2020 Applicant Profile

Forum for the GRE subject test in mathematics.
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Joined: Thu Dec 20, 2018 4:15 pm

2020 Applicant Profile

Post by internationalting » Thu Dec 20, 2018 4:25 pm

I posted on gradcafe yesterday and got some insight regarding admissions to PhD programs for statistics, but I was hoping you guys could help me out/let me know if I'm being realistic with respect to mathematics grad schools. My primary concern is no original research in mathematics, and would like your opinions on how much weight top programs put on this in admissions.

Undergrad Institution: Imperial College London (Mathematics 4 year MSci integrated masters, graduated June 2018)
GPA: ~3.9 to 4.0 equivalent
Type of Student: International Male

Masters Institution: Oxbridge (Masters in Mathematics, currently attending, will apply to schools next year with grades from this in hand)

GRE General Test:
Q: 170
V: 167
W: 4.5
GRE Subject Test in Mathematics:
M: 92%

Programs Applying:
PhD in Mathematics and Statistics

Research Experience:
Two summers with different professors in the stats department, one of which led to a paper being published. Expository final year thesis in probability.
Awards/Honors/Recognitions: Deans list.
Pertinent Activities or Jobs: Internship as a quantitative trader. Will be working as a quantitative researcher analyst from July 2019 (hopefully only for a year then entering grad school).
Letters of Recommendation: 1st from the stats professor where the paper was published, 2nd from an analysis professor (supervisor of thesis), 3rd from an algebraic geometer. Should be strong.

Relevant Grades: I thought I'd give a description as I will be an international applicant. I didn't officially take the courses written in italics (its rare if not impossible to be given permission to take extra courses for credit, certainly not for this many) but my letter writers verify that I studied them to a high standard independently either under themselves or their colleagues. "A" grade equivalent in everything but a couple courses taken in the first year.

Analysis -- Analysis I, Real Analysis, Complex Analysis, Measure and Integration. (Functional Analysis, Analytic Methods in PDEs, Fourier Series and Theory of Distributions, Stochastic Calculus)

Algebra -- Algebra I, II, III, IV sequence (starts from undergrad vector spaces/linear algebra, groups and rings and builds to homological algebra and graduate groups/rings). Then Galois Theory, Lie Algebras, Commutative Algebra. (Infinite Groups, Group Representation Theory, Modular Representation Theory)

Geometry/Topology -- Metric Spaces and Topology, Algebraic Topology, Algebraic Geometry, Differential Topology. (Manifolds, Riemannian Geometry, Complex Manifolds)

Probability/Statistics -- Probability and Statistics I, II, (measure theoretic) Probability and Markov Processes. Then Applied Probability, Time Series, Generalised Linear Models. (Statistical Theory, Statistical Inference)

Applied stuffs -- Methods I, II, DEs, Multivariable Calc/Fourier/PDEs, Applied Analysis. (Function Spaces and Applications, Advanced Topics in PDEs)

I have not yet decided what courses I will take to examinations this summer, but it will likely be a mix of analysis, stats and geometry right now.

Applying to where: Only really looking at top programs in either field tbh. Especially given that I may go back into industry at some point, branding is pretty important, and supposing I do want to come back to the UK it'd be very useful to have an internationally renowned name behind me.

Statistics - CMU, Berkeley, Stanford, Harvard, Chicago, Columbia
Mathematics - Berkeley, Stanford, Harvard, Columbia, Chicago, Princeton, MIT.

I'm not really sure if my profile is suited more to statistics or maths programs honestly - while I have research in statistics, and my job is also statistics heavy, my coursework and extra reading is dominated by maths.

Does anyone know what the calibre of incoming students at these programs is roughly like? Having checked the syllabi and done some timed past papers I know I could pass Harvard/Stanford quals and Berkeley prelims right now, and judging by the level of depth in some transcripts I'm almost ready to take Berkeley/Princeton style oral quals with concentration in say representation theory and algebraic geometry. But my concern is, if given the plethora of talent that these schools can select from, is basically everyone in my position or better with regards to mathematical knowledge upon entering the program? Because if so, I'm quite worried about my lack of original research now.

Thanks if you read, any thoughts would be greatly appreciated!

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Joined: Wed Jan 23, 2019 8:22 pm

Re: 2020 Applicant Profile

Post by gemach » Wed Jan 23, 2019 8:43 pm

I don't know how much I have to help here -- I have never sat on an admissions committee! However, I have this to contribute: I'm an international student who has received offers this round from multiple universities on your list. (Yeah, things have gone pretty well for me.)

I have roughly your scores on GRE + mGRE. I do not have your background -- I could not pass Harvard quals right now. (I have a *strong* background but generally know 80% of the things they expect for each topic, but not the last 20%. One of them, though, I've never taken a proper course in, so that would be a fair bit of work.) Two things that I suspect helped: I have done original research in maths -- a year-long thesis, which didn't quite get me anything publishable but got very very close. (That's the plan for my new few months of spare time!) As a result, that letter of reference was, I think, exceptionally strong, and I linked my work wherever I could in the application. (My other two letters were strong -- one based on a research project, one on coursework by someone who's a bit of a mentor -- but probably not quite as good.) All of my letters were from people who did PhDs and postdocs in the US at strong schools.

My read on things: you've done enough research that you can say, with evidence, that you like it and can do it. Most US students, from my understanding, have never spent e.g. six weeks working on a particular question while making no progress. (Joy of joys. I've done this twice; the second one I actually figured it out! Still was a pretty frustrating six weeks.) You also have, as you say, a very strong background. All of this is great.

However, the selection process is pretty random. A good friend of mine, who imo is a stronger mathematician than I am, did not get into one of the top universities that I did. (They've got into some awesome ones, though, but just to say that there's a lot of variance.) While obviously things have gone well for me, the (US background) researchers I talked to were very strong on not relying on getting into a top uni for me. I am not Terry Tao, I am not a shoo-in, and at the end of the day, there are 400 people applying for 12 spots at a lot of these places. More than 12 of those are going to be excellent.

Definitely think about how your interests fit with the uni you're applying to. What areas of maths are you interested in? Are there people at those unis who do what you want to do? Some of the ones on your list are ones I did *not* apply to because there were not enough potential supervisors in my field. Also, consider applying to some unis one step down in prestige that still have the name recognition you want. You don't want to put all your eggs in this highly nerve-wracking basket. (I'm thinking UCLA, Yale, Brown, Cornell...) Good luck! Maybe I'll see you in the US in a couple of years :)

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Joined: Sat Mar 02, 2019 12:54 am

2020 Applicant Profile

Post by Geraldhat » Sat Mar 02, 2019 4:55 pm

can someone please help me? I cant make picture appear in my signature? can someone make three pictures into one so i can have pic in my profile, I tried many times but best it came to is only link.. no pic.

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Joined: Mon Apr 22, 2019 2:42 pm

Re: 2020 Applicant Profile

Post by greedynripig » Mon Apr 29, 2019 7:02 pm

You will have to apply to find out; that is the best way. I'd recommend finding a topic you want to work on and a good mentor. Building a shiny profile isn't as respectful as doing something in mathematics that is your own. Most of these schools want good students who would become leaders in their fields. They're interested in future Godels, not just those with fancy diplomas. Can you show them that with the strength of your ideas? If you have the money, I would reach out to respective admissions directors and visit them. You can get a lot of insight about the process this way.

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Joined: Tue Jun 18, 2019 11:59 pm

Re: 2020 Applicant Profile

Post by moonbears » Wed Jun 19, 2019 2:41 am

Just posting my two cents here.

Your application looks great, and you've got some very impressive stats, course-work, and by the sounds of it strong letters; however, I wouldn't solely apply to the "top 10" schools - even if you're as strong as you claim. I honestly don't think it matters where you go that much as long as you're in a top 50 program, get a good advisor, work hard, and publish papers during your PhD. It's become apparent that top schools are more likely to burn students out, or shoo them away unless you're at the very tippy-top at a school like Harvard or Princeton (which is very unlikely). Even if you're a literal genius, you'd be surprised by the difficulty of the programs. Here's an interesting link https://web.math.princeton.edu/generals/tao_terence

The tl;dr is that Terry Tao didn't take his quals seriously and almost flunked them at Princeton. They said his harmonic analysis was unsatisfactory, which is surprising because when I was in his class he seemed to be quite good at all things Analysis. Also last time I checked he was, in fact, one of the best harmonic analysts in the world.

I would focus more on finding a place with a healthy work-life balance, one in which you think you'll be a good student and get lots of attention. It's super easy to get excited when you get into a top school and just go, but sometimes it can be beneficial to go to a less-well known school and just kick-ass.

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