International Medical student who wants to do a math phd
Much of this answer will depend on several variables that are currently not disclosed:

Where is your undergraduate degree from?

Have you taken classes in topology, analytic geometry, complex analysis, numerical analysis, computer programming, etc?

The rigor of the math classes you took during medical school.

A demonstrable capability to succeed in a U.S. top 20 math PhD program while having what would often constitute a minor in math at many universities in the U.S.

Why are you going to medical school, only to switch fields in a sense?



These are my thoughts on each of these points (as someone who has evaluated candidates for admission into graduate programs in mathematics):

If your degree is from a well regarded university in the U.S. or Europe, this will bode better in your favor. If your undergrad degree is from somewhere in the MENA region, your case will be harder. Right or wrong, many Top 20 programs in the U.S. would be hesitant to place great weight or significance on someone earning 90% in Calc II at a university in Morocco.  (I am perhaps overstating the situation here for emphasis).
I will be honest--when I get an application on my desk from the MENA region, especially if they do not have an undergrad degree in math, I tend to not place it on the top of my review stack. Applicants of this sort seem to rarely offer any reason for their attempt at admission beyond stating that they are &quot;interested in math&quot; and want to come to America to study it. (The MENA region is not the only area of the world that does this, mind you).

If you are interested in medical imaging, you will need to have a background in analytic geometry. My current area of research is in...yep...medical imaging from a mathematical standpoint. It is a field that requires abilities in graph theory, analytic geometry, statistics, computer programming (emphasis on computer programming). There would be absolutely no way that I would accept a student who could not program pretty well in an object oriented language (C++, Java, C#). Knowing some Python is usually not enough.

While I have not personally been to medical school, I have several associates who have. I must admit that I am rather dubious that one could take math courses while also succeeding in medical school. Maybe it is possible. I just know that there would have been no way that I could have pursued a second curriculum while I was working on a PhD.

One of my former institutions required (for admission) all of the classes you have listed, plus at least two other classes you have not. Exceptions were very rare. A minor in math was never enough for direct admission to the PhD program. A few exceptions were admitted provisionally (unfunded) to the master's program.

If I saw an applicant with a medical degree applying for a PhD program in mathematics, I would probably question the applicant's motivations (not how motivated they are, but WHY they are applying). A medical degree and a PhD in math are not usually seen in combination with one another (unlike an MBA/JD combo or something). I would question if the applicant had somehow been barred from practicing medicine or something. If you can explain your motivations clearly in an application, this would be wise.



I will say a few closing words on this subject.
Thinking math is &quot;interesting&quot; is likely never going to get you past the gates of a top 20 math program in the U.S. Nor will it be enough to sustain you through the 4 or 5 years it would take to obtain a PhD.
I have no idea what you finances are like, but it may be a wiser move to find actual employment in the medical imaging field with your medical degree itself. Obtaining a medical degree and then a PhD may complicate your ability to be placed in a residency as a physician.
Note that all of this is not to say that you cannot end up at a top 20 math program in the U.S. If you get a very high GRE score, maybe you can climb the wall and actually break in as a rather nontraditional student. Never say never I guess.
Best of luck.