Recently I've been toying with the idea of going through Crandall and Pomerance's Prime Numbers: A Computational Perspective cover-to-cover, to the best of my ability. However, it's a very difficult book, definitely for me and I think for anyone. The most difficult problems in each chapter are open research questions, so the book is as difficult as you want it to be. The non-starred, non-research problems are plenty hard for me.

If I were to slowly post questions I get stuck on here, then eventually math.stackexchange.com would have a partial solutions manual for Crandall and Pomerance. I've decided not to do this, because I love that book, and I wouldn't want to do something that would be harmful to it. I would anyway not do such a thing without asking the authors, which I am not willing to do.

I am anyway posting this question because I thought about it quite a lot over the last few days, and I think it'd be good if the community had their own answer. The same situation is bound to come up with self-study from other books. Maybe there's already an answer somewhere; I found this, but it doesn't quite answer my question.

Is it OK to slowly post a large number of textbook problems, with the motivation to get help when you get stuck with non-homework self-study questions, and the knowledge that this might render the book's problems unusable for a class by some people's standards?

  • This is also related. – Douglas B. Staple Apr 20 '13 at 1:49
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  • Keep in mind that much (most?) of the rationale behind asking people to show their work and such applies equally well to homework as to self-study. And asking good questions might obviate the concerns about having many from the book. – Hurkyl Apr 21 '13 at 1:42
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    I wonder if the scale of question asking you suggest might happen risks exceeding the limits of "fair use"? – Hurkyl Apr 21 '13 at 1:47
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    If you plan to read the whole book, there is a non-zero probability that you find someone on the site, who is reading the same book. Several people reading Atiyah-MacDonald used to frequent a chatroom created specifically for this subject. – Martin Sleziak Apr 23 '13 at 12:58
  • Of course there are problems which you don't know where to start. But often happens that you start to solve a problem and get stuck along the way. What about try to isolate the point you are having trouble with and post it as a new problem (which it is)? – leo May 1 '13 at 16:19
up vote 45 down vote accepted

Just a few comments on this.

  • Asking questions about mathematics is precisely the purpose of this site. It does not matter whether the questions come from the book you are studying or from elsewhere. What does matter is that you put an effort into your question and that you do not ask too many questions at once.

  • I definitely prefer when the OP mentions the origin of the problem, so I do not like the idea of asking questions and not saying from which book they are just to avoid the possibility that MSE can be used as a solution manual.

  • Over the time many problems from widely used textbooks appear on this page. Just a few examples of books which appeared here several times: Atiyah, Macdonald: Commutative algebra, Dummit, Foote: Algebra, Just, Weese: Set Theory or Golan: Linear Algebra. Probably some others. (Although none of the above cases have something like complete solution manual here at MSE.)

  • I fully understand the concerns about using MSE for cheating. But I do not think that we should complicate life to users who are trying to use the site correctly.

I generally agree with Martin on most issues. Let me add/expand some points.

  • The point of MSE is asking questions about mathematics, and as long as asking a question is not dishonest in any way, I see nothing wrong in it, whatever the origin.

  • Mathematical problems usually come from somewhere, and it is frequently not the case that it's the OP's own invention. I would imagine a lot of problems can be traced back to some textbook or exercise collection, only in some cases the path is more winding and includes a teacher somewhere along the way. Drawing a line at the point where the problem is directly taken from the book feels rather arbitrary.

  • There are a lot of solution manuals floating around, whether we like it or not. I generally consider it a good thing if a problem collection comes with a solution collection, be it official or not. In any case, it is a risky thing to give homework based on a well known book/problem collection in any case (at least, some level of trust is required in any case). Likewise, if one uses a book for self study, there will often be spoilers available in any case.

  • If a problem appears in a book, then it is the more likely than many people will be interested in finding a solution. Thus, such questions will be in a way more valuable than self-proposed problems.

I believe the question of wording and reference is an open one. Apparently, Qiaochu and Martin differ on this as well. I would again side with Martin, and argue that is the solution is out there, it's little use pretending it's not (it would be in a way like security through obscurity). On the other hand, it might be useful for those answering the question to know where it's from. Also, it's good if those looking for answer for legitimate reasons can find it easily. (Those who are dishonest enough to look for solution although they should not will probably find a way in any case). Nevertheless, I admit that this issue may be controversial.

I would prefer that this not happen. If you want to do this, don't indicate where the problems come from, and change their wording.

  • I agree with you that one should change the wording (although I have not been doing so because I assumed the general sentiment was to disclose the origin). Be that as it may, it seems to me that this perfectly valid answer got down voted because you did not give the reasons why you think that. Perhaps you could add an explanation and then people might understand your point of view and up vote instead. – Rudy the Reindeer May 2 '13 at 15:14

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