I've started self-studying analytic number theory from these lecture notes (I am currently attempting exercises from Chapter 2), and even though I enjoy the learning process, my main difficulty seems to be my intuition regarding bounds and asymptotic analysis. I got through introductory real analysis pretty well because I sorta knew what I was trying to bound, but here I am completely lost, to the point where I have to read each proof line-by-line again and again to develop an intuition about what the proof is trying to do. I know that the usual answer to these kinds of questions would be just to do more problems, but when I look at the problems (especially the later ones), I don't have a slightest idea where to start. This is almost demotivating because I am sure ANT has a lot of beautiful ideas and proofs rather than just bounding stuff endlessly, but it seems like the journey to get to those ideas is going to be painstakingly long. Therefore my questions would be:
- How can I get more comfortable working with bounds and integrals? Is it a thing that gradually comes with experience?
- Should I set aside my urge for developing intuition until a later time?
Thanks a lot!