What Math PhD Programs Can a Smart, Hardworking Student Aim For?

[owlpride]

Realistically speaking, what league of schools does a hardworking, smart but not brilliant math major have a shot at for a PhD in pure math? Let's say I might apply with 8 graduate courses at a "lower Ivy", coauthored 1-2 papers, solid recommendations.

I am not getting my hopes up for Stanford or MIT. But just how selective are Michigan and Wisconsin? Cornell? What about Berkeley?

I will probably have a conversation very much like this with my professors in the not-too-distant future, but I would appreciate your thoughts!

 

[mrb]

I don't have a direct answer for you, but I can say that I'm in a similar boat (only with 3 grad classes and no papers and at a school nobody's heard of, not a "lower ivy"... probably extremely good letters though), and it's not easy to get a solid answer to this question. I think probably ultimately it just comes down to, "No one knows for sure, and it's something of a crapshoot, so just apply to a lot of schools across the whole spectrum you would be willing to go to."

My professors have encouraged me to apply to Harvard and Princeton, but looking at the current grad students there and talking with some people, I'm sure I have exactly zero chance of getting in there. I've heard that admissions at top schools have become more competitive recently and that some profs aren't aware of that. So I actually am applying to MIT, but I'm not holding out a whole lot of hope about that one, and I'm also applying to 9 other schools across the range of the "top 25". It's possible even this is too ambitious, and I won't be shocked (very disappointed, but not shocked) if I don't get in anywhere.

The schools themselves aren't very helpful; the web pages of extremely well regarded schools will say something like "successful applicants to our graduate program usually have taken courses in advanced calculus, linear algebra, and a course in either abstract algebra or topology." ?? Well since that probably includes just about EVERY math major EVERYWHERE, what the heck is the point of even saying this? Obviously such a program wants to see a heck of a lot more than 3 math classes that everyone is required to take.