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Let me introduce my background first. I am now a mathematical physics master student in Germany. I obtained my Bachelor in physics in Asia, used to be a M.Phil student in my undergraduate's university, but then I decide to quit, switching to Germany.

I don't take many math course except calculus,linear algebra and topology. Rather I self-study mathematics, including abstract algebra,analysis,geometry,etc. So I am not sure my mathematics background is good enough or not. But at least I got 1.0 in both geometry in manifolds and group and representation. So I am optimistic about my background.

In next semester, I will choose as many math course as I can, but not all of them are basic course. So I do not have a formal background of a math undergraduate student as. Also I don't know if my master degree can be count as a master in mathematics.

Question: Based on my situation, do I have a chance(or how many chance) to get admitted in U.S or Canada school for a pure math Phd? I know that unlike Europe, it seems they required a background of mathematics. So I am afraid it may hurt my chance to get admitted.

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There is a chance, but you may need some preparation first. And you may need to make an appeal for a special situation.

In the US, the undergraduate math program consists of approximately 10 - 16 semester-length courses covering the major areas of math and a few less mainstream topics. If you don't have something very close to that, then there are probably gaps in your education that will affect your chances.

Pick a couple of graduate programs you are interested in, and look at the undergraduate math programs at those institutions, especially the required courses. That will give you a sense of where you stand.

But the only way to get a valid answer to your question is to apply for admission to a program, listing what you know and having letters of recommendation that attest to your likelihood of success.

But you can probably also talk to someone at a university you are interested in and ask them for an informal assessment of any gaps you need to fill. Then, you might need to take a year or so seriously filling those gaps, perhaps by enrolling as a non-degree undergraduate somewhere.

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    I would say 16 is a bit of an overstatement; I had 11 (and that counts 2 for my senior thesis). Most liberal arts colleges don't allow departments to require more than 9 or 10, and some limit students to counting at most 1/3 of their credits from any department. Departments do have to be more careful/efficient under such constraints. Aug 9, 2020 at 16:47
  • @AlexanderWoo, I made an edit. Thanks. I generally had two math courses per semester which is the source of the 16.
    – Buffy
    Aug 9, 2020 at 16:53

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