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This question is a variation of my earlier questions.

Okay so in the US, I guess one does not need a master's in math before pursuing a PhD in math since the US apparently usually assumes only a bachelor's.

What about in Europe? Technically, my master's is in mathematical finance not mathematics. So I didn't have research experience in looking through (pure) math books or articles in order to try to prove something theoretical or anything like that except for a few problem sets.

On an answer to one of my previous questions, user deviantfan commented that:

"In many european countries, it´s not even allowed/possible to skip the master degree."

Perhaps my question may be rephrased:

Is the master's in X PhD requirement in Europe satisfied by a master's in Applied X rather than Pure X?

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I will try to respond to the abstract question, with a perspective from Germany (that may or may not be valid for other European countries):

Is the master's in X PhD requirement in Europe satisfied by a master's in Applied X rather than Pure X?

The general answer to this is yes.

As opposed to the subject chosen for the Bachelor and Master degree, which is usually supposed to be the same or closely related in Europe, as Bachelor and Master curricula are closely coupled here, a PhD is often completely disconnected from the former studies.

Note that the Austrian website that Moritz linked to in the original version of his answer does not require a particular Master's degree, but a "relevant Master's degree". Without any further restrictions, this means that anything closely related to the subject (and the relationship between Applied X and Pure X might very well be sufficient) should do. At least, that would be the interpretation in Germany; it is possible Austrians interpret this differently.

However, it is also very well possible that the suitability of the Master's major is determined based on the research projects at hand. In that case, it depends entirely on the decision of the respective department chair, and it would be worthwhile to contact departments you are interested in. As a concrete example, it is completely normal in Germany to see Masters of Physics, Linguistics, and Maths starting PhDs in Computer Science, not only Masters in Computer Science.

EDIT: To clarify the last remark: None of them have to take any extra courses; rather, they are expected to bring their professional subject-specific knowledge from physics, linguistics, and maths, respectively, into their computer science research (while "informally" (i.e. without a class) catching up with the CS knowledge), just like Masters in CS are expected to use their professional CS-specific knowledge in their computer science research, while "informally" acquiring knowledge on (w.l.o.g.) physics, linguistics, and maths, as required for their respective research.

  • Where is relevant master's there? – Jack Bauer Jul 29 '15 at 17:11
  • Is the informal acquiring kind of like the brushing here? – Jack Bauer Jul 29 '15 at 17:13
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    @JackBauer: "Is the informal acquiring kind of like the brushing here?" - by "informally", I was trying to say that you do not have to attend any particular courses or acquire a certification of any kind, but that it is your own responsibility how you gain the knowledge required to being able to conduct the respective aspects of your research. – O. R. Mapper Jul 29 '15 at 19:57
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    @JackBauer: I'm not sure whether that is still the text I read when I wrote that, or whether the page has been changed meanwhile ... but anyway, the page linked from the page mentioned by Moritz says: "It has to be checked, however, whether the studies the applicant has completed so far can be considered as equivalent to an Austrian diploma or Master study for the purpose of the doctoral study", which seems to imply that whatever you have studied needs to be similar enough for the purpose of the doctoral study. – O. R. Mapper Jul 30 '15 at 16:16
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    @JackBauer: Oooh, it seems at some point, Moritz changed the link (check out the edit history of his answer). Now, he is linking to Universität Wien, but before, he was linking to Technische Universität Wien, which is a different university in Vienna. Their rules do indeed list "successful completion of a relevant master's, teacher training or other appropriate degree programme" as a "prerequisite for admission to a doctoral programme at TU Wien". – O. R. Mapper Jul 30 '15 at 16:24
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I'd say that one would need a Master's in Math or its equivalent. Then the question becomes, is your degree in Mathematical Finance an equivalent."

Hopefully, you will have had the core courses in mathematics such as real and complex analysis and advanced calculus. Perhaps your mathematical Finance degree will differ from a true math degree in "engineering type" applications, such as stochastic partial differential equations. If that is the case, you may be ok. Perhaps, at worst, you need to take 2-3 "traditional" math courses as a special student to make up for what you lack.

If you lack a traditional core curriculum, that would be different of course. Ultimately, it is for the faculties of the schools you apply to, to decide. And there is no one university "monolith" in Europe, only numerous schools, with meaningful variations in their admissions criteria.

  • Thanks Tom Au. 1. What is advanced calculus? I took vector calculus and an "advanced calculus" course which was a prerequisite for real analysis, which I had. No complex analysis. Is that that bad? I heard of someone who got accepted into a master's in math program which required bachelor's to have complex analysis even though she did not have complex analysis in undergrad. 2. "at worst, you need to take 2-3 "traditional" math courses as a special student to make up for what you lack." - Do you mean in the PhD program, if I get accepted? Or before the PhD program, I must take those classes? – Jack Bauer Jul 22 '15 at 21:55
  • Regarding the first question, in some engineering undergraduate programs or textbooks in economics, advanced calculus is used to refer to vector calculus – Jack Bauer Jul 29 '15 at 17:27
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It is a bit more complicated if you did not study pure math. You have to proof that your master degree is equivalent to a master in mathematics. If it is not, you will have to attend the necessary classes. It will get even more complicated if you studied abroad. It highly depends on the courses you took and on the amount of ECTS of each course. Furthermore, it will be decided individually by one or two people. At the bottom of the page from university vienna, you will find a text in english.

  • The OP has a Master's degree. The question is explicitly whether that particular degree is sufficient for a Math PhD. – O. R. Mapper Jul 2 '15 at 22:13
  • Thanks Moritz. What do you mean by attend necessary classes? I won't be accepted into the program until I take such classes either as a non-degree student or in another master's (in math)? Or I may be accepted, but then I will have to take such classes in the PhD program? I heard Europe's PhD programs have little coursework – Jack Bauer Jul 22 '15 at 21:52
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    Depending on the agreements between both countries it can be easy (or not) to prove that your master is equivalent to the demanded ones. You will have to hand in a list of your courses you passed. What might happen: you had a course of linear algebra and it was worth 3 ects but 5 ects are necessary, you might have to repeat such a course in order to inscribe for the specific PhD program. Best practise would be to contact the relevant university. – Moritz Jul 23 '15 at 8:27
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    be aware that I know these things from hearsay ! It could have changed in the meantime. – Moritz Jul 23 '15 at 8:29

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