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How important is it for an undergraduate student majoring in Physics and Mathematics (or any other science) to have experience in research (e.g., have a peer reviewed paper to his name most probably in collaboration with a professor) at the undergraduate level, keeping in mind that he will be applying for a master's or other postgraduate degree?

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If you want admission to the very best PhD programs in the US, prior formal research experience is very important, if not necessary. Admissions committees are primarily looking for evidence of research potential. The best possible evidence for "I'll be a good researcher someday" is "Look, I'm already a good researcher." So having formal peer-reviewed publications is better than having publishable but unpublished results, which is better than having research experience but no publishable results, which is better than having no research experience. If you're applying to the top PhD programs, you will be competing with applicants (yes, plural) who have peer-reviewed publications (yes, plural).

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What if someone is seeking admission to a MS or an Integrated MS/PhD programme (not a PhD, let us say that he will be applying for his PhD after his Masters). Do they also look for "evidence of research potential" like published papers? –  AchiralSarkar Jan 3 '13 at 3:35
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Applying for an MS program in the US is quite different, and varies from university to university, based on whether the MS is terminal, or is a pre-screen for a Ph.D. –  Suresh Jan 3 '13 at 5:34
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But if you mean a research masters (prep for a PhD), then yes. Not as much, perhaps, but only because most applicants with publications apply directly to PhD programs. –  JeffE Jan 3 '13 at 5:37
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In the U.S., in mathematics, it is a bit unusual to have a peer-reviewed publication from an undergrad, despite the recent years' push for "Research Experiences for Undergrads". In some cases there are group-written papers in second or third-tier journals, but nothing too serious. Or the undergrad gets to be the tag-along on an applied-math research "team". Indeed, it is exceptional, and only rarely happens, that an undergrad in mathematics has adequate background (disregarding future potential) to make a serious contribution. It does happen, but rarely, and is not at all "expected". Evidently the situation is much different in other fields.

In terms of literal admission to good-but-not-elite programs, the usual "publications" we on admissions committees see are "nice", but not really evidence of future potential so much as enthusiasm, ... which is a good thing, for sure! ... but the level of focus and effort required for these little papers is far, far different than the level of commitment required to do a Ph.D., with or without "talent".

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So, what you are saying is that though a not-too-serious paper looks nice on the CV yet it really does not affect the committee's decision? And this is restricted only to Mathematics? –  AchiralSarkar Jan 3 '13 at 3:38
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@AhiralSarkar: yes, not-too-serious papers on the CV have little effect on admission committees, for math grad school. I don't know about expectations in other fields. –  paul garrett Jan 3 '13 at 13:48
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During my studies it was relatively rare to publish as an undergraduate. The level of research needed for a peer reviewed publication is imo higher than what an undergraduate can produce. Maybe if the supervisor writes a paper based on your results, and with a lot of help with producing the results, this might lead to a co-authorship for the undergraduate. Therefor, I think that in the Dutch system (my experience) a peer reviewed publication would be a plus, but definitely not a requirement for admission into a masters program. Ofcourse, you need have written a thesis, but it does not have to published in a peer-reviewed journal. I do not know how this experience translate to, say, the US, but I know for countries like Germany it is not even always usual for a PhD to write peer-reviewed articles.

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I am from India but I have seen universities in the US prefers candidates having some publications co-authored with a professor and/or fellow students..However, you mentioned that one needs to have a thesis. Do you mean, like a special paper that one does during his masters? I don't think one has to do a thesis during one's bachelors under the usual curriculum in India. –  AchiralSarkar Jan 2 '13 at 19:12
    
In the Netherlands it is normal to write a thesis at the end of your Bachelor. It is meant to be the first independent research project you do. It normally takes around 3 months. But by publications do you mean publications in peer-reviewed journals, or conference publications (which can also be peer-reviewed, but often less stringent in my experience)? –  Paul Hiemstra Jan 2 '13 at 19:19
    
I meant an arxiv paper or one in a journal (not as high profile as the Letters of Physical Review but something having an impact factor of (say) 8). And no, most Indian universities do not have this thesis requirement at the undergraduate level. However,some meritorious students often do such projects in association with a research institute but that is by the virtue of the benefits they receive if they have won a scholarship or a fellowship of sorts. It is basically, a personal effort, not a formal requirement. –  AchiralSarkar Jan 2 '13 at 19:48
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The level of research needed for a peer reviewed publication is imo higher than what an undergraduate can produce — Nonsense. I can show you dozens of published counterexamples. –  JeffE Jan 2 '13 at 20:31
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for countries like Germany it is not even always usual for a PhD to write peer-reviewed articles — This obviously varies greatly by field. In computer science, it is very rare for a student to get a PhD without at least one formal publication. –  JeffE Jan 2 '13 at 20:37
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