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.