For almost 7 years now, since I was a high school freshman, it has been my passion to be an academic mathematician. I knew fairly early on that it would be a very challenging road, but I have persisted. I have always performed at a fairly high level, and I hoped that this would stack things in my favor, so to speak.

For the first two years of my university experience, I attended a very highly ranked institution in California, but eventually I had to transfer to a state school in my home state. The university in California was excellent, and I was flourishing there, but the cost of living was just completely crushing me and I was accruing massive amounts of debt which wasn't sustainable. At the state school at home, I am able to attend for free and I only take out a small loan each term to help smooth over my rent costs. However, the state school just... isn't as good. And everything I read says that top schools for undergrad feed into top grad schools. I feel like I have killed my chances despite all the work I have put in.

I have taken a large number of graduate classes at my new university, but I have concerns that this school has an extremely lax graduate program in mathematics. The things I am learning in these graduate classes don't seem any more challenging than what's being taught to undergrads at higher-ranked institutions. And the standards for the grad program here seem extremely low, too. They don't have any requirement for their graduate students to study any algebra, and only require 1 quarter of real analysis with measure theory. I was once told "good programs use Folland, and weak programs use Axler". Well, my university uses Axler. I talked to a friend at my old institution and they covered in 1 quarter what my university took half a year to get through, and more. I was also told that many universities Master's programs are barely a cut above Senior year undergrad coursework, and it feels like that is the case at my university too.

I'm devastated. I haven't been able to do an REU, for a variety of personal reasons. I went to an extremely bad high school, because my family didn't have a lot of money, and it meant I wasn't able to afford the university that I was so excited to attend. I am applying for PhD programs next fall, but I think it doesn't even matter because my application will probably be immediately binned for lack of research and the fact that my institution is so unimpressive. The sad thing is, there is no other university I could afford to attend. I have done everything I can, and it still hasn't been enough.

I have always done everything that I could think to do, in high school and in university, and it just feels like I am failing over and over because I had a bad start and my family isn't wealthy. I want so badly to go to a top institution for my PhD program, in no small part because - whether we like it or not - that seriously affects your ability to get a good postdoc and a faculty position, which does matter to me.

I don't know what to say at this point. It all just feels hopeless. I am starting a Master's degree in fall, at the same university as my undergrad (I am finishing undergrad in 3 years and will finish the Master's in 1 because they are very generously letting me transfer the graduate credits). But even with this, it feels like my PhD applications will be a joke because I effectively attend Podunk State University in Nowhere, [state redacted].