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I was just wondering how alarmed I should be if I have to read the hints that Rudin gives for the exercises. For example, this past weekend I spent probably over 10 hours (over the two days) trying to do #27 in Chapter 2 but couldn't figure it out (I spent that time trying to fix a fundamentally flawed approach). At the end of this, I gave up and read Rudin's hint. The hint pretty much gave away the problem, in my opinion, and I it was quite trivial after that. On the other hand, I think it would've taken me a long time (possibly an infinite amount) to think of the approach that his hint gave.

I have done all the problems in Chapter 2 up to number 27, and had to look at the hint on 22, 24, and then 27. So here is my question: the next time that I get stuck like that, should I go back and reread the chapter? Or do you guys think it is more efficient to take the "faster" route and just read the hint? For the record, I have been trying to prove all of the theorems on my own, and that went fine for chapter 1, and chapter 2 up until the compact sets section in which I got destroyed. Perhaps it would have been wiser of me to go work through the compact sets section again?

After this past weekend I felt quite sick of topology so I decided to move on to Chapter 3 which has been much easier so far. Perhaps I won't have to read the hints in chapter 3?

Austin Stromme
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    Chapter 3 contains one of the most painful and tedious sections of exercises in my opinion. It's a lot of series manipulation that struck me as highly unmotivated and hint-heavy when I did it. – jxnh Jul 19 '14 at 02:55
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    I just wish he kept the hints in the back of the book. The guys at Art of Problem Solving implement hints perfectly (IMO) - they keep them in the back and each problem has one or more hints with numbers associated to it. But, cleverly, the numbers are quite different (for example a problem could have hints numbered 127 and 249) so that, in the back where they are ordered, you don't accidentally see more than one hint at a time. This serves to reduce one's almost insatiable temptation to "peek" at the hint, and also allows them to dole out hints as needed. Great for learning. – Austin Stromme Jul 19 '14 at 02:58
  • Fair. I worked through Rudin in a class where we were doing basically every problem in one chapter a week, so I just gave thanks for the hints, but I could see why they'd be annoying if one was trying to get the most out of it at a more self-guided pace. – jxnh Jul 19 '14 at 03:07
  • Yeah I am just trying to get through chapter 8 by the end of summer, so I can go at a bit more of a leisurely pace. – Austin Stromme Jul 19 '14 at 05:02

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