After graduation, I will go to a graduate school to pursue a master by research degree in Applied Mathematics. The program will be research-based without any coursework.

The supervisors can suggest some courses to take if they think it's nececessary, but let's assume that the program will be research-based only.

I am confident with my mathematical skill. I believe it is good enough to understand research papers in the field I am interested. However, there are clearly a lot of advanced (applied or pure) mathematics topics that I have not learnt.

At the moment, it is not necessary for me to learn them, but I don't know if they will be useful in the future. For example, A gets inspired by a concept/technique in another field B to produce algorithm C in field D. Knowing things in B may help, but of course, it is not guaranteed and could be a waste of time.

Since the program is research-based, my time will be devoted mostly to research work, and there will be no time for any coursework. I wonder if it is a problem to start with research too early instead of spending time on taking advanced coursework to (at least) have a basic understanding of other fields in mathematics.

Should I delay the enrolment date to self-study some coursework, or should I just focus on doing research instead and learn things along the way?

  • Where do such programs exist? I assume you are an undergraduate. Yes?
    – Buffy
    Oct 14, 2022 at 11:37
  • @Buffy Exactly. This question is for Aus&NZ universities. I changed the tag
    – Neuchâtel
    Oct 14, 2022 at 11:48
  • but I have seen many situations where students went directly from 3-year bachelor to PhD in Australia. There was of course the influence of faculty members on these decisions. Still, I do not know if it is a good idea.
    – Neuchâtel
    Oct 14, 2022 at 11:49
  • 2
    Not sure how applicable that is to math, but in computer science many "research-based" programs still include a lot of studying. Not necessarily based on formal courses, but there is certainly still a lot that students (have to) learn "on the job". The expectation is definitely not that students already know everything they need to know in their subject at the start of the PhD.
    – xLeitix
    Oct 14, 2022 at 12:48
  • 2
    Every researcher necessarily needs to do some studying. Maybe not following specific actual courses, but reading text books, review articles etc. You seem to think that an NBA player does not need to practice or spend time in the fitness room. Oct 14, 2022 at 15:48

1 Answer 1


I don't know that Australian or New Zealand systems so this is a bit speculative. I'll assume, however that those systems are well designed and that accepted students are able to be successful and have good careers afterwards. Of course, if that were not the case those systems would change. So, as the kids say, obvs.

When students are accepted into a graduate program, someone makes an assessment that they are ready for that program and have a likelihood of success. It might be a committee, as in the US, or a specific advisor, as in Germany IIRC. But, the student's background is taken into account.

Once the student is in the system and has a (good) advisor, they are given advice (advisor -> advice). If the advice is good and the student follows it, they can prosper, though it takes work. Lots of hard work in math (been there, done that).

But, you don't seem to be trusting that the system is rational, when it actually is. Delaying your start for self study is highly speculative that you will focus on the right things, since you don't have an advisor to guide you. It might be ok and it might increase your odds of acceptance. OR NOT.

What you seem to want is something more like the US system, which would be fine if you are willing to move here. Lots of early coursework. Comprehensive exams to prove your readiness. Choose an advisor and a problem. Do the research. Write the dissertation. It is a fine system, but not the only rational system.

Expect that if you are accepted into a system then you are ready for study in that system. It works. Just. Do. It.

And, a life in academia is a life of learning. Don't fear to begin.

  • Thanks for your kind words!
    – Neuchâtel
    Oct 14, 2022 at 18:52

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