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At my current rate of taking classes I will be able to graduate from college with a B.S. in math from a top 50 US school in mathematics (according to U.S. news) in a total of 2 years with around 3.7-3.8 GPA. However, I am interested in pursuing a PhD within mathematics. If I do graduate within 2 years it will be somewhat of a "bare" degree, i.e. minimum requirements (3 quarters of Analysis, 1 quarter of Algebra, 1 quarters of Complex Analysis (at the time of application) and 2 more quarters of Algebra and 1 more quarter of Complex Analysis by the time I actually get my degree).

Reading this post it seems that the extra rigor is extremely valuable, and sticking around for another year or two would greatly help my application.

However, is applying still worth a shot? If I was to apply and get rejected would that negatively impact my application if I was to apply the next year or next two years? Would applying for a masters degree be worth it in this case, and then switching over to PhD later?

I do want to attend a top graduate program, and I will be talking with an adviser soon (I came here first to get an idea regarding this situation beforehand and not go in blind). So thank you for whatever feedback you give.

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    Do try to avoid graduating in December rather than May. Most programs are set up to have incoming students start in September and don't like to have incoming students start in the middle of the year. – Brian Borchers Feb 8 at 1:10
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    You linked to a previous post, for which mine was the accepted answer. I stand by what I wrote there. Just for the record though: what you describe as a "bare" degree is not bad, really: we have admitted people in my department with less coursework than this. – Pete L. Clark Feb 8 at 20:20
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Having been on the graduate committee of the departments I am/was in for the past six years, and having looked at around 500 applications over that time, I've got something to say about this:

  • The time it took you to graduate doesn't matter. 2 years is fast, and if you've got good grades, then you're clearly quite good and that speaks to your case.

  • If you're only doing the bare minimum of classes, then that raises questions about your preparedness. That's no different than the many applications we see from small liberal arts colleges whose math departments are so small that they can't run anything other than the standard set of courses. The question then always is how such candidates will do in advanced classes, given that they don't have as much background in the different branches of mathematics as applicants from larger schools. There is also the question of the level of courses you've taken: Many applicants take graduate classes in their last year as undergraduates, and if they do well there, that is definitely a plus on their applications.

  • You can always apply. If you get rejected, that's ok, and it won't be a stain on your file if you come back better prepared next year. But you'll have to have an answer to the question of what happens if you get accepted into a program of lesser quality: Are you going to take it, or hold out for something better next year. Declining an offer definitely will look bad if you try again next year, but of course there is also no guarantee that you'll actually get accepted at a better program next time around. So there is a risk involved in all of this.

At the end of the day, your best approach is probably to consider what happens if you graduate now, get accepted into a good program, and then find that you're not adequately prepared. Grad school is fast-paced, and you're thrown into the same pot as all of the other students, many of whom will likely have taken more (and more difficult) classes than you had -- in many cases, first year graduate program classes. You'll struggle -- I'm pretty confident saying that because essentially every graduate student struggles, and the question is only to the degree with which they do.

You can get ahead this curve a bit by staying for another year at your current institution, taking advanced courses, maybe a graduate course or two, and doing well. Your file is going to look better for it, and you'll have better chances of getting into the good graduate programs. On the other hand, your file is not going to look noticeably worse just because it took you three instead of two years to graduate -- your competition will have taken four years. The only real downside I can think to staying for a third year is the money you will have to pay for tuition and cost of living.

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    I completely agree with this answer. Just to underscore a key point that you make: the risk in applying now is not that the OP won't get in but rather that they will, in which case they will have to decide whether it is "good enough" and try to figure out the extent to which 1-2 extra years of schooling would get them into a better program. – Pete L. Clark Feb 8 at 20:18
  • Correct, that was the point I tried to make. – Wolfgang Bangerth Feb 10 at 18:50
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There is a good chance the admissions committee will not even see you've graduated in 2 years

There are a couple of questions here, let me address them.

1) It's likely worth staying the full four years and doing undergraduate research with a professor. This will put you in a much better position when letters of recommendation need to be written

2) Generally applying and getting rejected won't affect subsequent applications.

In general, the only advantage to graduating early is you get to make money sooner. If you're not careful, it can actually put you at a disadvantage as you'll likely have less work experience. You've enrolled at a university to learn, not plow through it as quickly as you can.

Slow down, take fewer classes (and make all As in them). Intern during the summers to both make extra money and gain experience. Finally, college (at least in the U.S.) is also about growing as a person. Take some time to get involved in extra-curricular and clubs.

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My advice is go for 3, not 2 or 4. Same applies if your Ph.D. is going fast. People have a hard tme taking 2 years seriously. But the 3 years shows credible acceleration. Even if you could be done in 2, just enrich during 3.

I gave a more detailed post earlier with several ideas on what to do during year 3 undergrad for similar question, but can't find it now (was during a previous guest).

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