Baby Rudin: Advice

Question

I am working through the first chapter of Principles of Mathematical Analysis and I am wondering how many of the twenty exercise problems I should do. I think the first ten are very to moderately easy (with 7 as an exception), but the next ten are much more difficult. I am of course trying to do all of them, but how many should I be content with doing successfully? Also, how many of the exercises would a college course using the book require? I am not trying to "get out of work" as I am doing this independently anyway, I just want to know what you would recommend.

Thanks

Answer 1

It looks as though Berkeley has posted their homework based on Rudin, to answer the question "what would a college course require?" The answer appears to be ~10 questions per chapter.

Personally, I make a list of the more straightforward questions for which learning the matter just requires repetition. These I carry in a notebook and do during meetings.

I then skim for more interesting problems, of which there are generally only one or two per section (based on my completely subjective definition of "interesting"). These I do when I have free time.

In summary: I do whatever interests me, and if the next section is too confusing, I go back and do more.

Answer 2

Do them all! But don't spend too much time on any one problem. After working on it for twenty minutes, move on, or take a break. Often times the hard problems will become easy after letting them sit in your head for a while. On the other hand, some exercises are intended to be brute-force and annoying, so that you appreciate the elegance of the machinery and results developed later in the book.

This is especially true for books like Rudin, Artin, etc., where most of the learning is intended to be in the exercises, and not in the exposition.