Difficulty deciding amongst Maths PhD offers!

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omegaSQU4RED
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Hello,

I'm a final year MMath student at Exeter and I have been given a couple of PhD offers - one at Exeter and one at Surrey. I am also awaiting one from Sussex. My favourite topics lie in the applied areas, namely PDEs and dynamical systems, but I would also like to expand my knowledge of pure mathematical analysis as the teaching on relevant areas is weak at Exeter - I'm talking areas like differential geometry, functional analysis, topology/metric spaces, measure theory and fractals.

The topics amongst those I have been offered/have applied for are:

Exeter: Geometrical methods for recurrence statistics and extreme events (this project is more pure, along the lines of the areas I want to learn more about as well as ergodic theory and real/complex analysis, but with repercussions for applied areas such as time series analysis and stochastic processes)

Surrey: Sleep-wake dynamics (this project seems to be a biosystems-type project but it is an application of dynamical systems and I've been told it can be tailored to make it as pure or as applied as I want, so it can effectively be made into a mathematics PhD as opposed to a biology one. This will involve quite a bit of MATLAB.)

Surrey: Fast numerics of the spin-orbit coupling of Mercury (this project is very applied, looking along the lines of astrophysics/numerical analysis - the work will be mostly computational, and seemingly less room for pure theory.)

Sussex: Theory of PDEs with applications to mathematical fluid mechanics (involves quite a few of the areas I want to learn more about, will involve mainly proving theorems and learning about analysis)

Sussex: Algorithmic construction of Finsler-Lyapunov functions (involves quite a lot of programming in C++ and knowledge of dynamical systems - sounds quite interesting.)

The problem I'm having at the moment is deciding which one to take! This is for numerous reasons:


  • I'm not 100% sure about the area I want to specialise in - I want to do a PhD which has the widest range of prospects possible, so that I'm not confining my field(s) of expertise by my PhD choice.
  • I'm not quite sure whether it would be better to do a PhD where I am already familiar with quite a few of the techniques involved (e.g. I am experienced with numerical analysis and dynamics) or to do one where I won't be too sure of my knowledge at the start but where I'll learn more in the first year of the PhD and then gain a better idea of which pure techniques to use.
  • I'm not sure which place I want to spend the next 3/4 years at - I've been to all three places and they're really nice; Exeter is great because it's a nice place and I know the department really well having done my undergrad degree there, but the other two would be a refreshing change and would provide me with a more diverse experience.
  • All of the universities are reasonably close to my home (Swindon) although it is considerably trickier to get there from Sussex.
  • Exeter is the only university that has a Russell-Group status, but none of the other universities are particularly bad department-wise, even if they are a bit small.
  • It would be more expensive to live in Exeter and Sussex than in Surrey.
  • If I stayed on at Exeter, potential employers/universities might view it as positive as it would demonstrate that I have a good standing reputation with Exeter already and they know that I'm a good student.
  • I have previously struggled with very pure mathematics such as abstract algebra, even though I feel like I want to give pure mathematics another chance.
  • All the offers require a 2.1/1st, and I am hoping for a 1st.


Basically I'm having a lot of trouble deciding which option would be the best for me. For previous/current maths PhD students, which factors made you want to decide where to go, and are there any other factors that I haven't considered?
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poohat
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Its a lot easier to get a permanent academic position or well-paying private sector job with a statistics related PhD than it is with either a biology or pure mathematics PhD, if that helps.

Also in my opinion, succeeding in pure mathematics requires more raw intelligence than succeeding in statistics/applied mathematics/biology - arguably pure mathematics requires more raw brainpower than any other academic field except maybe theoretical physics. So if you are struggling to get a first and/or dont have a PhD offer from a top department, then the applied fields are perhaps safer options.

On the other hand, I am slightly concerned that some of your projects look highly interdisciplinary. While this isnt necessarily a bad thing, you should really check that your supervisors and their collaborators are actually able to hit the top journals in established fields. You dont want to end up being too much of a mathematician to be employed in a statistics department, and too much of a statistician to get a mathematics job. Specifically, is work arising from "geometrical methods for recurrence statistics and extreme events " actually managing to get published in good statistics/probability theory/mathematics journals? It has a bit of a kooky complex systems vibe to me, but I could be totally mistaken since I dont know the area
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omegaSQU4RED
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(Original post by poohat)
Its a lot easier to get a permanent academic position or well-paying private sector job with a statistics related PhD than it is with either a biology or pure mathematics PhD, if that helps.
My interests lie in PDEs/dynamical systems - so these are applied areas but not necessarily related to statistics.

(Original post by poohat)
On the other hand, I am slightly concerned that some of your projects look highly interdisciplinary. While this isnt necessarily a bad thing, you should really check that your supervisors and their collaborators are actually able to hit the top journals in established fields. You dont want to end up being too much of a mathematician to be employed in a statistics department, and too much of a statistician to get a mathematics job. Specifically, is work arising from "geometrical methods for recurrence statistics and extreme events " actually managing to get published in good statistics/probability theory/mathematics journals? It has a bit of a kooky complex systems vibe to me, but I could be totally mistaken since I dont know the area
I will probably clarify this with the supervisors. Yes, quite a few of the projects are very interdisciplinary, but I've stressed to the supervisors that I'd prefer to distinguish myself as a mathematician as opposed to a biologist, so even though I won't be focusing purely on the biological part, I would be working with them and use mathematical modelling/analysis techniques to explain their models. Even though some of the topics are interdisciplinary, they apply a lot of general mathematical techniques that could potentially be ported over to another project. For example, my summer project last year was about tipping points in an ecological system, but my MMath project is on lasers - they are all governed by nonlinear dynamics!
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poohat
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Again its really about distinguishing yourself in a particular area. There are more than enough people doing (eg) mathematical/theoretical biology that if a biology department wants to hire a quant guy that they will go for one of these people, rather than considering a mathematician who's work can be vaguely applied to biology (and one of the reasons for this is as simple as the fact that you wouldnt be able to teach non-trivial undergrad/masters classes, since you would have almost no general background in the area outside your very narrow specialism). Ditto for statistics/ecology/etc departments. So I think you would probably be looking for jobs in mathematics departments rather than (eg) biology/statistics departments, unless you decided to go in a very different direction after your PhD and become essentially a mathematical biologist/statistician/etc. And this is certainly possible at postdoc level.

Getting a permanent job in a mathematics department isnt impossible, but it is insanely competitive and I would suspect that you would have the best chance if you were connected to a conventional area of mathematics, rather than something a bit 'out there' - departments usually a have a preference for hiring people in areas which they are already strong/established, rather than hiring people who are completely unconnected to the rest of the department's interest (an exception is the hiring of very senior people in areas where the department is hoping to expand). PDEs and dynamical systems are probably fine, but you do really need to check because its not as simple as saying "my work has some applications to biology therefore I can switch over into biology, at least not without spending several years as a postdoc essentially retraining as a mathematical biologist.

The questions to ask should be:

a) What journals does my supervior(s) regularly publish this work in, and are they considered good venues by non-interdisiciplinary mathematicians/biologists/whatever? Note: I'm not saying they have to have publications in ultra-elite journals, just that work related to the project should be hitting respectable and established journals rather than just going to low quality interdisciplinary outlets.
b) Is my PhD topic one of my supervisors main areas of interests, or is it just something they do on the side (some complex systems guys are traditional mathematicians/physicists and their complex systems work is just a side-project, that on its own would not be enough to have got them their jobs. This is probably less of an issue in an applied mathematics department, but its not uncommon in physics to see senior/tenured people branching out into other non-physics fields like finance/biology/etc that are very different to their core physics area)
c) How many other good departments in the UK (or elsewhere) have people interested in related areas? (this gives a very rough estimate of the academic career prospects)
d) Where have previous PhD students supervised by the advisor ended up?
e) Where have previous PhD students from the department ended up?
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omegaSQU4RED
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(Original post by poohat)
Again its really about distinguishing yourself in a particular area. There are more than enough people doing (eg) mathematical/theoretical biology that if a biology department wants to hire a quant guy that they will go for one of these people, rather than considering a mathematician who's work can be vaguely applied to biology (and one of the reasons for this is as simple as the fact that you wouldnt be able to teach non-trivial undergrad/masters classes, since you would have almost no general background in the area outside your very narrow specialism). Ditto for statistics/ecology/etc departments. So I think you would probably be looking for jobs in mathematics departments rather than (eg) biology/statistics departments, unless you decided to go in a very different direction after your PhD and become essentially a mathematical biologist/statistician/etc. And this is certainly possible at postdoc level.

Getting a permanent job in a mathematics department isnt impossible, but it is insanely competitive and I would suspect that you would have the best chance if you were connected to a conventional area of mathematics, rather than something a bit 'out there' - departments usually a have a preference for hiring people in areas which they are already strong/established, rather than hiring people who are completely unconnected to the rest of the department's interest (an exception is the hiring of very senior people in areas where the department is hoping to expand). PDEs and dynamical systems are probably fine, but you do really need to check because its not as simple as saying "my work has some applications to biology therefore I can switch over into biology, at least not without spending several years as a postdoc essentially retraining as a mathematical biologist.

The questions to ask should be:

a) What journals does my supervior(s) regularly publish this work in, and are they considered good venues by non-interdisiciplinary mathematicians/biologists/whatever? Note: I'm not saying they have to have publications in ultra-elite journals, just that work related to the project should be hitting respectable and established journals rather than just going to low quality interdisciplinary outlets.
b) Is my PhD topic one of my supervisors main areas of interests, or is it just something they do on the side (some complex systems guys are traditional mathematicians/physicists and their complex systems work is just a side-project, that on its own would not be enough to have got them their jobs. This is probably less of an issue in an applied mathematics department, but its not uncommon in physics to see senior/tenured people branching out into other non-physics fields like finance/biology/etc that are very different to their core physics area)
c) How many other good departments in the UK (or elsewhere) have people interested in related areas? (this gives a very rough estimate of the academic career prospects)
d) Where have previous PhD students supervised by the advisor ended up?
e) Where have previous PhD students from the department ended up?
I have asked all the potential supervisors quite a lot of questions, just to weigh everything up.

At the moment, I'm 80% sure that I would like to go to Sussex. Your response made me think quite a bit about the interdisciplinary studentships and I've decided to be on the safe side and go for something that is strictly pure mathematical, which can be applied to other things. This completely rules out Surrey.

I am leaning towards Sussex because, although a lot of the analysis in the PDEs studentship will be somewhat new to me, I can sit in quite a few modules (e.g. calculus of variations, Fourier analysis, functional analysis and so forth) that I never had the opportunity to learn at Exeter and these modules aren't really present at Surrey either. Even though I will need to read up on a lot of analysis for the Sussex studentships (I have done real/complex analysis and some stuff on nonlinear systems/PDEs but that's about it), I'm thinking it could be a breath of fresh air once I get stuck into it. I have found I do actually enjoy analytical proofs as they get me thinking, and because of the research environment it will be much easier to get into proving things at postgraduate than at undergraduate.

I'm probably going for the PDEs one, on the ground that I hope to expand my pure mathematical knowledge and become adept at analysing equations as opposed to just solving them.
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poohat
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The spin-orbit coupling one at Surrey didnt seem interdisciplinary at all, it looked like straight forward applied mathematics. For what its worth, an applied mathematics PhD would probably have a slightly easier job market than a pure one, but you have to do what you enjoy more. The one thing I would recommend though is that you become a very competent programming during your PhD (I dont mean 'able to string 10 iines of code together', I mean actually good) because this will be very important if you end up looking for private sector afterwards.
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omegaSQU4RED
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(Original post by poohat)
The spin-orbit coupling one at Surrey didnt seem interdisciplinary at all, it looked like straight forward applied mathematics. For what its worth, an applied mathematics PhD would probably have a slightly easier job market than a pure one, but you have to do what you enjoy more. The one thing I would recommend though is that you become a very competent programming during your PhD (I dont mean 'able to string 10 iines of code together', I mean actually good) because this will be very important if you end up looking for private sector afterwards.
The spin-orbit coupling one sounded a bit interesting but mostly computational - so not much room for dynamics. The PhD programmes at Surrey also seemed a little bit woolly, which made me a bit reluctant to commit to them. The ones at Exeter and Sussex are more clearly defined.

I want to do something that is in the applied dynamics/PDEs area but also very rigorous. However, I have programming experience in MATLAB, LaTeX and C so I would say I'm already competent at programming, but it'll be one of those things I'll always be learning new stuff about during a PhD even if the degree programme doesn't directly incorporate it.
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poohat
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(Original post by OL1V3R)
The spin-orbit coupling one sounded a bit interesting but mostly computational - so not much room for dynamics. The PhD programmes at Surrey also seemed a little bit woolly, which made me a bit reluctant to commit to them. The ones at Exeter and Sussex are more clearly defined.

I want to do something that is in the applied dynamics/PDEs area but also very rigorous. However, I have programming experience in MATLAB, LaTeX and C so I would say I'm already competent at programming, but it'll be one of those things I'll always be learning new stuff about during a PhD even if the degree programme doesn't directly incorporate it.
fair enough, good luck with what you end up doing!
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