Hello! I am about to enter my senior year of undergraduate and am planning on applying for Ph.D. programs in pure mathematics this fall. I am wondering if there is an effective way to go about searching for programs/how I can compile a reasonable list of schools given my credentials. I currently attend a small liberal arts college. My academics are fine but far from stellar (3.603 overall and 3.677 in math as of the end of junior year), I have one summer of research in chemistry, will be participating in a math REU this summer, and I have a position as a Learning Assistant (kind of like a TA on an undergrad level) for Calc II at my school. I'm planning on taking the GRE and GRE subject test this fall I'm assuming I'll perform fine, but not great. I think my main concern is my lack of research experience in combination with my nottoogreat GPA. Is one REU with no other math research enough? Will my experience in chemistry research mean anything at all? (This research only lasted for one summer after my freshman year, not published). Will my GPA knock me out of consideration from the getgo? I expect to have 2 very good, and one decent letter of recommendation.
I'm also concerned about the lack of courses I've had access to given the school I attend. The only higher level classes I will have completed by the time I graduate (in addition to the lower level required courses) are abstract algebra (my school only offers one course in this), number theory (this class is what killed my math GPA lol), complex analysis, chaos and fractals, advanced geometry, combinatorics and graph theory, applied mathematics and modeling, real analysis (my school also only offers one course in this as well), plus two electives in my final semester (not sure what they'll be yet, potentially a second course in linear algebra, and codes and ciphers). It actually sounds like a decent list when I write it all out in one place, but I will have taken every math course that my school offers upon graduating, aside from two statistics courses, and operations research which I have no interest in taking, and I feel as if my coursework is lacking if I look at the undergraduate courses that are offered at bigger schools. Will this be a detriment to me in the application process? I know there's nothing I can really do about it, but I know I will be up against super successful students at large research institutes who simply have a more developed program than I have access to.
As of now, I'm thinking of looking for programs in algebra I really enjoyed abstract algebra last fall and I would love to learn more about it, but what I'm seeing basically everywhere are things like algebraic geometry, algebraic topology, algebraic number theory, commutative and noncommutative algebra, etc. How do I know if I should apply to programs that have these research topics if I haven't had the opportunity to learn about them yet? Some programs I've found list group theory or algebra more generally, but this is not what I've been seeing in most cases. Should I be looking into these more specific fields of algebra (ha ha no pun intended) before narrowing down my list? Should I be deterred from applying to programs which have research I haven't been exposed to yet? Are there any specific schools with a strong algebra focus that I should be looking at? On another note, should I perhaps consider more than one field of mathematics when searching for programs? Putting all my eggs in one basket seems like not the best idea what if I take more advanced algebra classes and find that I'm not enjoying it as much as I anticipated? I did also enjoy my complex analysis course a lot more than I expected to, and would love to learn more about that. However, if I had to pick one right now, I'd go with algebra.
As a final thought, finding programs in the first place is proving to be very daunting. I've used the AMS search engine to try and filter my results, but I'm still left with an overwhelming number of schools. Should I be considering location as a major factor in narrowing down this list? It seems like a trivial thing to consider, but it would greatly help in shrinking the list, and I'm having a hard time thinking of any other way to do this.
This post is kind of all over the place, but any input regarding anything I mentioned in here would be greatly appreciated! Thank you so much!
How to find a good list of PhD programs to apply to?

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 Joined: Sun Jul 01, 2018 6:33 am
Re: How to find a good list of PhD programs to apply to?
The most reliable source you have is the professors in your school who knows you well and will write letters of recommendation for you.
You should be aware of the fact that often graduate students develop interest on new fields after they enter the grad schools, so unless you are completely sure about your current interest, you better not focus too much on one specific field of mathematics.
You should be aware of the fact that often graduate students develop interest on new fields after they enter the grad schools, so unless you are completely sure about your current interest, you better not focus too much on one specific field of mathematics.
Re: How to find a good list of PhD programs to apply to?
young556646 wrote:The most reliable source you have is the professors in your school who knows you well and will write letters of recommendation for you.
You should be aware of the fact that often graduate students develop interest on new fields after they enter the grad schools, so unless you are completely sure about your current interest, you better not focus too much on one specific field of mathematics.
Thanks for the feedback! My advisor has been pretty vague and not that helpful in searching for specific schools thus far, and he's (very conveniently) going on sabbatical next semester and will not be around to help me! I'll definitely reach out to other professors in the department to see what they have to say.
As to your second point, I guess I never really thought about it in that way. I think I'm very caught up in how I compare to others and thinking that everyone else has themselves more put together and organized with all of this than I do (but I know that's not the case and I need to calm down haha). I think that led me to believe that since (I have the impression that) everyone else knows exactly what they want to do and how to get there, that I need to figure all that out too.
Basically, I feel pretty alone in this process right now lol, I don't think anyone else at my school is planning on applying for graduate programs in math except for me, so I'm kinda stuck figuring out how everything works on my own. Thank you so much for your help though, I'll be sure to keep what you said in mind!!
Re: How to find a good list of PhD programs to apply to?
Unless you did something really significant in your REU i.e. being a primary author of a publication in a research journal or presenting at a national conference, only one REU for only one summer is simply not enough. You need to be looking around for multiple experiences, so you understand what different mathematicians do and how they approach different open topics. I don't know the answer as to whether your chemistry experience will help you, but in my personal opinion, I don't think so. Math graduate schools want to see your potential to do math research, whether it be in pure or applied math. You are correct in your assessment that your GPA is good, but not stellar. It could knock you out in many top places. You come from a small liberal arts school, which may or may not be known. I have heard that people who come from unknown schools typically get significant attention from a graduate committee by getting a near perfect math GPA (3.9+) and/or a very high subject GRE score (800+).Hello! I am about to enter my senior year of undergraduate and am planning on applying for Ph.D. programs in pure mathematics this fall. I am wondering if there is an effective way to go about searching for programs/how I can compile a reasonable list of schools given my credentials. I currently attend a small liberal arts college. My academics are fine but far from stellar (3.603 overall and 3.677 in math as of the end of junior year), I have one summer of research in chemistry, will be participating in a math REU this summer, and I have a position as a Learning Assistant (kind of like a TA on an undergrad level) for Calc II at my school. I'm planning on taking the GRE and GRE subject test this fall I'm assuming I'll perform fine, but not great. I think my main concern is my lack of research experience in combination with my nottoogreat GPA. Is one REU with no other math research enough? Will my experience in chemistry research mean anything at all? (This research only lasted for one summer after my freshman year, not published). Will my GPA knock me out of consideration from the getgo? I expect to have 2 very good, and one decent letter of recommendation.
I'm also concerned about the lack of courses I've had access to given the school I attend. The only higher level classes I will have completed by the time I graduate (in addition to the lower level required courses) are abstract algebra (my school only offers one course in this), number theory (this class is what killed my math GPA lol), complex analysis, chaos and fractals, advanced geometry, combinatorics and graph theory, applied mathematics and modeling, real analysis (my school also only offers one course in this as well), plus two electives in my final semester (not sure what they'll be yet, potentially a second course in linear algebra, and codes and ciphers). It actually sounds like a decent list when I write it all out in one place, but I will have taken every math course that my school offers upon graduating, aside from two statistics courses, and operations research which I have no interest in taking, and I feel as if my coursework is lacking if I look at the undergraduate courses that are offered at bigger schools. Will this be a detriment to me in the application process? I know there's nothing I can really do about it, but I know I will be up against super successful students at large research institutes who simply have a more developed program than I have access to.
It seems you did not do well in number theory. This could be a red flag, because number theory is central in pure (and even applied) mathematics, and you would need to explain why you got a low grade in your personal statement. I know that the lack of graduate courses at your school is something not under your control, but please be aware that graduate schools expect you to learn a vast majority of courses at the graduate level and pass exams in them to stay in the program (specifically Analysis/Algebra). You are going to have to selfstudy some books on your own to compensate. Google the classic graduate texts to read. Provided you selfstudy, you can say you were committed to learning challenging material in spite of the lack of courses at your school.
As of now, I'm thinking of looking for programs in algebra I really enjoyed abstract algebra last fall and I would love to learn more about it, but what I'm seeing basically everywhere are things like algebraic geometry, algebraic topology, algebraic number theory, commutative and noncommutative algebra, etc. How do I know if I should apply to programs that have these research topics if I haven't had the opportunity to learn about them yet? Some programs I've found list group theory or algebra more generally, but this is not what I've been seeing in most cases. Should I be looking into these more specific fields of algebra (ha ha no pun intended) before narrowing down my list? Should I be deterred from applying to programs which have research I haven't been exposed to yet? Are there any specific schools with a strong algebra focus that I should be looking at? On another note, should I perhaps consider more than one field of mathematics when searching for programs? Putting all my eggs in one basket seems like not the best idea what if I take more advanced algebra classes and find that I'm not enjoying it as much as I anticipated? I did also enjoy my complex analysis course a lot more than I expected to, and would love to learn more about that. However, if I had to pick one right now, I'd go with algebra.
So look up books/papers covering those fields you like and read them like right now. Find out what are the open questions in the fields you mentioned, and who is doing research to answer such questions. You can say in your personal statement that you read this article by Professor X from University Y, and you are interested in doing research under Professor X. If possible, try politely contacting professor X expressing interest. At this point, you should be mathematically mature enough to demonstrate selfreliance in this process of reading up on these fields. You should not be waiting for your instructor(s) to teach you anything.
As a final thought, finding programs in the first place is proving to be very daunting. I've used the AMS search engine to try and filter my results, but I'm still left with an overwhelming number of schools. Should I be considering location as a major factor in narrowing down this list? It seems like a trivial thing to consider, but it would greatly help in shrinking the list, and I'm having a hard time thinking of any other way to do this.
This post is kind of all over the place, but any input regarding anything I mentioned in here would be greatly appreciated! Thank you so much!
I think you should apply to a wide variety of places (if you can afford it). Don't concentrate on the very top schools. Look at those ranked in 2030, 3040. At the same time, don't aim too low.