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How does one apply to graduate school when he has been working for sometime? I am interested in pursuing a PhD in math and making a career switch. Would my work experience benefit my application (I am an actuary)?

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You may want to consider getting a masters first, then the professors in your masters program can write you recommendation letters. –  Noah Snyder Jan 24 '11 at 18:00
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A masters program should be much easier to get into, though. I am pretty sure that spending a lot of time on MO to get a high reputation is not the right way to go about it. –  Alex B. Jan 24 '11 at 18:07
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Not being on any recruitment committee, I shouldn't say more on this. If you already have an account with a high reputation, it won't hurt you to mention it, but I personally wouldn't expect it to magically open doors for you. If you don't, then I can think of many much better ways to employ your time between now and the application deadlines. –  Alex B. Jan 24 '11 at 18:22
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Having a high reputation on MO would be virtually useless. People want to see recommendations and GRE scores. To get into a masters program is much easier than to get into a Ph.D. program. You would ask your professors from undergrad for letters. They would write based on whatever recolletion they have of you, together with the information of the grades you got in your courses. –  Emerton Jan 25 '11 at 0:21
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The most important point to keep in mind about MO rep is that most mathematicians seem to still not know that MO exists (this is my experience from talking to people), and thus aren't even mentally prepared to be impressed. That said, there is some value to people having heard your name (it works for politicians, right), and MO could be a route to that. –  Ben Webster Jan 25 '11 at 4:03
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8 Answers

I am director of graduate admissions for a math Ph.D. program. My main advice is not to use recommendation letters from your current employment -- they are very unlikely to offer information relevant to your potential in research mathematics, even given that your job is highly quantitative. Instead, get letters from your undergrad math professors. You don't say how long you've been out of school -- if you're concerned your undergrad professors don't remember you, I would recommend sitting in on a course or two at a university near you, if the professor doesn't object. This will both a) give committees a chance to hear from someone who's talked math with you recently, and b) give you the chance to make sure that spending a lot of time learning math is what you want for the next phase of your life.

The advice to study hard for and do well on the subject GRE is also sound; the GRE has its problems, but it can be a good bolster for an applicant whose qualifications are unconventional in other ways.

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Please let me add (from experience) that it's a very good idea to do all of the homework, do it damn well, turn it in, and ask for feedback. I think most profs would be quite happy to do this, especially if you are obviously making a serious effort. –  Frank Thorne Jan 24 '11 at 23:36
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Yes, but if he's just sitting in the TA might (quite justifiably) not be willing to grade his papers. –  JSE Jan 24 '11 at 23:45
    
Very sound advice. In particular the bit about making sure going back to school in math is what the OP really wants. I remember a couple of older guys from grad school who came in from industry jobs; they found that the first couple of years challenged their motivation, and I can think of at least one who simply decided it wasn't for him after all, even though ability was not an issue. Whereas the temptation to drop everything appears weaker for students who have always been in school to begin with. –  Thierry Zell Jan 25 '11 at 3:08
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I was out of school for five years before grad school, and I did exactly what JSE recommended and I highly recommend it: I sat in on a graduate course at a (well-known) local university, to make sure I wanted to really quit my job to go to grad school, to give me some idea of what I might field I wanted to go into, and to make sure I had the mathematical chops to have a reasonable chance at success. My professor wrote a rec letter for me (which surely helped) and also gave me very useful advice on applying to grad school. All of this made a huge difference.

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That's a good point too: unvarnished advice on how to apply for grad school can't hurt. –  Thierry Zell Jan 25 '11 at 3:12
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The advice to apply separately for a master's program is very good. If you can take the GREs (general and math subject) and do well, then many institutions will be willing to take a chance on you as a master's student. Especially if you are willing to pay your own way even for the first year, then you should not have much trouble getting accepted at a decent program.

Reputation on MO is not worthless, but it is not a commodity with any recognized exchange rate. I am on the graduate admissions committee in my department, and I can't really imagine giving any weight to MO rep specifically. It is true that I have become deeply impressed by some undergraduates via their activities on this site. But this is not by virtue of having accumulated a certain amount of reputation per se but rather because of the deep knowledge and cleverness that oozes out of every corner of their posts. Anyway, I sincerely doubt that these pyrotechnic undergrads need a leg up in their graduate applications: there will be ample conventional evidence of their excellence.

As for whether being an actuary will be helpful in your application: that will probably be very department-specific. As others have said, if you can find a department which has some kind of actuarial program, it is worth contacting someone in that program (even if you don't want to pursue actuarial anything as part of your PhD) because they will be able to evaluate your skills and accomplishments and, if appropriate, convey their esteem to the admissions committee. To give one data point, I believe the current admissions committee at UGA has little or no experience with actuarial science, and it would be hard for us to evaluate a candidate with that background. I have the vague impression that actuaries are smart, mathematically minded people (and wasn't one of the biggest Jeopardy winners of the classical era an actuary?), but if you told me you had passed seven out of nine actuarial exams [note: I have no idea whether there are nine actuarial exams; I just made the number up], I wouldn't know what to make of it.

Come to think of it, perhaps a letter from someone with one foot in the actuarial community and another in academic mathematics would be a good idea. She could explain and translate your accomplishment into terms we would better understand.

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@Pete: FYI, the detailed syllabi for the exams and sample tests are available from the Society of Actuaries' website, soa.org/Home.aspx. The first couple of exam are at a nicely undergraduate-level, but as far as I can tell, beyond that it gets really into some heavy-duty probability (although obviously a bit specialized and, dare I say, quaint; I don't think you'll find measure-theoretic stuff in there). –  Thierry Zell Jan 25 '11 at 3:00
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Of course, your situation is not as mine was. If your undergraduate professors don't remember you, then it will be hard to get good letters of reference. In which case you need to develop or utilize your current relationships to get good letters of reference. For encouragement though, a brief telling of my experience follows.

I spent 5 years in industry between leaving my undergraduate institution and entering graduate school. I still had professors who remembered me and were willing to write letters of recommendation. That, combined with luck, a system for mass application (to over 70 programs, essentially down to 4 that I liked and 1 I really cared to attend), and a strong personal letter indicating a strong motivation for bringing my work experience into degree studies, was instrumental in my securing entry to graduate school. I did not need to provide references from work, but I was prepared to supply those.

One thing I could have done to improve my chances was to talk to some members of the department I liked and find out what parts of my situation would help my application. Igor Rivin seemed especially helpful in his comments and offer of time; if you get some one like that at the department you want to attend, pump then for all they are worth and repay them as appropriate, usually by thank you letters, acknowledgments in publications, and small tokens of candy or liquor or textbook or other appropriate treat. (Do this in a socially acceptable way, and not like bribing a member of an admissions committee.)

Gerhard "Ask Me About System Design" Paseman, 2011.01.24

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Also, there are several Related questions (listed on the right of my screen, perhaps your screen as well) on MathOverflow which may have useful information for you. Gerhard "Ask Me About System Design" Paseman, 2011.01.24 –  Gerhard Paseman Jan 24 '11 at 22:40
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I was in a similar position: I worked in a technical, mathematically sophisticated but very specialized job for ten years out of undergraduate before applying to an applied math PhD program. I am currently in my first year of this program.

In addition to taking the subject GRE, I got letters of recommendation from supervisors at various technical positions I had been in. I was lucky in that my employer is very well known in the academic circles in my area, so I think that the math department believed that the letters of recommendations knew what they were talking about, even if they didn't understand them exactly.

So, it might be helpful if you can get letters of recommendation from some colleagues who are at least in touch with academic circles. Depending on the size of your employer and/or the school, this might be easier or harder.

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I'm a faculty member who reviews many applications. I think that your actuarial experience would actually be a positive factor in your application to some graduate programs (particularly for programs with professional master's degrees and applied programs that focus on applications in financial mathematics, applied statistics, etc.), but it would not be helpful (and might even hurt) in other cases (e.g. the top PhD programs in pure mathematics.)

I would encourage you to either start taking graduate courses at a local university on a part time basis, or to enter a full time MS program with the intention of transferring to a PhD program after completing the MS.

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Maybe I'm being naive, but I have trouble imagining actuarial experience could actively hurt a candidate except in the most extreme of cases, maybe one or two dozen of the very top programs. –  Thierry Zell Jan 26 '11 at 1:25
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For what it's worth, I don't see how actuarial experience per se could hurt a candidate applying to any program. –  Pete L. Clark Jan 26 '11 at 8:11
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Pete- "actuarial experience" means "you wasted time working for a living rather than being a student, so you aren't sufficiently dedicated to the study of mathematics." I'm not saying that I agree with this attitude, but it's certainly an attitude that I've seen expressed in some quarters. –  Brian Borchers Feb 2 '11 at 1:52
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As an actuary, if you have passed a reasonable number of exams, you will have a proven record of mathematical ability. Most graduate programs should be familiar with actuarial science, and it might help if you apply to a school that does have an actuarial program (housed in math preferably), even if that's not what you're planning to specialize in.

There shouldn't be any resistance from the math department; there might be some administrative issues from the university-wide graduate school, which is usually the place where admissions take place. But in general, if the Math dept is interested, they'll be able to help you navigate these complications.

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By the way, I'm just addressing the issue of getting into a graduate school. Getting into the school of your choice might be trickier, and the masters-first route might make more sense there. –  Thierry Zell Jan 25 '11 at 4:35
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Assuming you are in the US and applying to US graduate school. Good GRE scores. Unless you are applying to Harvard or Princeton, that is your primary thing. These others (including recommendations) are secondary... They may be used when you have weak GRE scores, for a graduate program to admit you anyway.

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@Gerald: I am not at Harvard or Princeton (anymore!), but in our program along with GRE scores, we look just as carefully at the student's undergraduate coursework. We want to see both that they are well-prepared in things like algebra, topology and analysis and also that they have done well in at least one graduate level course (or the closest possible equivalent their program offers). –  Pete L. Clark Jan 26 '11 at 8:14
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I would go further and say a lot of places only use GRE scores as a safety check. That is mostly what we use them for, though a very high score does help your application. –  Kimball Jan 26 '11 at 10:31
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