Chances in Pure Mathematics

[3T113]

 

Undergrad institution: One of MIT, Princeton, Harvard, or Stanford

Majors: Mathematics

GPA: 3.78 / 4.0 overall and 3.85 / 4.0 in department 

Type of student: Domestic white male

Courses taken (+ Planned)

Math:

•  Accelerated Honors Real Analysis I (A-),  Accelerated Honors Real Analysis II- (A-),  Topology (A-), Complex Analysis (A-), Differential Geometry (A),  Modern Knot Theory (A)

Courses will take:

• Algebra, Measure Theory, Additional reading course in low dimensional topology 

Recommenders: One giant in the field of low-dimensional topology with whom I took the knot theory course and will complete an undergraduate thesis, one younger faculty member with whom I am doing an REU this summer, one giant in string theory with whom I did undergraduate research last year 

Research experience: Completed a semester long research project in Fall 2017 on random matrices and QFT with one recommender, received an A with submission of 20 page paper, though not for publication. Completing an REU this summer at my home institution on Lagrangian Floer homology and knot Floer Homology with the younger recommender. Will complete a year long undergraduate thesis with the remaining advisor, topic will be broadly in low-dimensional topology. 

Work experience: Nothing relevant 

Awards: None

GRE General: Taking in fall

GRE Math: Taking in fall

Here is a preliminary list of schools I am thinking about: MIT, Harvard, Chicago, Columbia, Cal Tech, UCLA, Texas, Georgia Tech, Duke, Indiana, UC Davis. In some regards I feel like I am being way too anxious, but at the same time, I feel a lot of pressure due to my peers. In any case, I would be thankful for any advice and feedback. 

Edited July 18, 2019 by 3T113

[bayessays]

You will have more luck at mathematicsgreforum.  This forum is focused on statistics because of how many math people already go to mathgre.

[3T113]

Thank you!

[MathStat]

While I applied to statistics PhD programs, I was also math major who did solely math research. Based on the experience of my peers who applied to math phd programs and on what some math professors have said, the single most important factor in math PhD admissions are your letters of recommendation.  Also make sure to score above 80% on the math gre. You sound like you have good chances, so apply to all the top schools and also a decent number of safeties. Good luck. 

[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:

1. Have a grounding in upper level/early undergraduate algebra, analysis and topology.
2. 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).
3. 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!

[Stat Assistant Professor]

I did a Masters in Applied Math. From what I could gather about PhD admissions at the department, it did seem as though the letters of recommendation were super important, as one poster above said. Grades in math classes were also very important. PhD programs in mathematics also like (domestic) candidates who have already taken a few graduate-level classes (most international undergrad math majors will have taken classes like measure theory, topology, etc. as part of their undergrad curriculum).

Since you're from a top school and are taking such courses, you should be in great shape for PhD admissions, provided you score decently on the subject test.

Edited July 26, 2019 by Stat PhD Now Postdoc