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I am a math major who will be a senior next year and hope to graduate a semester early for financial reasons. During my semester off, I plan to continue my (mostly trivial) research in algebra and independently work through three graduate level texts. However, I am going to apply to grad schools for pure mathematics in the fall and worry this may ultimately hurt my graduate school applications.

Will this have a negative effect on my math grad school applications? How can I best communicate that I will not slack off in the spring semester, but will continue working?

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2 Answers 2

Your application will be essentially complete by the end of fall term, but it should very pointedly mention what further work you will be doing in the spring term, whether or not you are paying tuition for the privilege of studying and thinking about mathematics.

There really needn't be a formal structure imposed on your work/study/research, and it needn't have any official label "research" versus "study". But do write what you plan to do, and do mention the guidance you hope/expect to have from more-experienced mathematicians (as opposed to just doing whatever strikes your fancy off in some closet). That is, do be sure to make the point that you will be engaged with actual contemporary mathematics, arguably more intensely, and at a more serious level, than the usual homework-exam model would encourage or allow.

If you can describe your plans for "spring term" in vivid and enthusiastic detail, you can make it sound far better than "taking classes". I'd not worry about hype-ing "research" too much, although, yes, it would be intellectually dishonest to not follow one's curiosity. But, of course, one's personal discoveries, however novel to oneself, may be old news to experienced professionals, so one should not presume.

Just tell your plans!

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Volunteer to do a research project with a professor in the department. This will demonstrate a continued effort in the field. Ultimately, however, what matters most is your grades and recommendations. If they say you're good, a semester off won't hurt.

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There was another question (can't look for it right now) for which the answers suggested this is probably not possible when not enrolled as a student. –  Nate Eldredge Jul 5 at 1:08
    
@NateEldredge From my experience (and what I've heard from other students in similar situations) universities sometimes allow students to continue as employees for one semester/quarter/unit of time after they graduate. I don't know how widespread this is. –  Mike Miller Jul 5 at 2:37
    
It's possible as a volunteer. What's tricky is getting paid to do this project. –  Ari Trachtenberg Jul 6 at 3:05

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