Advice on how to approach graduating early

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bucknuggets
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Joined: Sun Aug 04, 2024 6:42 pm

Advice on how to approach graduating early

Post by bucknuggets » Sun Feb 02, 2025 3:18 am

Hi everyone,

I've noticed that it seems to be common wisdom that graduating early is generally a bad idea, and that spending an extra year taking upper/graduate-level courses will fare you better with graduate applications. I was wondering if similar advice would apply in my case: I am a first-year at a low-ranked state school with a rather small math department, but by credits, I'm a junior thanks to AP/dual enrollment from high school. I have taken calc I-III, diff eq, discrete math (essentially intro to proofs), linear algebra I & II (LADR as textbook for latter), probability theory, and a course in Lie groups thus far. This semester, I am taking real analysis I, complex analysis, and dynamical systems. Next year, I plan on taking a yearlong sequence in graduate complex analysis, as well as abstract algebra I and graduate topology in the fall (among other courses). I'll be doing research this summer under a well-known program that will be fully funded (about ~8k in total) in the area of stability theory. My math GPA should be around 3.9 by the time I apply.

I was wondering if I should pursue PhD applications next fall, or if I should wait another year and complete a master's at my school through a 4+1 program. I have no apprehensions in the slightest about cheapening the college experience, and my main concern is whether or not I'd have a chance with apps this fall. My full-ride scholarship (the main reason I'm here) won't cover a year of a master's, and course offerings are rather limited and aren't too rigorous. I've talked to one masters student who told me that graduate analysis 1 was essentially a review of his undergraduate analysis at a top school. Of course, I'm planning on taking the math GRE, and I'm confident I can get a very good score (have always been a great test taker and I self-study well).

Open to any opinions on if I'd be good to apply next semester, or at least what I can do to maximize my chances. Thank you all!

EulerEnthusiast
Posts: 2
Joined: Tue Mar 19, 2024 6:25 pm

Re: Advice on how to approach graduating early

Post by EulerEnthusiast » Wed Feb 12, 2025 9:23 pm

A few random tidbits of advice:

1) You can always apply this fall and decide to postpone, but you can't decide you want to go to graduate school after not applying. I was on the fence about whether to go to grad school immediately after undergrad and my profs suggested to apply anyways and decide later. If I didn't get into a school I wanted to go to, I could do research for a year and apply next cycle. (I ended up deciding to go)

2) I ended up graduating a semester early (not two years early, which it sounds like you are on track for), so to spend my time productively while waiting for grad admissions results, I participated in the Department of Energy's SULI program for half a year. Could be worth looking into - I really enjoyed my experience. It also helped me in my research what knowledge I felt like I lacked such that when I entered graduate school, I had an idea for what sorts of things I wanted to learn. It also gave me ideas on what research direction to pursue. Also, since I felt a bit burnt out at the end of undergrad, it gave sufficient time to regain excitement to get back into school. If you don't feel a danger of being burnt out around this fall, then that may be a different story.

3) The main reason that I gathered on why an early graduation may be a bad idea: graduate school math is a different experience in terms of how you approach school. The danger with going to grad school so soon is if one treats grad school like a sprint and doesn't develop a well-balanced pace by which to go through it. Spending some time between undergrad and grad school or having a longer undergrad career can help with developing this kind of maturity. Make sure you develop a lifestyle in grad school such that it's sustainable. Taking a bit of a break (as mentioned above in (2)) can give some perspective to come into grad school focused and prepared.

4) If you find yourself wanting for coursework, you could add an additional area of interest to your studies - get another major or minor in physics, computer science, chemistry, biology, heck... philosophy or classics. Especially if you have a full-ride, since finances are likely not as much a worry. This can round out your education and your application. Or study abroad! Something like Budapest Semesters in Mathematics could give you a better idea of what grad school will be like (if it's pure math that interests you).

5) The benefits of doing the year-long masters:
- Could be helpful if you were planning on going into industry (doesn't sound like that's true in this case)
- If you had a mediocre GPA in undergrad, a masters could be a chance to remedy that
- If you were applying to PhD programs in the UK, some of them may require a masters. But since you'd already be paying for a master's, it would probably be better to see if you could do Cambridge's Part III math program.

But in many US PhD programs, you can already get a masters en route. So if it's not funded and you already have pretty decent coursework, GPA, and research, then a master's probably isn't worth it (unless you did the aforementioned Cambridge program, which (my impression is) is very good thing to have on a CV). But this is just my two cents and someone else may have very different anecdotes.

eternallyconfused
Posts: 12
Joined: Tue Oct 15, 2024 5:18 am

Re: Advice on how to approach graduating early

Post by eternallyconfused » Fri Feb 14, 2025 7:29 am

I am also enrolled in a 4 + 1 program, and I have only applied to programs that I really want to go to, as a PhD is a long-term commitment. I am sure I would benefit from doing a PhD in these places (and since you can get your master's en-route your PhD, I think not having done the master's will be fine). But I would rather stay an extra year than go to a place I am not too fond of, as I would regret not trying harder for a place I believe is better for me.

There are also some factors for me that make me really want a change, so I think this is a decision you can make by reflecting on what you think you might want, and how you feel about staying. But I think that applying to a few places that you really want to go to cannot hurt, and it'll prepare you for the process in case it doesn't work out (though hopefully, you'll be successful!)

caniusemyonetime
Posts: 52
Joined: Tue Jan 21, 2025 3:19 pm

Re: Advice on how to approach graduating early

Post by caniusemyonetime » Mon Feb 17, 2025 3:37 am

I graduated Fall 24, having taken a gap in spring 24 for a total of 3yrs for an American bachelors. The gap semester was to work on math and was funded by my profs DMS grant. I pulled some pretty good schools this round of admissions. Take that as you will

scrubm8
Posts: 9
Joined: Tue Jan 28, 2020 12:07 pm

Re: Advice on how to approach graduating early

Post by scrubm8 » Mon Feb 17, 2025 4:15 pm

I graduated a year early (so in 3 rather than 4 years) from a state school (at the time US News rank ~55 math department) and went to a top 10 PhD program (you can find my applicant profile from several years back if you want).

Questions for you
  1. How low-ranked is your school really?
  2. What kind of PhD program (both type and quality) are you aiming for?
Some comments about graduating early
In my case specifically, I strongly believe that graduating early was the correct decision. I was getting to the point of running out of math courses to take, I was very confident I could get into a top school, and I thought that I would benefit both mathematically and personally from a new environment.
EulerEnthusiast wrote:
Wed Feb 12, 2025 9:23 pm
3) The main reason that I gathered on why an early graduation may be a bad idea: graduate school math is a different experience in terms of how you approach school. The danger with going to grad school so soon is if one treats grad school like a sprint and doesn't develop a well-balanced pace by which to go through it. Spending some time between undergrad and grad school or having a longer undergrad career can help with developing this kind of maturity. Make sure you develop a lifestyle in grad school such that it's sustainable. Taking a bit of a break (as mentioned above in (2)) can give some perspective to come into grad school focused and prepared.
I understand this sentiment, but in my experience the leap between the period of the PhD where you are still taking classes and the period where you are exclusively doing research is much larger than the leap between the end of an American undergrad and a US PhD program. This cannot be simulated during an undergraduate degree by 99% of people (alternatively, you could go work in an actual job for a few years and then do a PhD). In particular, I think that graduating early is not a bad idea if you are mathematically ready for it.

Some advice for you (OP)
If your answers to the two questions are similar to my answers a few years ago, your profile is not strong enough to get into a top PhD program. This was already true when I applied, and since then the number of available spots has decreased because of COVID and because of more recent events. I would be very concerned that you do not have graduate courses in real analysis and abstract algebra, especially given your description of the graduate analysis course at your university.

I am also concerned that one year of studies is not enough time for you to obtain three strong letters that speak to your potential for graduate study (remember, when you attend a low-ranked university you really have to stand out). This is the most important part of the application, REU letters are extremely hit or miss (especially if the mentor delegates much of the mentoring), and of course it takes time for faculty to get to know you well.



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