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.