Everyone learned in high school that admissions to top colleges for undergrad is not a meritocracy because there are simply too many qualified candidates and not enough spots. After getting rejected from 9 top colleges and having to go to a state school, I knew that that at least would change for graduate school because achievements in college are easier to compare, harder to fake, and represent real effort. But now I have to question this belief given how acceptance rates are below 10% and taking tough courses, having a high GPA, and having great recommendations doesn't set you apart from the average applicant. So I wish to know what I could do that I'm not already doing or planning to do. To that end, here is a list of some things I've done:
- Courses taken by the end of this semester: MATH 340, 341, 403, 410, 411, 432 on this list, and STAT600, AMSC466. A+ in all courses so far.
- Established a good reputation with one professor after excelling in a seminar and a few math competitions, these being organized/proctored by him. Still need one more reputation like this to have 2 strong letters.
- Joined a directed reading program, currently reading through Graph Theory by Diestel.
- Published papers in high school journal and on arXiv.
- 4.0 GPA, more than half of credits towards degree done.
- By the end of this semester, will have satisfied all requirements outside math except for one writing course, and will have satisfied all criteria about specific math courses or topics. Thus, I have time to take plenty of graduate courses and the freedom to choose.
Here is what I'm planning to do:
- Summer 2021 REU. Didn't get into any REUs this year, probably because I only applied to several programs and had just one recommendation letter.
- Do even better in math competitions, simply for the fun of it.
- Take math subject GRE sometime in 2021 just to get it over with. I looked at a few practice tests and the questions look easy even once the time constraint is taken into account. However, I will still officially time myself on a few tests just to not let my guard down.
- Take more graduate courses, graduate with math department honors, and maintain a high GPA.
- Ask professors interesting questions outside of lectures so that they remember me. An instructor for a course I did very well in last fall told me he wouldn't be able to provide a good letter because interaction outside class was minimal (I never went to office hours or sent an email). This strategy should make me more than just a student who showed up to lectures and got good grades.
Is there anything significant I'm missing that would make me stand out among the applicants to top PhD programs? I heard that students from lower ranked colleges are expected to have higher statistics, but my academics with regards to grades and course offerings already seem to be maxed out, leaving only the option of making muself look better outside of courses. Surely the answer isn't to just continue doing what I was planning on doing given how competitive admissions are in the 21st century. These lists aren't complete, so a correction will be made if someone I already had in mind is mentioned.
A note about time: I should be on track to graduate spring 2022. If I don't get into a good math program for fall 2022, is taking an extra semester or 4th year and then reapplying for spring/fall 2023 a good idea?