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I have completed my undergraduate with a major in mathematics, however I was unable to properly apply myself for a variety of personal and medical reasons, and so was unable to achieve a suitable GPA to be accepted by any Masters Degree in Australia. However, I have not let my study lapse and have been applying myself, particularly to Analytic Number Theory (I've been through and completed the exercises of Apostol and am currently up to chapter 14 in Iwaniec and Kowalski) and Additive Combinatorics (Tao and Vu), and wish, if possible, to pursue further study with the goal of a PhD. Given my circumstances, are there any avenues that I should explore, or is this a pipe dream, and should I instead be more pragmatic and give up? I am aware, of course, that mathematics can be pursued as a hobby, but given my passion for it and improved medical and personal circumstances, I would wish to give it a try.

Apologies if this is not the proper forum to pose this question.

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    $\begingroup$ It’s Apostol $\endgroup$
    – J. W. Tanner
    Commented 22 hours ago
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    $\begingroup$ Thank you for this. $\endgroup$
    – everystringistaught
    Commented 9 hours ago

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It is a little difficult to answer this question without knowing more of your personal circumstances, but aiming to pursue a Masters degree instead of trying to enrol directly in a PhD programme might be a good direction. Some Masters programmes in European countries are not that competitive to get into, and have low fees, so this may be a viable avenue; students who do well in these programmes are then competitive applicants at worldwide PhD programmes. There are also institutions like ICTP (for students from the Global South) and AIMS (for African students) that look at applicants in the round and not just their Bachelor-level GPA, and offer scholarships at Masters level (called Diploma at ICTP).

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    $\begingroup$ I should clarify, I meant Masters degree (where I said programme) rather than PhD programme, I will amend it. I am in Australia and unfortunately cannot leave, but I really do appreciate your suggestions, thank you very much for your response. $\endgroup$
    – everystringistaught
    Commented 9 hours ago

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