SIAM News Blog

Ten Things I Learned During My Ph.D. Thesis

By Sam Relton

This article discusses the author’s experience as a Ph.D. student in numerical linear algebra at the University of Manchester. It is reproduced with permission and light edits from both LA Digest, the monthly newsletter of the SIAM Activity Group on Linear Algebra, and the author’s blog, where it first appeared on July 24, 2014.

For the past three years I’ve been doing my Ph.D. in applied maths at the University of Manchester. Now that I’m almost ready to submit my thesis, I thought I’d write up some tips for those who are just beginning their Ph.D. journey.

1. Use the best tools for the job

Spend some time at the beginning of your Ph.D. learning how to efficiently use the software necessary to research in your field. For example, learn LaTeX and pick an editor, learn how to use version control, and learn a programming language like MATLAB or Python. I like to use Emacs for writing up my research; it has great LaTeX support and numerous extensions for handling version control, code completion, blog writing, etc. A list of my favourite Emacs packages can be found here.

2. Write up EVERYTHING you do

I cannot overstate how important it is to write up your thoughts as you go along. Don’t just wait until the end; the following reasons demonstrate why:

  • Scribbled notes are easily lost
  • Writing a full argument helps you uncover any flaws
  • Written research is easy to share with your colleagues and supervisor
  • Writing” your thesis becomes a cut and paste job at the end

3. Keep a detailed bibliography

Keep the details of all of the articles and books you read while working on your Ph.D. You never know when something will become useful, and trying to find the same paper three months later is hard!

I recommend using BibTeX, which has great integration with LaTeX and Emacs, to store all citations. JabRef, which is available in the Ubuntu repositories, is great for managing your BibTeX database. It has some handy features for searching and outputting bibliographies based on a LaTeX .aux file that I use often.

4. Attend lots of conferences

At first, conferences might seem quite daunting; you get lost after slide three and spend the next 20 minutes thinking about your own research. STICK WITH IT!

After you’ve seen a few talks on a new subject, you’ll grasp the main concepts and be able to follow most presentations with no problems. Conferences are actually a great place to get new ideas, meet new collaborators, and learn about different areas. As a bonus you get to travel the world and try different cuisines – what could be better?

Charles Bridge, taken while at a conference in Prague.

5. Talk to people

This can be a little difficult (especially for us shy mathematicians), but speaking to people at conferences can be very rewarding. Trading expertise and ideas can really jump-start your own research and even lead to interesting collaborations. For example, two ideas that I’m currently exploring arose from idle conversations at conferences.

Conversation is also a great opportunity to network with current researchers and other Ph.D. students (they could be your future colleagues!) who you’re likely to meet again at future conferences. Getting to know researchers in your area can also help you choose an appropriate external examiner for your thesis.

6. Don’t be afraid to try crazy ideas

Sometimes weird ideas can lead to big insights and take your research in directions that you would never have thought of originally. Albert Einstein is quoted as saying “If we knew what it was we were doing, it would not be called research, would it?” For example, I had a little idea that I was working on for a few weeks, and a small part of it was proving quite difficult. Investigating the problem eventually turned into two journal papers and half of my thesis! 

On the other hand, if your quirky idea isn’t going anywhere after a couple of weeks, don’t waste your time. You’ve only got a few years to get your thesis together and your time would be better spent on something fruitful.

7. Work on your writing

In order to communicate your research to others, you have to write it down. Making your work easy to assimilate means that more people will read your paper and use your ideas, and your thesis will be easier to mark. The average quality of scientific writing is notoriously poor, so a good paper greatly increases your chances of publication as well.

For any subject reliant on maths, I’d recommend the Handbook of Writing for the Mathematical Sciences by Nick Higham as a good place to start.

8. Join a professional society

Another great way to meet people in your area (and get discounts on major conferences) is to join a professional society. For applied mathematicians in the UK, this typically means SIAM and the Institute of Mathematics and its Applications. Both offer student membership packages, and you receive a free subscription to SIAM News by joining SIAM.

9. Get involved with student societies

Organizing student activities is a great way to have fun while improving your CV. I’m president of the Manchester SIAM Student Chapter, and we get money each year to organize conferences for the Manchester Ph.D. students. If your university doesn’t have a SIAM student chapter, you can find information about starting one here.

I’ve really enjoyed organizing the conferences and recruiting some very interesting guest speakers. At our latest event, Pete Lomas from the Raspberry Pi Foundation spoke about the future of the device and education in computing. I wrote a blog post about this here.

10. Perform daily backups

This should be obvious, but many people forget to back up their work daily. I’ve personally been saved a few times by backups: once because my laptop died and a few other times when I accidentally deleted something important.

Your backups should not be on the same computer and should be automated, so you don’t forget to do it. For instance, I have the folder “Dropbox” in my Home folder synced with Dropbox (which automatically saves the last few changes to a file). I then run a backup script, written in Bash, on a daily basis to copy all new files across. You can automate this using cron in a Linux terminal. Windows users can automate this using the Windows Task Scheduler.

Finally: Don’t forget to have fun! Your Ph.D. is your project and there’s something wrong if you’re not enjoying your research.

Sam Relton is a postdoctoral researcher at the University of Manchester. His current research is on high-performance computing and task-based programming, and their use in large-scale linear algebra. Previously, he worked on theory and algorithms for computing matrix functions. His webpage can be found here:

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