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I am a Physics undergrad who is interested in pursuing a PhD in pure maths in the future (algebraic geometry/topology) but I am a bit unsure. My question is quite general, and I don't wish to provide more background for fear of bias in the answers.

My question: Is it is advisable/possible/unfavorable/favorable to apply for a PhD in a field, different from that in which you have done most of your undergraduate research?

My research (includes just reading and understanding papers, writing summaries until now, I havent published anything) mostly includes Quantum field theory, and gauge theory. Would the selection committee turn down an application to a pure maths field, if I have no research experience whatsoever?

I would also like to ask the question other way round. What if I concentrate my undergraduate research SOLELY on topics in pure maths such as algebraic geometry/topology and take other physics courses, would I be able to apply to a string theory PhD with a high chance of success?

Should I consider spending time on both of these (which is almost an impossible task), to improve my chances in both the areas or would research in one area, and grad level courses in the other suffice?

In brief: Should the PhD field you are applying to be the same as your undergraduate research area?

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See this answer for a related discussion. – eykanal Feb 11 '13 at 15:55
I thought we had covered this question somewhat in your previous question about recommendation letters.… – blackace Feb 12 '13 at 2:28
@blackace: I think that question is a bit different, as it asks about recommendation letters from physicists. So it maybe possible, that I get recommendation letters from mathematicians (under whom I have taken courses), but all my undergraduate research is in physics. Would it reduce my chances of getting into a good grad school? – user2734 Feb 12 '13 at 2:31

4 Answers 4

You can definitely apply in a different field than your undergraduate. Some major fields of research don't even exist as undergraduate majors in most colleges (e.g., neuroscience), so it's understood that many students will come from different backgrounds.

The more similar your major is to the new topic, the easier the learning curve. If your major is significantly different you may want to take some post-bachelors undergraduate courses before beginning the PhD program to bring yourself up to speed.

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You should do what makes you happy and you find interesting. PhD is a considerable investment and it is worthwhile only if you are highly interested in your research. It is quite common for people to change domain from undergrad to grad studies (between math/CS/physics/Bio-info).

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Yes, this is definitely possible.

When I was doing my undergraduate degree, I was pretty sure my interests lied within the area of nonlinear dynamics and systems of ODEs, and I had picked up some research experience in my third year as well as during my MMath dissertation. My third year summer project was on critical factors and tipping points (with application to a prey-predator population model) and my MMath dissertation was on nonlinear laser dynamics. However, I was finding towards the end of my undergraduate degree and the MMath project that I wanted to do something more rigorous, involving pure mathematical analysis and how this applies to partial differential equations (and I had taken some courses in fluid mechanics and PDEs beforehand). My current project is on statistical solutions of Navier-Stokes equations, which is a very different area to what I researched at undergraduate level. My ex-supervisor gave me vanilla advice, saying "your PhD topic should be the same as your MMath project" - in some sense this is true, because one piece of advice I've heard is that one should choose an area to specialise in as soon as possible, even though this may not suit everyone (and when applying for PhDs I was very unsure about the area of research I wanted to pursue, so I had offers to study a wide range of topics with varying mathematical backgrounds). I chose my current project because there would be opportunities to fill in the gaps from my previous university, the area of research is fairly lucrative, it would enable me to see things I had applied before in a new and rigorous light. I explained all this to my supervisor when I had my interview with her and admitted that my background of mathematical analysis wasn't as strong as it could be - but I emphasised that I was willing to learn and that the project in question would be one to help me become a better all-round mathematician. Subsequently I was accepted onto the project and (bar the usual PhD student woes) on the whole I am quite enjoying it as it's a completely different area to the ones my previous university offered. My background would imply that my strengths lied in numerical methods and applied nonlinear dynamics, and even though I would probably have much better luck at PhD programmes along the lines of these, I decided that I didn't want to spend my academic career simply "number-crunching" and doing stuff I found relatively straightforward. Doing more pure stuff is harder, but in my opinion, much more rewarding (as you can actually understand the background theory of why things are the way they are rather than just running a simulation and accepting that it works).

So to answer your question, if you apply to a PhD programme and explain your strengths and limitations of your background (be honest!) and explain why you would benefit from the programme, then that can be equally as important as knowing what the research itself is about I suppose. Some people may not advise making the change of topic, but if your heart is set on it, then grab the opportunity while you can.

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When you apply for a PhD, they are not expecting you to already be an excellent researcher in the field you want to go into, most early research is purely for experience and training and seeing whether you like research and they will understand that.

What's more important is that you can explain the choices you've made. They will look at your research history in context of your PhD choice. You just have to make sure that it shows off the skills they want you to have to do the PhD, those skills are not really subject specific.

I did an undergraduate and masters in Physics and got offers from Oxford, Cambridge and CRUK among other less well known UK institutions to do PhDs in cancer research so it's definitely not essential to have experience before hand, but will also depend on how competitive your chosen field is.

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