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I was not sure if I should even post this question at this site because it is not directly related to mathematics, but rather, careers in mathematics.

First of all, I have a B.S. in pure math. Currently I'm enrolled in a statistics graduate program. In my spare time I have been rereading my old algebra notes and I have studied analysis out of Royden and Follands book. Would it be possible to transition back into pure maths. I've noticed that it is easy to find individual who have moved to applied math from pure math, but I have not found anyone who has moved from applied math (or statistics) into pure math.

So my question...is it possible to move from a field like statistics back into pure math?

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Sure it is possible, at the usual cost of some time. But Statistics is very nice. If your tastes are "pure," then depending on research interests where you are, you can do stuff that is difficult or impossible to distinguish from pure mathematics. –  André Nicolas Oct 18 '11 at 3:36
    
I am eyeballing two areas. From my own reviewing to polish up on a weakness I had as an undergrad, I have been studying measure theory on my own so as to improve. Furthermore, I have been working through a O'Neill's Introduction to Differential Geometry book. So I've gained quite an interest in both measure theory and differential geometry. I'm okay with the time cost. I guess I'm looking at the admissions end. Will a statistics degree be an impediment to admission? –  S.Stein Oct 18 '11 at 6:19
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I am thinking in North American context only. You have an undergraduate degree in Mathematics. Many universities admit directly into the PhD program from the BSc. So why would they hold an MSc. in Statistics against you? Doesn't one welcome the return of a prodigal son or daughter? It will depend, as usual, on a suitable fit between grades, recommendations, and the level of the place you are applying to. Anyway, isn't Statistics Applied Measure Theory? –  André Nicolas Oct 18 '11 at 6:35
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I added a tag whose existence might allay your worries about posting a question about careers in mathematics :-) –  joriki Oct 18 '11 at 7:35
    
I would think a background in statistics makes you <b>more</b> rather than less interesting. Most departments look at a diverse background as a good thing. –  Bill Cook Oct 18 '11 at 13:07
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