It is irrelevant that your readers might be capable of managing to understand both examples at once. Moreover, people who really know the topic very well just skim through the easy part of the paper and then quickly get to the hard part.Īnd can't manage to understand both examples at once. In addition, it is, generally speaking, an advantage rather than a disadvantage if your paper can also be understood be people who are not experts for specifically this topic.
In this situation it is easy to get the impression that everybody else understands everything in your paper just as easily and clearly as you do. You have been dealing with the subject of your paper for probably quite some time and in a lot of detail. I think you might be overestimating the abilities of your readers: I feel like my advisor is telling me to write the paper as if the reader is some fool that knows nothing of the field (My apologies in case I am sometimes a bit too blunt - but I think it is important that somebody makes you aware of these points.) So I'll try to clarify those misconceptions in what follows. I'm under the impression that your perspective is influenced by a number of misconceptions which are very common for mathematicians writing their first papers. As well, I feel like my advisor is telling me to write the paper as if the reader is some fool that knows nothing of the field and can't manage to understand both examples at once.Īny general advice for what may constitute a preferable organization for such a case? However, shouldn't like ideas be considered together? With this organization, you basically need to read the paper twice, once for each case.
I see some merit in doing this, as (most) things are a bit easier for the Easy case.
Then, add another section, The Hard Problem (say), and show how everything can be extended into this case. However, my advisor believes that I should ignore the Hard Problem in both the Preliminaries and Results section, giving only the Easy results. The organization in this way makes sense to me because the reader can have in mind both examples in their mind, see how they are unified together, get the complete picture.
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There is also a bunch of statements about how to interpret some results which say things like "in the Easy case, we have the result A, but in the Hard case, it is similar to A, but for this slight difference". Then, in the Results section, I provide one statement that solves both the Easy and the Hard problem together. The way I have organized this paper is to discuss both cases together - in Preliminaries I discuss the Easy and Hard problems and show how they are unified, as well as providing separate statements / proofs for the preliminary theorems. But, they admit a more-or-less unified treatment, with much (but not all) of the Easy problem being a special case of the Hard problem. Most of the content, but not all, in "preliminary Results" and "Results" is considerably simpler for the Easy problem, and a bit more complicated for the Hard problem. There are also two natural cases of the problem, call them Easy and Hard, that we should look at (i.e., any reader would be confused if one case was covered and the other wasn't). The conclusion of the Results section is how to solve certain optimization problems. For the purpose of this discussion, say there are two sections: Preliminaries and Results - the former establishes some basic theorems and properties of certain functions which are then used in the results section. The field is operations research, and involves mostly a bunch of mathematical theorems. I have a question about how to organize a paper, and completely disagree with the way my advisor wants it done.
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