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As much as I have seen, actually mGRE seems to be even less acknowledged in pure mathematics admissions. I mean, after all, it is just a bunch of calculations, and anyone in math major can have a decent score by memorizing stuff. I have seen someone with ~60% accepted to Berkeley. The GPA is a bit of a concern, but maybe if you explain it well in the SoP, and since you came from a great university, I think it can be mitigated to a certain degree (although this is just guessing). The mathGRE forum is quite inactive, but indeed you should give it a try. But I think the best choice is to ask your professors about it.

It was a good thing that I didn't attempt to apply for CS since I do not have any formal research experience ? At least it is a good thing that I have genuine interest in CS as well. I wish I can study all the fun subjects.

@Sampaoli I really wish I had chance to get advice from you sooner. Personally, I thought mathematics might be too competitive, and one of my professors was worried that I might miss opportunities to study other subjects if I go to the math department, so I changed the universities one day before the LoR deadline for professors. This is my final list: Stanford, statistics Berkeley, statistics Upenn, statistics Cornell, OR (probability concentration) UNC-CH, statistics and operations research Michigan State, statistics and probability CMU, statistics (later joint Ph.D. for machine learning) Princeton, OR Georgia Tech, IR (statistics concentration) Purdue, statistics I wish I could have chance to apply for Courant and Chicago, but I was unsure whether I am qualified for it. The Math GRE forum was way too inactive to get an answer. I laugh at my own choice about CMU since there is no probability group there, but I was still attracted to TDA, networks, and ML. GT might be even worse, but seriously I lacked time and information. I really wanted to try Caltech's CMS but again I pulled back like a coward. Kinda depressing... I really wish there was someone who could have given me some advice near me. As someone who had to work and lacks information in the academia, this is really my best shot. The professors were not of much help. At least I wish this is helpful to future and current prospective applicants. Still, I want to sincerely thank everyone who have helped me deciding which universities I should apply for. My deepest gratitude to @bayessays and @Stat PhD Now Postdoc for honest evaluation of me and providing me with valuable information. I would have been still happy even if I was told that I should probably not apply for some of the top schools since I know that it is an honest opinion. Also many thanks to @Statmaniac for mentioning OR: I know it is not for everyone, but it definitely covers many of my interests. I made a convex optimization Python module myself (the core is from other packages, though) and I did not know it was an important topic in OR. And now I have to finish up the applications and rest... I am so exhausted now.

Unfortunately I got 860(87%) and it will hurt me at the top universities... I think it is kind of an embarrassing score for a quant haha... I am still thinking of opting for Michigan or other places where I can study stochastic processes and probability as well. I am trying my best to find a potential advisor looking through the faculty members. Sorry for hijacking the thread, OP. I just wanted to check the chance of getting into CMU.

Is it really that difficult to get into CMU unless the undergraduate university is super famous? I am wondering if this is true in my case as well... (I see a PhD student from the very top university but not from my university) I was almost decided to give it a chance but maybe I will fall back ? [Edited] Adding some information about PhD students and removing redundant things. Still, the scope of mathematics taught in Carnegie is quite narrow so I was keep hesitating about applying for it. Would I have chance to take classes from other universities or something if there is no class that I want to take? [Edited] Screw it, I might as well just apply for it cause why not. As for the OP, I also think you should apply for more higher-tier universities. I used stochastic processes and statistics frequently at my work but I cannot read most of the research papers either: sometimes it takes way too much time to read them at my level of training.

Thank you for your advice. I still decided to go for statistics since I want to focus on mathematical training. I guess I will take some deep learning courses later, if I am admitted somewhere.

Hey everyone, I actually found that OR works quite great for me. It depends on the department, but I just checked Cornell and it uses mathematics, statistics, ML, programming, optimization... I mean ML is really weak in the Statistics Department for some reason. So I'm thinking of adding some ORs as well. I am interested in optimization anyway. I would like to get some advice on universities with good OR department. [Edited] I am only considering OR if it has concentration on statistics and ML. Concentration on probability is also super welcomed. I am basically favoring academic flavor of OR more rather than its business one.

I had a brief discussion with one of my professors, and he advised me to apply for CS or ML. His opinion is that if I go to the statistics department, it is often way too theoretic (only dealing with something like Lasso) and he was worried that I might have way too few chances for applications. What is your opinion about this? Personally, I heard that CS focuses on research experience so I'm done for, but I might as well apply for some ML departments if this is the case.

@bayessays Oh... I might have to reconsider Purdue then... I need more research. Could you explain more about how Cornell is culturally different?

My friends actually pointed out that some of the schools are rather isolated (Cornell, Indiana, TexasAM, Virginia, Purdue) and expressed some concern about it. I have no idea about the researching environment in U.S., but what is your opinion on this topic? Will it be detrimental due to the lack of conference opportunities and what not? If you were in my case, would you consider choosing different schools considering the factor?

@bayessays That's good to hear. I think I will ask some of my friends with experience abroad(U.S.) on these issues as well; I cannot decide any of these on my own.

@Stat PhD Now Postdoc Thank you for your assessment! I am quite surprised and honored to hear my chance is still high for Purdue. I was also worried about University of Washington due to its weather. Is Seattle really that bad to live in? I actually prefer Purdue since the mathematics department there teaches model theory. I heard though that probability group in Seattle is quite big. I guess I have to look for quality of life in the case... [Edited] So I was worried a little bit about the low ranking of Indiana and Virginia in statistics, but I guess they are still great places to study statistics? In the case of Indiana, the ML was not in the curriculum but there was a separate center for machine learning so I think I can still learn various things.

Hello, I have mostly chosen my targets but I need some inputs. The following are almost 100% decided (except Michigan State due to its confusing policy about financial support): Stanford, statistics Berkeley, statistics Duke, mathematics Upenn, statistics Cornell, mathematics UNC-CH, statistics and operations research Michigan State, statistics and probability The criterion I used for deciding the department was where the probabilists belong. I think the lineup above is way too challenging so I want to add additional 3 from below: University of Minnesota Twin Cities, mathematics Purdue, statistics University of Washington, mathematics Indiana University, mathematics UCDavis, mathematics Texas AM, mathematics UCI, mathematics University of Virginia, mathematics If I had money to burn, I would have chosen more, but unfortunately I do not have that much money... Here are some questions I want to ask you: Do you think the lineup will be still a bit too tough even if I choose 3 from below? In that case maybe I indeed have to burn some more money... Do the universities I have chosen have strong a statistics department enough to offer rigorous statistics & ML program? Even if I end up going in the mathematics department, I will study statistics as well so this is an important question to me. I am particularly worried about Indiana University and University of Virginia. If possible, I am thinking of choosing University of Minnesota(19th math), University of Washington(26th math) and UCI(39th math). What is your opinion about it? Should I choose much lower? If you have no concrete opinion since they are math departments, then it would be OK if you comment about the level of strength in their statistics department. After checking the math GRE forum, I think it might be still too tough for me. Still, I would appreciate your honest opinion about it first. Thank you as always.

T_T I am now even more torn about which program I should pursue. It seems like I have to check each university how many Ph.Ds are admitted in each department(mathematics, applied mathematics, statistics, operations research). I have absolutely no idea how to get those numbers. I mean, I'm fine as long as I can study pure mathematics and statistics along the way. Do I have to use a random generator and... ha....... that doesn't sound good. Nonetheless your insight was indeed helpful.

Thank you for valuable advice. I still suppose that competition for pure mathematics is fiercer than statistics? I am not sure whether applied mathematics is easier than statistics for that matter. At least for me, considering operations research seems to be on option. What is the difference between statistics and operations research? Their focus might be different but it seems like they require equivalent courses in most cases (practically).