How do I know if I'm unprepared for my math PhD? I earned my B.A. in the U.S. but felt unprepared to go right into a PhD program due to the (extremely) limited math courses offered at my undergrad institution so I went into a masters program. I ended up doing really well (3.9GPA) and gained a lot of confidence and expanded my knowledge. A couple years later I decided I wanted to apply to programs for my PhD. I ended up selecting a foreign university where it is assumed you already possess a masters degree, which originally I though was great since it saved me a couple years of additional schooling that I though would be redundant. Now that I am about 6 months in however I am seriously questioning the quality of the master's program I was part of. It seems that others in the program are much more advanced than I am and I seem to struggle with everything, which is a brand new experience for me. I spend hours and hours spinning my wheels reading and trying to understand papers, feeling like I just don't know the background I need to. I feel as though after 6 months I have learned nothing and have wasted a lot of time on things that ultimately never became clear before I had to move on to the next task. I have somewhat discussed these concerns with my advisor but they seem confident that everything is fine.

I also find that now that I am here the project I am part of is much more applied than I had anticipated and I am unsure about if this will evolve to more closely match my interests over time or if this is just another indication of a poor match. 

I am not sure what to do. Is this a normal experience? If it truly is not a fit for me at my current level of knowledge, what are my options?

Any advice is appreciated.



EDIT: I have not discussed this as bluntly with my advisor as I am speaking about it here, primarily because it is just over the last couple weeks that it has become much more problematic. I do intend to speak to them about this more explicitly at our next meeting.
The fact that your adviser thinks you're doing fine, in particular, suggests to me that you may be dealing with some impostor syndrome.  

I think when most of us start out in PhD programs, we feel like everyone around us is doing much better.  Like they all belong here, but we don't.  This is usually accompanied with a feeling of "I had better keep my head down and stay quiet, so no one notices I don't belong here and kicks me out."

You don't say much about your conversation with your adviser.  Hopefully it was an honest conversation about why you're concerned.  As long as it was, consider trusting that they know what normal looks like.  You might also want to talk with some of your classmates more - you may be surprised to find that the ones who seem to be endlessly more successful than you are feeling identically.

PhD work is usually a whole new level of difficult, so it's not necessarily a warning sign that you feel like you have to study for hours to get anywhere.