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Most PhD programs in math has more applications that what the funding for program can afford if they admitted everyone. Assuming you have normal grades and good RLs, and you can fund your PhD program expenses, do your chances of admission increase?

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This is for the US. Most doctoral students in math hold Teaching Assistantships and the funding covers tuition, most fees, and a modest living stipend. Math departments need a lot of TAs so it isn't really the case that there are many unfunded doctoral students.

You would probably not have an advantage over any other student in admissions, however, if you choose to fund yourself. Or, I think it would be improper to make decisions based on funding in any case. Admittance is based on the likelihood of success in the program and the criteria are set as such. A low quality student with money wouldn't be seen as an asset, but as a liability. The money paid by such a student wouldn't show up in the department budget in most cases, but accrue to the system itself and is marginal in terms of the overall cost of running the system. Doctoral programs generally aren't "profit centers" for US universities.

But TAs provide a benefit in making the undergraduate (especially) program work smoothly. There are relatively few no-requirements scholarship.

The one advantage of self funding, however, might be that you could finish the degree a year or so earlier since you wouldn't have TA duties which take some time and effort. You might be able to pass comprehensive exams, which are normally required, a bit earlier.

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    There is still the issue of finding faculty mentors/advisors for everyone: capacity limitations. Not to mention a probable disinclination of many faculty to sponsor students not strong enough (in documentable potential) to be admitted. Feb 5 at 0:28
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    why the downvote then? Feb 5 at 9:20
  • I find it best to ignore downvotes that don't come with a comment. Especially on questions. But I don't think the downvote came from @paulgarrett as the comment is supplementary to the answer (thanks) not contradictory. But lots of downvotes are mystifying.
    – Buffy
    Feb 5 at 14:31
  • I did upvote just now, to help balance the drive-by downvotes. :) Feb 5 at 19:54

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