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What is the main difference between an integrated four-years MMath degree and a "standard" three-years Bsc followed by a one-year Master’s degree?

And what is the "natural" progression (if any) after a MMath: is it a PhD or it is not possible to apply to it and a further Master’s degree is needed?

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Assuming from the degree titles you're talking about the UK degree courses, the biggest difference is that an MMath student meeting the residence requirement receives some government support for the whole 4 years of her course, so that tuition fees are capped the whole time. This isn't necessarily true for a separate one year masters, which can make the courses significantly more expensive.

It's certainly possible to go straight on to a UK Ph.D after an MMath degree. However, that's actually possible after a undergraduate bachelors' degree as well, since by world standards, the UK entry requirements are relatively lax. Precisely what's required of a student will differ by field and institution.

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  • Going straight from Bachelor's to PhD in maths in UK sounds a bit unusual to me, but I admit I have not looked at the actual figures
    – Yemon Choi
    May 4, 2018 at 1:32
  • @YemonChoi At least from the applied side of the fence, it's all got a bit weird on that front at the moment, what with the new EPSRC doctoral training centres offering a vaguely US style Masters + PhD in a 4 year package. Although from our side, there's no reason an MMath/ Maths BA/BSc has to lead to PhD purely in a maths department.
    – origimbo
    May 4, 2018 at 4:51
  • @origimbo Oh you mean an integrated 1+3. Yes, Lancaster has one of those in (Maths+)Stats and no doubt other DTCs do the same. I thought you meant going straight from a BA/BSc in Maths to a regular PhD without any Master's type training (e.g. dissertation)
    – Yemon Choi
    May 4, 2018 at 13:26
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    @YemonChoi The 3 years BA plus 3 years PhD track is also still on the books as possible at a surprising number of UK institutions, although I don't think I've bumped into a case in several years.
    – origimbo
    May 4, 2018 at 14:10

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