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I would really appreciate any advice or suggestions anyone might have. I am currently a senior mathematics major, about to graduate in May. For two years, I have planned on going for my PhD in pure mathematics (my highest interests have been in algebra, number theory, and discrete math). I applied to 8 PhD programs and 1 masters program, the masters program just for the heck of it. I was accepted into the masters program, but I was rejected from 6 PhD programs and wait-listed on the other two. Neither of these last two would I really want to go to, but I would be happy at either of them nonetheless.

Now, the masters program is at Ohio State and gives full tuition waiver plus a minimum monthly stipend of $1950, plus a significantly reduced health insurance bill. The program specifically is the Master of Mathematical Sciences with concentration in Computational Sciences. The department is super lenient as to which courses I can take outside of their main core courses, as long as my course plan fits the computational theme and as long as my advisor signs off.

So, my question is, should I go to the masters program or should I go to one of the PhD programs (if I'm even accepted; again, I'm still wait-listed)? Will finishing this MMS program at Ohio State help my chances of getting in to a top-notch PhD program in the future? How common is it (in mathematics) for mathematicians to earn a (non-"incidental") masters degree before pursuing their PhD?

Thanks! Let me know if you want any clarification or further information.

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    I think its important for you to understand why you were turned down by 6 PhD programs in mathematics. This could be because you've aimed way to high, or it could be because of some specific flaw in your application, but you haven't provided us with much information. – Brian Borchers Mar 23 '15 at 2:15
  • Hello, this is the OP. Thank you all for your feedback so far. I should add that I believe my most significant flaw in my application materials was my Subject GRE score. It was abysmal, but I don't want to release any specifics. My grades have been really good (overall GPA of 3.80 and math/CS GPA of 3.90), I went to an REU, and I have several pre-print papers (although not actually published as of yet). I should also add that I come from a small, liberal arts college that is not well known. – user32088 Mar 23 '15 at 2:35
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    If you're serious about a PhD, you should take the subject again. At least for the general GRE (only one I had to take), that is very common. If it's very low, you might hit cutoffs where faculty won't even see an otherwise strong application (at least in my old field). – gnometorule Mar 23 '15 at 2:42
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I'm not in mathematics so take my answer for what it is. The fact that you were turned down by 6 PhD programs suggests that your applications probably weren't too strong. Maybe you had bad grades, bad test scores, bad recommendations, etc. Or you simply overestimated your application strength and applied to schools beyond your reach (i.e. top 15 schools).

Whatever it is, you need to overcome these shortcomings in your credentials. A Masters degree could be a great way to prove that you are grad school material, especially if you can demonstrate that you fit in academia by publishing article(s). This could be a jumping point to a decent PhD program. Generally, graduate programs would rather accept successful masters students over successful bachelors students, simply because good masters students already know the system and how to make it work.

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    I think this is generally good advice. However, a particular aspect of this that is discipline specific is that the OP wants to do a PhD in pure mathematics but has been accepted into an MS program in computational/applied mathematics. Having that master's degree isn't going to be particularly helpful in getting into a pure math PhD program. – Brian Borchers Mar 23 '15 at 2:13
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    @Brian Borchers. My plan as of now (if I go to Ohio State) is to plan my studies around algorithmic techniques in number theory or algebra. I'm hoping that focusing on either of these disciplines will help my application for a pure math PhD program. – user32088 Mar 23 '15 at 2:43
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    See the description of the MMS program's computational sciences track at Ohio State. It isn't a program that is designed for what you want to do, and it isn't clear to me that you'll be able to follow your interests within this program. math.osu.edu/grad/future/mms/computational-sciences – Brian Borchers Mar 23 '15 at 3:56
  • See also the list of required and elective courses: math.osu.edu/grad/current/mms/computational-sciences – Brian Borchers Mar 23 '15 at 4:04
  • That was the very first thing I did. Because it was not clear to me either, I contacted the director of graduate studies. He said that course plans centered around computational number theory and topological data analysis are especially encouraged. He also said that the department has been very lenient with elective course substitutions so long as they fit the computational theme and are approved by the advisor. – user32088 Mar 23 '15 at 5:10
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At this point it seems like your choice is actually whether to go for the Masters or not. So, you can either wait another year and apply again with the same application as before, hoping that you'll be luckier and get admitted somewhere... or you can get a jump-start on graduate studies, study for a couple of years, write up a good thesis (by all means, you should do a thesis) and then if you still want to go for the PhD you will have solid grades in graduate-level courses, a fresh batch of recommendations, some publishable work and a new perspective on whether to continue studies or enter industries, all of which would make you look that much better in the eyes of admissions committees -- all for $0. Given that you want to end up with a PhD, it seems like a no-brainer to me. :)

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I would recommend you start a program where you can begin your masters and then have the option to move on to a PhD (many programs have that option). I am just finishing my masters now in statistics and will not pursue a PhD anytime soon. Two reasons. One reason is because I want to work and make money. Second reason: I don't think I can stand being in school for another three years... in addition to more exams, thesis, and comp exams.

Maybe in the future I might change my mind. Or maybe an employer (like many do today) will help pay for me to pursue a PhD. You never know :)

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    The majority of this answer consists of information about yourself. Could you clarify how this information addresses the OP's question? – Pete L. Clark Mar 23 '15 at 1:20

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