Things are easily forgiven at the ends of sections if the section already had good results. These remarks could also lead onto the next section. But don't overdo that since the beginning of the next section is going to reintroduce itself anyway. E., if you're setting up the next section it should be in a subtle way that doesn't overlap with the official set-up which will appear there. General guide to Style, bad writing often goes hand-in-hand with murky thinking, so by writing clearly you are forced to clarify your understanding also. Thinking about layout, ordering of sentences and even simple things like punctuation are very important and can plan have a surprisingly good effect on your own understanding of the material. To some extent, the best rule of good writing is to write and write. Eventually it gets better. In the meantime, some things to watch out for are as follows.
Ideally, the proof of the main theorem should use as many as possible of the lemmas and propositions already proven, to show that they were all needed and worthwhile. Statements of theorems etc should be as self-contained as possible. Under this constraint, the shorter ones are the most powerful,. Pack the most punch. A punchy' theorem can be achieved by properly setting up the relevant background in the preamble and keeping background material out of the statement itself (as much as possible that is consistent with being self-contained notationally). The statement itself should be boiled down to the part that is really new and important. The end of the section is a good place to put any informal remarks. Anything you want to claim, assert or conjecture but which you haven't thought through formally to make a theorem, can appear here.
Smart Is the new Rich: If you can't Afford It, put It Down
Don't try to save space by building into your propositions repeats of other people's results. They should contain only results that are new, no matter how logical it would be to mention the other results not proven by you (that would be ok in a book or thesis or review article, but research papers should only contain the incremental data). In now other words, some of the stuff you want to put down is all part of the beautiful logical picture, but that's too bad. Unless you personally have something new and worthwhile to say about it, you have no business to be recalling it here (maybe in the intro with citations as motivation) and also should not be building it in mixed with your own results. As well as the logically-dictated tendency to repeat, we all have a human weakness to think that what we spent hours figuring out for ourselves is partly ours. This is a demon to be resisted.
Previous work is previous dealers work and don't be too proud to say you are using it, and whose it is you are using. You should ask yourself how would you feel if somebody developed your work and integrated it into theirs without being clear about your contribution. Results can be organised as lemmas technical results you need later but not of self-contained interest, propositions moderately interesting new results, and theorem main new results. Each of these should be an irreducible 'gem. Break up theorems etc with disjoint parts into propositions leading up to the denouement of your main theorem. You can follow these with some corollaries, which are more like tasty desserts. The proof of a theorems or proposition should be substantial and not a cheap logical trick in which it's immediate from some other work that's a corollary or a remark.
This should include technical remarks on notation to be used and basic references such as books for conventions. You can recall in this section for clarity things that you should be ashamed to publish in the later sections. If a lot of machinery which you did not invent is to be used, this is the place to develop it or give references. Remember, however, that you are not writing a thesis here: your goal is not to redo the work of persons a, b, c (which you may well have done in your notes while reading them, but that's tough). The goal is rather to make enough concise references or explanations so that exactly how you intend things to be defined, which conventions exactly you are using etc are all completely clear.
Find ways to state cut-and-dry and precise definitions that the reader will be able to refer back to when reading the paper, without digressions or story-telling. Anything in this section is 'safe' in the sense that the reader does not assume that this is your work. Indeed, the reader assumes it is not (and the referee can always make you delete it if it's too much). (Just the opposite is true in later sections, where you should not repeat well-known results or if forced to do so, explain that it is for completeness.' and give completely unambiguous references to the literature). So try to put most of what you will need here in the preliminaries. Sections 1, finally you get to explain your new results. Each section should begin with a recall of the goal and strategy of the section in case the reader forgot. Each section should have a main achievement. Then proceed as clearly as possible in the correct logical order.
Usda scientists have been Put On Lockdown Under Trump
Try to connect or reference all the relevant players in the field. This for takes knowledge of the literature and above all a sense of historical perspective. Who did really introduce the idea x that you are using and are giving him or her proper credit? This can also be woven into the above by way of making it interesting. Iv) Outline the organisation. This should be brief but not simply a list. State the goal and main achievement of each section. Make it into a story whereby each section is logically a precursor to the next section.
A good way is to tell a story, an interesting one that puts everything into perspective re the existing literature and conveys how it is you succeeded where others failed. What was the key idea which nobody else spotted? It should not reflect the actual historical progress of your research (which may have been long and winding) but rather based on how your thinking should have gone with the benefit of hindsight. This is not quite the same as the shortest logical path (which would not be understood until after the paper is read but rather involves an historical element with reference to works and ideas that the reader might already be familiar with. Note that it's rare for a young person to do something totally out of the blue, and worrisome for a referee. Iii) Survey statement the field so far. Make contacts with other aspects of the literature.
checklist. This should recall to the reader why the kind of result mentioned already in the abstract would be interesting and important. It also tells the reader what you think is the motivation, so that if he or she agrees with the way you are looking at the field, there's some probability that the paper will be useful for them. Keep it as down to earth as possible. Ii) The results and strategy. The key behind the work. Don't just repeat the abstract. Don't be ashamed or too proud to admit and reference the previous work the shoulders of giants which inspired and led up to your result.
The Abstract, the significance of a paper tends to be in inverse proportion to the length of the abstract. The shorter the abstract, usually the more powerful the results. So the challenge is beauty to keep it concise while at the same time conveying the key results and ideas behind the paper. The abstract should be self-contained and intelligible before one has read the paper. Keywords, this is for computer database searches to pick up on, along with words in the title and abstract. So think about what kind of search items you would want leading to your paper. This goes along with finding a math reviews code, which can be included in a foot note if you know. The Intro, many readers and (sad to say) quite possibly the referee will not get past the introduction. So it should be beautifully written with much work.
Late Breaking Website news!
The style and format of research papers varies from subject oliver to subject (and indeed journal to journal). This guide is aimed at students in the mathematical sciences. These are some hints for starting PhD students on how to write papers. It is assumed of course that you have some results worth presenting (as no amount of good writing can cover up a lack of content). How you write depends on the journal/type of reader you are addressing. Also, keep in mind some role models people you know or famous papers. The general aim is to be attractive to non-experts as much as can be expected, while interesting and not offensive to experts. The title, this should instantly convey why your work stands out from all previous ones. Should be intelligible to non-experts and down-to-earth though perhaps slightly enigmatic or 'catchy'.