Both style and format of a research paper are dependent on its subject (and hence, on the journal). The current guidance is prepared for students in the mathematical sciences [1–5].
A number of hints are proposed to show PhD students how to write research papers. However, it should be noted that the main factor of in writing a good paper is having some valuable results for presenting not good writing [1–5].
The writing method is a function of journal and type of reader addressed by author. Further, considering some known role models people or famous papers is useful. A favorite paper is attractive to non–experts as much as possible and is interesting and, of course, not offensive to experts [1–5].
Title of a paper should directly express its preference compared to all previously published works. It should be clear to non–experts and should be practical in spite of its possible unknowable or attractive inherence.
The importance of a paper and the length of its abstract are inversely proportional; it is usually established that the shorter the abstract, the more influential the results. Therefore, the abstract should be kept brief and simultaneously, it should express the key results and ideas of the paper. Independency and understandability of abstract for who has read it before the paper is of great importance.
Keywords
The aim of preparing keywords for a paper is for computer database searches. Therefore, author should determine his/her favorite search items that will lead to the paper. It would be useful to find a Math Reviews code and cite it as a foot note.
The Intro
The introduction is usually read, accurately, by many readers and the referees. As a result, writing the introduction with high quality is important. It seems be reasonable to use about 25% of manuscript for the introduction. The following issues will be considered in writing an introduction.
i) The Motivation
The introduction should clearly express the reason of importance and attractiveness of the results mentioned in the abstract. In addition, the factors which have been motivated author should be explained for reader. It will be very useful for reader to know the considered approach by author and hence, compared it with his/her attitudes about the problem to find if the paper will be useful for him/her. It should be as practical and realistic as possible.
ii) The Results and Strategy
It is the real essence of the work. It should not be similar to the abstract and should be including the previous works in this field which acted as a reliable base for the work. It would be appropriate to express the problem, the previous works aimed to solve it and the method which has been used by author to successfully solve the problem as a story. The new idea behind the paper should be explained. It is not necessary to explain whole of research history, as it may be very long and not be necessarily useful. However, explaining the way the author is approached to the problem based on his/her finding from previous works, that the reader might already be familiar with those, would be more useful. It should be noted that it is not easy for young authors to do such work without concerning referees.
iii) Literature Review
All aspects of the literature should be reviewed. All related works to the field should be cited to show the knowledge of author about historical perspective of the research. Further, if any ideas are used by author in the research, its first introducing to the literature should be clearly mentioned along with judgment of author about its appropriateness. Moreover, it may be useful to explain why it is interesting.
iv) Outline the Organization
A brief, but not only a list, explanation about the organization of paper along with the aim and the obtained results for each section should be provided so that each section acts as forerunner of the next one.
v) Preliminaries
All notations and key references should be technically remarked. It may be useful to address something which will not be published in the later sections. Any machinery which has not been invented by author but used in the research should be cited. However, it should be remembered that this is a paper not a thesis and hence, redoing the work of previous persons is not the aim but making the intends of author as clear as possible is the main goal. All mentioned definitions should be proposed so that reader can refer back to those during reading the paper.
As it is assumed by reader that this is not the work of author, it is considered safe. It will be useful to mention everything from the literature that will be needed in the following sections since in later sections it is not usual to repeat well–known results unless it must to do for comparing with previous results. In this case, references should be completely unambiguous.
Sections One
Ultimately, new results should be presented. At the start of each section, its goal and strategy should be clearly represented. In addition, each section should contain a specified achievement.
The manuscript should be written in a logical order. Although it is usual in books or thesis to represent previously published results, in a research paper, only new results should be represented.
It should be noted that mentioning the previously published results is only acceptable when the author have something new and worthwhile to say about it. However, it should not be mixed with new represented results. Although there is a tendency to repeat and proud to our previous works, it should be realized that previous work is for past and it should not be repeated when it is used as a basis to achieve new results. The understanding of this case will be easier when we ask our self how we would feel if somebody developed our work and integrated it into theirs without providing any clarity about our contribution.
The organization of results can be as following: lemmas technical results that will be needed later but not of self–contained interest, propositions relatively interesting new results, and theorem main new results. These should be the best peaks: i.e., if theorems are breaking up with disjoint parts into propositions, it will lead to the denouement of the main theorem.
The theorem or proposition should be proved so that its proof is not similar to a weak logical trick that it's immediate from some other work that's a corollary or a remark. The ideal form is that the proof of the main theorem uses as many as possible of the previously proved lemmas and propositions to demonstrate that they were all necessary and important.
Theorems should be stated as self–contained as possible. I this regard, the shorter the statement, the most powerful the statement. Achieving to a powerful theorem is possible by appropriately setting up the proper background in the introduction while keeping it out of statement to obtain self–contained statement from notational point of view. It should be pointed out that statement should be new and important.
Informal remarks can be mentioned at the end of the section. Any claim, hypothesis or argument which author is not able to explain those as a theory can mention in this section. By preparing good results in the section, it is possible to forgive things at the end of section.
It will be useful to have some brief explanation about what is stated in the next section. However, note that it will be reintroduced at the start of the next section.
General Guide to Style
As bad writing is accompanied by ambiguities, a method for clarification of the understandings is clear writing. Paying attention to layout, ordering of sentences and even simple things such as punctuation are greatly affected the understanding of the material.
Repeating the writing is the best method to achieve good writing. However, the following issues may be useful, too.
Avoid Non–Sequiturs
Passing through one sentence to the next one should be performed as smooth as possible. In English, short sentences are greatly preferred and the structure connecting across sentences also is of importance. Short sentences about an idea will be simply stored in the reader’s mind and hence, change of topic will not necessarily be shocking. When there is need for changing the topic, reader should be informed by key phrases such as 'on the other hand', 'meanwhile', 'in contrast to this', 'moreover', etc.
A new paragraph should be used to shift the general topic. However, as previous paragraphs are still active in the reader’s mind, huge shifts should be performed by providing an appropriate expression such as 'Now we come to ...' or 'To conclude this section' or other orientation signal. The signals may be refer back to the introduction or being a surprise for the reader.
Avoid Making Sandwiches
When an idea is discussed between discussions about another idea, a conceptual sandwich is happened. It would be within a paragraph, a section or in the overall layout of the paper. It is a sign of weal organization and is not appropriate. It is not possible to move the middle of the sandwich from the top or the bottom while pooling together the two related topic. It is usual to firstly introduce the more general topic and then, followed by sub–topics. The reason of avoiding a sandwich is saving the energy of reader since dealing with topics introduced in each other is difficult. Therefore, it will be useful to say all about a topic in the near future, before moving on to further questions arising from it.
It can be similarly happened with a sentence as when the second half of the sentence came as an afterthought but more properly belongs as the first half of the sentence. Therefore, the order of sentence should be checked.
Validation Status of Assertions
Assertions should be confirmed by a clear validation status. It means that reader should be clearly found from context or from signals in the syntax that how he/she can validate the assertion is correct. It should be clear that it can be validated through (a) a self–evident from what was said (b) following something said in the past (providing a signal to where) (c) a well–known fact that the reader should know anyway (d) a fact proven elsewhere by somebody else which had cited in the past (citing again ‘on the dot' to avoid any ambiguities) (e) a fact that will be justify later (giving the forward reference), etc.
Run–On Sentences
Opposite to some languages, English does not grammatically support long sentences with lots of commas. However, sentences should be short and sharp. Russians analogize English people sound to barking dogs. This is commonly afraid that finishing the sentence is leading to losing the context and hence, the author encourages to put a comma and continue with another one. However, this fear is not acceptable since words will still remain active for a short while after the period. It can be solved by looking for sentences which are longer than one or two lines and see if ', which' or ', where' etc. can be replaced by fresh sentences.
'This' and 'It'
Using pronouns such as 'this' and 'it' should be clear for reader. It should be clear that what they refer back to. In addition, 'this' should not be used for 'the present'.
'Never' and 'Only'
Using 'never' and 'only', which are strong assertions, is not suitable unless they are really proven. It may be better to reduce them with 'appears to be' or 'it seems'. However, 'probably' should not be used in this regard.
Commas
Although commas are very important, it is tough to give rules for them. When speaking, don't go by where you pause; the best commas can be used as a kind of 'conceptually pause' or to make an aside with the help of a later comma (brackets are usually better, however). While a fresh sentence would be better frequently, punctuation rules should be more followed when writing a thesis or for camera–ready work, and in these cases, a style manual like Fowlers should be consulted.
Math Symbols
A math symbol at the start or end of a sentence is not appropriate. In addition, math symbols should not have clash with textual punctuation. Displayed equations are exception to this. In this case, putting commas and a final period, if needed, to make easy reading through the displayed equation like text can be used as general rule. However, putting connectives such as 'and' or other substantial text into the displayed equation is not appropriate. The displayed equation is half–way to a table and hence, it should be laid out for visual clarity and without unnecessary text.
Definition of Symbols and Terminology
Any symbols and terminology should be defined, in a formal form, before it is used. In mathematical works, putting the term for an important concept in a different font when its usage is being specified for the first time is usual, particularly in preliminaries section. Any symbols should be clearly defined to show their meanings. Assumption about notations is not acceptable since notations may have other meanings in other conventions.
Conclusions
Although there is not necessary for a good introduction and well–written paper to have conclusions, epilogical comments based on the new presented results can be represented in this section. They are similar to corollaries or informal results or consequences that they have not been considered in detail. Suggestions for future studies can be provided based on the ideas resulted from the new presented results.
Bibliography
Performing a computer search (Bids, hepth, q–alg) for assuring about picking up all relevant recent work is useful. In addition, all the works and ideas which are used in the paper should be clearly cited. The birth time and place of an idea is important and should be cited not the time and place that it was read by author.
Spellchecking and punctuation checking are important. If possible, read the manuscript for last time after a week or month to discover typos that will be possibly ignored at the first reading.
References
[1] Manuela Farinosi, Christopher Lim, Julia Roll, Book or screen, pen or keyboard? A cross-cultural sociological analysis of writing and reading habits basing on Germany, Italy and the UK, Telematics and Informatics, Volume 33, Issue 2, May 2016, Pages 410-421.
[2] Seth Lindstromberg, June Eyckmans, Rachel Connabeer, A modified dictogloss for helping learners remember L2 academic English formulaic sequences for use in later writing, English for Specific Purposes, Volume 41, January 2016, Pages 12-21.
[3] N.J. Callaghan, Courts and Tribunal Report Writing in England and Wales, In Encyclopedia of Forensic and Legal Medicine (Second Edition), edited by Jason Payne-James and Roger W. Byard, Elsevier, Oxford, 2016, Pages 626-630.
[4] Julian M. Allwood, A. Erman Tekkaya, Writing for the benefit of the reader, Journal of Materials Processing Technology, Volume 227, January 2016, Pages A1-A5.
[5] John M. Swales, Configuring image and context: Writing ‘about’ pictures, English for Specific Purposes, Volume 41, January 2016, Pages 22-35.