2020 STATS / OR PhD Application Evaluation and Advice

[benz]

Undergrad Institution : Big State School in U.S., well known in mathematics.

Major(s): Mathematics
GPA: 3.86

Minor(s): CS

 

Type of Student: International male

 

Courses taken and taking:

Mathematics - Undergrad level: Honors sequence, covering single and multi-variable calculus, linear algebra, and manifolds.

Mathematics - Grad level: Combinatorics, all alpha courses (real / complex analysis, differential / algebraic topology, abstract algebra 1,2), some topic courses. Planing to take commutative algebra and algebraic geometry next semester.

CS - Undergrad level: C++, data structure and algorithms, computer organization, theoretical cs (Turing machine and complexity), one elective.

STATS: Took 1 intro course in freshmen year. Might take graduate level stochastic process, statistical inference or machine learning next semester.

 

GRE General Test: Not taken yet, but my vocabulary is very limited and I don't really expect to get higher than 325.

 

GRE Mathematics Subject Test: 89%, planing to take one more time.

 

Programs Applying: Statistics, Operation Research, Pure Math PhD.

Research Experience: 2 summers of REU, both in pure math (differential geometry and algebraic topology), one at home school, one ongoing.

Pertinent Activities or Jobs: Took part in some competitions, but the results did not meet my expectation (and were objectively not good). No job experience.

 

Letters of Recommendation: 3 professors from home school, one of whom is my REU mentor, expected to be good but not necessarily strong. I also have an option of asking my second REU advisor, but this might not be as good as the others.

 

Applying to where: (Since I intended to post this question to ask about STATS and OR, I will focus on these two subjects.)

 

Statistics: Stanford, Berkeley, Harvard, CMU, Washington.

Operation Research: Princeton, MIT, Columbia.

Mathematics: Most of the rest of the top 20s.

 

Remarks and Questions:

 

1. My grade is good (almost straight A) in general, except for one very bad semester (semester GPA~3.3; took 3 math and 1 eecs in that semester). This is one issue that I really worry about, and I don't know how much this would affect my application.

 

2. Previously my plan was to (only) apply for pure math PhD, so I have nearly no background outside pure math. However, my professor says that this does not really hurt because these subjects love math people, and historically, the application results in my department were indeed pretty good, where some students did not have much background either. In this case I have no idea which school in the list above I can probably get into. Could someone please comment whether this list is reasonable or not? Also, I could take some more STATS courses next semester, would it help?

 

3. Remark to question 2: This list is still under consideration. For example, I might apply for math to Berkeley and Columbia, or apply for OR to Cornell. But I think the big picture would not change, i.e. applying for math to most of the schools except the top 5-ish.

 

4. About the recommendation letters. I got A+ from real analysis (i.e. measure theory) which was taught by a professor in analysis, probability and random matrix theory, but I did not have much interaction with him. That said, he knows me, and I still have half a year to get in touch with him, maybe doing some reading. None of my other recommenders are in fields related to STATS and OR (they are in geometry and algebra). Would it make a difference if I ask the analysis professor for a letter when applying to STATS / OR?

 

5. About the difference between STATS and OR. To be honest, at this point, I think if I don't do math, I would most likely to go into industry in the end. On the other hand, I still want to do something that is more quantitative, and math related. For example, I know that ORFE at Princeton has a strong connection with math department, and there are even students doing mathematical physics; while, it seems that OR at MIT, Stanford, Columbia and Cornell are more towards engineering; and there are schools like Harvard and Yale whose OR department belong to business school. So I am wondering if research areas and tastes differ greatly between these schools.

 

 

Acknowledgements:

Thanks for any comments, and sorry about the long questions. I am going through lots of self doubts and anxiety. Not a long time ago I changed my mind about applying only for pure math, partly because of my grades and comparison to friends who just finished their application, and partly because my current REU (and seeing more math) makes me doubt whether I really want to do math. I hope that your comments would help me get a better understanding of my situation. I appreciate your kindness and help.

[Geococcyx]

I'm very much not the expert in how admissions for international students work, but I'll respond in the interest of giving you a timely(-ish) partial answer.

Responses to your remarks/questions.

1.  You didn't give us the grades for your classes, so how much that one lower-GPA semester would vary greatly depending on which math classes you took during it and what your grades were in them.  That said, the one I was worrying about most was Real Analysis, and you have an A+ in that, so I doubt it'll be an issue unless you got a C+ in linear algebra that semester or something.  Even then, your profile's pretty strong, one semester averaging a B+ probably shouldn't be something to really worry about.

2.  I'll get to the school list below.  Most stats classes aren't going to be a big help -- a grad level statistical inference class would probably help, if not that then an undergrad statistical inference class or the grad level stochastic processes class you mentioned. 

3.  Again, below.

4.  I don't really see an issue with asking your Real Analysis professor.  Presumably your other recommenders are your REU advisors or whatnot, that cohort of professors should be good.

5.  I can't comment on those schools' research areas.

OK, now your school list.  I'm not much of an expert in Math PhD applications either, so there's a limited amount I can comment on that.  That being said, your statistics list is really strong, and while you're a good enough applicant that you might get into some of those schools, I'm guessing you would want some safer choices in there too.  Part of that is that my limited impression of Math PhD programs is that they're really hard to get into, and part of it is that if all of your safety schools are math programs then that doesn't seem optimal for you -- if you're not sure you want to do math and are looking at statistics as an option, it doesn't make a lot of sense to strictly aim for some of the most difficult statistics programs to get into.  It's obviously fine if you would still probably prefer to do a Math PhD instead, but insofar as you want to explore statistics, it'll probably benefit you to apply to a few schools in the NC State/Texas A&M/UCLA range just for the ability to choose once you've visited them and make sure you have a non-math option.  

[benz]

Thanks for your comments!

In that semester I got a B+ from complex analysis, and a B- from the CS elective, security. My grades for other courses are all A range with 3 A-'s.

About safety schools: I will definitely add some safety schools. One issue is that my preference might still be in math, so given two schools that are similarly strong, I might choose math over stats. From previous students' results, it is quite possible that I will get into some top 20 math program, so I hesitate to really give up any reachable math programs. My plan has been changing a lot though. I will talk about school selections with my professors.

I guess my question about asking a letter from my analysis professor is that his letter may not be the best and I need to spend quite some time to do this, but his field seems to be more related to stats. I don't know how important the field of study of the professor matters.

Again, thanks for your reply and I benefit a lot from it!