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I have a master's degree (in maths) and would like to pursue a PhD in future and have at least a year in hand. So I thought of picking some new research topic by reading articles in journals. The problem is how do I know the material I am reading is of a suitable standard. I often hear (and I don't mean to belittle all researcher) rumours that few researchers publish for the heck of publishing. So I don't want to waste my effort in reading those papers. One of my criteria to shortlist papers is to look for the journal which has high brand value. But this method looks superficial to me. So can you suggest some pointer on how does one goes about finding a new research topic of which he/she has no advance knowledge (although I have the pre-requisite knowledge to pursue that topic).

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First, I think that a paper is a "good" paper if you can learn something from it. It doesn't matter what other, more experienced, people have to say. The reason for that is ....

Most serious researchers in various fields, math in particular, write for a certain audience. That audience doesn't include novices. Papers are written for other people at a similar level of sophistication as the writer and who are able to fill in details of argument without it being explicitly provided in all cases. Occasionally this leads to errors as you might guess, but it is the way of it.

But, on the other hand, most researchers also include a fairly complete list of references and perhaps an even richer bibliography. This is where the novice, even a beginning doctoral student, has to start. Read a paper that seems interesting or was given to you by an advisor. When (not if, when) you get stuck, go to the references for older papers that contribute to the ideas of the current paper. Start to read and understand them until you get stuck. Then, ... Do this recursively until you reach Euclid if necessary, or until you understand the current paper you are reading and then work forward through the stack (or the tree, actually) until you understand the paper of interest that started you on the quest.

Take a lot of notes as you do this. Don't depend on memory, especially short term memory to keep you on track.

You may need to do this process a few times until you become more accustomed to the ideas and gain insight into what is going on in that small part of math. The papers contain a lot of detail, but it is the insight, not the detail, per se, that gets you to true understanding.

But the notes you take will help guarantee that the whole (painful) process actually leaves you better off at the end. If you actually learn something, you have made a personal advancement.

I'll note for completeness that some people in science and math do write for a broader audience. Carl Sagan was noted for this, of course, as is Neil deGrasse Tyson. You can learn quite a lot from such authors, but not to the same depth you get from specialists writing for other specialists.

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  • My own repeated experience is that the backward tree of references is rarely helpful... though it surely seems that it should be. Maybe others have been luckier. Jul 31 '19 at 23:15
  • @paulgarrett, it is frustrating, of course. But it can also be short circuited if you have someone (advisor) who can close the gaps for you. In my era understanding deep papers required physical presence in a math library and a friendly librarian.
    – Buffy
    Jul 31 '19 at 23:18
  • Yes, a good advisor can tell the truth about the backstory, as opposed to the account seen "in the popular press". My own extensive experience with ingenuous belief that references really were what they pretend to be (in the hands of "expert discussion") mainly convinced me that they were not. Much "expert writing" is only narrative of some other activity, and not really that activity itself. Jul 31 '19 at 23:21
  • @paulgarrett When I was a novice, I found tracking references extremely helpful. Helpfulness of references does much vary from author to author. I would not be surprised if there are some variations in the reference culture between different fields.
    – Boris Bukh
    Aug 1 '19 at 12:43
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There is a complication that you should be aware of. (I'm thinking about mathematics.) Certainly in mathematics, the refereed-journal filter leads to more of the impress-the-experts writing than write-to-be-helpful-to-beginners. That is, not intentionally, but as a result of the filter, many of "the best" papers will be unintelligible to a beginner, and, worse, the degree of unintelligibility and details of what's missing are not possible to understand, either.

True, some familiarity with unintelligible things has its benefits, but not what one might have been led to expect from schoolwork.

In particular, I'd wager that deliberately-expository, but high-ish level, documents would be most beneficial to you. Certainly in mathematics. Not journal articles. And, best, get advice from faculty near you who're interested in the things you are. They can easily filter things in the direction you'd need.

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    Doctoral dissertations (and master's theses with original research) often have a good combination of more elementary exposition and new research results. Aug 1 '19 at 3:14
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I am nearly completed a Bsc in math, with plans to do grad school. I already have a fair amount of experience with research so far, but obviously am still rather new.

That being said, I would advise on top of looking at "high brand value" journals, find out who the big names in your topic are. IE who gets cited a lot, who receives press attention (if any), who's research is considered foundational or boundary pushing. Aside from looking at their papers and the journals they publish in, look at who they cite, and then the journals those people publish in. I think this method, while time consuming, will give you a much more complete overview of the literature than if you focused exclusively on "high brand value" journals.

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