I am starting to see a pattern in my math studies, and I'm interested in your thoughts on the subject.
It seems like there are certain things that are much easier for me to learn than others. For instance, I am a pretty quick learner when I can "visualize" what I'm learning, and logical thinking and rigid formalism seem pretty natural to me. I am also good with abstractions. On the other hand, I am painfully bad at calculations. I can make 5 mistakes when solving the simplest of equations (often not seeing my mistake even when I look for it, and then making 3 others when I try to fix it), and many mathematical tasks seem like meaningless symbol manipulations to me (calculating integrals, identities of all sorts, everything that involves unpleasant functions manipulations, complex numbers can reduce me to tears).
So, naturally I am a bit worried about my studies. Here are my questions:
- I think there may be something I am missing. For the things I am good at, I often have a strategy: an abstraction or a certain way of thinking that helps me deal with them. Do you have such a strategy for dealing with the problems I mentioned? How do you start thinking about them?
- How can I get better at these things? Trying really hard to do it a lot never seems to help. I just give up after making the same mistakes and reaching dead ends for two hours, look at the solution and don't understand how I could have come up with it on my own.
- Is all lost? What can I do with the skills I have?