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I'm a PhD student in applied mathematics

I’m in a quiet period since I’ve submitted all that my supervisor asked for (I’m a first year), I like to read as many articles as I can get my hands on. I’ll use connected papers and google scholar (as well as Microsoft academic) to find all the associated articles I can and then import them into notability where I highlight, read and find good search terms for future papers. I also like to make notes and repeat any calculations I see so i can gain a deeper understanding. What should I be doing so that I can develop my skills as a researcher?

Am I doing this right, is it good practice do this?

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  • You definitely need to add your field, otherwise this is way to broad.
    – Arno
    Commented Mar 8, 2021 at 12:05
  • @Arno just did :)
    – Roberto_1986
    Commented Mar 8, 2021 at 12:07
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    A key part of doing a PhD is learning to not just wait around for your supervisor to give you work to do, but to take the initiative and come up with some research problem or project on your own. Your time is probably better spent this way rather than repeating old calculations.
    – astronat supports the strike
    Commented Mar 8, 2021 at 12:09
  • Though not at the weekends! Hope you are giving yourself some time off :)
    – astronat supports the strike
    Commented Mar 8, 2021 at 12:10
  • @astronat I agree with that. A lot of the calculations link with the work I'm doing so it's often beneficial to see how quantities are derived and used etc.
    – Roberto_1986
    Commented Mar 8, 2021 at 12:27

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Research is about answering unanswered questions. Primarily those that are important in a field.

So, to get started, ask a lot of questions and keep a notebook. Find out if they are already answered by reading and asking others. Figure out if they are significant in some way or could lead to things that are.

Let the questions lead to hypotheses - what the answers to the questions might be.

In applied math (not my field) the questions might involve things that are particularly difficult in some domain. Ask why? Ask whether they can be simplified. Make a hypothesis about how they might be simplified. Then validate/invalidate the hypothesis. Along the way, other questions will occur to you. Write them down (notebook).

Then...

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