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