This is not a question related to a certain topic in mathematics, but more a question about studying mathematics generally. (please forgive me if my vocabulary isn't appropiate, I'm not a native speaker since I grew up and live in Germany)
Well, where to begin with? I started studying mathematics in October 2015, and I already passed my exams in calculus 1 and linear algebra 1, both with good grades. (and the exams in calculus 2 and linear algebra 2 are standing right in front of my door step) Before I started studying mathematics, I was a horrible math student, but when a good friend of mine introduced me to the world of mathematics on an academic level, I knew that this was actually what I wanted to do for the next few years or even the rest of my life.
Despite the typical problems that an average undergraduate math student has to face, I really like the subject itself, and I can clearly see that I get better and better at solving problems and understanding mathematics in general.
But there is one thing that bothers me: I feel like my skills don't develop fast enough, and therefore I don't know in which direction I'm heading right now. I don't know if studying mathematics is really worth it when I have the constant feeling of not being or not getting good enough at what I'm doing. I always think that there is something wrong with my way of approaching problems. (although there are a lot of people around me that tell me they wouldn't be able to solve those kind of problems that I solve, but I guess that's just a result of them not even trying to do so)
I wonder if my thoughts are normal and that everything gets much better when I give my skills plenty more time to unfold themselves - or if I should seriously consider to adjust myself in a completely new way. Do you recognize yourself when you reflect upon your time as an undergraduate student?
I would be glad if you could advise me on this topic.