kaehler

From what I hear for pure admissions at good schools, they want to know if you can pass quals, and then write a good thesis. You should try to: Have a grounding in upper level/early undergraduate algebra, analysis and topology. Show some evidence of research ability (not necessarily achieving any big results - just so they know that you know roughly what you're getting into in a PhD). Have recommendations from professors (preferably with some reputation) who can back up your grades and research experience with a "3T113 does know the basics of algebra/analysis/topology like the back of their hand, and I think they'll pass quals! 3T113 has had some research experience, they know what it's like, and I do strongly believe that they can do good research and write a good thesis!" If your undergraduate is at the university that your profile seems to suggest, then a lot of your undergraduate courses will cover early graduate content at a lot of places - you have great grades in major, so you're fine for 1. Clearly you seem to enjoy doing research, and you're spending a lot of time working towards an interest in low dimensional topology, so 2 is all good. Reputation wise, your recommenders are gonna be juuuuust fine :) so as long as you've left a good impression on them, 3 is sorted. I didn't mention the subject GRE because a student with those traits will do fine with a little practise to get the speed up. You should aim for 80% - any lower might be a red flag at the top few places you're thinking of, so winging it is most definitely not worth the risk. Realistically I think you'll get into 5 or 6 of the places you're applying to. Top 6 ranked programs (the top 3 in your list + Princeton/Stanford/Berkeley) are a crapshoot for pretty much everybody, and the next few on your list (Columbia, UCLA, Caltech) aren't far behind in that aspect. Good luck!

Ok, thank you! Do you think there’s a chance for consideration at Princeton or MIT?

Oh wow, thanks for letting me know, I’ll definitely keep that it mind. Do you know if any of the other programs in my match/safety list are significantly harder to get into than rankings suggest? I’m particularly interested in Columbia, as I don’t know if I’m going to enter academia after the PhD or not, and I’ve been told that they have excellent connections to industry.

Undergrad Institution : Imperial College London, 4 year MSci Major(s): Mathematics GPA: First Class (ranked top 5% of class) Minor(s): Statistics (took a bunch of courses but no official minor) Grad Institution: Toronto Major(s): Mathematics GPA: 3.97 Type of Student: International Courses taken and taking: (divided into what I think are normally undergrad/grad level in the US. Starred courses are at UofT, others are at ICL) Mathematics - Undergrad level: Linear Algebra, various methods courses (Vector calculus/Fourier/ODEs/PDEs), Dynamical Systems, Numerical Analysis, Abstract Algebra, Real Analysis, Complex Analysis, Topology, Differential Geometry, Probability Mathematics - Grad level: Measure, Probability, Functional Analysis, Stochastic Calculus, Manifolds, Riemannian Geometry, Algebraic Topology, Differential Topology, Complex Manifolds, Graduate Probability II*, Geometric Analysis: Brownian Motion on Manifolds*, Non-Linear Optimisation* Statistics - Undergrad level: Statistics, Statistical Modelling (both introductory courses) Statistics - Grad level: Statistical Theory, Generalised Linear Model, Stochastic Processes, Time Series, Computational Statistics, Bayesian Methods, Machine Learning, Methods of Applied Statistics I*, Methods of Applied Statistics II*, Topics in Statistical Machine Learning*, Theory and Methods for Complex Spatial Data* GRE General Test: Q: 170 (97%) V: 162 (91%) W: 5.0 (93%) GRE Mathematics Subject Test: 960 (99%) Programs Applying: Statistics PhD Research Experience: 2 summers of reading and writeup (1st on statistical learning, 2nd on topological data analysis). ICL thesis on Malliavin calculus, UofT project on information geometry. No real original work, just high level review/exposition. Pertinent Activities or Jobs: 1 data science internship at a tech company, working there full time from October. Proficient with Python and R, competent with C++ and Haskell. Letters of Recommendation: 6 options (4 from project supervisors, 2 from analysis/geometry professors who liked me), will choose most appropriate 3 for each program. Applying to where: (Probably not gonna happen, but one can dream): Stanford, Berkeley, Harvard, Princeton ORFE, MIT Applied Mathematics Reach: Chicago, CMU, Washington, Duke, UPenn Wharton Match: UWisc, UMich, Penn State, Columbia, Cornell, Purdue, Yale Safety: UCLA, UCD, USC, Rutgers, Northwestern, UIUC, MSU I have no idea exactly what I want to do, but I know I'd be happy working on anything along the lines of probability theory, statistical learning or the intersection of those fields with geometry/topology.