Need advice on choosing math/probability PhD program.

[Taxxi]

I am applying for a math PhD graduate program in probability (possibly in other pure math fields or statistics), but as an international student I'm having a hard time choosing which university offers good program related to probability theory. What I know is that some of the research is in conjunction with combinatorics and some go along the path of stochastic calculus. In short, I want to get some advice to the following questions of mine:

 

1. Which university offers strong PhD program related to probability theory? What I know is that most of the top 10 schools offer great programs, but I am also wondering other universities with good program in probability other than the top 10s for reaches and safer choices.
2. Which university offers a great degree of freedom regarding the fields I can study? I also wish choosing the advisor is flexible. As most applicants, I'm not firmly decided on my research field and I have a huge interest in nonstandard analysis and differential geometry as well(though I got a very bad grade in the subject due to some reasons...) As far as I can see, Cornell offers diverse opportunities by offering three faculty members to one student, and they can be changed as I study more and my subject of interest is changed. I'm not sure which university offers such flexibility.
3. Which university do you think is a reach and a safe bet for my profile listed below? I'm mainly thinking of applying for probability and statistics at the moment.

 

 

Undergrad Institution: Top 3 in my country.
Major(s): Mathematics, Economics.

GPA: 3.7/4.0

Type of Student: International (Asian)

Awards/Honors: Graduated with High Honors. Bunch of honors and scholarships (within the university).

Math/Statistics Grades: Mostly got As. Took many statistics classes(mathematical statistics, Bayesian statistics). Also took stochastic process class but received B+. Not bad in analysis but very strong in algebra including mathematical logics and algebraic combinatorics.

 

GRE General Test: 166V, 169Q, 4.5W.

GRE Subject Math Test: Waiting for the result. Expecting higher than 90% minimum.

Programs Applying: Probability or Statistics.

 

Research Experience: None...

Working Experience: Quantitative researcher in a fintech startup company (1 year). My researching area was asset allocation with weight constraints, and I actually implemented the program using quadratic programming in Python. Working experience in Python and ML. Working experience also includes the process of choosing preferable stocks by means of basic regression and time-series analysis. I have done so much since it was a small startup, working with a statistician in finance(Master) and a mathematician(PhD, probability and PDE).

Hobbies: Analyzing old classics games, finding the optimal strategy using probability theory and sometimes Python. Fun stuff. This is what got me the job.

Letters of Recommendation: I doubt they will be particularly strong but I doubt they will be detrimentally bad either. 1 from my set theory and mathematical logics professor, 1 from my linear algebra and abstract algebra professor, and 1 from my probability professor.

 

 

Thank you in advance sincerely for your advice.

 

Edited November 12, 2019 by Taxxi
Removing a few redundant phrases.

[bayessays]

You'll find better info about math programs over at the mathematics GRE forum. This forum is mostly populated by statistics people.

For statistics programs, many of the top programs have probabilists like Stanford and Berkeley. I'd also check out other top schools like Washington, Harvard, Chicago which all should have a couple.  Mid/lower ranked schools that have big probability groups are UNC and MSU. 

[Taxxi]

@bayessays Thank you! I wonder if I can pursue pure mathematics even if I choose statistics. I want to develop my mathematical skills with heavy emphasis on probability and statistics. Also thank you for the recommendation about the mid/lower ranked schools.

[Taxxi]

@bayessays Sorry for bothering you, but where is the mathematics GRE forum? The only forum close to it was here and I doubt people will answer to my question there...

[Edited] Well, the GPA is actually about 3.76 by converting the original score to the 4.0 scale. Couldn't edit the original post.

Edited November 12, 2019 by Taxxi
GPA score modified.

[Stat Assistant Professor]

UPenn Wharton Department of Statistics also has some very strong probability faculty (Bhaswar Bhattacharya and Jian Ding). In particular, Bhattacharya at Penn Wharton is an expert on combinatorial probability, so that would be an excellent fit for your research interests. And Jian Ding and his PhD students regularly publish in top probability theory journals like "Annals of Probability" and "Probability Theory and Related Fields."

Which Asian nation are you from, if you don't mind me asking? If you are from China, South Korea, or India, your profile is pretty strong and you stand a good chance. If you are from another country, competition will be tougher (only because there are already so many excellent applicants from the aforementioned countries).

Other than that, there will probably be a few differences between Statistics and Math programs. First, most Stat programs will tend to be dominated by statisticians rather than probabilitists, though I'm sure there will be at least one other member in your PhD cohort who will share your interest in probability. Second, the coursework will be different, i.e. you wouldn't need to take classes in topology, abstract algebra, etc. in a Statistics department like you would in a Math department. However,  you would still need to take a few proof-intensive, heavily theoretical classes in a Stat department like measure-theoretic probability theory, theory of linear models, advanced statistical inference/decision theory, etc.

As far as getting postdocs in the field of probability (many of which will be in math departments), this shouldn't be any problem for someone coming from a Statistics Department as long as they have great recommendation letters from well-regarded professors and as long as they have one article in a top journal like Annals of Probability or Annals of Applied Probability. As far as I'm concerned, as long as there are at least some probability theory faculty in a Statistics department, you could do just as well there as you would in a math department. Most of the stuff you do for your dissertation research is stuff you have to teach yourself on your own anyway, not things from classes (though the classes will give you a basic foundation for more advanced self-study).

Edited November 12, 2019 by Stat PhD Now Postdoc

[Taxxi]

@Stat PhD Now Postdoc Thank you for your detailed advice! I'm from South Korea. I do love mathematical treatment of statistics a lot; "Foundations of Linear and Generalized Linear Models" from Agresti and "Linear Regression Analysis" from Seber are what I used in my job in order to coordinate between my coworkers. My strong background in algebra enabled me to study linear models by myself. I was torn between choosing mathematics and statistics, but your helpful advice let me consider department of statistics with strong probability faculty. In any case, I also want to pursue pure mathematics along the way. I'll also consider Upenn Wharton Department of Statistics. Again, thank you sincerely for the valuable insight you have provided to me!

Edited November 12, 2019 by Taxxi

[Taxxi]

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):

1. Stanford, statistics
2. Berkeley, statistics
3. Duke, mathematics
4. Upenn, statistics
5. Cornell, mathematics
6. UNC-CH, statistics and operations research
7. 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:

1. 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...
2. 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.
3. 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.

Edited November 24, 2019 by Taxxi

[Stat Assistant Professor]

Of the statistics programs on your list, I think you will definitely get into MSU and Purdue. I wouldn't rule out any of the others in your top six, since a 3.7 from one of the top three schools in South Korea is very impressive. I have seen students from Indian Statistical Institute with cumulative GPAs in the low 80s (their grading scale is graded out of 100) get accepted to the likes of UPenn Wharton, Columbia, etc., and I assume that a 3.7/4 is similarly considered very good from a top school in South Korea. I think most adcoms are aware of the high level of rigor at the top math/stat programs in India, China, and South Korea, plus how advanced the coursework is (i.e. many undergraduates at these top schools take measure theory as part of their undergrad education, which is less common for domestic applicants).

I am not very familiar with the math programs on your list. I would recommend you post your profile at mathematicsgre.com to see what their opinion over there is about your chances. If you are trying to narrow your list to only three or so schools from the last eight schools on your list, though, I would definitely also consider things like quality of life (e.g. whether you strongly prefer to live in a city like Seattle vs. a small town like College Station, or if you are indifferent about that). This is somewhere you will be spending 4-6 years of your life, so don't discount things like that.

Edited November 24, 2019 by Stat PhD Now Postdoc

[Taxxi]

@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.

Edited November 24, 2019 by Taxxi

[bayessays]

I think most people would consider Seattle to have better weather than most the US.  It's a little cloudy, but the rain is greatly exaggerated and the climate is much more moderate than the Midwest or Northeast. The cost of living is the main issue there. 

[Taxxi]

@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.

[Taxxi]

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?

Edited November 25, 2019 by Taxxi

[bayessays]

The big conferences are national, so you'll have to travel to them anyways. You should look into whether the department helps students fund their travel. 

But you will have to determine for yourself whether the small town is good for you.  Texas A&M is very much a small college town in a pretty conservative part of the country, a couple hours a way from a big city. Cornell is in a small city too, but very culturally different. Some people consider Bloomington, Ithaca and Charlottesville as pretty desirable college towns, whereas Purdue and TAMU are in towns where most people would not choose to live. 

[Taxxi]

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

[bayessays]

I'm not saying TAMU or Purdue are in bad places. Most would just consider the towns to be pretty boring.

I meant that Cornell is an Ivy League school in a liberal state, whereas TAMU is in rural Texas, which is more conservative.  Very different environment in terms of religion and politics, so if that's an important factor, you may want to see which environment you'd be more comfortable in. 

[Taxxi]

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.

Edited November 28, 2019 by Taxxi

[Sampaoli]

I like your choices but you are missing a few excellent places. If you are interested in probability/stats, I would remove Purdue/TAMU/Indiana/UCI from your list. I would add Courant/Chicago/Northwestern. In probability, they beat most of the schools in your list in terms of pure research quality, they have incredible faculty in the field (Newman/Bourgade/Lawler/Smart/Auffinger/Zelditch/...) and their grad students have a record of finding top post-doc positions. Furthermore, location-wise it is hard to beat NYC and Chicago/Evanston if you like to live in a big city. 

In OR, you may want to consider MIT and Princeton. 

[Taxxi]

@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:

1. Stanford, statistics
2. Berkeley, statistics
3. Upenn, statistics
4. Cornell, OR (probability concentration)
5. UNC-CH, statistics and operations research
6. Michigan State, statistics and probability
7. CMU, statistics (later joint Ph.D. for machine learning)
8. Princeton, OR
9. Georgia Tech, IR (statistics concentration)
10. 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.

[ENE1]

Good luck @Taxxi! And congratulations on (nearly) finishing your applications.