nicole2 wrote: ↑Fri Jan 10, 2020 10:09 pm
Would you mind clarify as to why the materials on the math gre is not of graduate level?
Okay, if you people believe that I am being too ambitious, then doesn't that mean my advisor is purposely setting me up for failure by telling me I have an excellent chance of getting into these schools?
Also, what is the point of doing a PHD at a bottom tier school? I don't think there are any good mathematicians out there coming from tier 3 schools.
As to the gre question, the most advanced subjects covered are point-set topology, groups and rings, linear algebra, and some real analysis. I think the standard is to take a linear algebra, abstract algebra, analysis, and topology class by the fourth year of undergrad that covers these subjects.
I also wouldn't necessarily trust everyone on this anonymous forum more than your advisor, but I think it's important to get second and third opinions. Other faculty members would probably be your best bet. My opinion, for what it's worth, is that it's not a waste to apply to schools in the ~20-30 range, but you should research schools that fit well with your interests and strengths (instead of just looking at ranking) and write tailored statements for them.
You're probably right about no good mathematicians coming from tier 3 schools, but having a PhD in math can lead to plenty of other job opportunities. Being a good mathematician purely in terms of research, though, is a rare thing.
One additional point that I feel hasn't been discussed enough is the importance of having good armwrestling clubs near your graduate institution. For instance, Syracuse is a great school for this reason, as the great CNY armwrestling club is located there. (See
here) to find a list of clubs by location.)