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I have a very unusual profile for a PhD program applicant. I worked a few years in business after college and have recently completed a J.D. I did not have much research experience in college except my honors thesis. My grades in math are solid but I did not take any grad level classes. After the "distractions", I have decided that I would like to study math and do math research. I do love math and was quite good at it. I'm concerned that the admissions committee might view my trajectory as unfocused.

I would appreciate any feedback and suggestion as to how I can best remedy my situation.

Thank you so much for your help.

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    Put yourself in admission committee's shoes --- what evidence would you think convince them that Math PhD is not another "distraction"? Then do it! – Boris Bukh Mar 24 '15 at 0:55
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    You might consider taking some graduate level classes on a part time basis both to test the waters and to establish your credentials for admission to a graduate program. – Brian Borchers Mar 24 '15 at 1:04
  • Just worth a comment: Try to nail the Math Subject GRE. That will show programs that you haven't lost the math you knew back in undergraduate. – T K Mar 24 '15 at 15:18
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I don't know where you are, but at least in the US, research experience is not expected before enrolling in a PhD program. It is also not expected that you have take graduate-level classes, unless you are trying to get into a top program. However, it is true that admissions committees want to see that you are sufficiently motivated and committed.

My suggestion is that you apply to several masters programs and maybe a few PhD programs you are interested in. You may or may not get into the PhD programs, but it's easier to get into a master's program first. Having done a master's in math should be sufficient evidence that you're serious about doing a PhD (if indeed you still are), and this will make it easier to get into a better PhD program.

As you will need letters of recommendation anyway, I also suggest you contact some of your math professors from undergrad and let them know of your intentions. Then you can also ask about letters of recommendation and see if they have any suggestions for which kind of schools you should apply to. (By looking at your CV and transcripts, they should have a reasonable sense at what kind of schools you have a good shot at.)

By the way, as a bit of encouragment, many excellent mathematicians have started off in other careers, and your situation of wanting to do a math PhD after trying something else is not uncommon.

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I was successful in being admitted to top-20 Ph.D. programs in math in a similar situation. I had been out of school for 5 years, and I didn't do anything mathematically "serious" as an undergrad or in the interim.

I did exactly what Brian Borchers mentioned in his comment. I happened to live in the same city as an excellent university, and I asked a professor if I could sit in on his grad class. He kindly agreed, and I worked very hard, solved all the homework problems correctly and wrote them up, and slaved over my term project.

This gave me the confidence that yes, I really did want to go to grad school, and no doubt the professor's recommendation letter helped my case also. I recommend the same path to you if you have the opportunity.

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