I have been reading Rudin (Principles of Mathematical Analysis) on my own now for around a month or so. While I was able to complete the first chapter without any difficulty, I am having problems trying to get the second chapter right. I have been able to get the definitions and work out some problems, but I am still not sure if I understand the thing and it is certainly not internalized.
I am wondering whether I should take this shaky structure with me to the next chapters, hoping that the application there improves my understanding, or to stop and complete this chapter really well?
What do you think?
As for my background, I am quiet close to completing Linear Algebra by Lang (having done a course in Linear Algebra from Strang). I have completed Spivak's Calculus. I come from an engineering background and so I have done multivariable calculus, fourier analysis, numerical analysis, basic probability and random variables as required for engineering. One of the professors advised that I may be better off studying Part I from Topology and Modern Analysis by GF Simmons, but I am finding that completing that book itself may take a semester and I would prefer not to wait that long to start with analysis.
EDIT: If it makes any difference, I am studying on my own.
EDIT: So, I have accepted the answer by Samuel Reid. I too have found the limit point definition as illustrated by Rudin and the large set of definitions listed there somewhat dry and without any motivation or examples. This is one of the places in the book which makes it a little difficult for self-study. What I found working in this case is, taking some drill problems from other books and working through them. I will advise anyone to go real slow over the sections 2.18 to 2.32 . There are too many definitions and new concepts in that sections and to miss even one means you cannot move forward. To tell the truth, I found Simmons's 50 pages (from chapter 2 section 10 to the end of chapter 3) to be more useful than the corresponding 4.5 pages in Rudin.