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< ><FONT face="Times New Roman" size=3>The usual journal article is aimed at experts and near-experts, who are the people most likely to read it. Your purpose should be say quickly what you have done is good, and why it works. Avoid lengthy summaries of known results, and minimize the preliminaries to the statements of your main results. There are many good ways of organizing a paper which can be learned by studying papers of the better expositors. The following suggestions describe a standard acceptable style.</FONT></P>
< ><FONT face="Times New Roman" size=3>Choose a title which helps the reader place in the body of mathematics. A useless title: Concerning some applications of a theorem of J. Doe. A. good title contains several well-known key words, e. g. Algebraic solutions of linear partial differential equations. Make the title as informative as possible; but avoid redundancy, and eschew the medieval practice of letting the title serve as an inflated advertisement. A title of more than ten or twelve words is likely to be miscopied, misquoted, distorted, and cursed.</FONT></P>
< ><FONT face="Times New Roman" size=3>The first paragraph of the introduction should be comprehensible to any mathematician, and it should pinpoint the location of the subject matter. The main purpose of the introduction is to present a rough statement of the principal results; include this statement as soon as it is feasible to do so, although it is sometimes well to set the stage with a preliminary paragraph. The remainder of the introduction can discuss the connections with other results.</FONT></P>
<P ><FONT face="Times New Roman" size=3>It is sometimes useful to follow the introduction with a brief section that establishes notation and refers to standard sources for basic concepts and results. Normally this section should be less than a page in length. Some authors weave this information unobtrusively into their introductions, avoiding thereby a dull section.</FONT></P>
<P ><FONT face="Times New Roman" size=3>The section following the introduction should contain the statement of one or more principal results. The rule that the statement of a theorem should precede its proof a triviality. A reader wants to know the objective of the paper, as well as the relevance of each section, as it is being read. In the case of a major theorem whose proof is long, its statement can be followed by an outline of proof with references to subsequent sections for proofs of the various parts.</FONT></P>
<P ><FONT face="Times New Roman" size=3>Strive for proofs that are conceptual rather than computational. For an example of the difference, see A Mathematician’s Miscellany by J.E.Littlewood, in which the contrast between barbaric and civilized proofs is beautifully and amusingly portrayed. To achieve conceptual proofs, it is often helpful for an author to adopt an initial attitude such as one would take when communicating mathematics orally (as when walking with a friend). Decide how to state results with a minimum of symbols and how to express the ideas of the proof without computations. Then add to this framework the details needed to clinch the results.</FONT></P>
<P ><FONT face="Times New Roman" size=3>Omit any computation which is routine (i.e. does not depend on unexpected tricks). Merely indicate the starting point, describe the procedure, and state the outcome.</FONT></P>
<P ><FONT face="Times New Roman" size=3>It is good research practice to analyze an argument by breaking it into a succession of lemmas, each stated with maximum generality. It is usually bad practice to try to publish such an analysis, since it is likely to be long and uninteresting. The reader wants to see the path-not examine it with a microscope. A part of the argument is worth isolating as a lemma if it is used at least twice later on.</FONT></P>
<P ><FONT face="Times New Roman" size=3>The rudiments of grammar are important. The few lines written on the blackboard during an hour’s lecture are augmented by spoken commentary, and aat the end of the day they are washed away by a merciful janitor. Since the published paper will forever speak for its author without benefit of the cleansing sponge, careful attention to sentence structure is worthwhile. Each author must develop a suitable individual style; a few general suggestions are nevertheless appropriate.</FONT></P>
<P ><FONT face="Times New Roman" size=3>The barbarism called the dangling participle has recently become more prevalent, but not less loathsome. “Differentiating both sides with respect to x, the equation becomes---”is wrong, because “the equation” cannot be the subject that does the differentiation. Write instead “differentiating both sides with respect to x, we get the equation---,” or “Differentiation of both sides with respect to x leads to the equation---”</FONT></P>
<P ><FONT face="Times New Roman" size=3>Although the notion has gained some currency, it is absurd to claim that informal “we” has no proper place in mathematical exposition. Strict formality is appropriate in the statement of a theorem, and casual chatting should indeed be banished from those parts of a paper which will be printed in italics. But fifteen consecutive pages of formality are altogether foreign to the spirit of the twentieth century, and nearly all authors who try to sustain an impersonal dignified text of such length succeed merely in erecting elaborate monuments to slumsiness.</FONT></P>
<P ><FONT face="Times New Roman" size=3>A sentence of the form “if P,Q” can be understood. However “if P,Q,R,S,T” is not so good, even if it can be deduced from the context that the third comma is the one that serves the role of “then.” The reader is looking at the paper to learn something, not with a desire for mental calisthenics.</FONT></P> |
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发表于 2004-5-6 09:56:31
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