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A master's student in the department of mathematics that I work in has recently finished his master's thesis, on a topic that is well represented in the literature. There are several books and surveys concerning the subject but they are either semi-elementary treatises, or research level expositions.

He managed to write his thesis in quite a mature style and he treats results up untill 2022, (much like a survey). It should be noted that he has made no original contributions to the field, though he has written down some of his ideas and approach to the subject.

As such, I would like to ask wether he should publish his thesis, on the account of pedagogical reasons (and not only that) and if doing so could impact possible PhD applications? How whould the comunity recieve a survey-like publication from an unknown student?

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  • I think you should talk to publishers. My experience is that they are very keen on discussing planned books. I can't really predict whether this one will work well, but responsible series/field editors will have a qualified opinion, and if the opinion is positive, they will be keen to sign it (after the usual review stage). Commented Apr 18, 2023 at 13:37
  • Some math journals publish expository articles, for instance, L’Enseignement mathématique. Another possible venue are proceedings of math conferences. If the survey is high quality, it does not matter if the author is an unknown MA/PhD student. I suggest you talk to your advisor. Commented Apr 18, 2023 at 17:46

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It isn't obvious that he can publish the thesis other than on a private site or something like arXiv. Publishing with a formal publisher is decided by that publisher, not the author. It will need to pass muster by reviewers and an editor whose standards probably include some measure of novelty. And it isn't clear that what you describe has the required novelty.

But, if a reputable publisher will issue it then it is probably a plus for doctoral admissions. Private publication counts for much less if it isn't also formally published. For an established researcher that isn't quite the same, however, and preprints from known scholars can be highly valued, though also as a step along the way to formal publication.

But, the work may have pedagogical value. It might even be worth publishing as a separate volume as a service. Making it known to those who might want to see it is a major hurdle, however. Especially for someone new to academia.

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My best-placed publication is half of my MA thesis. I would suggest the student to try to add some original thesis/overall interpretative structure to the work and to publish it.

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