Applying to PhD programs in mathematics

Parents Forum
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<p>Everyone on this site was very helpful when S was applying to college as a math major. Now S is a junior in college and will be applying to PhD programs next year. I know he will be getting help with the process from his advisors at school and I've encouraged him to talk to grad students. He's not sure of his research interest at this time because he still interested in many topics. He's doing two research projects this semester and will be doing a senior thesis next year which will help him to more clearly define his interests.</p>

<p>My questions have to do with the application and selection process. Should he begin to visit programs before he applies and talk to faculty? How competitive are these programs and what do they look for in an applicant? At what stage in the process do the formal interviews occur? Are they at the candidate's expense? We've both hear that good students from good schools tend to not do well on the GRE's. What should he be doing to prepare?</p>

<p>I know there were a lot of math parents around these boards when S was applying to college and I'm wondering if any of you have kids who are also beginning this process.</p>

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<p>If you haven't already, post this on the graduate school board.</p>

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<p>I'm a history major going for history in grad school and have gone through the process (and unfaiirly/surprisely am STILL in it!).</p>

<p>Grad school is MORE competitive than you or your S can imagine- the acceptance rates are worse than Harvard and Yale for undergrad, especially for PhD. They are generally full-funded with TA-ships and stipend.</p>

<p>I would first recommend to your S to really figure out what he wants to study- really focus his topic. He might not have it down until he's half-way through his senior thesis (as I did) and that's okay. It's part of the reason why PhD programs like to see people taking a year off so they can get the best senior year work. See if his idea flies by his advisors, if it doesn't, he has to back to the drawing board.</p>

<p>The GRE will be incredibly important for him, especially the math. He just needs to get the minimum for his Verbal. He's got to shoot above 700.</p>

<p>Formal interviews tend to happen around January/February usually on the program's expense if they invite the student out or they just do a phone interview. I see it happen more often in lab sciences, not really for anything else.</p>

<p>Generally grad programs will pay for the student to visit for interview or admit weekends but not anything else- only if they really want the kid.</p>

<p>But... your S should be prepared to have some extra cash around if he has to apply to MA programs at the last minute if he still wants to go to grad school and not take a year off. Be prepared for the worst (My parents and I are still going through this shock that I'll have to apply to MA programs without funding!)</p>

<p>If the programs that he wants to go to are within his reach, by all means, go and visit the faculty. But he needs to be prepared for the <em>grilling</em> questions as the facutly will be "interview" him however informal the meeting will be. It's really scary because that's when students realize how stupid they are compared to these brilliant people and wonder why they're going to grad school again.</p>

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<p>Thanks s much ticklemepink!
I'll also post this on the grad school forum, but I thought I'd get more responses here.</p>

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<p>A good book to read: </p>

<p>Amazon.com:</a> A Mathematician's Survival Guide: Graduate School and Early Career Development: Steven G. Krantz: Books </p>

<p>Good luck. My S may be down that path several years from now.</p>

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<p>Mine has just been very successful with a top five program in Musicology studies - where they selected a total of 4 students for the entire musicology program! (to give you an idea of how competitive it is.)</p>

<p>You really must contact the specific faculty members you wish to work with before applying - otherwise, unless your application, recommendations, GPA, letter of interests, and etc. are absolutely incredible when compared with an already incredible group of applicants, you'll just get lost in the shuffle. </p>

<p>GREs just got you into the ballpark, though I have heard they have been used as tiebreakers between different size fellowships, not usually as a dealbreaker in admissions themselves. </p>

<p>Then you have to hone in quite specifically on what it is you wish to study, and why this particular faculty member should want to be your long-term mentor. It is understood of course that this can change once you are there, but if you can't make the case now as to why you should be a long-term colleague and someone who will carry the reputation of that faculty member forward, they would have no reason to believe you could do so once you are there. </p>

<p>Recs are extraordinarily important and, again, have to be written from the point of view of why this applicant would make a good future colleague. Famous scholars help, but not as much as one who really knows the applicant and can attest to her future promise. </p>

<p>Good luck! Mine is still basking in her good fortune (there are more applications still out.) Oh, and yes, once they want you, they will fly you there, wine and dine you, etc., etc. - there are little in the way of waiting lists, as those who would be on such lists are likely be snapped up by their competitors, so you do get the full-court press.</p>

<p>P.S. There are a lot of really good resources on this site: Find</a> the Graduate School That's Right for You — PhDs.org Graduate School Guide</p>

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<p>P.S. I explained it to my d. as the equivalent of applying for a 5-year/$300,000 job (tuition plus fellowship funding plus extras), and the chance to move up in one's career. You need to treat the application that way, because, in fact, that's what it is. And if you need to spend some extra money, etc. to do it, now's the time to spend it.</p>

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<p>cookiemom,
ticklemepink has hit the nail on the head.
1) Acceptance to top Ph.D. programs is phenomenally competitive-some with <5% acceptance rate.
2) It is vitally important for your S to narrow his focus to exactly what he wants to study. Graduate school acceptances really are all about the "fit." Is there a professor in the department who is doing the work/research that your S wants to do? When your S writes his "statement of purpose" for each application, he will have to define which area he wants to pursue.
3) My S did not go through interviews. He was invited to accepted students visits, at the university's expense.
4) I don't know that your S has to visit any of the programs before he applies. He should use his current undergrad professors as mentors to guide him to the best programs within his reach. He can read everything he needs to read about the programs online.
5) Not sure about your comment that good students from good schools don't do well on the GRE's. While I don't know anything about a math specific subject test for the GRE's, for the regular GRE's that everyone takes, there is a math component and a verbal component and a writing component. I remember my S saying that the math was basically the same as SAT math, and the verbal might have been a touch more difficult. He got the exact same score as he did on the SAT's.</p>

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<p>Some good guidance here on how to select a school: Harvard</a> Mathematics Department : Graduate Schools and Fellowships in Mathematics (2007-2008)</p>

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<p>i went through the process last year and, while much of the above advice is good, not all of it applies perfectly to phd admissions in pure mathematics. in regard to admissions in pure math, a few (chronologically ordered) thoughts:</p>

<p>1) begin talks about graduate admissions with some faculty at his university prior to summer break. they will have a decent idea of his abilities and as such will give him an idea of where he should begin to focus his search as well as provide some ideas in terms of research going forward.</p>

<p>2) take the regular gre before fall simply to get it out of the way. math departments arent going to care much about the verbal and writing scores. so long as theyre both good enough to validate a command of the english language, all is good. math should be 780+, though this shouldnt be much of an issue.</p>

<p>3) download the practice gre math subject exam from the ets website and take it. the exam is NOT terribly difficult, but IS difficult to perform well on. the earlier that is known, the better. by that, i mean this: most good math majors will be able to look through the exam and find only a handful of questions they simply dont know how to do. however, some of the questions prove more difficult than they initially look and, more importantly, time is a MAJOR issue. reading a difficult question, getting in the mindset to attack it, figuring out how to solve it, actually solving it (without a calculator) and then quickly dropping the entire mindset to attack a NEW, completely different question (focusing on something you havent thought about in two years) is a skill that few have mastered. it will prove particularly important on the gre math exam. </p>

<p>4) over the summer, become aware of what 'within reach' programs have strengths in some of the general fields of interest. at that point in my search, for example, i was pretty sure i wanted to do something in discrete mathematics or logic/foundations. being able to narrow things down to 15 or so schools at this point will make contacting faculty somewhat less daunting.</p>

<p>5) take the real gre math exam early in the fall. the late date is too late for some programs and will give you no leeway to retake should the score not be as good as desired. on that note, the gre math score IS important, and you will even see this confirmed on many programs admissions pages (berkeley and penn come immediately to mind). much like with ugrad admissions, a top score will not ensure admission to a top school, but a score less than 700 or so will make it virtually impossible to get into a top 20 program.</p>

<p>6) dont kill yourself over determining a very narrow research focus. while putting forward strong interests is an important part of a good statement of purpose, more than in some other fields, phd programs are focused on admitting on the most brilliant students over smart students who will best fit into their labs.</p>

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<p>have your son talk to his advisors about where they think that they would see him. Academia is very interconnected, and I think that coming from Princeton and my particular advisers helped me greatly in my applications to grad schools (biology). It's been my experience that grad schools are very excited to get students from Princeton, because of all of the independent work. I do not think that he needs to take a year off, although if he wants to, he is certainly welcome to. </p>

<p>I took the GRE subject test in april of my senior year, which turned out to be a very good decision as the fall of senior year is sorta stressful. I took the GRE general test in september right before school started-- but the location nearest princeton burnt down this fall, so he might want to look at taking it over the summer when it might be easier to get to (the closest ones are now sorta far away from princeton, ~40 minutes)</p>

<p>Don't worry too much about the gre scores, over 70% is usually considered fine. letters of rec and the independent work is much more important.</p>

<p>Definitely talk to the grad students, they've been through the process quite recently and so can have a lot of recent information and tips on what to do.</p>

<p>Feel free to pm me with more questions</p>

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<p>mini,tickle and momofthree got all the points right, but I wonder if Mathematics works more like the Sciences and less like Humanities..in that Sciences are grant funded to the supervising faculty to a great extent.I wouldnt think that the process is so different though.I can't emphasize enough having your Son use the resources/mentoring of the faculty at his undergrad institution.Not only will they have the contacts,be writing his reccs but they might be the most knowledgeable of what areas of research are "hot" right now.
D didnt make any visits as an Undergrad to Grad facilities.Her interview visisits were paid for.Her Dep't (also Musicology like Mini's D is now applying to) has just finished the visits for next years applicant finalists.They take in two per year,they had six visits....but its a small dep't.
D also thought the GRE's were similar to the SAT's.The math on them is not difficult.The hardest part was getting used to taking the timed test on a computer screen so practice is important.There is no paper test any longer.
I can't overemphasize the importance of the "statement of purpose" .Everything the student wants to do in Grad School is summed up in this document.Its not the equivalent of an undergrad why I want to attend XYZ College.In fact, the college itself may be meaningless.Its who you want to study with at that institution,what research you want to do, how you've prepared yourself to do that,etc.Yous S needs to structure this document so carefully and thats another area where his departmental mentors can help.
Best of luck to him!</p>

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<p>Yes it is extremely competitive. I was peripherally involved in looking at applicants for the PhD program in Computer Science at one of the very top schools in the country. I really did not have decision-making power, but, as part of the department, was able to look at the applications. What struck me was how hard a decision it would be - when there are literally a thousand applicants for a handful of slots, all the applications start to look alike - great recommendations, great scores, great gpas.</p>

<p>But here are some things that help: </p>

<p>FIRST, if you are going into a PhD program in Math, then you probably have a clue what focus/area you want to study. The PhD will be very narrowly focused.</p>

<p>WHICH MEANS that you probably had a mentor in Undergrad school in that same area, and that mentor can point you in the direction of schools who have faculty already involved in research in that concentration.</p>

<p>IT ALSO MEANS (hopefully) that the UG mentor is involved in that same area, and will know other professors at other schools doing the same kinds of research. And a recommendation letter from a mentor in the field to another person he/she knows in the field is worth much more that a standard recommendation.</p>

<p>ANOTHER APPROACH which can happen in parallel (sneaky, but works...) is to study conference/symposia literature for professors in the same research areas. Then contact them to discuss the papers, and have that lead to a discussion of other research at the school. And at some point have that lead into your interest in helping with that research... </p>

<p>Point is, having an inside person in a competitive field is worth a lot. The relationship between a PhD student and their advisor is closer than you can imagine, and you might want to approach this as finding an Advisor vs. finding a school.</p>

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<p>to mini #7- exactly my explanation to my clueless "non-academic" family! It's a cushy job! ;p Except you actually never see the money.</p>

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<p>Well, in my d's case, she actually sees a nice big chunk of it, well more than her vow of poverty would require. (It was comical trying to get her to shell out the extra money as an "investment" in the possibility.)</p>

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<p>I really doubt they do interviews for mathematics. They don't for chemistry. (They do for biology and biochem, I understand.) </p>

<p>From what I understand, the Math GRE is heavily applied, so this is why some excellent math students may not do well. They might not have seen diff. eqns./calculus/lin. algebra for 4 years. Just get a GRE Mathematics book at the bookstore and go through that. If he needs to, he can just bone up on some concepts he may have forgotten.</p>

<p>I don't know if applied and theoretical math grad schools are separated, but the theoretical PhD programs are insanely hard. One of the reasons John Nash (A Beautiful Mind) went to Princeton for grad school was because Harvard wouldn't give him a fellowship--because he had broken into the top 5 on the Putnam. If he's taken the Putnam and done very well (top 50) plus a similar performance in class, I think he's pretty set to get in anywhere. I imagine if he's at Princeton, they would be pushing the students to take the Putnam. If he isn't quite that high on the math competition, he's got to really shine in class--impress the faculty with his creativity, etc...Some people are really amazing at mathematics and just don't do well in competitions. I know a guy who made the faculty at Harvard and he wasn't as amazing at math competitions as you'd expect. I'm pretty sure he never got top 50 on the Putnam or made MOSP. He did win ARML nationals though in high school. I'm sure he was a phenomenal student (Harvard undergrad), and he really had that creative spark. There's some verbal, right-brained ability of developing a line of questioning that helps in research, and it doesn't always show up on these math competitions. Conversely, another guy (his roommate) that was incredible at math competitions didn't end up with any faculty job offers after graduation. </p>

<p>Apply for the NSF fellowhip. If he gets the fellowship, he can go to any school in America (at least that's the case with chemistry.) Even if they reject you, you could just call them up and tell them that you won it. As I said before, he shouldn't worry too much if he hasn't scored amazingly on the Putnam. I know a guy that won the NSF that barely made USAMO (top 160 in the country at the time) and never made honorable mention on the Putnam. The math faculty evaluating the NSF applications thought he still was one of the most promising math majors in the country though.</p>

<p>As for knowing research interest, I don't know if that is so important. Just say that you will pursue the same area that you did research in as an undergrad. I do know that math grad school is unusual in that you are taking a heavy classload for up to 3 years before you really engage in research. </p>

<p>Another thing--consider the Churchill Scholarship, a 1 year scholarship to the UK. Everybody lambasted me on the Rhodes scholarship thread for saying Rhodes scholars weren't that bright, but compared to the Churchill Scholars they really aren't. The Churchill Scholarship program is geared toward the people who are going to revolutionize science, mathematics, and technology. (I don't think it is for humanities majors, but I could be wrong.)</p>

<p>These are just bits and pieces of info I've heard from my friends. You should investigate any advice more thoroughly to confirm their veracity.</p>

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<p>Could we consolidate these threads? I posted on the grad school forum, but since this is more active, I'll just reinforce some of the points made here, based on my S's experience this year:</p>

<p>The general GRE math is easy and he should just take a practice exam or two and then get it out of the way before Fall. On the other hand, my S didn't bother to look at the Math Subject GRE until a week before he was to take it. He took one practice and realized he would need to study hard for it and there was no time. It included much math he hadn't seen in years because, as many math kids do, he'd had linear algebra and multivariable calculus while in high school. And the time pressure on the test is significant. In the end, he chose not to take it (he covered the fee which had already been paid, because he said it had been his mistake not ours.) Then he decided not to apply to any department that absolutely required it. This eliminated a lot of fine places, and we suggested he wait a year instead. But I was amazed to see he did quite well without it, even in departments that strongly recommended the subject test. On the other hand he is not in pure math.</p>

<p>Fellowship deadlines come very early, another reason to spend some time this summer researching departments and lining up letter writers. It's a good excuse to let faculty know you are applying next year and talk to them about various departments.</p>

<p>While I think it's true you don't necessarily need a very narrow focus to get in, that depends on the department. If your stated interests don't match anyone's there (especially a small department), you scores and grades don't matter. This can also be an excuse to contact faculty in departments, asking whether they are taking on new PhD students. With a larger faculty, there may be an assumption that someone will be available to work with you.</p>

<p>The application process is really a lot of work. Your S should be prepared for it, when he chooses his Fall courses. Mine had no idea how much time all the applications (they're all different -- no such thing as the Common App at this level) would take, and kept paring down his list out of sheer exhaustion. I was sure he didn't apply to enough departments. Again, luck was with him.</p>

<p>If your S's doing research, he will very likely go to conferences where he will have a chance to see some of the profs from his field without having to spend money to visit their institutions. And I'm sure they also come to his campus. My S only met with one prof, though he did e-mail a few. As others have said, there is no formal interview process the way there is in some fields. He's being flown to visit several departments that admitted him.</p>

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<p>
[quote]
Apply for the NSF fellowhip. If he gets the fellowship, he can go to any school in America (at least that's the case with chemistry.) Even if they reject you, you could just call them up and tell them that you won it.

[/quote]
</p>

<p>This is the way to end a career before it's even begun.</p>

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<p>"This is the way to end a career before it's even begun"</p>

<p>??
I'm not sure what you are saying...</p>

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<p>Maybe you're too brilliant for them :)</p>

<p>But oh my gosh, yes, I agree. The application process is extremely time-consuming because a lot of efforts go to thinking and writing the Statement of Purpose and dealing with LORs (and making sure that the profs aren't flaking out). At the same time, he HAS to write his thesis which will help him along the way in defining his interests for the SOP.</p>

<p>That was NOT fun. And now I'm just going through a bit of it again...still writing my honors thesis and now applying to MA programs. He's definitely going to want to take some easy courses.</p>

<p>Also your S also has to keep in mind that the academia is much smaller than he thinks. It's a big shock for many PhD applicants to discover those tight networks. Somebody always knows somebody through conferences, joint projects, etc. I've had at least 3-4 professors who tell me "Oh!! That professor at that grad school should know my name!!!" And it's a lot like high school all over again with the drama and politics.</p>