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I have a homework wherein a problem is eerily similar to a theorem we have proven and discussed before in class. Since we have a policy that the only concepts and theorems that we can apply to our homeworks and quizzes are those discussed in class, I figured that if I slightly modify a set defined in the proof of a previously discussed theorem, I would be able to prove my homework (I managed to prove it following the proof of the previous theorem).

Can I do this? Is this considered plagiarism?

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No, this bears no resemblance whatsoever to the concept of plagiarism. The goal of homework is to get you to review what you learned in class and demonstrate that you can apply it. That is exactly what you are doing.

Moreover, the purists who will wag their fingers at you and tell you to “cite” the earlier proof are part of why we have a generation of students who have no common sense understanding of what plagiarism is or what it means to plagiarize, and instead view the avoidance of plagiarism in terms of adherence to some mechanical set of algorithmic rules whose meaning they don’t understand (and I mean no offense to you personally, it isn’t your fault that you are being led astray in such a way by well-meaning but misguided — in my opinion — educators). The professor knows what they did in class, and know that you know it. There is no need to cite anything, just write a correct proof of the result you were asked to prove. If you want to mention that the proof is a variation of something that was done in class, that may be a nice way of showing a good level of understanding of the material, but it’s not required as some kind of plagiarism-avoidance algorithm.

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    @Buffy: Imagine a professor reporting a student to the academic integrity people and saying My student applied the material I covered in class without citing it, on a homework assignment that wasn't going to be seen by anyone other than me. They're a plagiarist! Can you honestly picture the student getting into trouble for that? It just seems too ridiculous to me. At most, I could imagine a professor saying something like "Next time, make sure you cite in-class discussions explicitly" - and even that would come across as pretty strict in my mind.
    – Kevin
    Sep 24 '20 at 1:24
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    I'm gonna have to start citing Ohm's Law.
    – D Duck
    Sep 24 '20 at 10:27
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    @Buffy the logical fallacy of your argument is that you are recommending to the OP to cite something just because they asked a question about plagiarism. If they asked about adding a legal disclaimer to their homework instead, would you then say “if you suggest to the OP that they do not include a legal disclaimer, then you are putting them potentially at risk. I object to that”? If they asked about encrypting the PDF of the homework, would you tell them it’s better to be safe than sorry and do that as well, and that anyone who says it’s not necessary is being irresponsible? ...
    – Dan Romik
    Sep 24 '20 at 13:37
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    ... The problem is that none of these things make any logical sense. Including citing the professor. It’s ultimately harmless to do it, just like it’s harmless to do other illogical things to avoid some perceived “risk”, but it’s pointless and unnecessary, and perpetuates an incorrect understanding of what plagiarism is that is actually quite harmful.
    – Dan Romik
    Sep 24 '20 at 13:38
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    I think this is a "common sense" response and I would upvote it. However, "common sense" has long gone out of the window to be replaced by "compliance", and "adherence to codes". In such times where responsibility is devolved to principles instead of thinking by one's own, it is probably safer to cite and appease the Vogonic gods of bureaucracy and technocracy rather than be sensible and end up inside their entrails (and leaving in who knows what state). I won't downvote either, because I personally actually would agree with the response except that "they" may not. Sep 24 '20 at 15:04
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In some courses it is strongly intended that you use the prior proofs. Rather than deriving everything from scratch, you're supposed to use the earlier results as building blocks.

You would write something like:

Using the proof obtained in example 3.2 from the lecture notes, we can here replace [this clause] with [another, more convenient clause]. We continue the rest of the proof as follows...

This isn't plagiarism, because you make it clear what is, and what isn't your work.

It's also good academic practice. Someone (say, the TA grading your homework) who needs to validate this sub-proof knows where to find it, and only needs to check if you applied the prior result correctly.

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  • 6
    While occasionally I might be okay with student just saying "this part follows as in the proof of ..." typically I would want to student to write a complete proof which only cites facts proved in lectures. This indicates they understand the whole argument and aren't just being lazy. Also, the grader who is not the instructor probably isn't attending lectures.
    – Kimball
    Sep 24 '20 at 13:07
  • Yeah. I was thinking of a course for which I TAed in which the lecturer would prove that a particular derivation was possible, and students then got homework where you were supposed to use that derivation about halfway through a different proof to connect the bits. The lesson was that a proof once done can be a useful building block for something else later on.
    – ObscureOwl
    Oct 1 '20 at 12:09
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You should cite the source to avoid all question of plagiarism or any other form of improper behavior or dishonesty, whether plagiarism or not. It shouldn't be a problem. "Following the proof of Prof. X for the YZ theorem as discussed in class ..."

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    I'd say in this case you probably don't need to cite Prof. X by name as it's not likely to be their work - they just taught it. There's another benefit to being upfront about what you're doing - if you start your answer with "Adapting the proof of YZ..." it's clear what you're trying to do; if this is correct but your attempt is otherwise a little muddled, it may save a mark or two
    – Chris H
    Sep 24 '20 at 9:37
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    What I like about this answer over the previous one is that it serves a double purpose: to emphasize the importance of citations by getting into the practice of citing things. Citation is not just something one does to avoid plagiarism, it is a positive good in academia to give credit where credit is due.
    – Lee Mosher
    Sep 24 '20 at 12:41
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    So did you also cite the actual course book in every homework assignment? (after all you surely applied things you learned in there for the homework) If not, what's the difference?
    – Voo
    Sep 25 '20 at 10:55
  • @Voo I think you should cite the book. Students usually say "using theorem 1...", and I think they should say "we adapt the proof of theorem 2...".
    – user129420
    Sep 26 '20 at 22:19
  • wait buffy, weird question, what if this were a quiz/exam/test instead of a homework? i guess we can't cite if we're answering only from memory...
    – BCLC
    Jan 25 at 15:46
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Plagiarism is passing of another persons work as your own. In this case you are using knowledge gained in class to solve a problem and therefore I don't see it as plagiarism at all. You understand the concept, or I will assume, and are using it to solve a later problem that is similar, now if you claim this as your proof then that would be plagiarism but that is not what you are doing. You are applying knowledge gained in class to another problem and that is not something to be concerned about. Most people know they are plagiarizing when word for word passing off something as their own. I assume the proof still requires you to apply what you learned not come up with your own theory.

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When in doubt, always cite the source. At worst you're verbose. At best you avoid a charge of academic dishonesty.

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NO.

Often there is only one right and or easy/short way to prove something.

I did that once on an exam in grad skl.

One direction I wrote 'obvious' for the other way I said 'clear' which was the profs proof in class. I got full credit which was lucky as I had not idea how to prove that theorem:)

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