A PhD is a daunting but ultimately rewarding undertaking. Mark, a Computational Applied Mathematics MSc student, shares how he decided to pursue further study, along with his tips on applying for PhDs.

By Mark Alvares

In March 2024 I went to TakeAIM, a conference showcasing some of the most exciting applied mathematics research by master’s and PhD students across the UK. At the time I was working as a data analyst, having graduated from my bachelor’s degree in pure mathematics the year before. I had been pretty burnt out with maths by the time I graduated, and was not planning on going back to university.

I had already started to miss studying maths, and this conference opened my eyes to the exciting research areas in applied and computational maths, to fields I had never paid much attention to before. I decided I wanted to do research, and the first step on that journey would be to complete a master’s degree.

Fast forward to now and I am completing my master’s dissertation, getting ready to start a PhD in Oxford in October. So how did I decide that a PhD was right for me? What did I do during my MSc to prepare for a PhD? And what should you do if you want to pursue a PhD?

Is a PhD right for me?

This is the first question you should ask yourself if you are interested in doing a PhD. A PhD is different to any other job, but also different to studying for a bachelor’s or master’s, so you should make sure you know what’s involved. I spoke to some friends that are doing PhDs, some of the tutors this year, some lecturers, and the Careers Service to get some different perspectives on what research and academia is really like.

You should also think about what you want to do in the medium-to-long term. Do you want to pursue a career in research? If so, then a PhD is the logical first step.

The reason I personally am doing a PhD is because I love doing maths and I’m excited to try and push the boundaries of human knowledge. The research I will be doing uses tools from a wide range of areas, including functional analysis, differential geometry, algorithms, and physics, combining them in amazing ways to simulate physical phenomena. When I try and read papers I often understand very little but I’m eager to dive into the details, to learn about how numerical schemes actually work under the hood, their theoretical justifications, and the physical validity of their solutions.

If you’re like me you may worry that you’re not good enough to make it in academia, that you weren’t a child prodigy or something. That’s okay! Maths ability is not a linear scale where everyone is either in front of or behind someone else – there are so many ways to do well, so many different problems to suit all kinds of people, so the most important thing is that you are really curious about finding out the truth and that you enjoy doing maths.

Applying for PhDs

Let’s say you have decided you want to do research – you know what’s involved, you’ve enjoyed the research aspects of your degree, and now you want to apply . How do you go about it?

First, you will need a topic. From what I’ve found, you’re not expected to have nailed down an exact research problem and know all the details around it, but you should know the rough area you’re interested in. Then, on most university websites, you can find a ‘research’ page for the maths department that lists the different research groups and the academics within them.

Research groups | School of Mathematics

Have a browse through the academics’ websites and see if any of them align with your research interests, and if they are taking PhD students – sometimes they will explicitly say they are looking for PhD students and sometimes they won’t. Try and read some of their publications. Don’t worry if you don’t understand the details, but try and get a high-level understanding of what they are interested in and where you might fit in. If they have written a survey paper (also known as a review), this is a great place to start as it will likely be aimed at non-experts in the field.

Once you’ve found a potential supervisor, it is a good idea to send them a concise email saying who you are, what interests you about their research, and some specific questions. There is plenty of good advice online on doing this, for example:

Notes for potential student collaborators | Bastian Rieck

The next step varies a lot depending on where you’re applying, not just across different countries but even within the UK. In some cases (like Centres for Doctoral Training in the UK or most US programmes), you apply to a general programme and get paired with a supervisor later, but I think it’s still a good idea to know in advance who you may want to supervise your project. In many cases, you will apply directly to a supervisor.

After you apply, you may be invited to an interview. You should hopefully be told what this will involve (if not, there is no harm in asking), for example, giving a presentation about a project. Like with any job interview, preparation is key. Make sure you know the details of previous research projects inside-out, for example, your undergraduate dissertation.

You should also have a very clear idea of why you want to do a PhD, why you want to work in your chosen area specifically, and what you want to do afterwards. From my understanding, competency-based questions are much less common than they are in graduate job interviews, but it won’t hurt to prepare for these too.

Competency-based interviews | Prospects

You should do at least one mock interview before, if not more. The University’s Careers Service offers mock interviews, and you can also ask a friend to do one with you.

Interviews and assessment centres | Careers Service

To summarise my tips:

• Find out what academic research entails and think why you want to do a PhD
• Build your CV by engaging with the research-focussed aspects of your course
• Find an area of maths that interests you
• Read about different university research groups, academics, and PhD programmes
• Contact potential supervisors
• Apply to a programme/supervisor
• Prepare for the interview
  • Know your motivation and the details of previous research projects
  • Do mock interview(s)

And make sure to enjoy yourself along the way!

Not quite ready for independent research?

The Computational Applied Mathematics MSc programme is an excellent way to learn how to do research, and will expose you to lots of difficult and exciting maths.

Learning to do research with an MSc | School of Mathematics blog

So you want to be a mathematician? / School of Mathematics by blogadmin is licensed under a Creative Commons Attribution CC BY 3.0

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