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So I am an undergraduate student in my third semester and I am mostly done with my double major in Pure and Applied Mathematics/Statistics. I will be done with the requirements for my bachelors by my fifth semester at the latest.

If I want to go for a PhD in Pure Math, would I be better off graduating after my 5th semester or pushing some classes back, taking graduate level classes and seminars in my 6th semester and doing an undergraduate thesis? I have some research done and will be doing more next semester, but that is nowhere near what I would do for the honors thesis.

Alternatively, I could go all out next semester and graduate then. However this would leave me very little time to study for the subject GRE (I am good with the general GRE) and to actually apply for schools due to how busy I will be.

I tried to make this a good question by including as much information as I thought was relevant, but if there are any questions or anything I forgot to mention then please let me know.

Does anyone have advice?

Mohammed Shahid
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  • I marked one duplicate, but if you check out the Related questions on the right you will find several existing questions that are similar to yours. I think answering beyond that is more of a matter of opinion or too tailored to your circumstances to be a good question for the SE format. – Bryan Krause Nov 27 '18 at 19:48
  • @BryanKrause that is an interesting post, thank you. I believe that the difference for me is that student loans are not the motivating factor for why I would like to graduate early. I go to a state school and I actually get paid to go here because of scholarships. My main concern is instead that there is a limit on how many graduate level classes an undergrad can take. I believe I will be capped at 2 classes. So even if I graduated a year early, I would have no more graduate level classes to take unless I started a masters. – Mohammed Shahid Nov 27 '18 at 19:58
  • The only person who can tell you about the number of graduate level courses you can take is your own school. You might inquire about exceptions to the rule, ways around the rule, etc. – Dawn Nov 27 '18 at 19:59
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    If I was reviewing your application and you had graduated in 5 semesters, I would immediately question the rigor of your program. A program that allows you to graduate that quickly would be a major worry for me. – Vladhagen Nov 27 '18 at 20:15
  • @Dawn there are no exceptions to that rule unfortunately. I know the graduate director at my school and have taken a class with him, but he said there is no chance of that happening. – Mohammed Shahid Nov 27 '18 at 20:22
  • @Vladhagen do you mean in regards to the difficulty of the classes or the amount of classes required?

    For the required classes, I would have taken the following:

    Logic, Language and Proof, Calculus 1, Calculus 2, Multivariable Calculus with Linear Algebra, Differential Equations with Linear Algebra, Applied Linear Algebra, Advanced Linear Algebra, Applied Algebra, Abstract Algebra, Introduction to Real Analysis, Real Analysis, Analysis in Several Dimensions, and Topology and Geometry.

    I also took some other Applied Math classes (Graph Theory, Stats, etc.) but those are less relevant.

     – Mohammed Shahid Nov 27 '18 at 20:28
  • Regarding the university, it is also an R1 university. Though I am not sure how relevant that would be to the rigor of the undergraduate major. – Mohammed Shahid Nov 27 '18 at 20:34
  • @MohammedShahid It would seem that many of those classes would build on one another. Calc 1 must proceed Calc 2 which must proceed DiffEQ and all three real analysis courses (in order). This is why I wonder how much you actually retained from these classes. If I was reviewing your application, I would be very incredulous that you actually learned in these classes. – Vladhagen Nov 27 '18 at 22:47
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    @MohammedShahid I am also a bit surprised that an R1 university actually allowed you to take 4-5 math classes a semester, especially when they seem to build on one another. – Vladhagen Nov 27 '18 at 22:48
  • Let us continue this discussion in chat. – Vladhagen Nov 27 '18 at 22:50
  • At most two graduate classes total (which seems utterly preposterous) or at most two graduate classes per semester (which seems completely reasonable, even for graduate students)? – JeffE Nov 28 '18 at 10:09

2 Answers2

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For the title question, graduating 1 year early and accomplishing more is definitely better than graduating 1.5 or 2 years early, and accomplishing less. In fact, there's a strong case to be made for taking four years and accomplishing as much as you can. In PhD admissions, you'll be competing against people who were also ahead of the game in their first few semesters, but stayed in school and kept gathering feathers in their cap. Some of these feathers will be more impressive than graduating early. Also, more time as an undergrad means more chances for professors to get to know you, and this is what translates into good letters of recommendation.

Now, that is all general advice. Factors particular to your situation may tilt the balance in favor of it making sense to graduate early. I would recommend talking this over with your professors, because they know your record and can give you realistic advice about your prospects after graduating in X semesters, for various values of X.

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Some things I would immediately question if I received an applicant who was in your situation:

  1. Getting into graduate school is a different beast than succeeding in graduate school. As someone tasked with reviewing your application, one of the things I need to consider is how successful a candidate will be in completing a degree. I need to assess mathematical maturity as part of that assessment. I would question if a student who took as many math classes as possible, as fast as possible, really has the academic maturity to succeed in a graduate program. Graduate school is much more than just burning through classes as fast as possible. We have had a few "younglings" who have tried to do our graduate program and they invariably lacked the maturity to succeed as a graduate student. We have stopped being so impressed by students who are fast graduates. (And have actually begun avoiding them admittedly).

  2. How did you manage to take 4-5 math classes a semester while also fulfilling general education requirements? In the US, most schools require 120 credits to graduate (with each math class being ~3 credits). If you did this in 5 semesters, you really took 20 credits a semester while at the same time fulfilling all prerequisites? Someone who took all three linear algebra classes in one semester likely did not really retain what they need to (and possibly circumvented some registration policies).

  3. If you have a gap year between your graduate degree and your undergrad, what were you doing during the gap year?

  4. Can someone who graduated 2 years early really establish a relationship with letter of recommendation authors?

Vladhagen
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  • Could you elaborate on what you mean by mathematical maturity?

    I made a comment in the chat explaining how I managed to take these classes.There was no overlap like you suggest with taking 3 linear algebra classes at once.

    In regards to what you mentioned regarding the general education requirements, I came in with 30 credits from AP exams which fulfilled most of them.

    What is the gap year you are referring to?

     – Mohammed Shahid Nov 28 '18 at 02:56
  • Regarding the letter of recommendation, I agree that might be an issue. I have somewhat of a relationship with the graduate director and I believe he would be willing to right a letter of recommendation, but I do not know if it would be as valuable since I have not done much research under him.

    However, I have done a bit of research under a postdoc here and I think he could write a sufficient letter of recommendation.

    Regardless, I agree that this would be greatly improved if I stayed longer and did the seminar classes and honors thesis that I mentioned.

     – Mohammed Shahid Nov 28 '18 at 02:59