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Mid-way through my undergraduate study, I realized that I am more interested in pure math than physics and wanted to apply for a PhD in pure math after my graduation. I had done research and written a thesis related to math (related to general relativity) for my undergraduate final year project under the supervision of a math lecturer. Unfortunately, after graduation I could not find a math research project for master’s degree and had to apply for a masters in another field. I ended up working on a project related to signal processing.

My undergraduate CGPA is not great (2.92/4.0). I worked hard in my master’s study and managed to publish a conference paper and a journal paper (one more currently requiring revisions for publication, and one more has not been submitted yet). This allowed me to graduate earlier. Now that I have completed my master’s degree, I want to apply for a PhD in pure math. I had consulted several lecturers/professors from my university as well as other universities at different countries, and I had been getting mixed opinions. I was told that transitioning to pure math is not that hard, I was told that my background is more qualified for applied math instead, some told me that I should consider PhD programs in the US since they generally offer coursework that can bridge the gaps in my background. I applied to five universities for PhD in applied math last year. I got rejected from four of them, the remaining one is still under review. This made me feel that my achievements in my master’s study are not helping me in the admissions at all.

But deep down, I am still more interested in pure math. Given my background, is it possible for me to get admitted to a PhD in pure math? I am aware that my background is not qualified for pure math. From what I have learned, it seems that I could either:

- Take the GRE general and math subject test (uncertain due to the pandemic) and apply to grad schools in the US or
- Apply to a master’s in pure math in other countries.

Did anyone have a similar experience? Or this is just a pipe dream?