I am currently a senior completing a Bachelors Degree of Science in Mathematics at Northern Arizona University. I am beginning to plan for graduate school. I will be applying to many Ph.D programs and a few Masters programs as a backup plan (all pure mathematics).

I am starting to think about how to write my personal statement. I am seeking advice regarding the process of writing a personal statement . I am mostly curious about what people usually talk about in these things. I obviously want to convey my interest and potential in mathematics research. But my problem is: I do not have the mathematical background to have an idea what I want to specialize in. I know that this hurts my chances at being competitive. My undergraduate degree has simply not exposed me to enough mathematics.

As far as research experience goes, I have done an undergraduate research project for credit for my degree. The topic was Hyperplane Arrangements. It culminated in a paper that will mostly serve as a summary of what we did as a resource for my adviser. It isn't something that is publishable since we did not prove anything significant.

I will also be participating in another project this year. We will be studying coxeter groups and their commutation graphs.

Both of these projects interest me but I do not have the breadth of knowledge to decide if these are something I want to spend years specializing in.

I appreciate any advice - relevant to my concerns or just advice in general.

Thank you.

closed as off-topic by scaaahu, Enthusiastic Engineer, user3209815, Fomite, louic Jun 29 '18 at 16:38

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    @EnthusiasticEngineer This is not a duplicate question. I am asking for advice on writing a personal statement. You have linked my question to a thread on "Advice for Weak Applicants." – johnny133253 Jun 28 '18 at 8:50
  • Questions seeking general personal advice are considered as shopping questions, so your question is subject to be closed. In the linked question you can find some good advice on your problem, if not you can easily ignore this little help and search for more advice on other questions. – Enthusiastic Engineer Jun 28 '18 at 8:53
  • @EnthusiasticEngineer Sorry, but I disagree with you. My question is specific to mathematics programs. The thread you linked does not answer my question. – johnny133253 Jun 28 '18 at 9:04
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    @EnthusiasticEngineer Actually, the SOP section of that question is actively harmful in math. Following the advice there would make you come off some mixture of pretentious and crazy. – Ben Webster Jun 28 '18 at 12:37

Honestly, it seems like you are worrying more than you should about not having chosen a specialization. I wouldn't worry about that: that's not something which is expected of students finishing a BA in the US. Even if you think you have, changing your mind about it is something which is normal and expected. So, it's very reasonable to worry about having less background than other students, but more in the context of general preparedness, rather than your personal statement.

So what should you write in your personal statement? Generally it's for things that the person considering your application would like to know, but which aren't clear from the other parts of your application. Things like: explaining about something unusual in your career path, like taking time off after finishing your degree; what your ultimate career plans are; how you became interested in mathematics; how your undergraduate research projects went and what you did in them; any work you did outside of courses (which is relevant to math! No one cares about your great success in the marching band). I have to admit, generally these personal statements contain no useful information, and a lot more attention is paid to transcripts and letters. I generally only read them carefully if there's something I'm confused about with the application they should explain.


I'll tell you how my experience went, maybe you'll have some ideas. I'm from Brazil, got a master's degree here, and I'm starting my PhD in the US next month (in a big state university, with a nice scholarship, in my opinion).

From what I saw, it is more about what you have accomplished so far, then what you want to specialize in, since there are programs on which you don't even choose an advisor until the end of your first year. This means you will have the time to get to know people and maybe change your mind along the way. Although, it can't hurt to look up the CVs and publications of professors you might want to work with, before choosing the universities to apply.

Anyway, I structured my SOP in four parts:

  • first: I started briefly telling my life history and how did I end up in mathematics. For example, during high school I took a two years technician course in Edifications/Civil Engineering, ended up screwing the entrance exams in the good universities here (because I focused only on the final project, which took 6 months), and was only accepted in a Licenciate course in mathematics (focused only in teaching). I ended up disliking working in Engineering, and disliking that math course. I was 18 at the time (I'm 24 now), and I wasn't aware that pure mathematics courses even existed (silly me, right?). But when I found out? Oh boy!

  • second: now I'm pursuing my B.Sc. degree. I had a fat scholarship, and I did a very long undergraduate thesis. My supervisor (which became my master's advisor later) suggested that we should revise it all, rewrite some things, add a topic or two, and throw in some exercises. Bottom line? I didn't even start my PhD, and our 560 pages book on introductory Lorentz Geometry (curves and surfaces) was accepted this month for publication with the Brazillian Mathematical Society. Go me! I went and finished my master's thesis in the same time we were finishing the book, ok.

  • third: if things were going so well, why did I want to leave? Basically, because the political and economical situation here in Brazil is crap (it definitely went downhill after the coup). I talked a bit about the budget cuts in science and education, and how I'd probably have to give up on mathematics if I stayed here.

  • fourth: if I decided to try going to the US, why did I choose to apply to this particular university? I concluded the essay with a personalized paragraph for each university.

Of course, what worked for me might not work for you, YMMV. You also have to consider other things in your application. I had a bad result in the GRE, but I got nice letters of recomendation (which were taken in consideration, despite my references not being world-class researchers). Also, even if the book (my main accomplishment so far) looks like a nuke, I only got accepted in one of the five universities I applied to.

I think that what you should take from my answer is the way that each part of the essay is connected with the previous one. That makes the text very fluid and the reading easier. I hope this is helpful and I wish you the best of luck.

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