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I am a Masters students in mathematics at a University in Asia.

I am applying to European Universities for Phd position in number theory.

I am interested in Analytic number theory and wanted to do my Masters dissertation in it, but no one in my university works in analytic number theory.

But fortunately, 1 professor from another Institute agreed to guide me . So, he has given me a research paper to study when I went to his institute to discuss with him but we couldn't discuss more about msc dissertation as he was very busy.

My question 1. what is exactly expected in a masters dissertation by European Universities in pure mathematics for admission to a PhD program? 2. Am I expected to prove new results? 3. If I am unable to prove new results then how many papers I am expected to read given that I have 4 months of semester for dissertation along with 3 compulsory courses?

What will European universities expect of me in my masters thesis?

  • There is really no substitute for working this out with the professor. He is your best, perhaps only, guide to what is acceptable. – Buffy Jan 22 at 11:37
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    Check here – luchonacho Jan 22 at 12:04
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    @Buffy I think your edit to the title has misunderstood the OP. As far as I can tell he is doing is MSc dissertation at an Asian university, and wants to know what kind of work would be expected if he is to have a chance at getting a PhD position in Europe. – mmeent Jan 22 at 12:58
  • @mmeent, you are right. Changed it again. Thanks. – Buffy Jan 22 at 13:05
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    @user2768, the OP states they are applying for a PhD. Actually, I think you can revert it. But maybe the OP should give an opinion here. – Buffy Jan 22 at 13:21
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+100

I think the most important thing is that you do well by the standards of your own institution and that you get good letters of recommendation from professors there.

Note that standards for a masters degree vary around the world. In some places very little research is required and the degree is based mostly on coursework. The "thesis" might be little more than an intelligent summary of some subfield. Perhaps something like a literature review for a doctoral dissertation. Other places the requirements are more research directed. While published papers are required in some places, it isn't universal.

But, it is in the nature of mathematics that if a research program is strictly time limited then what can be expected is also, necessarily, limited. Some problems remain unsolved after 100 years. Insight can't be scheduled.

Then, the question is, how will an admissions committee in a given place, say Europe, evaluate candidates from such a wide variety of programs and backgrounds.

Normally, it isn't a question of counting papers. Normally, it isn't any single thing. The admissions committee will be looking at what they hope is a complete record that indicates both the necessary background and a high likelihood of success in a PhD program at their university. Lots of things contribute to that. If you have done a dissertation, it will be a plus. If you haven't, but have done other "interesting" and relevant things, then those things will be a plus.

In the US this would be much less of a problem, of course. But, flexibility is required everywhere or a university would be forced to exclude too many good candidates based on things that matter less than qualities such as demonstrated focus, hard work, preparation, and potential.

Do good work by the standards of your own university, even if it isn't yet in the narrowly focused field you want to study for the PhD. Develop some insight, generally, into mathematics and especially number theory. Get good letters of recommendation.

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  • I don't think this is addressing the OP's question at all. – mmeent Jan 22 at 12:59
  • @mmeent, thanks. I misread the question initially. This answer has been heavily edited. – Buffy Jan 22 at 13:59
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what is exactly expected in a masters dissertation by European Universities in pure mathematics?

The answer will vary university to university. I suggest you short-list some candidate universities that might accept you and look at their dissertation requirements.

Am I expected to prove new results?

That's a possibility, but not mandatory.

If I am unable to prove new results then how many papers I am expected to read given that I have 4 months of semester for dissertation along with 3 compulsory courses?

That will depend on your dissertation topic, and could be as low as zero.

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  • But the first part of the answer is the important part. It may well be mandatory in some places. And it is unlikely (though possible) to be as low as zero. – Buffy Jan 22 at 11:36
  • @Buffy Which bit is important? What's mandatory? And what's possibly as low as zero? – user2768 Jan 22 at 12:56
  • I was just quoting you, actually. Your advice is in three parts. The first part is key. New results may be mandatory, for example. – Buffy Jan 22 at 13:00
  • @Buffy So, you're agree that: New results are possibly required, but not necessarily, and that the number of papers depends on the dissertation topic, and could be as low as zero. Also, you consider the first point to be the most important. – user2768 Jan 22 at 13:12
  • @Buffy can you please tell the name of the institutions in which it is mandatory to have new papers published? – user795826 Jan 23 at 6:01

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