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I am, or was, a math major in a big state university, and just graduated this year and I am taking a gap year. I finished my undergrad in three years and took some extra math courses. I also have one-year independent research experience with an Honors Thesis and a research award by the math department. The upper division courses that I have are : Linear Algebra, Analysis I&II, Adv Applied, ODE, PDE, Prob, Stats, Stochastics (All A's). some of them are in grad level. I also have an independent study on Fourier Analysis with Stien's book. As for the Application, I will have two very strong letters. Just haven't taken the GRE yet.

I understand that relatively good grad schools take the courses that students took seriously. And my problem is mainly about this.

However, every school's webpage that I looked at prefers students who also took Algebra and Topology, which I did not take for some reasons. But I am trying to learn Algebra with Artin's book and some more analysis with Stien's books myself in the gap year. Can someone please tell me just how much disadvantages would this bring me, and would what I am doing help with the admission process.

I am getting mixed messages about this. Some people say that I am pretty much locked out of top 50 schools, my professors could not really answer this, and my friends said it is not a big deal. I am very confused now. Any suggestions would be appreciated!

Thanks a lot.

closed as off-topic by Buzz, user3209815, Fomite, Enthusiastic Engineer, OBu Jul 15 '18 at 13:23

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  • Not a mathematician. But, being "locked out of top-50 schools" when you have a research award and top grades in grad courses seems manifestly wrong. I would just mention your self-study of the deficient coursework in your SOP. – cag51 Jun 14 '18 at 19:59
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    I’m honestly surprised your university let you graduate without taking Algebra and Topology, especially since you got honors. – Stella Biderman Jun 15 '18 at 5:46
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    It sounds like you have an excellent background in applied math, but are applying to pure math programs. Lacking courses in abstract algebra and real analysis is going to be a handicap in that context. Have you thought about applying to an applied math program? – Charles E. Grant Jun 16 '18 at 19:04
  • to answer Charles' question. Yes, I did consider applied math program. In fact, If my profile is determined to be too weak for pure, then I will go for applied. – Johnny Yang Jun 18 '18 at 1:07
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I have never been on an admissions committee and can’t really speak to if it’s actually disqualifying or not. However, even if we operate under the assumption that it is disqualifying that doesn’t mean you can’t go to graduate school, it means you can’t go to graduate school this year. You can enroll as a non-degree student in the university of your choice and take the necessary courses. This may be expensive or difficult depending on the country / situation, but if you really do need the courses it’s an option available to you. I know several people in the US who have done this in math and math-adjacent fields, more commonly for a MS degree but also for a PhD.

  • Thanks, Stella. That is what I am trying to do. I am trying to get a job in the university I just graduated, so the tuition would be very cheap – Johnny Yang Jun 18 '18 at 1:09
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To be honest, I wouldn't worry a lot about what "some people say." Locked out is a pretty strong statement. I think you have a gap in your education, but you have filled that with other, also valuable, things.

I think that any reasonable admissions process will raise an eyebrow and look at what you have to offer overall. They may suggest a plan for filling the gap.

You are also well placed for applied programs by the way, if that is your interest and the reason that you took the courses that you did.

But when you apply, stress what you can do and have done, not your "weakness".

However, the best answer to this question is from someone in the admissions process (or a department head) at one or two of the universities you'd like to apply to. Likely they are willing (eager) to spend a bit of time with a prospective grad student.

My own history probably isn't relevant now (too far in the past), but I had only a very simple Intro to Topology as an undergraduate, but it became one of my top subjects in grad school. Likewise the first graduate course in Analysis (Measure Theory) was completely different from my undergrad experience. I loved it. Best. Thing. Ever. You can think. You can do math. No problem.

However, it will serve you well to try to fill what ever gaps you think you have. I would think that if you feel you lack in both Algebra and Topology that you work first on one, then the other, rather than getting too much on your plate at once.

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