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How much of an advantage does an Applied Mathematics PhD applicant have if he/she has a publication under his/her belt?

Of course, this depends on the "prestige" of the journal that he/she published in. I suppose publishing in a top tier journal like Nature or Science would be a major advantage, but would the applicant be one of the first picks because of it?

More pertinently (I suppose seekers of such advice would not have a top tier journal publication), what about those with publication/publications in lesser journals?

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    A publication demonstrates your ability to do research, which is highly valued. The better published the article and the more "yours" it is, the better. – Dave Clarke Sep 6 '12 at 18:15
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    a top tier journal like Nature or Science — Careful! Depending on what you mean by "applied mathematics", Nature and Science might not really be top-tier journals. – JeffE Sep 6 '12 at 22:05
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    "About yea big" (extends arms) – David Ketcheson Sep 7 '12 at 5:04
  • To elaborate on JeffE's comment, some applied math departments are open to students simply applying math (like engineering) and some applied math departments require their students effectively be pure mathematicians that are only "applied" in the sense that they prove abstract theorems in the fields of PDEs, dynamical systems, numerics or probability. Most applied math departments fall somewhere in between: they'd like you to prove something in your thesis and would like to see some actual application, but the rest is up to you. – WetlabStudent Jan 17 '14 at 17:01
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The question is not answerable at this level of abstraction, because grad school admission is not decided on the basis of easily described rules. If you're a coauthor on a brilliant and important paper, you may still be rejected if the committee doubts you were a major contributor to the paper. On the other hand, some applicants with no publications at all may be accepted.

As a general rule, nobody on the committee will read the paper itself. That would be both time-consuming and unlikely to be fruitful, since the committee probably doesn't even have an expert in this specific area. They may get a little information from the abstract or your personal statement, but everything else they know about the paper will come from your letters of recommendation.

The letters need to indicate why this paper should help your case for admission. Specifically, they need to explain why the paper is interesting, what you contributed to it if you are not the only author, and why your work was impressive.

This task will be easier if the paper is really good, and that's correlated with being published in a top journal, but this is not really necessary. For example, if an undergraduate makes a major contribution to a solid but not exceptional research paper, then that could mean a lot, even if the paper doesn't get accepted to a leading journal. Of course the paper needs to meet at least some standards - publishing in a junk journal or vanity press doesn't count. However, the most important issue is demonstrating that you can carry out good research, not getting your name in a prestigious venue.

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    "If you're a coauthor on a brilliant and important paper, you may still be rejected [...] everything else [...] will come from your letters of recommendation." Actually, it's sad. It means basically that actual accomplishments are worth less than networking, being at a prestigious university, having a recognized and diplomatic advisor, etc. – Piotr Migdal Oct 16 '12 at 17:30
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    I see it as the opposite: it means you need actual accomplishments, not just the ability to attach your name to things. Sometimes people get their names on papers because of minor contributions or networking. Letters give a way of distinguishing this from serious contributions. If you are the sole author of a paper in a top journal, then that may mean a lot by itself, but few grad school applicants are in that position. If you are one of several authors, or the quality of the paper is less obvious, then letters are crucial. – Anonymous Mathematician Oct 16 '12 at 18:18
  • OK, you are right with this "appending risk". However, the first author in a decent-class journal is not that rare. – Piotr Migdal Oct 17 '12 at 21:51
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The answer depends on how the admissions process works. In my school you need to find someone who is willing to be your primary advisor to have any chance of being accepted. I am much more likely to spend a few extra minutes considering a candidate with a publication. In fact, I would say that I would schedule an informal phone interview with anyone with a publication nearly independent of the CV. Beyond this initial stage, which in my opinion counts for a lot, but not everything, things get too complicated to speak generally.

  • PhD admission works like this in the UK too: students usually have to contact a supervisor/advisor beforehand. – Legendre Nov 5 '12 at 2:54
  • In applied math this is not always and often not even usually the case. Many applied math programs, like math, admit students and then they find their advisors after they have finished some coursework and passed their quals, in the meantime they are assigned a temporary advisor before hand. – WetlabStudent Jan 17 '14 at 16:53

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