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.


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    $\begingroup$ Do as many as you can, and then move on. Keep in mind those which you cannot solve. Do not fixate yourself on an exercise which you cannot solve for more than 30-60 minutes. Sometimes the solution comes when you're doing something else. $\endgroup$ Oct 15, 2011 at 19:55
  • $\begingroup$ I don't know the book, but does it really contain only 20 exercises? $\endgroup$ Oct 15, 2011 at 19:55
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    $\begingroup$ @HenningMakholm The first chapter has only twenty exercises. $\endgroup$
    – analysisj
    Oct 15, 2011 at 19:56
  • $\begingroup$ The more problems you do, the more mature you become in the subject. $\endgroup$
    – user9413
    Oct 15, 2011 at 20:00
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    $\begingroup$ @analysisj, Henri Poincare supposedly only worked four hours a day on research, two hours in the morning and two in the evening. It was his conviction that our subconscious minds can be used to great benefit; it certainly benefited him to a great extent! If it worked for him, maybe it can work for you too. $\endgroup$
    – user4536
    Jan 1, 2012 at 20:14

2 Answers 2


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.


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.


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