数学专业英语－How to Write Mathematics?

yunjiang · 发表于 2004-5-6 09:55:13

<H1 ><A>How to Write Mathematics?</A></H1>
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align=center>------ Honesty is the Best Policy
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>The purpose of using good mathematical language is, of course, to make the understanding of the subject easy for the reader, and perhaps even pleasant. The style should be good not in the sense of flashy brilliance, but good in the sense of perfect unobtrusiveness. The purpose is to smooth the reader’s wanted, not <v:shapetype><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></v:shapetype><v:shape><v:imagedata></v:imagedata></v:shape>pedantry; understanding, not fuss.
 The emphasis in the preceding paragraph, while perhaps necessary, might seem to point in an undesirable direction, and I hasten to correct a possible misinterpretation. While avoiding pedantry and fuss, I do not want to avoid rigor and precision; I believe that these aims are reconcilable. I do not mean to advise a young author to be very so slightly but very very cleverly dishonest and to gloss over difficulties. Sometimes, for instance, there may be no better way to get a result than a cumbersome computation. In that case it is the author’s duty to carry it out, in public; the he can do to alleviate it is to extend his sympathy to the reader by some phrase such as “unfortunately the only known proof is the following cumbersome computation.”
Here is the sort of the thing I mean by less than complete honesty. At a certain point, having proudly proved a proposition P, you feel moved to say: “Note, however, that p does not imply q”, and then, thinking that you’ve done a good expository job, go happily on to other things. Your motives may be perfectly pure, but the reader may feel cheated just the same. If he knew all about the subject, he wouldn’t be reading you; for him the nonimplication is, quite likely, unsupported. Is it obvious? (Say so.) Will a counterexample be supplied later? (Promise it now.) Is it a standard present purposes irrelevant part of the literature? (Give a reference.) Or, horrible dictum, do you merely mean that you have tried to derive q from p, you failed, and you don’t in fact know whether p implies q? (Confess immediately.) any event: take the reader into your confidence.
There is nothing wrong with often derided “obvious” and “easy to see”, but there are certain minimal rules to their use. Surely when you wrote that something was obvious, you thought it was. When, a month, or two months, or six months later, you picked up the manuscript and re-read it, did you still think that something was obvious? (A few months’ ripening always improves manuscripts.) When you explained it to a friend, or to a seminar, was the something at issue accepted as obvious? (Or did someone question it and subside, muttering, when you reassured him? Did your assurance demonstration or intimidation?) the obvious answers to these rhetorical questions are among the rules that should control the use of “ obvious”. There is the most frequent source of mathematical error: make that the “ obvious” is true.
It should go without saying that you are not setting out to hide facts from the reader: you are writing to uncover them. What I am saying now is that you should not hide the status of your statements and your attitude toward them either. Whenever you tell him something, tell him where it stands: this has been proved, that hasn’t, this will be proved, that won’t. Emphasize the important and minimize the trivial. The reason saying that they are obvious is to put them in proper perspecti e for the uninitiated. Even if your saying so makes an occasional reader angry at you, a good purpose is served by your telling him how you view the matter. But, of course, you must obey the rules. Don’t let the reader down; he wants to believe in you. Pretentiousness, bluff, and concealment may not get caught out immediately, but most readers will soon sense that there is something wrong, and they will blame neither the facts nor themselves, but quite properly, the author. Complete honesty makes for greatest clarity.
 ---------Paul R.Haqlmos

yunjiang · 发表于 2004-5-6 09:55:24

<

0cm 0cm 0pt; TEXT-ALIGN: center" align=center>vocabulary<

0cm 0cm 0pt">flashy 一闪的 counter-example 反例 <

0cm 0cm 0pt">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

yunjiang · 发表于 2004-5-6 09:55:37

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0cm 0cm 0pt; TEXT-ALIGN: center" align=center>notes<

0cm 0cm 0pt 18pt; TEXT-INDENT: -18pt; tab-stops: list 18.0pt; mso-list: l62 level1 lfo30">1. 本课文选自美国数学学会出版的小册子How to write mathematics 中

aul R.Halmos. 的文章第9节2. The purpose is smooth the reader’ way, to anticipates his difficulties and to forestall them. Clarity is what’s wanted, not pedantry; understanding, not fuss.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’s wanted以避免重复。3. I do not mean to advise a young author to be ever so slightly but very very cleverly dishonest and to gloss over difficulties.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．Here is the sort of thing I mean by than complete honesty. 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：Here is 的意思是：“这里就是---”，然后把要说的事情在随后给出，若用This is the sort of thing---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．In any event: take the reader into your confidence. 意思是：在任何情况，要敢于对读者讲出真相。这里take---into one’s confidence意思是：“对---吐露秘密；把---当成心腹朋友”。6．Don’t let the reader down.. 意思是：不要使读者丧气。这里down是形容词。7．Complete honesty makes for greatest clarity. 意思是：彻底的诚实就是最大的明嘹。 Make for 是“有助于”的意思。这样简洁而又充满哲理的句子还有 Emphasize the important minimize the trivial.

yunjiang · 发表于 2004-5-6 09:55:53

<

0cm 0cm 0pt; TEXT-ALIGN: center" align=center>Exercise<

0cm 0cm 0pt"> (Miscellaneous Exercises)<

0cm 0cm 0pt">Ⅰ.Fill in each blank with a suitable word.1. <v:shapetype><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></v:shapetype><v:shape><v:imagedata></v:imagedata></v:shape>is called the ________ ________of <v:shape><v:imagedata></v:imagedata></v:shape>.2.p (x)= <v:shape><v:imagedata></v:imagedata></v:shape> is a_________of_________n.3.<v:shape> <v:imagedata></v:imagedata></v:shape>called a __________ _________.4. <v:shape><v:imagedata></v:imagedata></v:shape> is called the________of <v:shape><v:imagedata></v:imagedata></v:shape>.5.The graph of <v:shape><v:imagedata></v:imagedata></v:shape> (p>0) is a___________.6.<v:shape> <v:imagedata></v:imagedata></v:shape>then <v:shape><v:imagedata></v:imagedata></v:shape>is called a________ _________sequence.7.<v:shape> <v:imagedata></v:imagedata></v:shape>is a_________of two equations with three_______.8.Numbers such as<v:shape> <v:imagedata></v:imagedata></v:shape>and πare called________numbers.9.The relation between the celements of a set <v:shape><v:imagedata></v:imagedata></v:shape>of real numbers denoted by<(or<;>;>) is called an_________relation.10.The relation between sets, denoted by<v:shape> <v:imagedata></v:imagedata></v:shape>is called an_________relation. Ⅱ.Each ofthe following sentences is grammatically wrong. Correct these sentences.1. Let <v:shape><v:imagedata></v:imagedata></v:shape> is a continuous function defined on[a,b].2. Differentiating both sides of<v:shape> <v:imagedata></v:imagedata></v:shape>with respect to x, the equation becomes y’=—x/y3. Take the derivatives of both sides of the equation <v:shape><v:imagedata></v:imagedata></v:shape>,we get x+yy’=0.4. The primtive of<v:shape> <v:imagedata></v:imagedata></v:shape>here C is a constant.5. We say that<v:shape> <v:imagedata></v:imagedata></v:shape>has a limit A at<v:shape> <v:imagedata></v:imagedata></v:shape>if<v:shape> <v:imagedata></v:imagedata></v:shape>approaches to A when X tends to<v:shape> <v:imagedata></v:imagedata></v:shape>.Ⅲ.Translate the following sentences into Chinese (pay attention to the phrases underlined):1. We are now in a position to prove the main theorem.2. An analogous argument gives a proof of the corresponding theorem for decreasing functions.3. An immediate consequence of Bolzano’s theorem is the intermediate-value theorem for continuous functions.4. We claim that <v:shape><v:imagedata></v:imagedata></v:shape>has no real solution, In fact if <v:shape><v:imagedata></v:imagedata></v:shape> is a real solution, then we have <v:shape><v:imagedata></v:imagedata></v:shape>which is impossible.5. It is clear that the method described above also applies to the general case.6. It is easy to show that <v:shape><v:imagedata></v:imagedata></v:shape>has derivatives up to order n at the point x=0,where n>1. Ⅳ.Translate the following passage into Chinese:1. It is helpful to introduce the words”local”and“global”to contrast two types of situations that frequently arise. If we are considering a given set D, then we say that any specific property holds“locally”at <v:shape><v:imagedata></v:imagedata></v:shape>of D if it is tre at <v:shape><v:imagedata></v:imagedata></v:shape>if and at all points near <v:shape><v:imagedata></v:imagedata></v:shape>；thus there will be an open ball B apout <v:shape><v:imagedata></v:imagedata></v:shape> and the property will hold for all <v:shape><v:imagedata></v:imagedata></v:shape>.On the other hand, a property that holds at all points in D is said to hold “globally”in D.2. The study of sequences is concerned primarily with the following type of question:if each term of a sequence <v:shape><v:imagedata></v:imagedata></v:shape>has a certain property, such as continuity, differentiability or integrability, to what extend is this property transferred to the limit function?

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