A showy way to say "use no superfluous letters" is to say "use no letter only once". The way to make the human reader's task less demanding is obvious: Is your research purely theoretical mathematics, in the theorem-proof sense, or does your research involve several different types of activity, for example, modeling a problem on the computer, proving a theorem, and then doing physical experiments related to your work? A reader who likes your paper may want to continue work in your field.

However, you will almost always include a few standard sections: The overworked period is no worse than the overworked comma. Is it a special case of a larger question? A meaningful statement can be false, but a theorem cannot; "a false theorem" is self-contradictory. research paper help in mathematics Since your reader does not know what you will be proving until after he has read your paper, advising him beforehand about what he will read, just as the travel agent prepares his customer, will allow him to enjoy the trip more, and to understand more of the things you lead him to.

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Does your result strengthen a previous result by giving a more precise characterization of something? Does it provide a new proof for an old theorem? Once you have considered the structure and relevance of your research, you are ready to outline your paper. By "theorem" I mean a mathematical truth, something that has been proved.

The primary goal of mathematical writing is to assert, using carefully constructed logical deductions, the truth of a mathematical statement. The statement of the theorem should, first of all, contain exactly the right hypotheses. Remember at this point that although you may have spent hundreds of hours working on your problem, your reader wants to have all these questions answered clearly in a matter of minutes.

If you do mathematics purely for your own pleasure, then there is no reason to write about it. These two goals--to convince your reader of the truth of your deductions, and to allow your audience to see the beauty of your work in relation to the whole of mathematics--will be critical as you develop the outline for your paper. March , , Copenhagen, http: The background will serve to orient your reader, providing the first idea of where you will be leading him.

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Now that we have discussed the formal structure, we turn to the informal structure. In the background, you will give the most explicit description of the history of your problem, although hints and references may occur elsewhere. dissertation equation numbering The presence of "then" can never confuse; its absence can. The body, which will be made up of several sections, contains most of your work.

You should take care not to disappoint them! It goes without saying that any assertion should follow the lemmas and theorems on which it depends. By the time you reach the final section, implications, you may be tired of your problem, but this section is critical to your readers. essay editing software in mobile phone On the contrary, most proofs could be modeled with very complicated graphs, in which several basic hypotheses combine with a few well known theorems in a complex way. Have you proved a stronger result of an old theorem by weakening the hypotheses or by strengthening the conclusions?

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Asking several questions may help you discern the shape and location of your work: Formal and Informal Exposition. It is available from the American Mathematical Society, and serious students of mathematical writing should consult this booklet themselves. Also, for some papers, there may be important implications of your work. You have the latitude to develop the outline in a way which is appropriate for your work in particular.

The primary goal of mathematical writing is to assert, using carefully constructed logical deductions, the truth of a mathematical statement. To honestly and deliberately explain where your work fits into the big picture of mathematical research may require a great deal of humility. March , , Copenhagen, http: