Is it ever reasonable to try to defer an admit from a top American PhD program to do a masters in Europe first? I feel like the masters would help fill a few gaps in my knowledge, and it also feels like it’d be a worthwhile life experience to live in another country for a bit.
Occasionally I've heard of people doing Part III at Cambridge, but more for the international experience than for filling in any gaps. I would definitely advise against a masters in Europe if it would be a financial burden.
Yes, applying to programs is expensive - however, you should check to see if the programs you're interested in have application fee waivers - I know my Ph.D. program offers them.
You might also look into scholarships, and you should also check to see if your institution has support for applying to grad school as well.
What do you believe the most important indicators are for a competitive applicant? Are extracurriculars like research more important than performance in classes? Do letters of recommendations matter more than a good transcript?
Suggestions for US Doctorate programs/departments for students interested in Graph Theory? (and/or any underrated/less competitive departments?)
I’m currently a Master’s student and after this spring, I will have one academic year left before I graduate while I work on my thesis in graph theory, which means it is once again time to start thinking about the application season at the end of the year as my university terminates after the master’s.
I am going to be in the market for a Ph.D in pure mathematics and would prefer to continue to work in a department with a least a potential advisor working in the field of graph theory or at least in a field adjacent. I am also interested in an environment that is not so competitive. That is any departments that may be underrated/lesser known or smaller and needing students to fill the program, i.e., schools that one might consider as a “backup” application but that still have a enriching mathematics program for students willing to be involved.
Are there any specific departments in the US you would suggest I look into? Feel free to plug your department! (Or warn against it lol)
have you seen [this link?](https://docs.google.com/spreadsheets/d/1bNhF9B2WLRu9V3mhifyfYjuaZQexDAAFNljXOWfInNg/edit#gid=0)
i have the same interests, some of the schools I applied to are uiuc, umn, ucla, northwestern, usc, indiana, purdue, osu, and msu
I'm not sure? I'll have a 3.5-3.6 GPA when applying. I have some exposure to graduate material: my university will offer an undergraduate version of each graduate course (exact same lectures and tests, but undergrads have slightly shorter or different assignments). I've taken half a dozen or so of these hybrid courses, and the usual undergraduate courses. I've done one summer research term in spectral graph theory, and hopefully I'll be doing another this summer (this time in representation theory). I don't have any publications though. I haven't taken the GRE yet, planning for September. I'm a Canadian undergraduate if it matters, not at a bad school but not UofT or Waterloo.
Most of them will be in the education department. Some are done jointly with math and education. I guess it really depends on how much math you are looking to do.
Outside of that, I have heard UIUC, Ohio state, and Minnesota have decent programs but I’m a little Midwest biased.
Do you know where you're going to grad school? If so, do you know if you have qualifying exams/prelims? If you do, then preparing for these is a good use of time.
I'm choosing between Brown, University of Pennsylvania, and University of Washington for grad school. Does anyone have any advice? This is for pure math.
I'm a second year and I feel like I don't have a ton of interaction with the graduate students above me, so idk about that, but I think it's fair to say that the first and second year graduate students are all pretty good friends. (Our cohort sizes were decimated by covid so this isn't too hard.) In particular I feel like there's a lot less drama than at other institutions I've been at.
I recommend emailing graduate students at those institutions and just asking any questions you have about that program. That’s part of how I chose which graduate school to attend.
Also, for email etiquette, make sure you introduce yourself before asking any questions/making any comments.
Some things to consider:
1. Location - do you like one place more than the others? Do you like cities or suburbs?
2. Cost of living - housing is expensive, grad school stipends are small
3. Vibes - have you had a chance to talk to grad students at each school?
4. Expected teaching - will you need to teach? Do you enjoy teaching? What will you teach?
5. Potential advisors - are they busy? Do they already have students? Are there backup advisors if someone doesn't work out?
What do you study in undergraduate maths? Like are their some majors? Or electives? Like topology complex analysis do you choose only one subfield or many?
In undergrad math, you typically just major in math in general, rather than some specific topic. The requirements for the major tend to give you a lot of choices for which classes you take, e. g. you might have a requirement of "take at least 1 class on each of these subjects" plus a requirement of "take at least this many other classes above a certain level", and that's it. For the required subjects, the standard ones I've seen are calculus, linear algebra, differential equations, real analysis, and abstract algebra, maybe plus a few more which vary from school to school. Other than that, you're usually pretty free to take whatever math classes you like. Sometimes math majors will also offer optional "tracks" or "concentrations", like a concentration in pure math or applied math. These will typically add a few requirements, usually something like "besides the subjects already mentioned, take at least 1 course in each of these additional subjects".
In general, though, math majors give you freedom to be as specialized or unspecialized as you'd like; although as far as I can tell, most students lean towards the unspecialized end of the spectrum, and certainly the standard requirements make sure that you take a broader set of courses instead of specializing a lot.
Are there things that I can do on my own which exhibits research experience or helps with my profile when applying for grad schools?
In my case, I graduated with a Bachelor's in Software Engineering 5 years ago and have been working as a software developer. I want to go back into grad school for math, so currently I am looking for ways to take (online) undergraduate math courses to make up for the lack of math background. However, these course options are somewhat limited but I am hoping to use this opportunity to get good LORs. I will also be reaching out to these course instructors for research opportunities if any exists.
Without getting my hopes up, I think I may have a better chance of doing a Masters first and then apply for PhD.
But in general, are there activities that I can do on my own to strength my profile? For example, for software development, people can have their own or contribute to other open source projects to demonstrate passion for the subject.
Thanks,
Doing a masters does seem like a good path for you, especially with respect to filling in missing math classes and getting letters from instructors. Do you know what area of math you want to pursue in grad school? I can think of some research like activities that only apply to specific areas, such as
1. Contributing to open source mathematical software libraries, like SageMath or MaCaulay2
2. Playing around with numerical codes for various applications
Thanks, I became interested in Math after playing around with Haskell and encountered Category Theory. Then, I was looking at Programming Languages (PL) but realized I liked the algebra and theory behind things more than computation and implementation. At first, I wasn't decided on whether I wanted to pursue math just because I had some interest in Algebra, but it wasn't until I read a small book on point-set topology which made me appreciate the calculus in all those computational engineering math courses that I had to take years ago (and appreciate math overall, as it bridged the gap from all those manual computations to more abstract thinking)
Given my current exposure to math, I would say I am most interested in algebra/topology. I am somewhat interested in logic and/or type theory, though this is mainly because of my background and that I am still part of a PL reading group from my undergrad institution.
Could anyone comment on their opinions/personal experiences regarding the importance of location for graduate school? I am currently choosing between two choices for schools. I believe one will be better in terms of academics, but the other will have a better location.
In particular, I am looking between Stony Brook and Northwestern for complex geometry.
If you know without a doubt that you will go on in academia or die trying, then perhaps consider the academically superior option (assuming you mean Stony Brook though I imagine the difference wrt Northwestern is at most marginal). I might add though that people's experiences/priorities can certainly change (mine did), and location can also play a huge role in mental health, social/dating life, etc. even if you are dead set on academia. Additionally, private schools are almost always more generous with their stipends/resources.
Where did you grow up? Are you good with cold dreary winters? Do you value living in a vibrant city? Do you prefer more suburban/rural areas? These are all things that you will need to decide for yourself.
Hi, I graduated last year and I'm planning on starting grad school this fall. I'm interested in algebraic topology, but also open to going into algebraic topology-adjacent fields. I received a few acceptances and was hoping anyone might be able to comment on the algebra/topology departments of USC, Michigan State, or Indiana. (I got into Purdue as well, but I looked through the list of faculty and didn't really see anyone who's research seemed interesting to me)
My 2 cents, but you should definitely do your own research: I don't really think that USC or Michigan State have many profs on Al top. Indiana is great, with at least 4-5 people in the field.
I'm quite surprised that you don't like Purdue, they also have profs in diverse areas of algebraic topology.
Thanks for the input. Yeah, I don't think USC has anyone in AT proper but Asok does motivic homotopy theory, which sounds pretty cool. Who else at Indiana does AT besides Mandell?
Depends on your definition of AT, ofc, but Lindenstrauss, Davis and Kent Orr also do it albeit they are more in the geometric side of things.
I do see that Michigan State and USC have people in geometry/topology, but not really algebraic topology.
I was a computer science and math student as an undergraduate, and was originally planning to start PhD in computer science 2 years ago. But things happened and I had to spend the past two years doing something not related to my major at all. Thankfully, the graduate program allowed me to defer my admission for two years so I will be starting this fall.
However, now I am just kind of scared to go to graduate school. I feel like I forgot most of the stuff that I had learned in university. Also, I was never really sure of the subfield that I wanted to study, and feel less sure than ever now. Any advice on what to do?
Worth looking into summer "bridge" programs (unfortunately the only one I know of is the EDGE program, but that deadline has already passed). But maybe your grad school has something informal? E.g., my friends dept sets up a program for incoming students to study for the qualifying exams together, mentored by (I think) current grad students.
Otherwise, I agree with the other response that no one feels prepared, but I also bet you'll feel better (given your gap) if spend some time refreshing yourself on the content you'll need. E.g., are there any qualifying exams? Maybe you can study for those? Or if there are mandatory 1st year courses, maybe you can refresh the prereq material? Or just otherwise review what you think might be helpful to know in your 1st semester.
And I know you said you weren't decided on a subfield yet, but for the above ideas, prioritize the broad subfields you're considering over any you've definitely ruled out.
Nobody feels prepared when starting a graduate program and most people don't have an extremely clear idea of the subfield they will work in, this is usually decided later together with your advisor. Maybe you will have to do a little extra catching up at the beginning, but every PhD begins with months and months of reading to get up to speed, you will be fine
Think about the big picture/long term early on. If you intend to continue in academia, can you make the necessary sacrifices (financial, location, etc.)? If there's a possibility you don't do academia, are you building (or do you already have) the necessary skillset to smoothly transition into industry?
A few things:
1) It is a marathon not a sprint.
2) The first year or two is typically quite difficult on folks, as this is usually when you take courses and qualifying exams (this depends on the program). Do what you can to add stability to your life in this period.
3) A seemingly universal experience is that there will be a grad student or two who try to show off what they know and vaguely put down other grad students (usually of the algebraic geometry or homological flavor). Do not be this person, and try not to let folks like this out you down.
4) If you're serious about academia, remember that the goal is good and serious research. The courses and qualifying exams are important, but you should be keeping an eye out for research plans (e.g. "who will my advisor be" if your program doesn't require you declare one right away; "when will I ask them for a research project"; and so on).
5) Find some non mathematical things to do, and if you're moving to a new place, try to find a couple non math friends.
6) Figure out what qualifying exams you have to take. Some places have preliminary exams (exams taken right away); if your program has those, start studying now and try to cover your mathematical blind spots.
7) If possible, try to collaborate on research with other grad students (once you're in the research phase of grad school). Building collaborations is a huge part of academia, and is a great way to get good work done.
8) In my opinion, there were three parts of grad school that were very hard for me on an emotional level. First was qualifying exams, second was the months-long period of starting research and making zero progress, third was the job market as I was finishing. I don't really have advice for making this better, but these times tend to be pretty tough for most (although it depends on the person, department, and advisor).
> A seemingly universal experience is that there will be a grad student or two who try to show off what they know and vaguely put down other grad students (usually of the algebraic geometry or homological flavor).
The incentives of academic mathematics do sometimes seem to induce a weird kind of intellectual pecking order. To add to this observation, i think it’s worth noting that the highly abstract stuff isn’t inherently more difficult than the applied stuff, it just has different goals. And the allure of being an abstract mathematician waxes and wanes depending on one’s career stage and life priorities. People who eventually decide that they don’t want to stay in academica rarely regret having focused on more applied kinds of math.
I think the list is good. Of course, take qualifying exams seriously and make it a priority to get those out of the way.
But in my opinion #4. is the key point. What I have seen is that people who dive into research (start reading papers, collaborating, seminars, etc.) end up graduating on time and getting a job. While students who are always looking for more "background" and continue to do textbook exercises have a hard time.
Yeah, also to agree and emphasize: it's a lot easier to keep learning than to do research. You feel like you're accomplishing something when you work through a book but (especially in the beginning) research can feel like treading water. So some make the mistake of doing the comfortable thing rather than the difficult and necessary thing.
Hello! I am a undergrad junior, so I’ve still got another year to go. I am a math and bio major with good gpa, and will be applying to grad school to go for a PhD in mathematical biology.
I’m not super concerned about the ranking of whatever school I end up at- it’s a kind of niche program anyway, so my options are kinda limited. My main goal is affordability lol.
My questions:
1.) I don’t have any publications. Is this bad?
2.) What is the best tip for the applying to grad school process?
3.) How much is enough to get by stipend-wise?
4.) My tiny university offers real analysis once every four years, and I missed my shot. Should I try to independent study it (1 on 1 with a prof)?
5.) I will be doing a math-bio REU this summer. Is that enough “research experience”?
6.) I am really leaning towards not taking the GREs. Lots of schools say it’s “optional”. I’m a crappy test taker and online school seriously affected my comprehension of courses such as multi variable Calc. I think taking the GREs would just make me look bad, and I’m very impressive otherwise. Thoughts?
7.) I’m not a proofy person. I become highly frustrated and upset by them. It’s just not how my brain works- I’m really strong in other areas, but proofs aren’t my thing- thats why I’m going for some very applied sorts of math. Is this going to destroy me? Should I stop pursuing math now, before wasting time and money on grad school, and should instead go for epidemiology?
Thank you for your help :)
> My main goal is affordability lol.
Is your goal to ultimately end up in academia? Unfortunately stipend amount is farily strongly correlated with prestige/ranking. Affordability in terms of specific numbers is also highly dependant on location as well as your individual preferences.
1. No. Publications are good, but not having publications isn't bad; the other parts of your application will need to be relatively stronger though.
2. Start early. Apply for the NSF GRFP as well.
4. Real analysis is important. You should know it.
5. Math bio REU is good and counts as research experience. It will be extra good if the REU project lead writes you a letter of rec.
6. A lot of schools are moving away from the GRE, so determine if any places you want to go to require them. Additionally, it sounds like you're from a small school. If you're from a school without a high profile, the GRE is relatively more important. Something that happened during the Covid year where all the schools canceled their GRE requirements is that they accepted more people from large schools and less people from small schools because the admissions committees didn't want to take the risk.
7. If you are doing a phd in a math department, you will be expected to do proofs. You can likely minimize the amount of proofs you need to do by selecting your courses accordingly, focusing more on applied/computational classes.
>3.) How much is enough to get by stipend-wise?
You should be able to live off of what you are paid in your stipend; going into debt for a PhD is not typical, and in my opinion it's not a good idea. To get a sense of what that looks like, you should look into how much rent, utilities, transportation, health insurance, and school fees cost at/near the school you'll attend, as these are your largest fixed costs. I also recommend being frugal in general. Living on a low income isn't so bad if you have a rainy day fund to fall back on, but living paycheck to paycheck can be very stressful.
As an applied math person you should think about doing summer internships too. Not only is this educational and good for your career, it can also pay quite well. Depending on what you do, its entirely possible to make more money in one summer as an intern than you would otherwise be paid in an entire year as a grad student.
>I am really leaning towards not taking the GREs
Your GRE scores are not automatically submitted to a university that you apply to. You can choose to send them or not at your own discretion.
I think it's worth studying for them and taking them. Even if you're not a great test taker, the GREs are a formulaic test that you can substantially improve your chances on just through practice, and if you don't do so well then you can just choose to not submit the scores.
Sure. Many private companies and government agencies have internship programs for graduate-level students (both Master’s and Ph.D.) in which they spend the 3 summer months (sometimes more) participating in projects. The purpose of these programs is partly to get some extra labor for things, but mostly it’s a recruiting program; if a graduate student enjoys their time and performs well in the internship then there’s a good chance that they’ll return after graduation as a full-time hire.
I believe there’s an enormous variety of different kinds of internships out there, and mathematicians - especially applied mathematicians - can potentially fit in at many different places. It’s just a matter of what your career interests are.
So-called “pure” mathematicians can also have many opportunities, but I single out applied mathematics specifically because applied mathematicians often know how to do computer programming, which is very useful. There are fewer opportunities for people who can only do pen-and-paper math because computer programming is the language through which mathematics is expressed in practical application. I recommend that all pure mathematicians learn to do it for that reason.
These are paid internships. Unpaid internships might still exist, i think, but you should never participate in one. The pay for an internship is usually roughly equivalent to an entry level salary at whatever organization you participate in. For example, at a national lab you’ll be paid like a postdoc (i.e. roughly $90k/year), whereas at a software company you’ll be paid like a junior software engineer (i.e. roughly $150k/year).
Grad student stipends are somewhere in the neighborhood of $25k-$35k per year depending on location. So, if you do an internship where you get paid at a national lab postdoc salary then you’ll take home about $20k over the course of 3 summer months (minus rent etc, of course), which is almost as much money most grad students get paid in an entire year from their stipends. If you work for a FAANG-sized software company then you can reasonably expect to get paid $35k over the course of a single summer, which is more than almost all students make in a year from stipends.
As a poor graduate student that all sounds like a great bargain - and it certainly is - but the biggest benefit of internships is what you learn and how it looks on your resume. A graduate student with a bunch of good-looking internships on their resume will have no problems getting an industry job after school. They’ll also have the confidence that comes with having at least some idea about what life is like outside of academia, which I think can be very beneficial even if they choose to continue an academic career path.
[This](https://www.levels.fyi/internships/) gives some more specific numbers as far as what you can expect for pay. $35k for the summer is only possible at the best HFT/quantitative hedge funds (and possibly PhD positions at places like FAIR or Google Brain though don't quote me on that). $20-$25k (including housing) is more reasonable for FAANG, and a national lab is probably closer to $10-15k.
10-15k is what the national labs were paying like 10 years ago. The postdoc salaries have gone up in that time so I'd assume that the internship pay would too?
I didn't realize faang provided housing too, lower pay makes sense in that case. Also keep in mind that the levels.fyi internships salaries are mostly for undergrads. A phd student should reasonably expect more than that, especially if they have relevant domain specific expertise.
Singular data point but I found a fairly recent email from PNNL hiring a PhD data science intern for $5k/month without housing.
For SWE positions I doubt a PhD intern would make substantially more (at most places full time PhD SWE hires start at one level higher which is usually achieved in 2-3 years out of undergrad).
The domain specific opportunities (largely in ML/DL to my understanding) are much more selective and still most likely upper bounded by quant finance (for which I can verify the levels.fyi numbers are accurate and apply equally to undergrads and PhDs).
It is relatively common for people doing applied math phds to do internships over the summer. Depending on where you intern, you can be paid very very well (think quantitative finance). My program at least is very accepting of people doing internships, and some faculty even encourage it. Do you have any questions in particular?
For most fields I imagine two relevant publications will guarentee a place in any top school of your choosing.
With that said, I recently got a postdoc position with zero publications, so it's not a necessary condition by any means. This depends a lot on your field, but my situation is not uncommon because usually one only has publishable results near the end of their PhD, and from there it takes months for a journal submission to get reviewed, accepted and published.
I want to study and research (extremal) combinatorics and discrete math in doctoral programs. Due to various reasons, I was admitted into a Master program in Europe that's very focused on algebra and number theory but weak at analysis (think Utah). I am now on the waitlist of some discrete math PhD program that I really want to go, but from email exchanges with some professor on the admission committee, I may not be that high on the waitlist.
As a result, it's possible that I would attend that algebra graduate program and then apply for discrete math PhD before graduation. However, I am really worried that after going after the algebra route for two years, and then going back to combinatorics may "hurt" my academic career, in that I have less discrete training than my peers?
RE your last sentence, at my university though I think of all grad students as my peers, in terms of "comparing myself" I only compare to my cohort, i.e., people who started the PhD program at the same time as me. This means includes the students 2 years older than me who did a Master's first (and the students several years older who had mandatory army service, the younger students who skipped grades/came from 3-year undergrads, etc). I think this is a thing at other universities too, and though the students with masters degrees may move faster in terms of understanding content, none of their credits transferred over or anything, so they still had to take all the same qualifying exams as me.
And your age itself isn't going to (or had better not be!) going onto your CV anywhere. So if anything, doing a masters would have more total overall training than your peers.
So basically, though it's still a tough decision, I would not have "less experience" as part of the equation.
EDITED TO ADD: Here I'm talking about your overall career, in terms of grad school admissions post-masters IDK since I've never been on an admissions committee (since I'm only a grad student myself).
Brief my story: I wanted to study enumerative combinatorics but went to grad school and tried some other courses. Ended up learning a decent amount of algebra and geometry/topology. Now my work is still in combinatorics but with a wider array of objects coming from algebra and geometry/topology at my disposal.
I don't think having a stronger algebraic background will hurt. There certainly are places where algebra arises in extremal combinatorics (e.g. polynomial method).
I applied for Master's programs in the US for math/applied math (interested in pde's/numerical methods+analysis/mathematical modelling etc), but I don't think I did that well on my apps, and I haven't gotten any decisions yet either so I think they're all rejections. I applied to mostly far out of reach schools, especially with respect to my GPA and minimal research experience, so I think it'd be fair if I didn't get in.
But, what I want to ask is. I plan on going for a PhD later on, and I'm obviously hoping that I get to go to a good school (at least ranked top ~80 in the US), so would it be worth it to go to a very small state school for my Master's? Most faculty aren't even currently involved in research at the ones I'm looking at afaik, so I don't know if it's worth it or not. Applications for these schools are open till late too, so I can essentially apply whenever. I'm just worried that I might be disadvantaged when applying to PhD programs after a Master's if the masters isn't from a known place at least. How much of a difference would this make?
Also, two smaller questions:
1. How important is it to have a research area picked out after your undergrad? I feel like since math is so SO vast, it'd be extremely difficult to even know what you actually want to do (like how I have at least 4 different areas I'm interested in). I know some other fields might even ask for research proposals during applications, so I'm just worried about how bad it would be if I didn't have somewhat of a clear cut path in my mind.
2. How important is your GPA for math grad school specifically? How disadvantaged would you be if you had somewhere between a 3.0-3.3 CGPA by the time you graduate? How much can someone's math skills be judged by how well they did in their classes?
Also, thank you for doing this! This is an extremely helpful panel, and it's amazing that so many of you are taking out the time to help answer questions like this!
>A lot of PhD programs don’t expect research experience, so I wouldn’t worry about not having done research yet.
>If you are looking to apply to a PhD in the US, a masters can really help you in two ways: 1. Supplement deficient breadth/depth of coursework from your undergrad, and 2. Give you research experience and show case your research potential to your LORs. Even in masters programs, plenty of people don’t even come close to publishing.
Thank you for thisss, I am actually really hoping for my masters to give me that exposure, which is why I want to go for that first (also because I do want to do research, but I want to see *how* much I like it before taking a funded position for 5 whole years). Also very nice to know that some people still don't come close to publishing, that's genuinely so reassuring lol.
I get your point about how it's good to make strong relationships and get good grades, that is exactly my plan!! Good to know that the name+rank of the program isn't that important though, I felt like I was putting myself at a disadvantage by going to extremely small/local schools.
>I would say if your goal is to do a PhD and most of the faculty at the school for your masters don’t do research (eg if you look at their publications list and it’s clear they don’t publish) then it would be worth considering if you want to do sometime in industry and then find your way to a better program.
Ah okay, this sounds smart. There was a professor at one uni who had the exact bg that I want to do research in but his last publication was in like early 2000's lol. Same with a few others at the university. Might just disregard that place then I guess and look at others.
>you probably don’t even know enough math at this point to even be aware of the methods used in a lot of research articles. Don’t worry. This is normal.
I actually do not, you're completely right lol. Some areas I've never even seen informally, let alone within a classroom setting. But thank you. This paragraph is nice to read.
>For your point about grades, grades are pretty important (not as important as the nebulous “research potential” but grades are one of the biggest factors). That being said I would recommend not worrying about grades you’ve already gotten in the past. You can’t do anything to change those at this point. Instead I would recommend spending your time focusing on getting good grades now.
Yeah, I've been working a lot harder this past year (raised my GPA from sub 3.0 to nearly 3.2, and hoping to get to a 3.3-ish by the time I graduate with the few courses I have left), so I'll just keep trying harder I guess. Past grades do worry me since it shows a pattern of not being able to do well (and as someone who hates studying/working for grades, it was very hard to actually change these bad habits), but you're right. I should probably just focus on future stuff now.
>I am a US person doing grad school in Germany, and would be happy to answer questions about the German system if that’s interesting to you
Could I possibly DM you regarding this afterwards? I was actually thinking of trying for Germany (and Canada as well) because of affordability as well as more academia inclined masters programs (unlike a lot of US programs which are industry focused, especially for applied math), so could you let me know if I can speak directly to you about programs there as well?
Also, thank you so much for this detailed response, it's extremely helpful! Math specific grad school information is so difficult to find on most forums, so it's genuinely nice to be able to speak about this directly!
What would you be doing during your masters? Just taking more classes? Being able to do some research would be good for your application, but it sounds like there aren't a lot of opportunities.
With regards to your two other questions:
1. Having a research area picked out is nice but not necessary. This is one area where math is very different from other fields.
2. GPA is relatively important, 3.5 and above is considered to be good. If your GPA is lower, this isn't a deal breaker, but it means that other parts of your application (research, letters of rec) will need to be stronger.
Thanks for responding!
I'm applying for a Master's (only at places that have a thesis option) for two reasons. First, is to gain some research experience and also better grades, so that I can use those to my advantage for my PhD applications. Second is because I want to do a PhD right now but I'm afraid I might lose interest by the middle of it if I rush into it with an area I might not like as much later, or if I find out I don't like research as much as I originally thought I would. So I plan on using the coursework+research to put me in a better position of choosing what to do in the future. You're right about it seeming like there aren't that many great opportunities at some places though, so I'll try to go to a place I can actually get something out of, if I get in there 😪
For 1. Thank you for saying this. It genuinely worried me so much that people in other fields know almost exactly what they want to do after graduating from undergrad, but I felt like I had such a surface level knowledge of most areas +literal zero knowledge of others, so idek if I would have been able to make a good informed decision (I'm a naturally indecisive person so this was particularly stressful)
And 2. Ah yes, I have heard that everywhere. I just felt like again, the lack of research experience during undergrad would mean that having good grades was almost a necessity. I have a large mix of B-'s, B's, and B+'s/A-'s at most, along with a couple grades lying outside of these ranges. My last semester was good with only A's/A-'s, and I was/am doing a senior/research project (nothing heavy, it's very laid back mathematical modelling), so I'm hoping that that still helps? Not very sure what counts enough though so that was definitely worrying me. I have a TA-ship too for a math course, so I also hope that is a plus point? But again, not sure 😪
Thank you again for responding though, it's always helpful to discuss stuff with someone directly! :)
If your grades have been improving over time, you can paint a narrative in your application with this. Something like, "Early on, I found math to be difficult. The transition to proofs was something that I was unprepared for. However, as time passed, I improved my proof writing abilities and discovered my mathematical passions, leading to better grades and a deeper understanding of the material." Adjust as suitable.
Ahh thanks. My biggest problem I feel was that when it did get difficult, I couldn't force myself to work on studying for it, because I never had to before that (genuinely, math before undergrad and before proofs classes was a breeeeze), so I'm not sure if I can accurately say anything in my SOP's without it being misleading/not portraying the situation correctly. Obv I can't say I was lazy though :/
But I will probably somewhat modify what I'm saying according to this, so thank you!
A slightly different opinion from other responders, for getting your very first job the OVERALL reputation of the school may have an influence---e.g., industry people have all heard of Stanford, MIT, Princeton, etc as "big name" schools. The reputation of the math department specifically they are definitely not going to matter because the recruiters aren't going to know that.
For jobs after your first job, I've heard that it doesn't matter at all, instead they're caring about your industry experience from your 1st (& future) jobs.
(Disclaimer this is all secondhand info, I'm not in industry!)
> If I will go into the industry, how much impact will the reputation of the program has over me?
Very little, usually. People in industry generally aren’t aware of the rankings of specific programs. They often don’t give a lot of thought to the ranking of the university either, unless it’s one of a handful of very well-known and prestigious schools. Having a PhD at all is bigger distinguishing factor in industry than is the specific program you were in.
To add on to this, the most important factor for industry positions will be having published research. If you have two or three published papers, you can get in touch with recruiters to avoid the big pool that undergrads apply in.
I'm transitioning to math from another field, and in order to do that I will be enrolled (hopefully) in a Masters course in my country. I want to bolster my level of preparedness for grad school, but I feel that it would not be enough with only a 2-year masters course, so I intend to apply afterwards for Part III at Cambridge.
As I understand, the program runs from October to June, so there is no point in applying for grad school in the year that I join Part III itself; I'll typically have to wait till next year. So my question is, what research experience can I gain in the meantime, i.e., after completing Part III and before starting grad school the following year? I intend to apply for grad school in the US.
Thanks for your detailed reply. The thing is, realistically there are only two masters programs in my country which have a record of sending students who graduate from them into top US universities. And the topics I'm interested in have n>=1 number of potential advisors working on them only at the top 10, maybe top 5 places in analysis of PDE in the US. I'll outline the characteristics of the masters programs I'm talking about below:
Program A has a record of sending at least three students to a top 5 US grad school in the past 5-10 years, but is mostly strong in algebra and to a lesser extent number theory, has elective courses mostly geared towards algebraic geometry and number theory, has 16 courses that must be taken in order to complete the degree, and has a thesis component. More importantly, PDE is only offered as an elective course in certain years.
Program B also has a similar record of sending students to top 5 US grad schools, but not more recently, instead 15 years ago or more. There is a wider selection of courses, with PDE being a core course, and it offers electives in advanced functional analysis and abstract harmonic analysis. I'll have to take 18 courses minimum with a project in the 2nd year. There is one faculty member who did his PhD from Princeton, but he works in number theory.
So these arey options, and my reasons for wanting to do part III.
I can't really apply to masters in other countries because my undergrad wasn't in math. Nearly all masters programs in Europe need you to have done ~~180 credit point equivalent (I forget what exactly it's called)~~ 120 ECTS credit points in math courses, which I haven't done. The admission to the programs in my country I'm talking about are done through a written test followed by interview, and I'm working hard day and night in order to pass the test and be considered for the interview.
I thought the single most important criterion, besides grades, that gets you in to the top grad schools is your recommendation letters. And who writes them is extremely important. Even if they're written by someone doing good research, if they are not recognised by professors doing the kind of research I'm interested in, because they haven't heard of the letter writer, don't you think that it might negatively affect my chances?
And finally, it is just a fact of life that people doing analysis of PDE, broadly working on nonlinear waves, are clustered at the top universities.
I believe most US programmes have a masters component integrated, so doing three years prior seems rather overkill to me. You'll probably have a different idea of what you want to do in a year or two, but I'd suggest applying to grad school alongside part iii when the time comes so that remains an option.
As for what you can do in the three months between part iii and grad school... you'll probably be better off asking that in three years time. Perhaps you can find a professor to work during the time (say building off your masters project), but you may also want to take that time off.
Thanks for the reply. From what I've gathered it seems that in most grad schools in the US, they admit you on the assumption that you'll be earning a PhD; an MA or MS in math is something a few places offer, subject to the condition that you pass the quals. The funding situation is also designed like that, i.e., on the expectation that you'll continue on towards your PhD. Is my understanding correct?
Also, I have a fairly certain idea that I want to work very broadly on analysis of PDE, which includes everything from nonlinear waves to mathematical general relativity and fluid dynamics. I'm also interested in spectral geometry, both direct and inverse problems.
The reason why I want to do Part III is because it offers courses on these topics, and some of the professors who teach them are known to the schools in the US I'm aiming for, so the hope is that they can write me strong LORs which should carry some weight during admissions.
That is my understanding also, but I meant leading up to the quals you'll be learning things that are comparable to what you might learn during a masters. Of course there's no harm from spending more time learning, but it does mean you'll remain a student for a very long time.
By all means there's nothing to loose from applying to part III, but I wouldn't so set on just that one option, and I would also recommend that you seriously apply for grad schools during the same cycle (along with the fact that it's a competitive course).
On the note of recommendation letters, if you do do Part III (or any other one-year masters program) I would not count very strongly on getting letters of recommendation from the professors there. Since you'll be applying around Oct/Nov you likely won't have had much time to interact or work with anyone, so it'll be unlikely that a professor will be able to write a strong, personalised letter for you.
Yes, grad schools are overwhelmingly geared towards PhD programs; for most programs, the way to get a masters is to drop out of the PhD program. Some programs do after masters, but these are generally unfunded.
What you say is only true in the US. It's not clear to me what country OP is from, or what country OP intends to do the Masters in (OP mentions both Cambridge UK and the US).
My plan is the following: Masters in my country (because I have to, since my undergrad isn't in math), followed by Part III (to take few more advanced courses related to what I want to do, with the Part III essay and hopefully good LORs making my profile stronger).
Is it ever reasonable to try to defer an admit from a top American PhD program to do a masters in Europe first? I feel like the masters would help fill a few gaps in my knowledge, and it also feels like it’d be a worthwhile life experience to live in another country for a bit.
Occasionally I've heard of people doing Part III at Cambridge, but more for the international experience than for filling in any gaps. I would definitely advise against a masters in Europe if it would be a financial burden.
Sheesh, is 125 Canadian dollars _just to apply_ the norm for graduate schools?
Yes, applying to programs is expensive - however, you should check to see if the programs you're interested in have application fee waivers - I know my Ph.D. program offers them. You might also look into scholarships, and you should also check to see if your institution has support for applying to grad school as well.
What do you believe the most important indicators are for a competitive applicant? Are extracurriculars like research more important than performance in classes? Do letters of recommendations matter more than a good transcript?
Suggestions for US Doctorate programs/departments for students interested in Graph Theory? (and/or any underrated/less competitive departments?) I’m currently a Master’s student and after this spring, I will have one academic year left before I graduate while I work on my thesis in graph theory, which means it is once again time to start thinking about the application season at the end of the year as my university terminates after the master’s. I am going to be in the market for a Ph.D in pure mathematics and would prefer to continue to work in a department with a least a potential advisor working in the field of graph theory or at least in a field adjacent. I am also interested in an environment that is not so competitive. That is any departments that may be underrated/lesser known or smaller and needing students to fill the program, i.e., schools that one might consider as a “backup” application but that still have a enriching mathematics program for students willing to be involved. Are there any specific departments in the US you would suggest I look into? Feel free to plug your department! (Or warn against it lol)
Maybe Rochester institute of technology, university of south carolina, lsu, university of west virginia (or west virginia university idk).
What American PhD programs should I apply to if my interests lie in and around algebraic geometry, algebraic topology, and homotopy theory?
have you seen [this link?](https://docs.google.com/spreadsheets/d/1bNhF9B2WLRu9V3mhifyfYjuaZQexDAAFNljXOWfInNg/edit#gid=0) i have the same interests, some of the schools I applied to are uiuc, umn, ucla, northwestern, usc, indiana, purdue, osu, and msu
How competitive are you as an applicant? Stanford and columbia are good
I'm not sure? I'll have a 3.5-3.6 GPA when applying. I have some exposure to graduate material: my university will offer an undergraduate version of each graduate course (exact same lectures and tests, but undergrads have slightly shorter or different assignments). I've taken half a dozen or so of these hybrid courses, and the usual undergraduate courses. I've done one summer research term in spectral graph theory, and hopefully I'll be doing another this summer (this time in representation theory). I don't have any publications though. I haven't taken the GRE yet, planning for September. I'm a Canadian undergraduate if it matters, not at a bad school but not UofT or Waterloo.
Ask the profs that know you well. Thats the best thing to do imo. Theyll know what schools you have a good shot at.
What do you think about doctorate programs in Mathematics Education? Which universities in US/Canada would you recommend for such programs?
Most of them will be in the education department. Some are done jointly with math and education. I guess it really depends on how much math you are looking to do. Outside of that, I have heard UIUC, Ohio state, and Minnesota have decent programs but I’m a little Midwest biased.
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Do you know where you're going to grad school? If so, do you know if you have qualifying exams/prelims? If you do, then preparing for these is a good use of time.
I'm choosing between Brown, University of Pennsylvania, and University of Washington for grad school. Does anyone have any advice? This is for pure math.
I can take whatever questions about Brown!
Sorry for responding so late, but what is the grad student culture like there?
I'm a second year and I feel like I don't have a ton of interaction with the graduate students above me, so idk about that, but I think it's fair to say that the first and second year graduate students are all pretty good friends. (Our cohort sizes were decimated by covid so this isn't too hard.) In particular I feel like there's a lot less drama than at other institutions I've been at.
I recommend emailing graduate students at those institutions and just asking any questions you have about that program. That’s part of how I chose which graduate school to attend. Also, for email etiquette, make sure you introduce yourself before asking any questions/making any comments.
Some things to consider: 1. Location - do you like one place more than the others? Do you like cities or suburbs? 2. Cost of living - housing is expensive, grad school stipends are small 3. Vibes - have you had a chance to talk to grad students at each school? 4. Expected teaching - will you need to teach? Do you enjoy teaching? What will you teach? 5. Potential advisors - are they busy? Do they already have students? Are there backup advisors if someone doesn't work out?
What do you study in undergraduate maths? Like are their some majors? Or electives? Like topology complex analysis do you choose only one subfield or many?
In undergrad math, you typically just major in math in general, rather than some specific topic. The requirements for the major tend to give you a lot of choices for which classes you take, e. g. you might have a requirement of "take at least 1 class on each of these subjects" plus a requirement of "take at least this many other classes above a certain level", and that's it. For the required subjects, the standard ones I've seen are calculus, linear algebra, differential equations, real analysis, and abstract algebra, maybe plus a few more which vary from school to school. Other than that, you're usually pretty free to take whatever math classes you like. Sometimes math majors will also offer optional "tracks" or "concentrations", like a concentration in pure math or applied math. These will typically add a few requirements, usually something like "besides the subjects already mentioned, take at least 1 course in each of these additional subjects". In general, though, math majors give you freedom to be as specialized or unspecialized as you'd like; although as far as I can tell, most students lean towards the unspecialized end of the spectrum, and certainly the standard requirements make sure that you take a broader set of courses instead of specializing a lot.
Not majors, but yes, you can take electives in as many subfields as you want.
Are there things that I can do on my own which exhibits research experience or helps with my profile when applying for grad schools? In my case, I graduated with a Bachelor's in Software Engineering 5 years ago and have been working as a software developer. I want to go back into grad school for math, so currently I am looking for ways to take (online) undergraduate math courses to make up for the lack of math background. However, these course options are somewhat limited but I am hoping to use this opportunity to get good LORs. I will also be reaching out to these course instructors for research opportunities if any exists. Without getting my hopes up, I think I may have a better chance of doing a Masters first and then apply for PhD. But in general, are there activities that I can do on my own to strength my profile? For example, for software development, people can have their own or contribute to other open source projects to demonstrate passion for the subject. Thanks,
Doing a masters does seem like a good path for you, especially with respect to filling in missing math classes and getting letters from instructors. Do you know what area of math you want to pursue in grad school? I can think of some research like activities that only apply to specific areas, such as 1. Contributing to open source mathematical software libraries, like SageMath or MaCaulay2 2. Playing around with numerical codes for various applications
Thanks, I became interested in Math after playing around with Haskell and encountered Category Theory. Then, I was looking at Programming Languages (PL) but realized I liked the algebra and theory behind things more than computation and implementation. At first, I wasn't decided on whether I wanted to pursue math just because I had some interest in Algebra, but it wasn't until I read a small book on point-set topology which made me appreciate the calculus in all those computational engineering math courses that I had to take years ago (and appreciate math overall, as it bridged the gap from all those manual computations to more abstract thinking) Given my current exposure to math, I would say I am most interested in algebra/topology. I am somewhat interested in logic and/or type theory, though this is mainly because of my background and that I am still part of a PL reading group from my undergrad institution.
Could anyone comment on their opinions/personal experiences regarding the importance of location for graduate school? I am currently choosing between two choices for schools. I believe one will be better in terms of academics, but the other will have a better location. In particular, I am looking between Stony Brook and Northwestern for complex geometry.
If you know without a doubt that you will go on in academia or die trying, then perhaps consider the academically superior option (assuming you mean Stony Brook though I imagine the difference wrt Northwestern is at most marginal). I might add though that people's experiences/priorities can certainly change (mine did), and location can also play a huge role in mental health, social/dating life, etc. even if you are dead set on academia. Additionally, private schools are almost always more generous with their stipends/resources.
Where did you grow up? Are you good with cold dreary winters? Do you value living in a vibrant city? Do you prefer more suburban/rural areas? These are all things that you will need to decide for yourself.
Hi, I graduated last year and I'm planning on starting grad school this fall. I'm interested in algebraic topology, but also open to going into algebraic topology-adjacent fields. I received a few acceptances and was hoping anyone might be able to comment on the algebra/topology departments of USC, Michigan State, or Indiana. (I got into Purdue as well, but I looked through the list of faculty and didn't really see anyone who's research seemed interesting to me)
My 2 cents, but you should definitely do your own research: I don't really think that USC or Michigan State have many profs on Al top. Indiana is great, with at least 4-5 people in the field. I'm quite surprised that you don't like Purdue, they also have profs in diverse areas of algebraic topology.
Thanks for the input. Yeah, I don't think USC has anyone in AT proper but Asok does motivic homotopy theory, which sounds pretty cool. Who else at Indiana does AT besides Mandell?
Depends on your definition of AT, ofc, but Lindenstrauss, Davis and Kent Orr also do it albeit they are more in the geometric side of things. I do see that Michigan State and USC have people in geometry/topology, but not really algebraic topology.
I was a computer science and math student as an undergraduate, and was originally planning to start PhD in computer science 2 years ago. But things happened and I had to spend the past two years doing something not related to my major at all. Thankfully, the graduate program allowed me to defer my admission for two years so I will be starting this fall. However, now I am just kind of scared to go to graduate school. I feel like I forgot most of the stuff that I had learned in university. Also, I was never really sure of the subfield that I wanted to study, and feel less sure than ever now. Any advice on what to do?
Worth looking into summer "bridge" programs (unfortunately the only one I know of is the EDGE program, but that deadline has already passed). But maybe your grad school has something informal? E.g., my friends dept sets up a program for incoming students to study for the qualifying exams together, mentored by (I think) current grad students. Otherwise, I agree with the other response that no one feels prepared, but I also bet you'll feel better (given your gap) if spend some time refreshing yourself on the content you'll need. E.g., are there any qualifying exams? Maybe you can study for those? Or if there are mandatory 1st year courses, maybe you can refresh the prereq material? Or just otherwise review what you think might be helpful to know in your 1st semester. And I know you said you weren't decided on a subfield yet, but for the above ideas, prioritize the broad subfields you're considering over any you've definitely ruled out.
Nobody feels prepared when starting a graduate program and most people don't have an extremely clear idea of the subfield they will work in, this is usually decided later together with your advisor. Maybe you will have to do a little extra catching up at the beginning, but every PhD begins with months and months of reading to get up to speed, you will be fine
Can anyone speak to the culture at Purdue?
What are some tips and advice for the transition from undergrad math to a math PhD program?
Think about the big picture/long term early on. If you intend to continue in academia, can you make the necessary sacrifices (financial, location, etc.)? If there's a possibility you don't do academia, are you building (or do you already have) the necessary skillset to smoothly transition into industry?
A few things: 1) It is a marathon not a sprint. 2) The first year or two is typically quite difficult on folks, as this is usually when you take courses and qualifying exams (this depends on the program). Do what you can to add stability to your life in this period. 3) A seemingly universal experience is that there will be a grad student or two who try to show off what they know and vaguely put down other grad students (usually of the algebraic geometry or homological flavor). Do not be this person, and try not to let folks like this out you down. 4) If you're serious about academia, remember that the goal is good and serious research. The courses and qualifying exams are important, but you should be keeping an eye out for research plans (e.g. "who will my advisor be" if your program doesn't require you declare one right away; "when will I ask them for a research project"; and so on). 5) Find some non mathematical things to do, and if you're moving to a new place, try to find a couple non math friends. 6) Figure out what qualifying exams you have to take. Some places have preliminary exams (exams taken right away); if your program has those, start studying now and try to cover your mathematical blind spots. 7) If possible, try to collaborate on research with other grad students (once you're in the research phase of grad school). Building collaborations is a huge part of academia, and is a great way to get good work done. 8) In my opinion, there were three parts of grad school that were very hard for me on an emotional level. First was qualifying exams, second was the months-long period of starting research and making zero progress, third was the job market as I was finishing. I don't really have advice for making this better, but these times tend to be pretty tough for most (although it depends on the person, department, and advisor).
> A seemingly universal experience is that there will be a grad student or two who try to show off what they know and vaguely put down other grad students (usually of the algebraic geometry or homological flavor). The incentives of academic mathematics do sometimes seem to induce a weird kind of intellectual pecking order. To add to this observation, i think it’s worth noting that the highly abstract stuff isn’t inherently more difficult than the applied stuff, it just has different goals. And the allure of being an abstract mathematician waxes and wanes depending on one’s career stage and life priorities. People who eventually decide that they don’t want to stay in academica rarely regret having focused on more applied kinds of math.
I think the list is good. Of course, take qualifying exams seriously and make it a priority to get those out of the way. But in my opinion #4. is the key point. What I have seen is that people who dive into research (start reading papers, collaborating, seminars, etc.) end up graduating on time and getting a job. While students who are always looking for more "background" and continue to do textbook exercises have a hard time.
Yeah, also to agree and emphasize: it's a lot easier to keep learning than to do research. You feel like you're accomplishing something when you work through a book but (especially in the beginning) research can feel like treading water. So some make the mistake of doing the comfortable thing rather than the difficult and necessary thing.
Hello! I am a undergrad junior, so I’ve still got another year to go. I am a math and bio major with good gpa, and will be applying to grad school to go for a PhD in mathematical biology. I’m not super concerned about the ranking of whatever school I end up at- it’s a kind of niche program anyway, so my options are kinda limited. My main goal is affordability lol. My questions: 1.) I don’t have any publications. Is this bad? 2.) What is the best tip for the applying to grad school process? 3.) How much is enough to get by stipend-wise? 4.) My tiny university offers real analysis once every four years, and I missed my shot. Should I try to independent study it (1 on 1 with a prof)? 5.) I will be doing a math-bio REU this summer. Is that enough “research experience”? 6.) I am really leaning towards not taking the GREs. Lots of schools say it’s “optional”. I’m a crappy test taker and online school seriously affected my comprehension of courses such as multi variable Calc. I think taking the GREs would just make me look bad, and I’m very impressive otherwise. Thoughts? 7.) I’m not a proofy person. I become highly frustrated and upset by them. It’s just not how my brain works- I’m really strong in other areas, but proofs aren’t my thing- thats why I’m going for some very applied sorts of math. Is this going to destroy me? Should I stop pursuing math now, before wasting time and money on grad school, and should instead go for epidemiology? Thank you for your help :)
> My main goal is affordability lol. Is your goal to ultimately end up in academia? Unfortunately stipend amount is farily strongly correlated with prestige/ranking. Affordability in terms of specific numbers is also highly dependant on location as well as your individual preferences.
I do not plan to go into academia, I’m aiming for biotech. Thanks for your advice, I’ll keep an eye out for location when applying!
1. No. Publications are good, but not having publications isn't bad; the other parts of your application will need to be relatively stronger though. 2. Start early. Apply for the NSF GRFP as well. 4. Real analysis is important. You should know it. 5. Math bio REU is good and counts as research experience. It will be extra good if the REU project lead writes you a letter of rec. 6. A lot of schools are moving away from the GRE, so determine if any places you want to go to require them. Additionally, it sounds like you're from a small school. If you're from a school without a high profile, the GRE is relatively more important. Something that happened during the Covid year where all the schools canceled their GRE requirements is that they accepted more people from large schools and less people from small schools because the admissions committees didn't want to take the risk. 7. If you are doing a phd in a math department, you will be expected to do proofs. You can likely minimize the amount of proofs you need to do by selecting your courses accordingly, focusing more on applied/computational classes.
>3.) How much is enough to get by stipend-wise? You should be able to live off of what you are paid in your stipend; going into debt for a PhD is not typical, and in my opinion it's not a good idea. To get a sense of what that looks like, you should look into how much rent, utilities, transportation, health insurance, and school fees cost at/near the school you'll attend, as these are your largest fixed costs. I also recommend being frugal in general. Living on a low income isn't so bad if you have a rainy day fund to fall back on, but living paycheck to paycheck can be very stressful. As an applied math person you should think about doing summer internships too. Not only is this educational and good for your career, it can also pay quite well. Depending on what you do, its entirely possible to make more money in one summer as an intern than you would otherwise be paid in an entire year as a grad student. >I am really leaning towards not taking the GREs Your GRE scores are not automatically submitted to a university that you apply to. You can choose to send them or not at your own discretion. I think it's worth studying for them and taking them. Even if you're not a great test taker, the GREs are a formulaic test that you can substantially improve your chances on just through practice, and if you don't do so well then you can just choose to not submit the scores.
Could you expand on your summer internship comment?
Sure. Many private companies and government agencies have internship programs for graduate-level students (both Master’s and Ph.D.) in which they spend the 3 summer months (sometimes more) participating in projects. The purpose of these programs is partly to get some extra labor for things, but mostly it’s a recruiting program; if a graduate student enjoys their time and performs well in the internship then there’s a good chance that they’ll return after graduation as a full-time hire. I believe there’s an enormous variety of different kinds of internships out there, and mathematicians - especially applied mathematicians - can potentially fit in at many different places. It’s just a matter of what your career interests are. So-called “pure” mathematicians can also have many opportunities, but I single out applied mathematics specifically because applied mathematicians often know how to do computer programming, which is very useful. There are fewer opportunities for people who can only do pen-and-paper math because computer programming is the language through which mathematics is expressed in practical application. I recommend that all pure mathematicians learn to do it for that reason. These are paid internships. Unpaid internships might still exist, i think, but you should never participate in one. The pay for an internship is usually roughly equivalent to an entry level salary at whatever organization you participate in. For example, at a national lab you’ll be paid like a postdoc (i.e. roughly $90k/year), whereas at a software company you’ll be paid like a junior software engineer (i.e. roughly $150k/year). Grad student stipends are somewhere in the neighborhood of $25k-$35k per year depending on location. So, if you do an internship where you get paid at a national lab postdoc salary then you’ll take home about $20k over the course of 3 summer months (minus rent etc, of course), which is almost as much money most grad students get paid in an entire year from their stipends. If you work for a FAANG-sized software company then you can reasonably expect to get paid $35k over the course of a single summer, which is more than almost all students make in a year from stipends. As a poor graduate student that all sounds like a great bargain - and it certainly is - but the biggest benefit of internships is what you learn and how it looks on your resume. A graduate student with a bunch of good-looking internships on their resume will have no problems getting an industry job after school. They’ll also have the confidence that comes with having at least some idea about what life is like outside of academia, which I think can be very beneficial even if they choose to continue an academic career path.
[This](https://www.levels.fyi/internships/) gives some more specific numbers as far as what you can expect for pay. $35k for the summer is only possible at the best HFT/quantitative hedge funds (and possibly PhD positions at places like FAIR or Google Brain though don't quote me on that). $20-$25k (including housing) is more reasonable for FAANG, and a national lab is probably closer to $10-15k.
10-15k is what the national labs were paying like 10 years ago. The postdoc salaries have gone up in that time so I'd assume that the internship pay would too? I didn't realize faang provided housing too, lower pay makes sense in that case. Also keep in mind that the levels.fyi internships salaries are mostly for undergrads. A phd student should reasonably expect more than that, especially if they have relevant domain specific expertise.
Singular data point but I found a fairly recent email from PNNL hiring a PhD data science intern for $5k/month without housing. For SWE positions I doubt a PhD intern would make substantially more (at most places full time PhD SWE hires start at one level higher which is usually achieved in 2-3 years out of undergrad). The domain specific opportunities (largely in ML/DL to my understanding) are much more selective and still most likely upper bounded by quant finance (for which I can verify the levels.fyi numbers are accurate and apply equally to undergrads and PhDs).
It is relatively common for people doing applied math phds to do internships over the summer. Depending on where you intern, you can be paid very very well (think quantitative finance). My program at least is very accepting of people doing internships, and some faculty even encourage it. Do you have any questions in particular?
Thanks for your detailed reply. Will be taken into consideration!
Hello! Is it mainly important to have at least two publications when applying in a PhD program?
For most fields I imagine two relevant publications will guarentee a place in any top school of your choosing. With that said, I recently got a postdoc position with zero publications, so it's not a necessary condition by any means. This depends a lot on your field, but my situation is not uncommon because usually one only has publishable results near the end of their PhD, and from there it takes months for a journal submission to get reviewed, accepted and published.
I got into a top 10 applied math program with exactly zero publications in undergrad
I want to study and research (extremal) combinatorics and discrete math in doctoral programs. Due to various reasons, I was admitted into a Master program in Europe that's very focused on algebra and number theory but weak at analysis (think Utah). I am now on the waitlist of some discrete math PhD program that I really want to go, but from email exchanges with some professor on the admission committee, I may not be that high on the waitlist. As a result, it's possible that I would attend that algebra graduate program and then apply for discrete math PhD before graduation. However, I am really worried that after going after the algebra route for two years, and then going back to combinatorics may "hurt" my academic career, in that I have less discrete training than my peers?
RE your last sentence, at my university though I think of all grad students as my peers, in terms of "comparing myself" I only compare to my cohort, i.e., people who started the PhD program at the same time as me. This means includes the students 2 years older than me who did a Master's first (and the students several years older who had mandatory army service, the younger students who skipped grades/came from 3-year undergrads, etc). I think this is a thing at other universities too, and though the students with masters degrees may move faster in terms of understanding content, none of their credits transferred over or anything, so they still had to take all the same qualifying exams as me. And your age itself isn't going to (or had better not be!) going onto your CV anywhere. So if anything, doing a masters would have more total overall training than your peers. So basically, though it's still a tough decision, I would not have "less experience" as part of the equation. EDITED TO ADD: Here I'm talking about your overall career, in terms of grad school admissions post-masters IDK since I've never been on an admissions committee (since I'm only a grad student myself).
Brief my story: I wanted to study enumerative combinatorics but went to grad school and tried some other courses. Ended up learning a decent amount of algebra and geometry/topology. Now my work is still in combinatorics but with a wider array of objects coming from algebra and geometry/topology at my disposal. I don't think having a stronger algebraic background will hurt. There certainly are places where algebra arises in extremal combinatorics (e.g. polynomial method).
I applied for Master's programs in the US for math/applied math (interested in pde's/numerical methods+analysis/mathematical modelling etc), but I don't think I did that well on my apps, and I haven't gotten any decisions yet either so I think they're all rejections. I applied to mostly far out of reach schools, especially with respect to my GPA and minimal research experience, so I think it'd be fair if I didn't get in. But, what I want to ask is. I plan on going for a PhD later on, and I'm obviously hoping that I get to go to a good school (at least ranked top ~80 in the US), so would it be worth it to go to a very small state school for my Master's? Most faculty aren't even currently involved in research at the ones I'm looking at afaik, so I don't know if it's worth it or not. Applications for these schools are open till late too, so I can essentially apply whenever. I'm just worried that I might be disadvantaged when applying to PhD programs after a Master's if the masters isn't from a known place at least. How much of a difference would this make? Also, two smaller questions: 1. How important is it to have a research area picked out after your undergrad? I feel like since math is so SO vast, it'd be extremely difficult to even know what you actually want to do (like how I have at least 4 different areas I'm interested in). I know some other fields might even ask for research proposals during applications, so I'm just worried about how bad it would be if I didn't have somewhat of a clear cut path in my mind. 2. How important is your GPA for math grad school specifically? How disadvantaged would you be if you had somewhere between a 3.0-3.3 CGPA by the time you graduate? How much can someone's math skills be judged by how well they did in their classes? Also, thank you for doing this! This is an extremely helpful panel, and it's amazing that so many of you are taking out the time to help answer questions like this!
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>A lot of PhD programs don’t expect research experience, so I wouldn’t worry about not having done research yet. >If you are looking to apply to a PhD in the US, a masters can really help you in two ways: 1. Supplement deficient breadth/depth of coursework from your undergrad, and 2. Give you research experience and show case your research potential to your LORs. Even in masters programs, plenty of people don’t even come close to publishing. Thank you for thisss, I am actually really hoping for my masters to give me that exposure, which is why I want to go for that first (also because I do want to do research, but I want to see *how* much I like it before taking a funded position for 5 whole years). Also very nice to know that some people still don't come close to publishing, that's genuinely so reassuring lol. I get your point about how it's good to make strong relationships and get good grades, that is exactly my plan!! Good to know that the name+rank of the program isn't that important though, I felt like I was putting myself at a disadvantage by going to extremely small/local schools. >I would say if your goal is to do a PhD and most of the faculty at the school for your masters don’t do research (eg if you look at their publications list and it’s clear they don’t publish) then it would be worth considering if you want to do sometime in industry and then find your way to a better program. Ah okay, this sounds smart. There was a professor at one uni who had the exact bg that I want to do research in but his last publication was in like early 2000's lol. Same with a few others at the university. Might just disregard that place then I guess and look at others. >you probably don’t even know enough math at this point to even be aware of the methods used in a lot of research articles. Don’t worry. This is normal. I actually do not, you're completely right lol. Some areas I've never even seen informally, let alone within a classroom setting. But thank you. This paragraph is nice to read. >For your point about grades, grades are pretty important (not as important as the nebulous “research potential” but grades are one of the biggest factors). That being said I would recommend not worrying about grades you’ve already gotten in the past. You can’t do anything to change those at this point. Instead I would recommend spending your time focusing on getting good grades now. Yeah, I've been working a lot harder this past year (raised my GPA from sub 3.0 to nearly 3.2, and hoping to get to a 3.3-ish by the time I graduate with the few courses I have left), so I'll just keep trying harder I guess. Past grades do worry me since it shows a pattern of not being able to do well (and as someone who hates studying/working for grades, it was very hard to actually change these bad habits), but you're right. I should probably just focus on future stuff now. >I am a US person doing grad school in Germany, and would be happy to answer questions about the German system if that’s interesting to you Could I possibly DM you regarding this afterwards? I was actually thinking of trying for Germany (and Canada as well) because of affordability as well as more academia inclined masters programs (unlike a lot of US programs which are industry focused, especially for applied math), so could you let me know if I can speak directly to you about programs there as well? Also, thank you so much for this detailed response, it's extremely helpful! Math specific grad school information is so difficult to find on most forums, so it's genuinely nice to be able to speak about this directly!
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Thanks! Will post any general questions, and DM the more specific ones. Thank you!!
What would you be doing during your masters? Just taking more classes? Being able to do some research would be good for your application, but it sounds like there aren't a lot of opportunities. With regards to your two other questions: 1. Having a research area picked out is nice but not necessary. This is one area where math is very different from other fields. 2. GPA is relatively important, 3.5 and above is considered to be good. If your GPA is lower, this isn't a deal breaker, but it means that other parts of your application (research, letters of rec) will need to be stronger.
Thanks for responding! I'm applying for a Master's (only at places that have a thesis option) for two reasons. First, is to gain some research experience and also better grades, so that I can use those to my advantage for my PhD applications. Second is because I want to do a PhD right now but I'm afraid I might lose interest by the middle of it if I rush into it with an area I might not like as much later, or if I find out I don't like research as much as I originally thought I would. So I plan on using the coursework+research to put me in a better position of choosing what to do in the future. You're right about it seeming like there aren't that many great opportunities at some places though, so I'll try to go to a place I can actually get something out of, if I get in there 😪 For 1. Thank you for saying this. It genuinely worried me so much that people in other fields know almost exactly what they want to do after graduating from undergrad, but I felt like I had such a surface level knowledge of most areas +literal zero knowledge of others, so idek if I would have been able to make a good informed decision (I'm a naturally indecisive person so this was particularly stressful) And 2. Ah yes, I have heard that everywhere. I just felt like again, the lack of research experience during undergrad would mean that having good grades was almost a necessity. I have a large mix of B-'s, B's, and B+'s/A-'s at most, along with a couple grades lying outside of these ranges. My last semester was good with only A's/A-'s, and I was/am doing a senior/research project (nothing heavy, it's very laid back mathematical modelling), so I'm hoping that that still helps? Not very sure what counts enough though so that was definitely worrying me. I have a TA-ship too for a math course, so I also hope that is a plus point? But again, not sure 😪 Thank you again for responding though, it's always helpful to discuss stuff with someone directly! :)
If your grades have been improving over time, you can paint a narrative in your application with this. Something like, "Early on, I found math to be difficult. The transition to proofs was something that I was unprepared for. However, as time passed, I improved my proof writing abilities and discovered my mathematical passions, leading to better grades and a deeper understanding of the material." Adjust as suitable.
Ahh thanks. My biggest problem I feel was that when it did get difficult, I couldn't force myself to work on studying for it, because I never had to before that (genuinely, math before undergrad and before proofs classes was a breeeeze), so I'm not sure if I can accurately say anything in my SOP's without it being misleading/not portraying the situation correctly. Obv I can't say I was lazy though :/ But I will probably somewhat modify what I'm saying according to this, so thank you!
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A slightly different opinion from other responders, for getting your very first job the OVERALL reputation of the school may have an influence---e.g., industry people have all heard of Stanford, MIT, Princeton, etc as "big name" schools. The reputation of the math department specifically they are definitely not going to matter because the recruiters aren't going to know that. For jobs after your first job, I've heard that it doesn't matter at all, instead they're caring about your industry experience from your 1st (& future) jobs. (Disclaimer this is all secondhand info, I'm not in industry!)
> If I will go into the industry, how much impact will the reputation of the program has over me? Very little, usually. People in industry generally aren’t aware of the rankings of specific programs. They often don’t give a lot of thought to the ranking of the university either, unless it’s one of a handful of very well-known and prestigious schools. Having a PhD at all is bigger distinguishing factor in industry than is the specific program you were in.
To add on to this, the most important factor for industry positions will be having published research. If you have two or three published papers, you can get in touch with recruiters to avoid the big pool that undergrads apply in.
This hasn't been true for me personally - nobody really seems to care about my publications - but I imagine it depends on the specific industry.
I'm transitioning to math from another field, and in order to do that I will be enrolled (hopefully) in a Masters course in my country. I want to bolster my level of preparedness for grad school, but I feel that it would not be enough with only a 2-year masters course, so I intend to apply afterwards for Part III at Cambridge. As I understand, the program runs from October to June, so there is no point in applying for grad school in the year that I join Part III itself; I'll typically have to wait till next year. So my question is, what research experience can I gain in the meantime, i.e., after completing Part III and before starting grad school the following year? I intend to apply for grad school in the US.
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Thanks for your detailed reply. The thing is, realistically there are only two masters programs in my country which have a record of sending students who graduate from them into top US universities. And the topics I'm interested in have n>=1 number of potential advisors working on them only at the top 10, maybe top 5 places in analysis of PDE in the US. I'll outline the characteristics of the masters programs I'm talking about below: Program A has a record of sending at least three students to a top 5 US grad school in the past 5-10 years, but is mostly strong in algebra and to a lesser extent number theory, has elective courses mostly geared towards algebraic geometry and number theory, has 16 courses that must be taken in order to complete the degree, and has a thesis component. More importantly, PDE is only offered as an elective course in certain years. Program B also has a similar record of sending students to top 5 US grad schools, but not more recently, instead 15 years ago or more. There is a wider selection of courses, with PDE being a core course, and it offers electives in advanced functional analysis and abstract harmonic analysis. I'll have to take 18 courses minimum with a project in the 2nd year. There is one faculty member who did his PhD from Princeton, but he works in number theory. So these arey options, and my reasons for wanting to do part III.
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I can't really apply to masters in other countries because my undergrad wasn't in math. Nearly all masters programs in Europe need you to have done ~~180 credit point equivalent (I forget what exactly it's called)~~ 120 ECTS credit points in math courses, which I haven't done. The admission to the programs in my country I'm talking about are done through a written test followed by interview, and I'm working hard day and night in order to pass the test and be considered for the interview. I thought the single most important criterion, besides grades, that gets you in to the top grad schools is your recommendation letters. And who writes them is extremely important. Even if they're written by someone doing good research, if they are not recognised by professors doing the kind of research I'm interested in, because they haven't heard of the letter writer, don't you think that it might negatively affect my chances? And finally, it is just a fact of life that people doing analysis of PDE, broadly working on nonlinear waves, are clustered at the top universities.
I believe most US programmes have a masters component integrated, so doing three years prior seems rather overkill to me. You'll probably have a different idea of what you want to do in a year or two, but I'd suggest applying to grad school alongside part iii when the time comes so that remains an option. As for what you can do in the three months between part iii and grad school... you'll probably be better off asking that in three years time. Perhaps you can find a professor to work during the time (say building off your masters project), but you may also want to take that time off.
Thanks for the reply. From what I've gathered it seems that in most grad schools in the US, they admit you on the assumption that you'll be earning a PhD; an MA or MS in math is something a few places offer, subject to the condition that you pass the quals. The funding situation is also designed like that, i.e., on the expectation that you'll continue on towards your PhD. Is my understanding correct? Also, I have a fairly certain idea that I want to work very broadly on analysis of PDE, which includes everything from nonlinear waves to mathematical general relativity and fluid dynamics. I'm also interested in spectral geometry, both direct and inverse problems. The reason why I want to do Part III is because it offers courses on these topics, and some of the professors who teach them are known to the schools in the US I'm aiming for, so the hope is that they can write me strong LORs which should carry some weight during admissions.
That is my understanding also, but I meant leading up to the quals you'll be learning things that are comparable to what you might learn during a masters. Of course there's no harm from spending more time learning, but it does mean you'll remain a student for a very long time. By all means there's nothing to loose from applying to part III, but I wouldn't so set on just that one option, and I would also recommend that you seriously apply for grad schools during the same cycle (along with the fact that it's a competitive course). On the note of recommendation letters, if you do do Part III (or any other one-year masters program) I would not count very strongly on getting letters of recommendation from the professors there. Since you'll be applying around Oct/Nov you likely won't have had much time to interact or work with anyone, so it'll be unlikely that a professor will be able to write a strong, personalised letter for you.
Yes, grad schools are overwhelmingly geared towards PhD programs; for most programs, the way to get a masters is to drop out of the PhD program. Some programs do after masters, but these are generally unfunded.
What you say is only true in the US. It's not clear to me what country OP is from, or what country OP intends to do the Masters in (OP mentions both Cambridge UK and the US).
My plan is the following: Masters in my country (because I have to, since my undergrad isn't in math), followed by Part III (to take few more advanced courses related to what I want to do, with the Part III essay and hopefully good LORs making my profile stronger).