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As a new PhD student, how to balance learning and researching? I am in Australia and here we don't have any course in PhD period. I know I need to learn something about my programme, but sometimes just studying what I need immediately is not enough and not systematical. Could you give me some suggestions? or more generally, how to be a PhD student? I just want some advice!

My programme is on mathematical general relativity. In this area, we need knowledge from PDEs, geometry and algebra, and of course general relativity. I mean, so many fields are involved in this areas, how could you arrange your time to leaning new staff and researching and reading papers. I have some basic knowledge on all these area, but there still so many thing I need to learn. So many classic reference and book in this area I should read, But I don't think I could cover all this books in just few years. and I also want to spend more time to research.

Actually, just in order to understand a new paper or learn a method, I could study relevant materials very quickly, but always feel this is not systematical. I want know all of them, but the other problem emerges: I don't have enough time.

In the other words, if I call learning referred to read classical books and classical papers, and researching referred to think and read recent papers. I would like to learn how to split my time to do these two kinds of activities.

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To make this more specific (and more appropriate for math stackexchange), you should say what country you're in and give an idea of your background and future desires. For example, just speaking from my own perspective, your question almost doesn't make sense because my experience has been that studying for and passing the Ph.D. Qualifying Exams was the main focus for a student planning to get a Ph.D. But this was in the U.S., mostly at Group II departments and one middle-ranked Group I department. For some years/universities I've had experience with, the failure rate was nearly 70%. –  Dave L. Renfro May 13 at 13:51
    
@Dave L. Renfro Thanks for your advise. I have revised it. –  chuck May 13 at 22:01
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I think this is a bit of a unique problem to some extent. At least in the US and Canada, math students often take lots of courses in the first two years or so in order to completely prepare them (at the base level) for real research. What you could do is put together learning seminars with your fellow PhDs on topics that are of interest and necessity to you (and others). This way you can get exposure to those things that you need to learn without divesting too much of your own time. We do such things at my university, but more because we otherwise would never see certain topics in class. –  Cameron Williams May 13 at 23:18
    
@CameronWilliams Thanks, Cameron. Although I don't like courses actually, your advice is still helpful because this gives me a method to split my time. And actually I have already learned the most basic knowledge, I want to expand my knowledge in relevant area which you may not study in the classroom and you should extensively reading classical books and classical papers. So if I call learning referred to read classical books and classical papers, and researching referred to think and read recent papers. I would like to learn how to split my time to do these two kinds of activities. –  chuck May 14 at 8:34
    
The advice given here is relevant. " For example, in an undergraduate class any Ph.D. student at Stanford will have tried to learn absolutely all the material flawlessly. But in order to know everything needed to tackle an important problem on the frontier of human knowledge, one would have to spend years reading many books and articles. So you'll have to learn differently. But how?" –  littleO May 14 at 8:46

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