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What is the level of work expected in the masters thesis of a student of maths?

I know some people's works are worthy of publications while some involve only studying some topic in detail from a book and submitting a summary (since this is akin to a couple of courses, a year worth of work, in that topic in terms of content covered, I would consider this,which I believe is called a literature review thesis, as an extreme opposite of independent research work thesis).

But what is the "average" level of a MS thesis of a mathematics student? Is it usually closer to a literature review thesis or a research work thesis?

In particular, I would also like to know:

  1. How much is it valued (if at all) when one applies for PhD?

  2. I have heard that its value is more in Europe than America, which if I were to guess I would say, may be due to absence of GRE like criterion there. Is this true?

Edit: After the wonderful existing answer explaining the case in Germany, I would really like to know the situation in US too. I expect a drastic difference due to the presence of GRE system but would like to know how much importance the thesis has, there.

PS: Please excuse me if one can find answers to some of these questions in already existing questions. I have searched, but couldn't find them. Please provide the links in those cases.

Also, anecdotal details will also be greatly appreciated. Thanks!

  • @user54981 Of course that would most certainly be there. – NeerajKumar Jun 6 '16 at 6:01
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    The difference between US/Canada and Europe is mainly due to the fact that in most European institutions, applicants to a PhD program are expected to held a Masters or equivalent degree, and the PhD program is often research only with close to no coursework. Compare to North American institutions where applicants to a PhD program are not expected to hold a Masters, and generally only hold a Bachelors degree, and where the program tends to be longer with a more significant coursework portion. – Willie Wong Jun 8 '16 at 13:40
  • Note also that the European application process for entering a PhD program is often quite different from the typical North American one. (Search on this site if you want to know more; I'm sure it has been asked before.) – Willie Wong Jun 8 '16 at 13:41
  • @NeerajKumar Not necessarily equations. Almost certainly inequalities such as the element relation. – Jacob Murray Wakem Jun 8 '16 at 15:35
  • @JacobWakem I don't understand what the term element relation is but isn't the presence of inequalities dependent on the topic? For example, a thesis in algebraic topology or geometry is most likely to not use any inequalities but one in functional analysis or number theory may have a lot of it.. – NeerajKumar Jun 9 '16 at 4:03
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I think this varies a lot. But for Germany your first question can be answers succinctly: In a Master's thesis you should show that you have potential for research.

On the other hand, expectations vary a lot between advisors. But certainly you do not have to prove a new theorem or develop a new theory.

  1. How much is it valued (if at all) when one applies for PhD?

I can only answer for the situation where you apply in Germany. The thesis can be a door opener if it is topic closely related to the field where you want to do a PhD. Also a good mark is important. But also in Germany hiring professors will often contact your advisors or request a reference letter and this is much more important.

  1. I have heard that its value is more in Europe than America, which if I were to guess I would say, may be due to no GRE like criterion. Is this true?

Not sure on this point since I can't provide a comparison with the US and also I am not sure if the situation is uniform with the EU.

  • Thanks for the answer. As I mentioned, there are the two extremes in the kinds of thesis. In the first I can imagine the potential for research to be clearly visible( since they are doing actual research work) but how about the second case? If the work is only the study of a topic then? I doubt if it would reflect much on the potential to do research. Though one consideration that I can imagine is if the person spends his thesis studying on a certain topic then would it be of any advantage if person applies into that topic for PhD. Are such considerations taken into account? – NeerajKumar May 26 '16 at 15:37
  • Sorry if this is not getting more concrete, but, e. g., a literature review thesis can or can not show research potential. If your question is: What do I have to do in a Master's thesis do get a PhD position, the answer is "Nobody can tell you in advance." Go ahead and choose a thesis topic you find thrilling and write a good thesis. – Dirk May 26 '16 at 16:27
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+100

From my knowledge of the US system (I did my graduate work in the US, and am currently a professor in the US), the average level of a masters thesis is relatively low. (That said, it usually does involve at least some original research).

The reason for this is the structure of Ph.D. programs in the US. Usually students are admitted to Ph.D. programs directly as undergraduates, and the first two years of the Ph.D. are similar to an MS program in Europe. Students who complete a Ph.D. don't generally write a masters thesis along the way. Rather, masters theses are usually written by students who decide in their second year not to continue with our Ph.D. program, but would still like to earn some sort of degree for their efforts. These theses are often weak (but sometimes are quite good).

Some students do use an MS as a stepping stone to Ph.D. programs elsewhere; indeed, I personally know students who successfully transferred to much stronger programs. Their MS-level work was much better than average.

In short: The degree itself won't be highly valued in the US, but doing an MS can lead to strong letters from your professors and research advisors, and these will be highly valued.

  • Another complication with master's theses, in the U.S., is a perception that the student "will do a PhD thesis anyway" if they go on to a PhD program, and so there is less need for the master's thesis to include challenging research. The motivation for writing a master's thesis becomes different from the motivation for writing a PhD thesis. – Oswald Veblen Jun 9 '16 at 21:19
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A great resource I have used to understand the quality of final thesis work for my primary focus is the Open Access Theses and Dissertations which has thousands of master's and Ph. D. final publications. Research this website using your topic and you will see what amount of research is involved, differences and similarities between schools, methodologies, etc.

In addition, a great site for further publications is http://Arxiv.org . Many thesis in the U.S. are 'sandwich' publications, involving an assortment of publications published while student is performing research.

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