I'm in a rather unique situation, and if possible would like some advice. I'm trying to figure out where and if I should go for a Masters in math, based on how it would help my PhD applicant profile.
Undergraduate Institution: Decent Public School. Top school in state, 30-50 USNews national ranking.
Major: Physics, Math
GPA: 3.66
Math GPA: 3.65
Type of Student: International ethnically Indian male.
Masters Institution (Ongoing) Small Public School. Not well-known at all. :
Major: Physics
GPA: 4.0
Note: I started this program in January, as a fallback plan in case I got into nothing for the 2024 cycle.
I've recently decided to switch fields from physics to math. I applied to math PhDs in the 2024 cycle and got rejected everywhere. Based on the profiles here I feel like I'm a really weak applicant, so I'm trying to remedy that. Long story short, I have only one graduate class in math, Bs in a significant number of my upper level math classes, no math professors I could ask a letter of recommendation from, and no research experience in math at all. I do have research experience but it's in physics. It focuses on PDEs and solitons, and I have a paper under review. I know it's a sorry profile, but I've had a series of unfortunate happenings in the past few years, including the pandemic (or as a math prof of mine liked to put it, the "scamdemic").
I'm hoping for a really good school for my math PhD, focusing on PDEs. Based on my profile I've been thinking that a Math Masters would be helpful. But my current school doesn't have a math department, so I'm looking for other schools. Here's the thing though: I can't leave the US, so I can't do any European masters program, however much stronger they may be.
Now I've identified a few programs that may be worth doing. I've seen UIUC's, UWisc-Madison and UMich's program among others. UMich and UWisc look good since they have people I'd like to work with for my PhD there.
They are also expensive, so I've been looking at instate programs as well since I will pay much less for housing that way. I have found an instate program, but the math department seems fairly average. It's certainly not as well-known as UWisc or UMich. I do know one prof at that school who's willing to work with me and who does very interesting research in PDEs and analysis, but that's about it.
Now my question is: would going to the instate program affect my chances of getting into a top PhD program? In other words, is it significant that the instate program is less prestigious than programs like UWisc and UMich, in terms of PhD admission prospects?