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I was browsing questions for category theory, and this question caught my eye due to familiarity:

is there a property of a category that is preserved by category isomorphism, but not equivalence?

I further looked into the users questions and there were only two, the other being the following:

Initial and terminal objects in $\textbf{FinVect}_R$

Both begin with "I am trying to teach myself category theory and," don't have a label for homework, and have sufficiently detailed answers with no effort shown prior to the answer being provided. What I am getting at is that these were 2 of three questions on a take home final for a class I was in and we were given a week to complete. Note the dates of the questions and the due date of the final show below: enter image description here

Based on this, I was wondering how does math.se differentiate between how they treat a question labeled as "self-study" vs being tagged as a "homework" question. As an undergrad, this person essentially had half of this final completed (1.5 out of 3 questions), and I feel a bit cheated due to the work I put in to receive my A in this class. Should homework and self-study be treated synonymously?

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    $\begingroup$ Do you recognize the name? If it bothers you that much, make the professor aware of what happened. $\endgroup$ – Ron Gordon Jul 25 '13 at 18:53
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    $\begingroup$ So, we see that questions identified by OP as "self-study" may or may not be self-study; questions identified as homework may or may not be homework, etc. The conclusion I draw from here is to pay little to no attention to the claimed source of questions, and answer (or not answer) them based on their mathematical content. $\endgroup$ – 40 votes Jul 25 '13 at 19:11
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    $\begingroup$ @AlexMardikian: my philosophy is innocent until proven guilty. I am happy to answer questions that are well-posed in the spirit that mixedmath outlines in his terrific answer. If, however, I do find that cheating is occurring, I will do everything possible to bring it to a halt, including notification of an instructor that cheating has occurred in his/her class. Your post makes it pretty clear to me that someone is acting inimical to this site. $\endgroup$ – Ron Gordon Jul 25 '13 at 19:44
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    $\begingroup$ Unfortunately, it is logically impossible to prevent this behavior. Cheating is even harder to detect if the person isn't lazy and stupid about how they pose the question. The best we can hope for is to alert those wronged by the action, and hope some sort of justice will come of it. Ultimately I think the solution of testing in a society with freely accessible information will be for educators to modify their testing accordingly for students they don't trust, like in-person tests where info access can be controlled. $\endgroup$ – rschwieb Jul 25 '13 at 19:53
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    $\begingroup$ Self-study questions are easy to spot. They are the ones which show some effort. (He says wistfully...) $\endgroup$ – user1729 Jul 25 '13 at 20:19
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    $\begingroup$ (Also, I think that the professor should be made aware of this. There seems to be some thinking that this isn't necessary. The name is probably made up, but I think that the professor would like to know that someone was cheating! At the very least, they might keep a close eye on here next year...) $\endgroup$ – user1729 Jul 25 '13 at 20:23
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    $\begingroup$ I feel a bit cheated due to the work I put in to receive my A in this class. Why? You put in the work, you apparently mastered the material, and you were appropriately rewarded. That’s the ideal outcome. The possibility that someone else was rewarded inappropriately in no way detracts from your achievement. $\endgroup$ – Brian M. Scott Jul 25 '13 at 21:38
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    $\begingroup$ @BrianM.Scott It detracts from the achievement by making it less valuable if more people have achieved the same thing. Comparing other courses for example, with CompSci Cryptography I was the only A+ in the class out of about 70, however with Into to AI about 10% of the class is easily capable of attaining an A+. That makes an A+ in crypto more distinguishable than an A+ in AI, no? $\endgroup$ – Alex Jul 25 '13 at 21:56
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    $\begingroup$ The only real value is what you learned. That isn’t changed by the grade that you or anyone else got. $\endgroup$ – Brian M. Scott Jul 26 '13 at 8:56
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    $\begingroup$ @BrianM.Scott I disagree! In an ideal world, yes, but if you and this person apply for the same job and he gets offered it because he cheated then...... $\endgroup$ – user1729 Jul 26 '13 at 9:24
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    $\begingroup$ @user1729: I consider that a somewhat unreasonable response to a pretty remote possibility. The only outcome that I think genuinely ought to be infuriating is actually losing a job to a genuinely less well qualified person simply because that person cheated at some point. (Note that the fact of having cheated does not imply that one is less well qualified.) It’s a waste of emotional energy to worry about it before it actually happens, or at least looks moderately likely. It also leads to the guilty until proven innocent approach that seems to be deplorably common. $\endgroup$ – Brian M. Scott Jul 26 '13 at 10:04
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    $\begingroup$ @BrianM.Scott I wasn't claiming that the response was reasonable, just that it was likely. I am coming to the end of my PhD, my funding is about to stop and, having been searching for a year, I still haven't found a postdoc. I would be pretty pissed off (to say the least) if someone got a postdoc ahead of me after they plagiarised someone else's work or they got their supervisor to write half their thesis for them. Sure, they maybe learned some maths on the way, but the warm, cozy feeling that I get from someone else knowing maths isn't going to get me a job! $\endgroup$ – user1729 Jul 26 '13 at 10:17
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    $\begingroup$ @user1729: Of course. So would I. But (a) that would be a case of reacting to an actual injury, and (b) in the present case we’re not talking about cheating of that level of significance. In any case, we’ve come rather far from the actual statement to which I initially objected. I still maintain that the OP has not been cheated and has no reason to feel cheated. There is a very remote possibility that the OP might as a result of this be cheated in the future, but that’s a rather different thing. (I do hope that your luck in finding a position improves.) $\endgroup$ – Brian M. Scott Jul 26 '13 at 10:33
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    $\begingroup$ Most of the problem questions begin with worthless titles, like "function derivative" or something similar. This is because the leeches aren't clever enough to understand the context of their question. If we insist on having the question, can't we just repost it -- properly written -- and let the leeches try to find it? I bet they won't be able to, and we'll get higher quality posts. $\endgroup$ – Emily Jul 26 '13 at 12:59
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    $\begingroup$ Sounds like something you should email your professor about. $\endgroup$ – Alexander Gruber Jul 26 '13 at 15:48
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It is tremendously dissatisfying how many people use MSE as a source for homework/test answers. The issue behind what you talk about, i.e. how are homework questions received here, is one that is frequently asked around here.

There is an argument that being a repository where students can freely and easily cheat does a disservice to both the educational math community and the practicing math community. And this argument has merit, especially given how low the bar is set for asking questions here on average.

One potential response is for people to give out hints only to suspected homework questions. This has the extreme disadvantage of limiting that question's future appeal. Recall that a deeper goal of MSE is to provide a searchable repository of questions and answers. Each question can be useful to many different people, not just people who currently have a homework question about the topic. One of the amazing things about SO is how often I can look up a topic as a nonexpert and find an answer that completely and clearly answers my question. Hints are good for the OP, but not so good for others. An interesting solution to this is to later go back and edit your hints into a full solution. I haven't done this, nor have I seen it done, but it makes sense to me. (I'm not discouraging hints - I sometimes give them too - but I acknowledge that they do not improve the quality of the site. They will never be pearls, as I reference below).

But hints aren't the answer. There is an argument that says that the crime is the asker's and not the answerers'. This also has a lot of merit. But it is also an ethical dilemma. Did you know that at my undergrad, if a student cheats on another student during an exam by looking at their paper, both students are brought up to the student honor code advisory council for potential punishment? They believe that in general, students are aware of being cheated on and this is unacceptable. But at my grad school, only the cheater's offense is actionable. That is more cut and dried, and yet still has inconsistent treatment.

This side has the benefit of having a site full of complete answers rather than half-answered hints. And that is good! I, for one, have wanted to know something about differential geometry (likely as I use it, but have too many other things to do to merit really learning it instead of using much of it as a black box), found an answer that was hinted, and did not comprehend the hints. But this side has two major downfalls as well: it does nothing to discourage rampant cheating (as you mentioned) and encourages/rewards generic homework questions, which is another way of optimizing for sand instead of pearls. (I'd like to emphasize how good of a read that last link is. Reading it gave me a deeper understanding of the SE model and purpose).

This is a fundamental divide in approach to this site that has caused much heartache and even a few high-level departures from the site. To answer your question, there is no consensus (that I know of) about either distinguishing between self-study and homework or simply answering homework-style questions. The current status quo is for users to choose for themselves what is appropriate within reason. However, do not reward poorly written questions with no research effort (part of the hovertext for downvoting). Even homework questions can be well-written, and in fact any well-written well-researched question, homework or not, can lead to a pearl.

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    $\begingroup$ At the university where I am working on my graduate degree, there is a single punishment for cheating: automatic expulsion. $\endgroup$ – Emily Jul 25 '13 at 18:33
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    $\begingroup$ The last link is interesting. But if you think about it from a biological point of view, a pearl is nothing but the cyst of a mollusk in a shell. Kind of creepy that people wear that, isn't it? $\endgroup$ – Asaf Karagila Jul 25 '13 at 18:40
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    $\begingroup$ @mixedmath Perhaps I'm reading things into what you're saying, but... Are you saying that asking for help on MSE is cheating? I've been encouraged by my teachers to search online for answers to my questions, I've always figured that it's what I do with the given information that's important; if I simply copy from, say, MSE and it's discovered I'd assume I'd get zero points. But if I rephrase and, in particular, fill in any possible blanks to really show that I understand the help I've been given, it's ok. Asking online is no different from searching for answers in a different book, IMO. $\endgroup$ – Erik Vesterlund Jul 25 '13 at 22:47
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I really don't make any distinction between the two. I may help someone a bit more if they claim self-study, but that really depends on how much work they show. In general, I don't really care if it's self-study instead of homework.

However, this is an instance of cheating, which isn't looked favorably upon in this site. But, I'll let a moderator deal with that aspect of this question.

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  1. That you feel cheated is understandable. In your place, I would certainly tell the professor about the situation - otherwise it will be certainly reproduced in the next years and there will be much more people cheated.

  2. In my opinion, however, the site has little to do with this. The problem is the examination model which allows easy cheating (and even, in a sense, encourages it).

  3. Now that the people ask here about their homework is okay for me provided their questions are not just copy/paste of the problem statements. If I find a question too boring, I simply don't answer it. But if somebody else is ready to do other people's homework for free without even being properly asked - well, it is their right after all.

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    $\begingroup$ I agree. It's easy to mistake for a flaw of MSE what is actually a flaw of academic system being exposed by MSE. $\endgroup$ – 40 votes Jul 25 '13 at 21:20
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    $\begingroup$ Concerning (3): But you go out of your way to try to deny them that right. $\endgroup$ – Brian M. Scott Jul 25 '13 at 21:43
  • $\begingroup$ @BrianM.Scott I am not sure to understand what do you mean. $\endgroup$ – Start wearing purple Jul 25 '13 at 21:46
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    $\begingroup$ You’re one of the more rabid closers of such questions. The last sentence of (3) is sheer hypocrisy. $\endgroup$ – Brian M. Scott Jul 26 '13 at 8:54
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I'm not sure if this student really cheated.

I think when a professor gives homework to do in home, the student is suppose to make some searches in books, sites, asking people, etc... the goal of this kind of test is not only evaluate the capability of the student to solve the questions, but judge if he or she can't solve them in almost any way, how he or she is capable to surpass this to finally solve the question.

So, this is my opinion...

Remark

Following the comments below, I think I didn't make myself clear, I'm against someone ask someone about full solutions about homework tests, but maybe the professor didn't give really hard questions, I think the only way to prevent such behaviors is asking really difficult questions which can't be solved in one post here as a full solution.

As I said above, for me the goal of such tests is supposed to be different than tests in class.

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    $\begingroup$ Broadly speaking, yes. However, "getting the complete solutions of some guy on the internet" doesn't count. $\endgroup$ – user1729 Jul 27 '13 at 14:35
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    $\begingroup$ I don't think that the intent of a take-home exam is to test a student's ability to find someone who can solve the exam problems. $\endgroup$ – 40 votes Jul 27 '13 at 15:10
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    $\begingroup$ The intent of a take home final in my opinion was more or less to allow the professor to give more interesting problems to solve rather than being restricted to a collection of problems that can be solved within 2 hours. $\endgroup$ – Alex Jul 27 '13 at 16:22
  • $\begingroup$ @user1729 I didn't say that. $\endgroup$ – user42912 Jul 27 '13 at 19:02
  • $\begingroup$ @AlexMardikian I don't understand how a question which can't be solved in 2 hours can be answered in only one post here. $\endgroup$ – user42912 Jul 27 '13 at 19:04
  • $\begingroup$ @40votes I didn't say that. $\endgroup$ – user42912 Jul 27 '13 at 19:05
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    $\begingroup$ @user42912 "I don't understand how a question which can't be solved in 2 hours can be answered in only one post here." What's hard to understand there? SE sites, including this one, daily give answers to questions that baffled the askers for days or weeks. $\endgroup$ – 40 votes Jul 27 '13 at 19:30
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    $\begingroup$ "really difficult questions which can't be solved in one post here as a full solution" -- what kind of questions are those that can't be solved within $30000$ character limit of one post? $\endgroup$ – 40 votes Jul 27 '13 at 19:37
  • $\begingroup$ @user42912 Reread what I said, a collection of questions is what a final consists of; to be a final taken in the standard setting it must be viable to complete all questions within the classroom in two hours, generally without any references to the text, notes, or outside sources. Having a take home final allows for more difficult or interesting questions. A short answer in one post here can give away the difficult factor to the problem, not to mention be a giveaway to a person who may not have put sufficient effort to actually researching the problem themselves. $\endgroup$ – Alex Jul 27 '13 at 19:46
  • $\begingroup$ @AlexMardikian why doesn't take an exam which you can search in books in class? I think the professors has to change their methods, we are in 2013, it's impossible to prevent this. $\endgroup$ – user42912 Jul 27 '13 at 23:07
  • $\begingroup$ @AlexMardikian I've already had an exam during all day long with a lunch pause, we began the exam in the morning and finished in the evening, this exam was taken in class. $\endgroup$ – user42912 Jul 27 '13 at 23:08
  • $\begingroup$ @40votes I'm not speaking about the length of the post. It depends of the subject anyway. $\endgroup$ – user42912 Jul 27 '13 at 23:13
  • $\begingroup$ @user42912 It is a standard for the UC system to have two hour long finals. It is up to the professors digression whether or not a "cheat sheet" is permitted, but even this is uncommon for all the classes I have taken; I personally have only had one such exam. The two hour final exams for the UC system will likely not change, nor do I see much of a reason for that to change. $\endgroup$ – Alex Jul 27 '13 at 23:58

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