kieroda wrote:Your profile looks fine so far. Here are some bullet point answers:
- Research experience isn't too important, but if you can get an REU it's a good place to make connections and it does look good.
- Letters of recommendation are arguably the most important part of the application, so try and get to know a few professors.
- The math subject GRE is far more important than the general GRE, I'm pretty sure most schools don't care about the general GRE at all. Take the subject GRE whenever you can find time to study and do the practice tests beforehand.
djysyed wrote:I've reached out to Northwestern and UChicago since I am a student at UIC (Top 30 Graduate Program so definitely apply here as well). Based on the responses I've received from Northwestern faculty, you'd want to do as many guided readings and REUs as possible since you don't have access to graduate courses. In addition, keep your MGRE as high as possible (preferably 90%). Many of the incoming students don't have previous graduate study. Unlike Northwestern, UChicago is a top 5 program so they expect you to have seen a fairly large amount of math and possess the ability to pass their first year sequence, which is very very intense.
ArtinWedderburn wrote:As for your number theory and topology interest:
1. If you want to take number theory (or any algebra class), you should take commutative algebra as soon as possible. A friendly introductory text is Atiyah's "Introduction to Commutative Algebra". If you want to study number theory, you should read through the first ten chapters and pay attention to topics in integral dependence, discrete valuation rings, Dedekind domains, and completions. If you want to study algebraic geometry, the first eight chapters should suffice (though chapter 11 contains something that will appear in Hartshorne chapter 1). Unfortunately, I don't know any number theory so I cannot give you any further advice.
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