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Mathematics PhD Watch

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    Hi I have some questions specifically about doing a PhD in maths.

    - How well formed does your idea of what research you'd like to do need to be (at the application stage)? Is it sufficient to know that you'd like to explore a particular area (eg. differential topology, fluid mechanics, w/e) or do you need to have some question or problem that you want to pursue?

    - How does the work done during the PhD differ qualitatively from the work done, say, on an undergraduate project? Are they meaningfully comparable?

    - Roughly what is the ratio of time spent between reading/review work and actual new mathematics? (I know this probably varies a lot depending on the subject, but answer from personal experience)

    - Does anyone know anything about attrition rates? I can only find US-related stats. What (in your experience) are the most common reasons for dropping out of a programme?

    Hopefully some of you can help me with these.

    Thanks.
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    bump. (would it be better if this were moved to the maths forum?)
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    (Original post by em12)
    - How well formed does your idea of what research you'd like to do need to be (at the application stage)? Is it sufficient to know that you'd like to explore a particular area (eg. differential topology, fluid mechanics, w/e) or do you need to have some question or problem that you want to pursue?
    You probably want to know enough to know who you might like to supervise you so then you can discuss a more detailed research proposal.

    (Original post by em12)
    - How does the work done during the PhD differ qualitatively from the work done, say, on an undergraduate project? Are they meaningfully comparable?
    Some of the best MMath students can produce project work which would not look out of place as a first year PhD report.

    (Original post by em12)
    - Roughly what is the ratio of time spent between reading/review work and actual new mathematics? (I know this probably varies a lot depending on the subject, but answer from personal experience)
    I think you answered your own question! It completely depends on your area. In applied mathematics, you don't often see a lot of "new" mathematics.

    (Original post by em12)
    - Does anyone know anything about attrition rates? I can only find US-related stats. What (in your experience) are the most common reasons for dropping out of a programme?
    This is hard information to obtain but I have to say I have never known anyone to drop out of a Maths PhD. Loads in other subjects, but Maths, nope.
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    I am not a Math PhD, so I can only tell you my views on PhD in general

    (Original post by em12)
    How well formed does your idea of what research you'd like to do need to be (at the application stage)?
    In first year one typically takes PhD level courses. So you are not expected to start writing your dissertation immediately after you join. However, in the UK your PhD application is reviewed based on your research proposal, which should show that you have a more or less clear idea of what you are going to work on.

    (Original post by em12)
    How does the work done during the PhD differ qualitatively from the work done, say, on an undergraduate project?
    I don't know about mathematics and what kind of projects you had, but PhD is nothing like what typical undergraduate dissertations are. It sounds like you are doing similar stuff (writing a huge paper), but it can be very hard to manage and finish a serious research project.

    (Original post by em12)
    Roughly what is the ratio of time spent between reading/review work and actual new mathematics?
    Again, no idea about math, but you are supposed to review the literature. Let's say you have three subtopics for your dissertation, and for researching each topic you review 30 articles on average. Each article reads like a chapter in a book. So it is already quite a lot of reading! And 30 articles is very little to survey a topic, as there really is no limit to the depth, and you are tempted to go on reading and pursuing interesting questions.

    (Original post by em12)
    What (in your experience) are the most common reasons for dropping out of a programme?
    The biggest problem is to choose a good topic where you can produce nontrivial results and actually manage to finish it. As an undergrad you have never worked on the same thing for three years.
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    I have only just started my maths PhD so I can't offer a great deal of guidance but...


    (Original post by em12)
    - How well formed does your idea of what research you'd like to do need to be (at the application stage)? Is it sufficient to know that you'd like to explore a particular area (eg. differential topology, fluid mechanics, w/e) or do you need to have some question or problem that you want to pursue?
    I would say that 99.9% of prospective PhDs in maths only know what area they want to work in. The fact is that it is pretty tough to know what a good, appropriate, manageable program/question is from the outset. When I applied, I found people who worked in the areas I was interested in and they told me a little about what they did and what type of things they had in mind for PhD students.

    On the other hand, if you have a good problem and a considered justification of its importance, interest and approachability then I would definately mention it and can only see it supporting your application.
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    Am not sure about this particular PhD but some general things to note: The literature review consists of a substantial part of the first year. It should be carried out systematically and evaluated. It also continues and goes on in the background. The methods that comprise the methodology are also developed and formulated by this. I've been carrying out analyses and am going to be conducting pilot experiments for the data collection, analysis and interpretation aspect of it. Basically, you define the question, you deliver the answer. Doing a PhD is a non-linear process. That is, a number of tasks are likely to be carried out simultaneously. It's great!
 
 
 
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