刚度,刚性

proportionality成比例地

inclusion包含,包括

magnitude数值,大小

substantiallyadv.实质上的

perturb干扰,扰乱

resonancen.共振

vibratoryadj.振动的,可知的

perceptible可见的,可知的

adudible听得见的,可闻的

foregoing前述的

impulsive冲击的

shock冲击

Fourierseries傅里叶级数

excitation激发,激励

discrete分离,离散的

contendwith向…作斗争

compressor压气机

fatigue疲劳

perceptible可见的,可知觉的

shredder切菜器

disposal处理

urban都市的

metropolitan大都市的

at-grade在同一水平面上

elevated高架的

guideway导轨

Lesson25AprefecttotheContinuumMechanics

preface序言

continuum连续pl.continuua

rigidbody刚体

contemporary当代的,同时期的

widespread分布广的,普及的

accommodate容纳,使适应

medium介质

plasticity塑性

residual剩余的,残留的

creep蠕变,爬行,塑性变形

aging老化

polymeric聚合(物)的

sandy沙的,沙质的

aubterranean地下的,隐藏的

essence精髓,本质

thermodynamics热力学

self-similar自相似

expedient方便的

sonsolidate把…联合为一体,统一

justify证明…有理

radically根本地,本质上

deliberate从容不迫的,深思熟虑

Lesson33whatisacomputer

Attributev.赋予

medieval中世纪的

astronomer天文学家

Mars火星

resemblevt.像,相似

tediousadj.冗长乏味的

pulp浆状物,果肉

filtervt.过滤

underlyingadj.潜在的,基本的

oren.矿沙,矿石

perceivev.察觉,看见

interventionn.干涉,插入

intelligentadj.有智力的,聪明的

Lesson34Acomputersystem

manipulatevt.操纵,使用

chipn.

芯片

etchvt.蚀刻,蚀镂

fingernail指甲

mountvt.安装,安置

assemblevt.集合,聚集

cabinet橱柜

executevt.执行,实现

paycheckn.支付薪金的支票

barchart直方图

joystick游戏杆

encountervt.遇到,遇上

MathematicalModeling

industry

n.工业,产业,行业,勤奋

commerce

n.商业

complexity

n.复杂(性),复杂的事物,复杂性

career

n.(原意:道路,轨道)事业,生涯,速度

outset

n.开端,开始

essence

n.基本,[哲]本质,香精

advocation

n.(=advocacy)拥护支持

provision

n.供应,(一批)供应品,预备,防备,规定

publicize

v.宣扬

roundabout

adj.迂回的,转弯抹角的

n.道路交叉处的环形路,迂回路线,兜圈子的话

trial-error

vt.n.试制,试生产

maneuverability

n.可操作性,机动性

vehicle

n.交通工具,车辆,媒介物,传达手段

junction

n.连接,接合,交叉点,汇合处

ponder

v.沉思,考虑

contrive

v.发明,设计,图谋

snooker

n.(=snookerpool)彩色台球,桌球

context

n.上下文,文章的前后关系

deviation

n.背离

数学专业英语－Groups

and

Rings

Duringthepresentcenturymodernabstractalgebrahasbecomemoreandmoreimportantasatoolforresearchnotonlyinotherbranchesofmathematicsbuteveninothersciences.Manydiscoveriesinabstractalgebraitselfhavebeenmadeduringthepastyearsandthespiritofalgebraicresearchhasdefinitelytendedtowardmoreabstractionandrigorsoastoobtainatheoryofgreatestpossiblegenerality.Inparticular,theconceptsofgroup,ring,integraldomainandfieldhavebeenemphasized.

Thenotionofanabstractgroupisfundamentalinallsciences,anditiscertainlypropertobeginoursubjectwiththisconcept.Commutativeadditivegroupsaremadeintoringsbyassumingclosurewithrespecttoasecondoperationhavingsomeofthepropertiesofordinarymultiplication.Integraldomainsandfieldsareringsrestrictedinspecialwaysandmaybefundamentalconceptsandtheirmoreelementarypropertiesarethebasisformodernalgebra.

Groups

DEFINITION

Anon-emptysetGofelementsa,b,…issaidtoformagroupwithrespectto0if:

I.

Gisclosedwithrespectto0

II.

TheassociativelawholdsinG,thatis

aо(bоc)=(aоb)оc

foreverya,b,cofG

Ⅲ.

ForeveryaandbofGthereexistsolutionsχandУinGoftheequations

aοχ=b

yοa=b

AgroupisthusasystemconsistingofasetofelementsandoperationοwithrespecttowhichGformsagroup.WeshallgenerallydesignatetheentiresystembythesetGofitselementsandshallcallGagroup.Thenotationusedfortheoperationisgenerallyunimportantandmaybetakeninasconvenientawayaspossible.

DEFINITION

AgroupGiscalledcommutativeorabelianif

aοb=bοa

Foreverya

andb

of

G.

Anelementaryphysicalexampleofanabeliangroupisacertainrotationgroup.WeletGconsistoftherotationsofthespokeofawheelthroughmultiplesof90ºandaοbbetheresultoftherotationafollowedbytherotationb.ThereaderwilleasilyverifythatGformsagroupwithrespecttoοandthataοb=bοa.Thereisnolossofgeneralitywhenrestrictourattentiontomultiplicativegroups,thatis,writeabinsteadof

aοb.

EQUIVALENCE

Inanystudyofmathematicalsystemstheconceptofequivalenceofsystemsofthesamekindalwaysarises.Equivalentsystemsarelogicallydistinctbutweusuallycanreplaceanyonebyanyotherinamathematicaldiscussionwithnolossofgenerality.Forgroupsthisnotionisgivenbythedefinition:letGandG´begroupswithrespectiveoperationsoando´,andlettherebea1-1correspondence

S:

aa´

(ainGanda´inG´)

betweenGandG´suchthat

(aοb)´=a´οb´

foralla,bofG.thenwecallGandG´equivalent(orsimply,isomorphic)groups.

Therelationofequivalenceisanequivalencerelationinthetechnicalsenseinthesetofallgroups.Weagainemphasizethatwhileequivalentgroupsmaybelogicallydistincttheyhaveidenticalproperties.

ThegroupsGandG´oftheabovedefinitionneednotbedistinctofcourseando´maybeo.whenthisisthecasetheself-equivalenceSofGiscalledanautomorphism.

I:

aa

OfG,butotherautomorphismsmayalsoexist.

Rings

AringisanadditiveabeliangroupBsuchthat

I.

thesetBisclosedwithrespecttoasecondoperationdesignatedbymultiplication;thatis,everyaandbofBdefineauniqueelementabofB.

II.

multiplicationisassociative;thatis

a(bc)

=

(ab)c

foreverya,b,cofB.

Ⅲ.Thedistributivelaws

a(b+c)=ab+ac

(b+c)a=ba+ca

holdforeverya,b,cofB.

Theconceptofequivalenceagainarises.

Weshallwrite

B≌B′

tomeanthatBandB′areequivalent.

Vocabulary

Group

群

rigor

严格

ring

环

generalization

推广

integraldomain

整环

Abeliangroup

阿贝尔群

commutativeadditivegroup

可交换加法群

rotation

旋转

automorphism

自同构

数学专业英语－Historical

introduction

of

Calculus

TheTwoBasicConceptsofCalculus

Theremarkableprogressthathasbeenmadeinscienceandtechnologyduringthelastcenturyisdueinlargeparttothedevelopmentofmathematics.Thatbranchofmathematicsknownasintegralanddifferentialcalculusservesasanaturalandpowerfultoolforattackingavarietyofproblemsthatariseinphysics,engineering,chemistry,geology,biology,andotherfieldsincluding,ratherrecently,someofthesocialsciences.

Togivethereaderanideaofthemanydifferenttypesofproblemsthatcanbetreatedbythemethodsofcalculus,welisthereafewsamplequestions.

Withwhatspeedshouldarocketbefiredupwardsothatitneverreturnstoearth?WhatistheradiusofthesmallestcirculardiskthatcancovereveryisoscelestriangleofagivenperimeterＬ?Whatvolumeofmaterialisremovedfromasolidsphereofradius2rifaholeofredius

r

isdrilledthroughthecenter?Ifastrainofbacteriagrowsatarateproportionaltotheamountpresentandifthepopulationdoublesinonehour,byhowmuchwillitincreaseattheendoftwohours?Ifaten-poundforcestretchesanelasticspringoneinch,howmuchworkisrequiredtostretchthespringonefoot?

Theseexamples,chosenfromvariousfields,illustratesomeofthetechnicalquestionsthatcanbeansweredbymoreorlessroutineapplicationsofcalculus.

Calculusismorethanatechnicaltool－itisacollectionoffascinatingandexeitingideathathaveinterestedthinkingmenforcenturies.Theseideashavetodowithspeed,area,volume,rateofgrowth,continuity,tangentline,andotherconceptsfromavarictyoffields.Calculusforcesustostopandthinkcarefullyaboutthemeaningsoftheseconcepts.Anotherremarkablefeatureofthesubjectisitsunifyingpower.Mostoftheseideascanbeformulatedsothattheyrevolvearoundtworatherspecializedproblemsofageometricnature.Weturnnowtoabriefdescriptionoftheseproblems.

Consideracruve

C

whichliesaboveahorizontalbaselinesuchasthatshowninFig.1.Weassumethiscurvehasthepropertythateveryverticallineintersectsitonceatmost.Theshadedportionofthefigureconsistsofthosepointewhichliebelowthecurve

C,abovethehorizontalbase,andbetweentwoparallelverticalsegmentsjoining

C

tothebase.Thefirstfundamentalproblemofcalculusisthis:Toassignanumberwhichmeasurestheareaofthisshadedregion.

Considernextalinedrawntangenttothecurve,asshowninFig.1.Thesecondfundamentalproblemmaybestatedasfollows:Toassignanumberwhichmeasuresthesteepnessofthisline.

Basically,calculushastodowiththepreciseformulationandsolutionofthesetwospecialproblems.Itenablesustodefinetheconceptsofareaandtangentlineandtocalculatetheareaofagivenregionorthesteepnessofagivenangentline.Integralcalculusdealswiththeproblemofareawhiledifferentialcalculusdealswiththeproblemoftangents.

HistoricalBackground

Thebirthofintegralcalculusoccurredmorethan2000yearsagowhentheGreeksattemptedtodetermineareasbyaproceeswhichtheycalledthemethodofexhaustion.Theessentialideasofthis,methodareverysimpleandcanbedescribedbrieflyasfollows:Givenaregionwhoseareaistobedetermined,weinscribeinitapolygonalregionwhichapproximatesthegivenregionandwhoseareawecaneasilycompute.Thenwechooseanotherpolygonalregionwhichgivesabetterapproximation,andwecontinuetheprocess,takingpolygonswithmoreandmoresidesinanattempttoexhaustthegivenregion.ThemethodisillustratedforascmicircularregioninFig.2.ItwasusedsuccessfullybyArchimedes(287－212B.C.)tofindexactformulasfortheareaofacircleandafewotherspecialfigures.

ThedevelopmentofthemethodofexhaustionbeyondthepointtowhichArchimcdcscarriedithadtowaitnearlyeighteencenturiesuntiltheuseofalgebraicsymbolsandtechniquesbecameastandardpartofmathematics.Theelementaryalgebrathatisfamiliartomosthigh-schoolstudentstodaywascompletelyunknowninArchimedes’time,anditwouldhavebeennexttoimpossibletoextendhismethodtoanygeneralclassofregionswithoutsomeconvenientwayofexpressingratherlengthycalculationsinacompactandsimpolifiedform.

Aslowbutrevolutionarychangeinthedevelopmentofmathematicalnotationsbeganinthe16thcenturyA.D.ThecumbersomesystemofRomannumeralswasgraduallydisplacedbytheHindu-Arabiccharactersusedtoday,thesymbols“+”and“-”wereintroducedfortheforsttime,andtheadvantagesofthedecimalnotationbegantoberecognized.Duringthissameperiod,thebrilliantsuccesseoftheItalianmathematiciansTartaglia,CardanoandFerrariinfindingalgebraicsolutionsofcubicandquadraticequationsstimulatedagreatdealofactivityinmathematicsandencouragedthegrowthandacceptanceofanewandsuperioralgebraiclanguage.Withthewidespreadintroductionofwell-chosenalgebraicsymbols,interestwasrevivedintheancientmethodofexhaustionandalargenumberoffragmentaryresultswerediscoveredinthe16thcenturybysuchpioneersasCavalieri,Toricelli,Roberval,Fermat,Pascal,andWallis.

Fig.2.Themethodofexhaustionappliedtoasemicircularregion.

Graduallythemethodofexhaustionwastransformedintothesubjectnowcalledintegralcalculus,anewandpowerfuldisciplinewithalargevarietyofapplications,notonlytogeometricalproblemsconcernedwithareasandvolumesbutalsotojproblemsinothersciences.Thisbranchofmathematics,whichretainedsomeoftheoriginalfeaturesofthemethodofexhaustion,receiveditsbiggestimpetusinthe17thcentury,largelyduetotheeffortsofIsaacNewion(1642—1727)andGottfriedLeibniz(1646—1716),anditsdevelopmentcontinuedwellintothe19thcenturybeforethesubjectwasputonafirmmathematicalbasisbysuchmenasAugustin-LouisCauchy(1789-1857)andBernhardRiemann(1826-1866).Furtherrefinementsandextensionsofthetheoryarestillbeingcarriedoutincontemporarymathematics

Vocabulary

geology

地质学

decimal

小数，十进小数

biology

生物学

discipline

学科

socialsciences

社会科学

contemporary

现代的

disk(disc)

圆盘

bacteria

细菌

isoscelestriangle

等腰三角形

elastic

弹性的

perimeter

周长

impetus

动力

volume

体积

proportionalto

与…成比例

center

中心

inscribe

内接

steepness

斜度

solidsphere

实心球

methodofexhaustion

穷举法

refinement

精炼，提炼

polygon

多边形，多角形

cumbersome

笨重的，麻烦的

polygonal

多角形

fragmentary

碎片的，不完全的

approximation

近似，逼近

background

背景

学专业英语－How

to

Organize

a

paper

(For

Beginers)?

Theusualjournalarticleisaimedatexpertsandnear-experts,whoarethepeoplemostlikelytoreadit.Yourpurposeshouldbesayquicklywhatyouhavedoneisgood,andwhyitworks.Avoidlengthysummariesofknownresults,andminimizethepreliminariestothestatementsofyourmainresults.Therearemanygoodwaysoforganizingapaperwhichcanbelearnedbystudyingpapersofthebetterexpositors.Thefollowingsuggestionsdescribeastandardacceptablestyle.

Chooseatitlewhichhelpsthereaderplaceinthebodyofmathematics.Auselesstitle:ConcerningsomeapplicationsofatheoremofJ.Doe.A.goodtitlecontainsseveralwell-knownkeywords,e.g.Algebraicsolutionsoflinearpartialdifferentialequations.Makethetitleasinformativeaspossible;butavoidredundancy,andeschewthemedievalpracticeoflettingthetitleserveasaninflatedadvertisement.Atitleofmorethantenortwelvewordsislikelytobemiscopied,misquoted,distorted,andcursed.

Thefirstparagraphoftheintroductionshouldbecomprehensibletoanymathematician,anditshouldpinpointthelocationofthesubjectmatter.Themainpurposeoftheintroductionistopresentaroughstatementoftheprincipalresults;includethisstatementassoonasitisfeasibletodoso,althoughitissometimeswelltosetthestagewithapreliminaryparagraph.Theremainderoftheintroductioncandiscusstheconnectionswithotherresults.

Itissometimesusefultofollowtheintroductionwithabriefsectionthatestablishesnotationandreferstostandardsourcesforbasicconceptsandresults.Normallythissectionshouldbelessthanapageinlength.Someauthorsweavethisinformationunobtrusivelyintotheirintroductions,avoidingtherebyadullsection.

Thesectionfollowingtheintroductionshouldcontainthestatementofoneormoreprincipalresults.Therulethatthestatementofatheoremshouldprecedeitsproofatriviality.Areaderwantstoknowtheobjectiveofthepaper,aswellastherelevanceofeachsection,asitisbeingread.Inthecaseofamajortheoremwhoseproofislong,itsstatementcanbefollowedbyanoutlineofproofwithreferencestosubsequentsectionsforproofsofthevariousparts.

Striveforproofsthatareconceptualratherthancomputational.Foranexampleofthedifference,seeAMathematician’sMiscellanybyJ.E.Littlewood,inwhichthecontrastbetweenbarbaricandcivilizedproofsisbeautifullyandamusinglyportrayed.Toachieveconceptualproofs,itisoftenhelpfulforanauthortoadoptaninitialattitudesuchasonewouldtakewhencommunicatingmathematicsorally(aswhenwalkingwithafriend).Decidehowtostateresultswithaminimumofsymbolsandhowtoexpresstheideasoftheproofwithoutcomputations.Thenaddtothisframeworkthedetailsneededtoclinchtheresults.

Omitanycomputationwhichisroutine(i.e.doesnotdependonunexpectedtricks).Merelyindicatethestartingpoint,describetheprocedure,andstatetheoutcome.

Itisgoodresearchpracticetoanalyzeanargumentbybreakingitintoasuccessionoflemmas,eachstatedwithmaximumgenerality.Itisusuallybadpracticetotrytopublishsuchananalysis,sinceitislikelytobelonganduninteresting.Thereaderwantstoseethepath-notexamineitwithamicroscope.Apartoftheargumentisworthisolatingasalemmaifitisusedatleasttwicelateron.

Therudimentsofgrammarareimportant.Thefewlineswrittenontheblackboardduringanhour’slectureareaugmentedbyspokencommentary,andaattheendofthedaytheyarewashedawaybyamercifuljanitor.Sincethepublishedpaperwillforeverspeakforitsauthorwithoutbenefitofthecleansingsponge,carefulattentiontosentencestructureisworthwhile.Eachauthormustdevelopasuitableindividualstyle;afewgeneralsuggestionsareneverthelessappropriate.

Thebarbarismcalledthedanglingparticiplehasrecentlybecomemoreprevalent,butnotlessloathsome.“Differentiatingbothsideswithrespecttox,theequationbecomes”iswrong,because“theequation”cannotbethesubjectthatdoesthedifferentiation.Writeinstead“differentiatingbothsideswithrespecttox,wegettheequation,”or“Differentiationofbothsideswithrespecttoxleadstotheequation”

Althoughthenotionhasgainedsomecurrency,itisabsurdtoclaimthatinformal“we”hasnoproperplaceinmathematicalexposition.Strictformalityisappropriateinthestatementofatheorem,andcasualchattingshouldindeedbebanishedfromthosepartsofapaperwhichwillbeprintedinitalics.Butfifteenconsecutivepagesofformalityarealtogetherforeigntothespiritofthetwentiethcentury,andnearlyallauthorswhotrytosustainanimpersonaldignifiedtextofsuchlengthsucceedmerelyinerectingelaboratemonumentstoslumsiness.

Asentenceoftheform“ifP,Q”canbeunderstood.However“ifP,Q,R,S,T”isnotsogood,evenifitcanbededucedfromthecontextthatthethirdcommaistheonethatservestheroleof“then.”Thereaderislookingatthepapertolearnsomething,notwithadesireformentalcalisthenics.

Vocabulary

preliminary序,小引(名)开端的,最初的(形)

eschew

避免

medieval

中古的，中世纪的

inflated

夸张的

comprehensible

可领悟的，可了解的

pinpoint

准确指出（位置）

weave

插入，嵌入

unobtrusivcly

无妨碍地

triviality

平凡琐事

barbarism

野蛮，未开化

portray

写真，描写

clinch

使终结

rudiment

初步，基础

commentary

注解，说明

janitor

看守房屋者

sponge

海绵

danglingparticiple不连结分词

prevalent流行的，盛行

loathsome可恶地

absurd

荒谬的

banish

排除

sustain

维持，继续

slumsiness

粗俗，笨拙

monument

纪念碑

calisthenics

柔软体操，健美体操

notes

1.

本课文选自美国数学会出版的小册子Amamualforauthorsofmathematicalpaper的一节，本文对准备投寄英文稿件的读者值得一读。

2.

Chooseatitlewhichhelpsthereaderplaceinthebodyofmathematics.

意思是：选择一个可帮助读者进入数学核心的标题。

3．Foranexampleofthedifference,……inwhichthecontrastbetweenbarbaricandcivilizedproofsisbeautifullyandamusinglyportrayed.

意思是：作为这种差别的一个例子，可参看J.E.LittlewoodAmathematician’sM