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I am applying to grad school this year for PhDs in mathematics. I have done four projects overall. One was a REU through which I published paper, and the second was my undergraduate thesis, where we solved an original problem (My professor said it wasn't enough to publish in a journal just yet, and unfortunately I don't think I'll have the time to work on that problem further). However, both these endeavors resulted in original work, so I don't mind categorizing them under "Research experience" in my CV.

In two other summers, I worked under different professors where I basically studied Coding Theory in one and Homological Algebra in the other. Both these projects led to me writing exposition on the topics I covered. However, I am unsure what I should categorize this under in my CV as it seems incorrect to categorize it as "research". I would like to know what should I classify my expository summer projects as in my CV, if not for "Research Experience"?

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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
    – Community Bot
    Sep 22 at 16:50
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    I think the question is clear. But perhaps you should explain what you mean by exposition and expository. You wrote a summary of what you had learned?
    – Oliver882
    Sep 22 at 17:15
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    I don't think it counts as research experience. Maybe "Further study"?
    – Oliver882
    Sep 22 at 17:16
  • Yes, I wrote a summary of the topics covered. Sep 22 at 19:16

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No, it’s not research, and I’m not even sure it’s accurate to refer to these experiences as “exposition”. It sounds like you studied some math under the supervision of some professors, and wrote up a summary of what you learned. “Exposition” would really only make sense if you published or are intending to publish what you wrote (even if it’s just in the sense of making the document freely accessible online on some web page) with the goal of creating a useful resource for other people; and it carries an added implication that what you wrote is polished enough and of high enough quality to serve as a resource in such a way. So claiming the “expository” designation might come across as a bit presumptuous. Most write-ups of this sort written by undergraduates are pretty far from living up to this standard.

In addition, describing the project as “exposition” also puts the emphasis on the writing you did rather than on you having learned some advanced math, which may be actually the more relevant information you want to convey.

So basically there isn’t really a standard term to refer to such projects, but I’d stay away from “research” and “exposition”. I’d suggest putting this under a general heading such as “Miscellaneous”, “Other educational activities” or something similar, and describing the projects as something along the lines of:

  • “Summer reading project on [name of topic] (supervisor: Professor [name])”.

  • “Summer reading course” (only if this was done for academic credit)

  • [name of the program you participated in] if this was done as part of a formal program, e.g., “Advanced Math for Undergraduates (summer project, Department of Mathematics, University of X)”.

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  • Fair enough. Thank you for letting me know. Will keep that in mind. Sep 22 at 19:42
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Deep reading on a narrow topic is often the preliminary to research, so it is related but not exactly the same thing. Dissertations, for example;le, often have a "literature search" section that places the current study in what is already known.

So, since a CV doesn't normally have a fixed format, you could use a section such as "Research Related Study" an list those other things, especially if you have written them up and presented them somehow, such as to a professor. "Specialized Independent Study" might also work.

If one or more of your professors who write your letters of recommendation mention your "deep dives" it will reinforce it.

If you intend to follow up with those studies then "Work in Progress" might be appropriate. Or "Early Stage Work In Progress", perhaps.

But I agree that they probably don't belong in the Research section itself.

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  • "Research Related Study/Specialised Independent Study" would work I think. As one of my letter writers is the professor I did my study under, I think that would reinforce the point as well, just as you mention. Sep 22 at 19:19

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