text:
Accused of cheating due to the time accounted by Blackboard
Since the exams this year for college is online, there is a timer. Usually, when I start an exam I click a random answer choice or what I think is right at that moment. Once I finish most of it, I go back to look it over.
I got accused of cheating since I answered the questions in 15 mins, and the system recorded that automatically once clicked, instead of recording the time of completing the whole set of questions.
When reviewing my answers after the 15 minutes, I realized I guessed correctly and there was no need to pick another answer. But I got accused since I finished so fast and so accurately.
We were allowed to use cheat sheets with equations and info, allowing me to finish so fast, so I do not understand why I am being accused. And some of the questions were similar to the homework which helped even more. So how do I prove that I did not cheat. It took me an hour and 9 mins to take the exam.
The only information that they kept repeating over and over again was the timing. I clearly stated that I did not look up anything and I had other tests to take the same day. i went over the review powerpoint which had very similar questions to the test once I started taking it. They flagged my test when they were looking for people that posted it on chegg.
There was no other allegation made besides the timing and I have all the proof that I did not cheat. The person telling me the allegation did not give me the chance to clearly defend my self.
Please help me prove that I am not cheating.

To the close voter(s). I think that this problem is now general enough and serious enough that "personal factors" doesn't really apply anymore. The details may be personal, but we need systemic solutions.

This question is very light on important details. How were you accused of cheating? Did the online exam environment say something to that effect? Did you get an email from your professor? From someone else? A phone call? What exactly was the message? etc. This matters a lot going forward.

The answers will depend on the standards that define how accusations are to be made in your country. What course of action you have in the US will not necessarily be appropriate in other countries. Where are you located? Finally and most importantly, are you presenting ALL aspects of your case honestly?

Please don’t write answers in comments. It bypasses our quality measures by not having voting (both up and down) available on comments, as well as having other problems detailed on meta. Comments are for clarifying and improving the question; please don’t use them for other purposes. Existing answers in comments and other extended discussion has been moved to chat.

Unfortunately you can't prove a negative. You have been "caught" by a system that is insufficiently accurate to properly evaluate your actions (and those of many others).
All you can really do is insist (and keep insisting) to your professor that you didn't cheat and explain how you actually acted. If you don't get satisfaction then escalate the issue to higher authorities.
And keep insisting. People have an obligation to be fair.
A recent article in the Washington Post explores how badly online testing systems are performing. While the article focuses on fully automated systems, the problem is much wider, even when human "proctors" are used in conjunction with webcams. In my view the real problem is in trying to apply solutions from a different era into the current pandemic/online situation. Those solutions no longer work and the workarounds are badly failing. They make assumptions that are not valid given the range of normal human actions.
Any cheating detection system, automated or not, needs to have the property that it produces zero false positives. The meeting is part of that system and should assure that you aren't accused wrongfully. But it isn't well understood that a system permitting no false positives will almost invariably produce some false negatives. But the consequences of error in a cheating detection system are so asymmetrical that such a rule is required.

Artificial Intelligence is certainly artificial but it is definitely not intelligent.

Note that I hesitated to edit this after so many votes had been cast, not wanting to invalidate decisions made already by users. The advice remains the same. Insist that you didn't cheat and stick with it.

I got flagged at the same time as they were looking for those who posted the entire test online on chegg. So how am I trying to prove a negative?

Proving that you "didn't do something" is what I mean.

@Nan Was the test posted online before or after the start of the exam?

@Nan one more example how other people cheating might affect you. I'll just link this to a question on that subject.

I don't know why the idea that you can't prove a negative perpetuates, but it is not true 1 2. For example, I can prove that my mug on my desk doesn't have any tea in it, by showing you that it is empty. OP could (theoretically) prove that he didn't cheat by recording himself during the exam and submitting the recording. In general, you can (theoretically) prove that you "didn't do something". This happens all the time in court rooms.

Let us continue this discussion in chat.

That last one about AI was a good one. I'm saving that one for later.

-1 The linked Washington Post article is a red herring: it's about third-party video surveillance systems, but no such system is being described as used by the OP. In comments the OP says they're on Blackboard which does not have any such feature for surveillance or flagging suspicious activity. It does happen to record time that questions and tests are submitted; the instructor took initiative to manually make use of that data. No part of the OP's story is asserting any attempted use of AI; that's a complete distraction in this answer.

@DanielR.Collins, I pointed to the story simply for context about the state of online testing and the uprising against it. I have no specific knowledge of the internals of Blackboard. On this site there have been many questions relating to this issue and how people are being unfairly accused. The WaPo story is simply context. Whether the "automation" is AI or other is not material. A machine judged that the OP cheated.

Who has the burden of proof? If it is the instructor, then they have to prove it. If it is the student, they should ask the professor - how can I prove to you I didn't cheat?

@Buffy: "A machine judged that the OP cheated." This is absolutely false, to the point of malicious misinformation. I am deeply experienced with Blackboard, and no such machine judgement exists in the system, nor ever has. The story here is purely a manual decision by the human instructor.

Hmmmm, @DanielR.Collins, so the instructor times each student? The OP describes something that seems very automated. Or does the OP have it wrong somehow? Maybe just forbidding students to return to already answered questions. There is a discrepancy here. Is it possible that "Blackboard" was used in a generic sense?

@Buffy: None of that. Blackboard logs access and submission times to all works. Assignments, tests, questions, accessing videos, what have you. The instructor has made a proactive choice to manually look at those time logs and make inferences from them. It's one click away from any test submission if one wishes to view them.

Depending on where the OP is located, he/she is not responsible to prove the negative. In the USA, the standard of proving guilt is the preponderance of evidence or the harsher beyond a shadow of doubt. Also in the USA, the faculty have an obligation to follow these standards in making accusations, and it is the OP’s right to stand firmly on them.

It's not that "these systems no longer work". They never worked. They were adopted as a cost-cutting measure. Now there are additional reasons for using them, and they're still trash, but now they hurt more people to a greater extent. There isn't some new, better alternative that isn't utter trash.

The answer uses the phrase “such systems” without really explaining what systems it is referring to. I can see why someone would think the Washington Post story is a red herring.

@DanielR.Collins Since you have a good knowledge of Blackboard, can you confirm something? Would Blackboard have recorded that the OP spent a further 54 minutes reviewing their answers after the initial 15 minutes spent answering them? Could OP cite this as evidence in their favour? Everyone seems to be ignoring this point.

@DanielR.Collins: The focus isn't on the automated nature of the flagging, but the overreliance on an automatically observed metric (and nothing else). The one who raises the flag, whether it's an algorithm or a person relying solely on the same data that an algorithm would be relying on, is completely irrelevant. What is relevant is that there is no sanity (or redundant) check occurring, but rather a blind adherence to a single flawed metric with a limited scope, without accounting for its flaws. In that, the article is perfectly on topic with the question that was asked here.

@DanielR.Collins I do agree with you that "A machine judged that the OP cheated." is an incorrect description of the question. However, what is a correct description is that "The professor blindly believes that a machine judged that the OP cheated." If the professor defers to the machine's report, then the machine has in fact done (or at least singlehandedly caused) the judging, albeit indirectly. But again, the point of the article is not to point out who made the final ruling, but rather that blindly relying on arbitrary metrics is going to lead to frequesnt false flagging.

"You have been "caught" by an automated system that is insufficiently accurate to properly evaluate your actions (and those of many others)." Who cares? In my country you need to be proven guilty, not innocent.  Can they prove you cheated in front  of a court? No they can't, how would they with that silly software and everything else is irrelevant. As way to often with these issues on academia SE: Don't bother with the prof, escalate it to the next instance. In Germany this would be the "Prüfungsausschuss". Nuclear option: Get legal advise from your students union lawyer and threaten to sue.

@TheoreticalMinimum You seem to be thinking of criminal offences, which probably don’t apply here.

@BrianDrake Of course the presumption of innocence applies. At least in the jurisdiction I'm familiar with. If some prof would make up rules inverting this principle in Germany I'm 98% sure this would give a fun little law suit, as it is a violation of the State University Act. More likely it would trigger direct intervention by the university administration, overruling the professor and putting him back in place.

@BrianDrake (Looking at access data from my Blackboard tests this week): The system only logs clock time when individual questions are saved and when the overall test is finally submitted, plus a time-delta from the last event (labeled "Time Spent"). There's no record of what happens between then. Footnote on the log says, "* The times appearing under the Time Spent column may not accurately represent the time the student spent on each question. The student may have looked at other questions before answering and saving individual questions."...

There's even the possibility, say, that a student quickly fills in answers, closes the web browser, and then the system auto-submits the test when a timer elapses later on. So there's no data that a student was specifically viewing or reviewing questions at any time -- at best, a big unexplained gap between last saved question and final test submission.

@Buffy Thanks. For the record, I don’t think editing misinformation after votes is misleading — it’s definitely standard practice across the network. And your answers get upvoted because they’re good, not because users agree with specific mistakes (if they do — that’s too bad for them; they can revoke their vote after the edit, if they catch it; but this shouldn’t prevent you from editing).

@TheoreticalMinimum Presumption of innocence is a red herring.  The question is whether the professor needs to know beyond a reasonable doubt, or be 51% sure.  If this is in the USA, this isn't criminal-law (the government isn't attempting to arrest you, fine you, etc).  This is probably a civil lawsuit, which usually uses the 51% standard.  I agree the OP should fight this, but the professor is unlikely to need to prove this beyond a reasonable doubt (unless that happens to be the university's policy).

@PatrickM, The standard you suggest is an ethical minefield. It is an invitation to unfairness. How can you imagine that there is enough certainty to apply such a standard. An unfair accusation of cheating can be devastating to a person's future. It isn't a game to win or lose.

@Buffy You're talking about the ideal though. It is far more likely to be the scenario Patrick described though, and that's the situation OP needs to deal with.

@Buffy The standard I described is an ethical minefield. I am not trying to suggest how the school should handle cheating. I am doing my best to guess how the school currently handles cheating, based on my knowledge of US law, and reading the policies of collages I’ve attended.

Let us continue this discussion in chat.

I’ll just leave this bit here: your suggestion of taking legal action is an answer, and answers belong in answers, not comments.

@TheoreticalMinimum Some of your comments have been copied to the chatroom and should be deleted. Please delete them, then flag this comment for deletion too.

No. I advise to escalate it internally and make clear you are willing to pursue this further (by legal action) if necessary.

A simple solution would be to demonstrate the flaw in the system to the professor by recreating the scenario in which you were accused of cheating.

This. The main problem here is that the university administration believes that the online system records the time it takes for a student to complete the exam, and it simply does not do that.

And I would definitely downplay the "random guessing". I really hope you didn't already tell the administration that. It's really difficult to believe that all the questions you guessed on just happened to be correct the first time, especially in an college exam involving equations (or any exam involving equations). It's a little bit more believable if you only ever picked the answer you initially thought was correct.

@DKNguyen Yes, I assumed OP really meant something more like "educated guessing."

Reproduce the things you did to demonstrate the facts.  Note that if the OP was online and logged in to a system, there should be records on servers that show that that (and as it's an exam, the institution should still have them).  If the OP was logged in much longer than they timing system claims it took, then it backs up the OP's claim.

@DKNguyen It was in the question right from the start (before it was edited): “Usually, when I start an exam I click a random answer choice or what I think is right at that moment.” (emphasis added)

@BrianDrake I know that, but also having educated guesses in addition to random guesses in no way increases the probability of those random guesses all being correct.

@DKNguyen Actually, it does increase the probability of the random guesses all being correct, by decreasing the number of random guesses. Also, none of the guesses are truly random. Or at least, they shouldn’t be, assuming the student actually knows the material.

@BrianDrake That's splitting hairs. It doesn't increase the chance of the random guesses actually taken being correct. And why would the professor assume the student knows the material if he think he's cheating? If the student says he guessed even some questions randomly that just adds fuel to the fire. That's exactly why you should not say that.

@DKNguyen It kinda does. If you have a 4 choice question and your educated guess eliminates two of those, you've gone from a 1/4 chance to a 1/2.

@JSLavertu You are ignoring that OP specifically said random guesses are in the mix too. The questions with educated guesses do not increase the chances of your randomly guessed questions being correct.

@DKNguyen I get what you mean now, my bad for the misreading. That being said without knowing the number of questions and their number of choices for each, we can't really make a judgement about the odds of the situation happening. Randomly guessing 100 questions and 5 educated guesses is extremely suspicious, but the reverse isn't.

@JSLavertu Even 95 non-guessed questions with 5 random guessed questions all being correct is suspicuous. <0.1% chance with 4 choices.

When questioning or complaining about a decision, it is best to offer a solution.
All correspondence should now be in writing (or at least email) so that you have a record of anything said and any accusations made. People will be cautious of accusing you of anything in writing. If things go badly, you can copy your emails to a senior person and be open about that.
Never say anything in anger and never accuse or criticise. Simply state the facts in a dispassionate way.
For example
You could offer in writing to take a similar test whilst being observed.
It is unlikely that you will be taken up on this but the fact that you have offered will make them think twice.
If there is any disciplinary action, you can then point out that you were willing to demonstrate your strategy and your ability.  Of course you have to make sure that the new test is not made especially hard, so specify "at the same level of difficulty".

Important
Never act in the heat of the moment. Take your time, stay polite but be insistent. Do not give up.

Example email
Dear X
With regard to our conversation about possible cheating.
I note that the automated timing system may have indicated something unusual. My exam strategy is to hurry through all the questions and then return to check my answers. In this case the initial stage took me about 15 minutes and the checking stage took a further x minutes. I checked thoroughly but did not need to correct any answers.
If there is any doubt at all of my skills or ability I will be willing to take a further such test (at the same level) under supervision
I am willing to take such a test online or manually with an observer present.
Nan

Note I have added a sample email. Use your own words and check the content carefully before sending. I take no responsibility for the result - I'm just saying what I would do.

I don't have much experience in this, but is it really necessary to offer to take an additional test? OP did the exam like everybody else. If the universities policing strategies are not effective, why should it be the students' problem? They really cannot prove OP was cheating, it looks like they can be at best suspicious, not sure. Taking another exam on these ground is not only a great source of stress, it's unfair on many levels.

@user2723984 - There is a very good reason. If this escalates, the OP has shown willing to provide a way out. Merely having a "he said, she said" argument causes bitterness and resolves nothing.  The only argument that actually proves the competence of the student is another test.  The test is unlikely to take place but the offer puts the student in a very strong position.  The reply to any question by the opposition is, "Fine, Let's have another test!"  The offer to prove oneself takes away a cloud of suspicion that would otherwise hang over the student for the rest of their studies.

I see your argument, however doesn't this amount to an admission that something may have gone wrong with the initial assessment? I think it somehow implicitly states that the university is right to trust this system and if the system says "cheat" then at least a re-test should be done. I wouldn't be inclined to grant them this.

@Lewian - I don't quite understand your argument. How else can someone objectively prove their innocence in this situation?  My point is that, whether or not the re-test is administered, the offer is there. When and if the OP wishes to escalate to a higher level a method of proof of innocence has been offered.

I don't buy that the student has to prove their innocence if there's actually no evidence at all of their guilt. (What was presented in the question surely doesn't constitute evidence of guilt in any credible sense.) Apart from this a re-test doesn't prove innocence. Just because you pass a re-test doesn't imply you haven't cheated in the initial one.

@Lewian - I see what you are saying, however the OP's question is "So how do I prove that I did not cheat ... Please help me prove that I am not cheating."  (final sentences of the question).  I am simply answering that question as requested.

@chasly-supportsMonica also what if all questions were correct in the first exam, and second a few wrong, should he then accept a B? or is it proof of cheating an gets an F?

@lalala - That is for the OP to judge. Firstly I don't think it will come to that but if the OP shows confidence about getting a good result even if assessed under strict conditions,  the accusers will have to choose between re-testing or accepting the original result. They can't have it both ways. If it were me, I would insist (in writing) on having either a withdrawal of the allegations or a re-test. Being accused of cheating is a serious matter in academia - people who are accused should be allowed to clear their name. I would keep insisting and escalating until one or the other was done.

Showing you are willing to take a second test to prove your innocence might appear to be the most logical course of action - but when witches are being hunted for, logic doesn't come into the equation. In the same perverse way that those who drowned were judged innocent while those who floated were supposedly witches, showing willingness to cooperate is likely to be perceived as an attempt to sway the accusers to your side because you are guilty. Don't make that offer - you know you are innocent, other answers  (e.g. @Buraian's) have suggested far better ways you can prove it.

@chasly-supportsMonica you are conflating demonstrating competence and proving innocence. Your stated reason for suggesting that OP retakes or offers to retake the exam is that you are answering the direct question about proving innocence. You are not, because it does not.

@Corey - My answer is aimed at proving competence. A demonstration of competence gets as near as can be obtained in real life to proving that one did not cheat  (or, more accurately, that one did not need to cheat).  I can see no other way of proving it without the OP having access to a time-machine. If you have one then I shall be very interested to hear it.

The problem is, from experience, that explanation sounds fake -- what someone caught cheating makes-up. An explanation of the weirdness and an acknowledgement about how weird it is might do some good. Instructors don't always know how on-line tests work, so pointing out the format and problems types and how your process isn't completely crazy might help:

Many on-line tests don't allow you to go back and change. Checking one at random and assuming you can change it later is very, very, very odd. If you've been using this test format for a while and it's well known the system is "change any time, submit when done", that might make it seem less weird.

Guessing an answer and moving onto the next Q is a terrible way to work. So terrible it seems like no one would do it. I mean, you need to do some work to have a decent guess, why not do a little more work right then to get a real answer? Explain the details. Maybe in one Q you picked "B) using Hanson's method" because most titration's use it, and obviously reading the details would take a while and the tests don't have lots of extra time. Or is it a look-up thing? You thought you remembered Whistler was a member of the Surrealists, checked A), then came back and looked it up in your messy notes -- sure enough, Surrealist.

15 minutes? How many Q's? 30? Explain how a Q can be read in 30 seconds and an educated guess made. Pick out 1 or 2 (again, instructors may be doing their best with pre-set quizes they haven't had a great chance to look over).

Explain what "random or guess" means. Under a "best guess using 2 minutes" process, it makes much more sense to leave it blank if you have no idea. When you come back, it's a reminder. Sure a random guess is standard, but only at the end of the test. What's the reasoning behind random answers right away?

You wrote than you usually do this. If your last quiz was also answered in 15 minutes, but then you changed answers over the next hour, that proves you work this way. If they can't get records of your last quiz, then just how good is this anti-cheat software anyway?

Right, if this were say a 15 question 4-multiple choice calculus test, OPs story is very very implausible.  I don't know what the topic or the length of this exam is, so maybe OP is telling the truth.  But OP's story is highly highly unlikely with "random" guesses, unless there's very easy ways of being pretty confident of the right answer (in which case you'd expect people finishing the exam in 15 minutes not to be unusual).

It's a common time management strategy.

The online tests which don't allow to go back and change are stupid for a serious exam. I haven't seen any and I do hope they are not so common as you believe. (Also, all such "tests" I have seen make it very clear that you can't go back - you have to not only do the multiple choice, but also click on an "okay" button.) If I had an exam with 50 questions on one page with radio buttons I would as OP assume one can change the answers later.

@NoahSynder: I had such a test (multiple choice linguistics exam, questions were mostly about definitions "The following is an example of which concept?"). Went through the exam (written, not online) and chose my first feeling for every answer I could easily answer. Then I looked through them in more detail and then to the harder questions (maybe 5 percent). What OP describes sounds similar to what I did.

Personally, if I was told that some questions were guessed random and they all happened to be correct the first time, I would be suspicious. Much less so if the OP only said they just pick the answer that initially seems correct. Also depends on the nature of the test and subject itself. The fact that this test had things like equations doesn't help since that decreases the probability of questions with answers that can initially look correct.

@NoahSnyder Sure, but I think I address that. As you say you only wrote "every answer I could easily answer". You left some blank. And you probably didn't finish phase-I in 15 minutes of an hour-long test. But then again, the OP's test could be easy, 15 mins being about right, and given an hour just because.

“… assuming you can change it later is very, very, very odd.” Why? That’s exactly what you would do on a written exam. I hope user111388 was correct that this generally carries over to online exams.

"Explain how a Q can be read in 30 seconds and an educated guess made." There are are often good strategies for selecting the right answer to (poor quality) multiple choice questions which don't involve working out the correct answer for yourself. All you have to do is identify the wrong answers as being "obviously wrong" for some reason.

@industry7: It's not the time management strategy that surprises me, it's the guessing 100% correctly part.  If it's that easy to guess correctly in 15 minutes then lots of students would be done after 15 minutes, and if it's not easy then depending on the length of the exam this situation is very implausible.

I would +1 this but for the last line: "how good is this anti-cheat software anyway?". There is no anti-cheat software involved in the OP's story, and none exists in the platform they reference (Blackboard). The instructor is manually checking submission time logs and deciding to draw inferences from that.

@DanielR.Collins I stand by it as broadly "correct enough". The software logs are an anti-cheat feature.

@NoahSnyder - Anecdotal, but: When I did my (freeform) maths Abitur exam, due to a miscommunication, I arrived 30 minutes late, without the required books and calculator, had to borrow a pencil and rely on educated guesses and intuition for most questions. Finished 30 minutes early and still got a good grade (with some absurdly accurate guesses). And no, I'm not that good at math, it was 50% luck and 50% ad-hoc reasoning. It happens.

@RutherRendommeleigh: Yes, lots of people take exams quickly.  Finishing in half the time is quite common.  What isn't common is one person finishing way faster than everyone else and getting all the questions correct!

Even well-written questions can sometimes be answered very quickly.  I'm thinking of one of my father's (college professor) quizzes.  I was in the room because he wanted me to see the film he was showing the class, I took a stab at the quiz afterwards.  His questions were dead easy if you knew the material (and woe to the student who didn't--his questions required applying knowledge, open book/open note didn't mean just look up the answer)--and in this case I did.  Did the whole thing in 5 minutes and astounded the class--more so when I aced it.

@LorenPechtel (and Ruther and Noah): Maybe done-in15-minutes shouldn't have been flagged, hard to say. But the OP didn't tell the instructor they finished that quickly.. Maybe a stone-cold cheater would have. And now the oddball explanation is the issue.

@noah-snyder "or what I think is right at that moment". Again, this is a very common strategy, and in my personal experience, I rarely ended up changing any of my answers.

Explain to your professor that you did not cheat, and that you think the automated system is measuring something other than 'cheating.' Speed is not cheating after all.
If the professor will not consider your arguments and decides to fail you anyway, there is a process you can follow. It is called a grievance. File a grievance with the university, and the Dean or other administrators will have to conduct a fair hearing based on evidence. Hearings like this usually include your academic peers, and there may even be academic attorneys who can be hired to assist you.

I can't imagine the instructor being willing to fight this in grievance. "What evidence do you present?" "Time logs. This student is too fast." "... Okay but what evidence of cheating? What did they do to cheat?" "I don't know, I just know they did!" If the OP's description is accurate, there's no way the instructor's case can hold up. This answer hopefully will help future students in the same position who read this though to know what to expect if the advice in the top voted answers don't resolve their issue.

Long story short, consider offering to retake the test, to validate your innocence.
I've been accused of cheating, by my college environmental chemistry professor.  The man literally went page by page, from the book, and used his handwritten overhead projector slides from 1969, for his presentations 20 years later.  I like to read, and the class was for non-Chemistry majors, so no in depth topics were put in the tests.  Additionally, he had a test "preview" class, and he outlined exactly what he'd be putting on the test, every time.  After the first exam, I simply read through the chapters, and I never attended any of his classes afterwards, except the previews and exams.
He got quite upset that I kept getting perfect scores on his exams, whilst not attending class.  He was so adamant, that he brought in the Dean of Academics into the fray.  I calmly explained my process to both, and offered to retake the exam on the spot, saying if I got 90% or better, that my 100% exams would stand.  They both agreed.  I finished the exam in under 10 minutes, and got another 100%.
It also didn't hurt that I am an avid Chemistry person, and got a 99 out of 100 on the New York State Regents back in high school, plus A's in Chem I and Chem II already, so I was fairly prepared for this class anyway.

But should they take longer than 15 minutes AND not get 100%, wouldn't this validate that they "cheated"?

In parallel with following one or more other suggestions, please contact your student union, and specifically your faculty/department/semester representatives if you have them, and whoever is in charge of student rights in academic affairs.
First, they might offer material or procedural advice. Second, they may intervene on your behalf. It is a very different thing to railroad a single isolated student, and to go against something the student union objects to (and, hopefully, will not stand for). I'm not sure if that capability is as strong as it is usually in these days of Covid, but still.
Also, as @Buffy points out, it is not possible to prove a negative - and it's quite likely that some guidelines of rules for disciplinary procedures require that concrete evidence be provided of wrongdoing, rather than merely suspicious circumstances. So you (or your student union rep) might be able to "throw the book" at your professor, so to speak.

This is a partial answer, to be read in parallel with the other answers.
The question says:

Please help me prove that I am not cheating.

That is not the real question. The question is:

How can I convince the university that I did not cheat?

My partial answer is that before you can convince the university that you did not cheat, you should try to convince others that you did not cheat. You need to learn to clearly state the relevant information. Your question suggests that you have trouble with this.
For example:

I clearly stated that I did not look up anything

Well, of course you would say that. It doesn’t prove anything.

and I had other tests to take the same day.

It is not clear how this is relevant.

i went over the review powerpoint which had very similar questions to the test once I started taking it.

This sounds like you were looking at the review PowerPoint file during the test. I don’t think that’s what you meant.
Other answers have suggested contacting student unions etc; they would probably be best placed to help you with this.

Exactly how are you accused of cheating?

I got accused of cheating since I answered the questions in 15 mins

As others have already noted, finishing a exam quickly is not cheating.  It could be a visible symptom of cheating, but it could caused by something else.  You provides one possible explanation:

I answered the questions in 15 mins, and the system recorded that automatically once clicked, instead of recording the time of completing the whole set of questions.  When reviewing my answers after the 15 minutes, I realized I guessed correctly and there was no need to pick another answer.

But you also provide one other small detail that has been overlooked by other answers:

They flagged my test when they were looking for people that posted it on chegg.

And later in a comment to buffy's top rated answer, you reiterate:

I got flagged at the same time as they were looking for those who posted the entire test online on chegg.

This seems to be a major point in the accusation, so I'll focus my answer on it.
An alternate explanation the university may believe for why you finished the exam quickly is that you were copying the answers from the chegg post; which would be rightfully considered cheating.
Others have noted that you can't prove a negative, but in this instance that may not be the case.  Quoting from Chegg's Honor Code:

Copying solutions or requesting unexplained final answers promotes completion without comprehension, which is something we don't support at Chegg.
Furthermore, you should be aware that in the event your institution contacts Chegg as part of an investigation into academic integrity, Chegg is authorized under our Terms of Service and Privacy Policy to cooperate fully in that investigation and we commonly do. This can include providing information to your institution about your user profile, account, site usage activity, and interactions with Chegg Tutors.

If the university really suspects you of using the answers posted on Chegg to finish the exam quickly, the burden of proof rests with them.  If the univeristy is not currently working with Chegg to determine if anyone viewed the answers, it might be beneficial to suggest that course of action instead of continuing to speculate.  Being cooperative in the process can only help determine the truth and clear your name more quickly.

I would ask, first, is there any evidence that the OP was using Chegg other than the timing? Does the OP have an account there used for other purposes? Does OP routinely attempt to disguise their identity online (which might itself be considered suspicious, even if it has nothing to do with the current question)?

To clarify my earlier comment: The university has already shown a tendency to misinterpret the evidence. So be careful about bringing them new evidence; you should expect them to misinterpret this new evidence too. So I would first ask if there is anything specific about the new evidence that I would expect to be misinterpreted, and see if I can deal with it early on. Still, from the university’s point of view, working with Chegg should be a no-brainer, so good answer overall.


text:
Advice for getting a paper published as a highschooler
I have possibly found a somewhat novel method of proving a famous theorem, and after some research, I found a variant of the method published as a paper. So, naturally, I reached out to the professor who wrote that and asked him for opportunities and I am waiting for a reply.
If he declines my request for help on publishing the paper, what other ways is it possible to get a paper published as a person who isn't affiliated with a university/ Has major connections?
Other than that, the process from an outsider's perspective looks a bit tedious right now, but what are the general things to keep in mind while approaching it?
My educational details are that I've passed out my HS this year.
Note: I've checked with some grad students, the result is indeed correct. The current state of whether they'll help me follow through with publishing however is a 'maybe'
Update: Got in touch with the prof and sent the tex file containing the paper to the publisher which he had published too. Hopefully gets some acknowledgment :-)
Update 2.0: Seems to have been done already (See here), not sure if there exists a paper on this but that killed of the novelty.
A word from me to all the answerers: Thank you all. Turns out that my proof was posted before on MSE and I do not wish to publish something already done before. However for the actual question which I had asked, I have received many great answers and I honestly can not objectively choose a single answer which have helped me the most since all of them provided value to me in one way or the other.
As is most relevant to my individual problem of me publishing this result, I will accept Kostya's answer as they were the ones who found that the proof was done before. Again, thank you all.

I could have sworn this was asked already, but google-foo fails me.

Possible duplicate: https://academia.stackexchange.com/questions/6191/academic-journals-aimed-at-publishing-work-by-high-school-students

The most important thing is to get feedback from an experienced mathematician to judge your proof. As a high school student it is difficult for you to see what is noteworthy in the field. There are often many ways to prove a result and it could be that your way is considered obvious and doesn't bring anything new to the table. I am not saying that is the case, but you should keep that option in mind when communicating! E.g. when emailing a professor I wouldn't "request help with publishing" but ask for feedback on whether the result could be noteworthy. You're more likely to receive a reply!

Noted, sent a reply to the prof

Most research journals want to publish new research, not a variant of something they already published.

This has indeed been done before. But you still basically reinvented the concept of generating functions as a high scjooler, which is quite impressive in itself!

Congratulations on finding the proof!
I have looked into your comments and also your MSE post. Here are some remarks:

you are mis-attributing the field of your result. It is not 'related to algebra'; modern algebra studies general, abstract features of structures. Neither is it related to operator theory as your tag suggests. If I were to name a field, it would be combinatorics, but the right venue for your proof are indeed high school/recreational math journals, like American Math. Monthly. (Although AMM is quite demanding on the quality.) Serious research-oriented journals are unlikely to be interested.
it is not true that posting your solution on MSE diminished your chances to publish it a journal. In Maths, most of papers are submitted to journals after they've been already published as pre-prints on arxiv.org website. For example, here you have a paper in an area similar to yours published in AMM. Posting to arXiv requires an endorsement of your paper from someone who has regularly posted there before, but no peer-review process. Publishing to a journal is then merely a "quality stamp" (of course, if it's AMM, more people will actually read it.)
you seem to think that what you need from academics is their "affiliation" and "connections". This is not really the case. What you need is their expertise to decide whether the result can merit a publication, and if so, how to make a convincing case for that. You can see from a linked example above how such articles are written. First, you need to briefly review the history of the problem and known proofs. You then need to compare your new proof with existing ones, and make sure that it is not one of them, and even not one of them in disguise, make the case about it in the paper, and ideally explain what is the advantage of your proof over known ones. (In the case of the paper above, their proof speaks for itself, in that it is just 7 lines long, and relies on an elementary identity whose proof is another 4 lines, so more elementary than existing ones.) You should also  place your method of the proof in a context. Is it new? Is it a standard tool to prove identities which somehow was never applied to this particular problem? Are there other problems it can be applied to?

For an editor to give it a serious look, it shoulnd't feel like it's written by a know-nothing amateur who just came up with this proof, typed it and sent to a journal, because in that case, priors are heavily infavor of that proof being either wrong or a (variant of) something known. It must be clear that you have done your homework, know where your result stands in the context, and have a credible claim for novelty.
UPD: as I see now, there is an earlier MSE answer with essentially the same proof as yours. I don't know if there's a published reference, but (a) I would be very surprised if there weren't and (b) it's beside the point, as it would be inappropriate to publish this proof under your own name anyway.

Thank you! I had not seen that.

I asked him for a published reference, but what did you mean that it's in appropriate to publish under my own name?

A scientific article needs to contain an original contribution. If you re-discovered something, it would be a major violation of norms not to cite prior work (regardless of whether it's actually formally published or not) if you are aware of it. And if all you have in your publication has already been done before, why would you write it? Many a mathematician have been there, and usually they just write off losses and move on to the next project.

In fact, one way to salvage some output is to write a survey article on the topic. Recently, something like that happened to non less than Terry Tao (with co-authors), when he though to have proved a new identity about eigenvalues, only to have been told that this identity has been already discovered and re-discovered multiple times. What resulted is https://arxiv.org/pdf/1908.03795.pdf, which surveys prior publications with a claim of originality much scaled down.

But then again, the value of such a survey depends much on the situation. A topic that is scattered over many obscure publication but deserves to be better known - yes. Textbook material - not so much. And the requirements to the survey are different; if you write about history of the subject you really got to know the history very well.

I mean it's similar but not exactly the same.. I used the Taylor's theorem while he used the Cauchy product rule. How similar should something be before it loses novelty?

You should rather ask: how different should it be before it gains novelty? What is it new in you proof that would be of interest to others? It is quite usual that a proof contains many steps, and each of them can be done in several ways. Tweaking any number of them does not produce a new proof, especially if these steps are standard. There must be a new non-trivial idea.

I'd recommend not trying to submit a paper to a journal without guidance from a more experienced academic. That academic doesn't have to be a professor; anyone with more experience with the field than you should be good.
You've contacted the professor, which is a great start. If they don't reply, you can/should also talk to your teachers. Since you're fresh out of high school, there's a good chance your somewhat novel method might be wrong, or not novel. Your teachers have been in the field longer than you, so they probably know more than you; furthermore they know you personally so they'd be more likely to look at your method. If your teachers are unable to help, you could also ask friends/family for anyone with more formal training in the field.

I've checked with some grad students, it's correct for that matter.

@Buraian you might want to edit that comment into the question, as it is very relevant.

Anyone can publish a paper, regardless of age or affiliation, provided that it meets the (rather high) standards of a journal. The standards will include things like understandable writing, but more important is whether the paper solves an "interesting" question in a "novel" way.
"Interesting" can mean new and important, or classic, or other things. "Novel" means that the approach is new, and for mathematics at least, something that might be exploited for solving other problems. A "famous theorem" is itself interesting, of course.
You don't need a professor's help to do this, but they might be able to give you some advice on your paper and how and where to present it.
But even your secondary school math teacher can probably help you with this, provided that they read enough of the literature.
But the way to get started with a publication is to submit it (probably online) to a suitable journal. You will hear from them fairly quickly if it is rejected. If they find it "interesting and novel" it will be assigned to some reviewers for deeper analysis.

Do you know of journal's which accept results related to algebra? and how exactly do I submit?

Sorry, no. But I do know that there is a math journal whose mission is to publish work by students. Look at websites of the American Mathematical Society and the Mathematical Association of America to start. Those two organizations (among others) also have more general journals.

Perhaps "may not need" ... most people need a lot of guidance in prepping their first ms (no shame), although I'm not in math

A particularly challenging aspect of writing a paper is the introduction. At least in my field of research, I expect this to contain a reasonable overview of related work. Context ist very important to appreciate the value of a paper. The standard is that this needs to be provided by the author, not by the reader. This was a major challenge for me for many years despite working at a top research institute where I have access to very knowledgeable people. For a newcomer this is even more challenging, since you won't have anything close to the broad overview which comes from many years of experience.
I would still encourage you to try. If you're lucky you could get an editor or referee who writes some useful feedback. And if you get it published, even on arXiv, you can be extremely proud. Just don't be discouraged if it doesn't work out.

I was in your same position in high-school, and not to come off as discouraging, but the results you have most likely do not settle the “famous” open problem you’re interested in.
In high-school, I believed I had proved P=NP by coming up with an algorithm that solved an NP-Hard problem. I even typed the solution and emailed it to a few Professors who, rightfully so, did not reply me. I had a look at that paper a few weeks ago and I chuckled at what I had wrote then. I did not understand what P, NP,  correctness proofs, or even polynomial time algorithm meant, I just wholeheartedly believed I had solved P=NP.
You mention that your area is in algebra. If you have no formal training in math, the techniques you are familiar with from high-school will most likely be elementary algebra. It is likely that extremely brilliant mathematicians tried to tackle the problem, and failed to do so. Do you think they lacked your intuition or algebraic techniques?
If I were you, I would hold on to this paper for a few years and I would continue to study math. I hope I don’t come off as discouraging, it is just that peer review can be absolutely soul crushing for new researchers, and I would hate for that to happen for you when you’re still exploring Math.

not 'open', I have posted the result on MSE, see the latest question about Faulbaher's formula.

And a problem doesn't need to be "open" to be interesting.

@Buffy I never claimed the problem must be open to be interesting?

@Coconut The question seems clear enough: "a somewhat novel method of proving a famous theorem" (emphasis added) It's not an "open problem". The OP has updated the question to state that their solution has been verified. Also, as stated in the comment above, the OP posted the result on MSE and asked for feedback.

Congratulations! Even if your paper contains errors, the mere experience of writing it and submitting it for evaluation by others is hugely valuable and shows superb skill and dedication from you!
Please don't stop! I'm not clear if this is something you have already written, or is still unfinished. I am not a published researcher, but I have many friends who are published academic researchers. What I have picked up from them is that papers are never 'finished' and never 'perfect'. So please, don't aim for 'perfection' otherwise you risk never completing it.
Do a rough draft from top to bottom including the end. Don't worry about formatting or grammar. This is the creative part, where you are getting your thoughts on paper and explaining how you got from A to B. Ignore any small errors.
Importantly, wait till after you have a complete rough draft to go back and polish it.  Then read it again to catch out any embarrassing mistakes or formatting issues.  Then ask your grad friends or a teacher you know to read it for an outside perspective.  I apologise for the repetition if you've already done all this, I'm just trying to cover the bases.
As for publishing, go ahead and publish it!  Another poster, @Buffy, has mentioned the American Mathematical Society and others. If you're not American, maybe your country has a similar organisation.
Another place to publish is arXiv.org, an open academic publishing forum. They may or may not require you to get endorsement from another academic before allowing you to register with them to publish your paper. Using your school or college email address will help. If they need an endorsement, look for who is publishing papers most similar to yours on arXiv, and email 1 or 2 per day with a copy of your paper and a polite request to ask them to endorse you. Be sure to briefly mention your age and background.
Good luck! Getting a paper published on arXiv is a major achievement! It's not a peer review forum, but it's a big milestone.

Even if the result is not new, if your proof is short (and, by definition, does not require more than what a high-schooler knows), then it might be possible to publish in say American Math. Monthly, or similar. They accept short, nice proofs.

"by definition, does not require more than what a high-schooler knows" You mean "does not require more than what this high-schooler knows". If their high school is anything like my high school was, then they have progressed way beyond what their school teaches (see, for example, their MSE post containing the proof that is the subject of this question).

The OP stated in a comment on another answer:

I have posted the result on MSE, see the latest question about Faulbaher's formula.

It looks like the question they are referring to is: Faulhaber formula from geometric series and operators?
As far as I know, academic journals generally do not accept work that has previously been published elsewhere. According to a Physics Stack Exchange meta post by Emilio Pisanty:

Of course, pre-publication on Stack Exchange could make some journals and publishers refuse to publish the material, but that is a question that we cannot answer for you.

damn this was a true catch-22 situation. I had not many friends to discuss this with so I had posted on MSE for checking, but posting on MSE reduces my chances for getting published.

source: Stack Exchange

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

sort: votes


text:
Would it be a good idea to drop out of my Bachelor's program and look for scholarships to restart abroad?
Currently, I study BA in Mathematics, and because of some problems related to the environment I found myself in, I cannot complete my studies in this place.
I studied most of the courses, except Topology, Fields & Rings, Real Analysis 2, Numerical Analysis, and some elective courses. In general the education level here is not that good, so I have decided to drop it and start again in another (good) place.
But, if I do this, I don't know if it will be good for me and for my journey. I plan to move from the Middle East either to Europe or the USA, to study there and start the bachelor's again. Moreover, I'm 23 years old now. and I don't know if my age will cause a problem.
Any advice?

Not sure, but this might be off-topic since it is related to undergraduate admissions.

It is unlikely that you would need to "start over", but the US system is probably very different from what you are used to with many required courses outside maths.

There are very few scholarships for international students at the undergraduate level in the United States.  Most foreign undergraduates in the US are supported by their relatively wealthy parents.  The situation is very different for MS and PhD degrees.

How much longer before you could finish the degree? One year? 2 years?

@mkennedy I think I need two year.

Different countries in Europe have a different opinion on what constitutes "old" for a student. There are countries where 23 would still be quite young.
You may want to have a look into whether programmes in the EU or USA would allow you to transfer (part of) the credits for courses you already passed. Some programs will, some programs won't. If you find a program that allows this, it might make your journey substantially smoother.

Yes, look for a program in several places to see what the real effect would be. Guessing about this is not a good idea. You may need to speak with some admissions people to learn what the outcome might be.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Doing a PhD at a famous football school: how can I ask for time off to attend games?
Consider a famous football school in the U.S., for example Penn State, Michigan, Nebraska, Wisconsin, Auburn, and Ohio State.
I am doing a PhD in a STEM field at one of these schools, and on 6 or 7 Saturdays of the semester, there is a home game for the football team, and I'd like to attend the game and be a part of the tradition.  It's likely an all-day affair, pre-game, going to the game, and more festivities after the game.
My research advisor isn't into sports — at all.  And the expectation is that we're doing work on these Saturdays, while our football stadium nearby is filled with 80,000 or so fans cheering on our team.
Would it be reasonable to ask my advisor for Saturdays off, so that I can participate in our school's football tradition?
How could I go about saying this to him, without upsetting him, or coming off as "unfocused"?
Clarification: Plenty of communication takes place on weekends. My advisor is very intense, micromanages almost, but that style suits me well, and I find his dedication really admirable. But I don't want to miss out on football either; I'm not in graduate school for very long.

So is he reasonable enough that you can ask him to not work this one weekend?

Is there a reason he might consider you unfocused other than that you might ask for a day off? (in the weekend...)
And are there other PhDs in your research group that want to attend the games?

Comments are not for extended discussion (nor for answers); this conversation has been moved to chat. Please see this FAQ before posting another comment.

FWIW with covid this fall the stands are empty. Next fall is a long time away.

Please clarify whether you are being saddled with an impossible/unfair schedule overall, or just that you would like a different schedule than what you have? People are making assumptions here that might not be valid. You have a right to time for yourself, but not  necessarily every Saturday, depending on the field and the projects. Fairness might require that you coordinate/compromise with others.

And is this by mutual consent or are you coerced? I worry that it is a path to early burn-out, even if agreed to.

What is the nature of your Saturday work? I.e., is it work that could just as easily be done at another time, or is the lab full of people who are working in teams? Is he expecting you to be physically in the building, or just reachable by e-mail?

"I'm not in graduate school for very long." You're not? Five+ years is long, longer than typical undergraduate courses in the US, which is when people usually really get into football

@AzorAhai These days 5 years is actually pretty typical for undergraduate students in the US. Course loads are much, much bigger and universities do exceedingly little to encourage students to graduate in 4 years, since extra years means extra tuition.

@tyler More common than a few years ago? Sure. "Typical," no. Maybe in some fields, but not for all undergraduates.

It’s a tricky situation and you will want to filter any advice given here (including mine offered below) through your own understanding of the details of the situation and the personalities involved.
That being said, my tentative guess as to the best strategy for handling it is to do two things:

Don’t mention to your advisor your football game attendance plans. It’s your private business what you do on weekends. Simply go about your private business as a normal person does. (And for heavens’ sake don’t “ask for Saturdays off”. You don’t ask for what is rightfully yours.*) Any work can wait until after game day festivities are over. You’re a grad student not an indentured servant.

Work hard and be productive and responsive to your advisor during normal work hours/days (including non-game weekend days if you feel like doing work on those days).

If you do the combination of those two things, I suspect (but cannot be certain) you’ll be fine and your advisor will be completely happy with you, perhaps after an initial adjustment period where you might have to deflect some questions from him about why you didn’t answer some email right away on a Saturday. If that happens you can just say you were busy, had an event to go to, or, if sufficient trust has had time to develop between the two of you, simply tell him the truth (but make sure to state this as a statement of fact, not a request for permission or validation, and not stated in an apologetic tone where you volunteer unnecessary details about why you want to attend football games as you sort of did here).
*
If this is a problem, I’m sorry to have to tell you but you’re in an abusive relationship and you likely should be expecting much bigger problems in your relationship with your advisor than a conflict over attending football games.

This might depend on the field. In some lab intensive situations it might be necessary to cover and monitor experiments 'round the clock. No one should have to work all the time, of course, but "weekends" may not be a meaningful distinction.

@Buffy - sure, but people need 'own' time. Yes, I worked many long hours on weekends tending an accelerator running experiments. But I also went climbing, skiing, or just slept in late and had a lazy day many other times. Or just took a day off during the 'normal work week' to compensate.

@JonCuster, yes, of course. Everyone needs reasonable work conditions, even as a student. And it may also be possible to trade off a weekend duty day with someone else. But, again, the research itself may not respect "traditional" weekends. It isn't necessarily like making widgets, which can happen anytime. I think this would be less of an issue in math, say, where the time is easier to schedule. But, you might not get the ability to completely define your own schedule in some fields.

@Buffy - I spent many long weekends tending an accelerator. The 'me' time was just put somewhere else on the schedule. Days of the week were pretty interchangeable as a grad student...

Depends. As a student I had to run experiments. The success of the setup was always a hit and miss and depended on a lot of factors. When the experiment worked at 6pm, you go and do the measurements while it works. Whatever plans you had for the night, went right out of the window, including whatever tickets you had, dinner or sleep. And if you were unfortunate enough that it started working on Friday...

Equally, in some labs people just think that a particular piece of apparatus needs seven-day-a-week nannying because no-one's ever done the experiment of taking a weekend off and observing whether the oojamiflip trap really does fail adequately to control the cowabunga medium, or whatever the purported problem is.

@Buffy the characteristics of an abusive adviser-student relationship do not depend on the field. Even in experimental disciplines where there is work that needs to be done over the weekend, a non-abusive adviser will involve their students in the process of scheduling activities and make sure that weekend work is distributed equitably, that students who work weekends get the same number of days off as everyone else, and that students enjoy a reasonable flexibility to attend cultural events in their area. The duty to treat students in such a way is not discipline dependent.

Yes, I have no problem with your characterization. But we don't know if this is indeed a case of abuse or just scheduling. The OP hasn't charged overwork, just the desire to be free on Saturdays. They may well have a reasonable overall schedule, or not, but haven't said.

While I agree with most of this answer, if there's already an expectation of working on Saturdays, simply silently skipping one and ignoring their emails until afterwards seems likely to go poorly. I also agree with not asking for permission, but it seems like you should at least tell them that you won't be available beforehand.

@NotThatGuy vague informal expectations that are unreasonable do not require special consideration or action - ignoring them is precisely the way to send the signal that they are unreasonable, and I would recommend doing that as long as the adviser isn’t abusive (and if they are, as I said you should expect much bigger problems anyway). As for telling people beforehand that you won’t be available, that makes sense if you’ve been specifically scheduled to do something on a given Saturday. In that case obviously you’re already committed and need to make arrangements to get out of the commitment.

do you disagree with lalala's answer? it apparently has 3 downvotes

Having worked at Penn State I can assure you that no one in their right mind will be anywhere near downtown on game days. The majority of our graduate students went to at least some of the home games and I don't know of anyone who questioned their commitment.
Update
Just to clarify for anyone unfamiliar with "big" football schools - on home game days Penn State's stadium becomes the third biggest city in Pennsylvania (after Pittsburgh and Philadelphia). Fans begin arriving in town on Thursday (parking their RVs in the Walmart lot). By Saturday there isn't any easy way to drive into or out of town due to the amount of traffic generated.
The local paper includes a special route to the hospital (which is next to the stadium) along back roads that the police keep clear of football traffic. If you are pregnant, you get a special number to call to get a police escort if you go into labour.
So home games are a big deal.

I had a similar experience at UGA. As a chemist I wasn't even allowed in the building on gameday. If there were an explosion or a chemical leak, the stadium might need to be evacuated. I'm sure the boosters would not look favorably on that.

You don't seem to have addressed the question of how to ask for time off, but rather only that taking time off would probably be okay.

This.  There is no reason for anyone to be on campus unless there is some sort of presence-critical experiment going on.   Don't mention going to football mention the fact that getting to campus is damned near impossible, unless he can score you a big school in the South like Alabama, even faculty permits aren't worth the paper they're printed on from Friday afternoon through Saturday evening).

Is the university near downtown? It seems to be implied it is, but I don't know where Penn State is

The town is the university :-) the stadium is just out of town but you still avoid the whole town. There are other Big10 towns were the stadium is right in the middle of town/campus (Ann Arbor for example) where I imagine it is even worse.

Good answer, but regarding the issue of being on campus during game days, it’s worth noting that research in many disciplines is done sitting at a desk. This can be done from home, so an adviser’s unreasonable expectations to work on weekends and game days may not be affected by the crowded campus/downtown area.

do you disagree with lalala's answer? it apparently has 3 downvotes

Don't.
That is, don't ask for time off to attend games--moreover, don't ask for time off on Saturday. Why? Because it's not a work day and your advisor isn't your mom.

Would it be reasonable to ask my advisor for Saturdays off, so that I can participate in our school's football tradition?

No, because as Dan Romik said, you don't ask for what's rightfully yours. Also, your advisor in a professional capacity doesn't need to know what you do on your time off.

How could I go about saying this to him, without upsetting him, or coming off as "unfocused"?

You don't come off unfocused by taking Saturdays off. On the contrary, you come off as someone who is trying to strike a good work-life balance and refresh yourself. This is very important to learn if you continue in academia (and frankly probably any profession).
As long as you do your job during the week, and are meeting the expectations that were laid out when you accepted your job (that is, if you're a laboratory experimentalist maybe you were told some experiments would require some attention on weekends), then you have nothing to worry about. If your advisor is getting upset at you for not coming in every Saturday, that's a separate question and I wouldn't want to work for such a person. Just because it might not be an uncommon problem doesn't mean it's an acceptable thing to do.
Source: Recently got my PhD in STEM from a R1 school with a big football program.

God bless you and your answer, good sir/madame

do you disagree with lalala's answer? it apparently has 3 downvotes

This is up to you, I went to a university which had saturday attendence requirements, so one would have to apply for official leave. Probably this is not the case where you are, but I agree if everybody works on Saturdays, it is not good not to come. Personally I would talk to the supervisor tell him you want to see the games and if it is ok to come in on Sunday instead.

why does this have 3 downvotes?

@BCLC I am wondering myself...


text:
Rules or Laws to guide sectioning and sub-sectioning
Regardless of the field or subject, is there a website or organization that has rules on how to section and sub-section a document? I have a document on which I have randomly chosen a layout.
project document outline:
1. Define Goals to stakeholders
2. Product/ Objective/ Expectations
3. Scope
4. Time Frame with phases and processes
5. Project Budget
6. Risk and Benefits
7. Team members and organizational chart w/ roles and responsibilities matrix
8. Rules of Communication
9. extra docs include:
    a. action and issue tracker
    b. project charter
    c. project organization
    d. project roles and responsibilities
    e. project plan
    f. project budget breakdown
    g. stakeholder matrix
    h. risk log
    i. project communication plan
    j. scope statement/requirement specification
    k. change request tracker
    l. design document
    m. possible obstacles & problems

10. Full visualization of organization and process.

This layout is completely a guess, and I am wondering if there is a guide to how to section and subsection, some law or rule to do sectioning or sub-sectioning the proper way that anyone from any field can follow

This question appears to be about a business document, not an academic document.

@AnonymousPhysicist is there any stack exchange for business?

Or Writing SE. They deal with technical writing. Please check their guideline and help center.

You asked a question How to move back to main section after finishing a sub-section on Writing SE in June, 2016. You forgot about it?

Yes, the are such organisations and rules.
In fact, there are various standards for formatting documents, including sectioning. See e.g. the APA 6th or 7th edition, or the Chicago Manual of Style; these are widely used.
If you want to publish in a formal outlet, most likely you'll have to apply whichever standard the outlet requires, which could be a custom one.

Certainly there are no laws on such things. In general the layout depends on the material and the audience.
But it looks like you are writing something as part of a proposal, maybe for a research grant. In that case, the recipient might have requirements for what to include in the application. You need to cover all of those things, of course. And it is often best to include them in your application in the order of the requirements listed. This makes it easier for the reader, who has some power to accept or reject, to quickly check that you have all of the needed elements.
But as a general outline, what you have seems to be reasonable.  As a "working document" is is fine. Tailor it to the requirements of the audience, however.


text:
Instructor's manual -- model answers from it by instructor
For a textbook, there is an instructor's manual provided by the publisher to the instructor that has prescribed the textbook in a course. The instructor sets some questions from the textbook as assignment. After the assignment is due, the instructor takes the solutions from the instructor's manual verbatim for the questions on the assignment and shares with the students as model solutions without stating that they are from the instructor's manual that he has access to. In this particular case, it seems clear that if students also have access to the instructor's manual (via free document repositories) and turn in answers verbatim from the instructor's manual, that would count as academic indiscipline. But what of the instructor's actions?
Another variation of this is the following. The students at the beginning of the course, ask for some model questions with answers to help them prepare. The instructor chooses questions and answers from a different textbook (for which he has the instructor's manual) than the one prescribed for the course. He shares with them at the beginning of the course these questions with solutions without citing the source.
If the source is cited by the instructor, and the students ask for access to the instructor's manual, on what basis can access to it be denied? At present, it seems that the only basis for such denial is an agreement with the publisher that the instructor will not share the complete instructor's manual.
What is the consensus view on these issues?

The view is that students should learn, so copying answers doesn't help them. The instructor is not there to learn.

So what you are saying is that in both cases, the instructor is just fine taking answers verbatim from the IM without saying so, creating a new document and sharing it with students.

@user111388 'The instructor is not there to learn.'  It ain't necessarily so.  On a couple of occasions, I've volunteered to TA on a course primarily because I wanted an excuse to schedule some time to learn the content of that course.

I don't.know what you mean by fine and if you are asking from a law perspective if the instructor can prevent cheating or if they teaxh well or something. But of course, tge students goal is to learn, so they should not look at the questions before. If the questions are good, it doesn't matter where they come from (at least feom an educational perspective).

@DanielHatton: What I mean is that it is not the course goal. Similar to industry - you may learn something while working, but this is not the company's goal of your employment.

What I meant was, is it plagiarism for the instructor to provide a verbatim copy of the IM's answers to students as model answers without citing its source.

@Tryer: Then remove the case about the students, its irrelevant. I'd say in an exam its okay, otherwise blindly copying is not okay for.an instrcutor when the source is hidden. But on this site, many people told me it is okay when a prof copies blindly teaching material and hides the source, because in teaching nobody expects new material, so there cannot be a plagiarism.

How is that not relevant? If student do it, we are all agreed that it is plagiarism. The question is, is it plagiarism if the instructor does so. You don't seem to be taking any stance on this issue. You say that "this site" says professors cannot plagiarize while teaching.

You asked for a consensus, I told you that this site's concensus (by a recent question ) seems to be that an instructor may copy, hide the source and this is okay (and for some reason may be better than copying and stating the source). My stance is that this is not okay for normal teaching, here the prof may copy, but should not hide the source imo (especially in public lectures), but in exams it's ok. And I think we all agree it's beyond unacceptable if students copy answers.

Ok, could you please share a link of that question with me?

https://academia.stackexchange.com/questions/159072/is-this-tenured-professor-plagiarizing-his-lectures/159237?noredirect=1#comment426111_159237

Assuming that you want to teach your students good academic practice in general as well as your specific subject, then you should let them know the source of the answers you provide, at least in general. "This comes from the book's authors" is probably enough. Otherwise they might get the idea that copying and plagiarism is fine. And if you represent the answers as your own work, then, yes, it is a form of plagiarism..
However, providing the answers verbatim, raises also the issue of over-copying from published material. It may be, however, that the instructor's guide provides specific guidance for use, possibly granting (or forbidding) such release. For some books, the questions/exercises are the most valuable part, and releasing this information can definitely lessen the value of the book, especially if students are likely to put such things online or otherwise cache them for others. That would be a copyright problem, but not a plagiarism issue if you give the source.
Third, while not an ethical issue, courtesy and respect for the authors might imply that you not give out answers verbatim, to protect the investment they made in producing it. And also courtesy and respect for future instructors (and students) who want to use the book in a way that maximizes learning and lessens the likelihood of student cheating.
Finally, there is the issue of serving your students. This can raise many issues, but, in general, hints for producing solutions are more valuable to their learning than just providing answers. In fact, minimal hints, that help them develop insight, are more valuable than extensive hints. There is a vast difference between developing an answer on your own and reading a solution. Developing a solution with minimal hints is very much closer to the former than the latter. This will aid their education rather than giving them the false impression that they have developed some skill or insight when they have not. Hints are also sometimes necessary to dispel misconceptions. Unfortunately, tailored hints don't scale very well.
To answer one of your concerns directly, you can deny them access on the basis that having those answers would inhibit their learning and that they should try a bit harder to work out the answers themselves.
So, my suggestion, as an experienced educator, is that you don't give these out for a variety of reasons, the most important one is the value that actually doing the exercises has for your students. Even if they struggle. Perhaps especially if they struggle. The purpose of education isn't "answers", but learning.

Thank you for taking time to answer in detail. However, it is unclear to me what the specific answers are to my specific questions in the OP. Reading between the lines of your paragraph beginning "Third, while not an ethical issue, ", I suppose that you would say that while not optimal, it is not plagiarism or academic-indiscipline if the instructor reproduces verbatim answers from the IM. Am I right or am I misstating your position?

Courtesy and respect are a bit different from plagiarism and copyright violation. It is an orthogonal issue. I don't imply that it isn't plagiarism. "It" refers to courtesy and respect, not to copying verbatim.

'It may be, however, that the instructor's guide provides specific guidance for use, possibly granting (or forbidding) such release.'  Here in the UK, if any such guidance were stricter than the default position in public law, I think the guidance would be rendered void by section 32(3) of the Copyright, Designs and Patents Act 1988 (but IANAL).


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My assignment answers show similarities to my friends', though they differ in content. Can I be accused of plagiarism?
So for an assignment one question has been causing me great worry. After we all submitted, some of us sent each other our work so we can compare, and some of my friends' answers have some similarities to mine. Here is one:
There are very minor and sometimes subtle similarities in our word choice with some similar phrases. Our actual answers themselves were completely different though, different logic, flow and different points. We did chat about the questions which was allowed so maybe I might have subconsciously remembered them saying something like that. There are a few more kind of like that, mainly only single words though, nothing in terms of our actual content.
In another question our points are similar, but we made them in a different order and different wording, and my friend has more to say after the question is answered. We did also discuss this one as well.
So should I be worried of a case or am I blowing this out of proportion?

Yes, you might be accussed of plagiarism for work that bears strong similarity to someone else's work even if there is no verbatim copying.  However, no one can answer this question without having the documents in front of them and even then people might differ in their judgements.

Please do not vandalize your own post. See here for an explanation, and some other options.

Well, it isn't a problem until it's a problem, so don't panic.
But, there might be explanations that account for it. They are your friends, so you may have developed similar speech patterns that make the same phrasing natural for all of you. You are in the same class so you might have picked up the phrasing from the professor and used it in the same context. Or from a textbook.
But the key is that the answers are different. I doubt that it will become a problem. If you are called on it and didn't cheat/coordinate, then saying that you can't account for it is accurate. It is doubtful that if you did cheat/coordinate that this would be how your coordinated. Relax.


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Legal responsibility of a university for international students (Europe)
I am a non-EU student in a European university that has international master and doctoral programs for foreign students.
I have found the university does not offer important forms in English that would also benefit international students (e.g., tuition fee reimbursement application form that describes various contexts sufficing such application). I wonder if there is any legal document describing responsibilities or duties of universities having international students.

If the country is not an English speaking one, it is likely that any legal documents will be in the official language (or languages), whatever they might be. If they have an international students office/association, likely they can help.

It's quite possible that such laws would vary from country to country, if any exist.

Thank you @JonCuster for your comments. It is an Austrian university. I wonder your thoughts on the context, they might help guiding me. I missed the opportunity of the application due to my lack of German skills. Do you think international students have a right to demand such forms to be also in English? They do inform the deadline to pay tuition fee in English as well.

I meant the above message for you too, @Wetenschaap.

You can demand, but there likely is no legal requirement. Living in Austria is, of course, a wonderful opportunity to learn German.

It baffles me again and again how people (academics!) first relocate to a foreign country without a base knowledge of the language and then don't try to learn it as fast as possible.

What language is the program conducted in? Does your university have an international office? I have seen instances where all official documentation was in German, but human assistance was provided to non-speakers for tasks such as filling out forms. And any reason why you cannot translate the forms yourself, using online tools?

@GoodDeeds I'm a PhD student, all lectures I attended and the communication within the university was in English. The university does not have a designated international office. Filling out the form would not have been a problem (using online translation even by typing), but I simply did not know the option I could have used for the reimbursement or waiver of the tuition fee. If I did not look up the form somehow, I would not have known it at all.

I completely doubt students have a right to this form in English.  It would immediately be perceived as another example of English imperialism.  I would think that your department is aware of such forms and would make you aware of them.

@ZeroTheHero, unfortunately not. My institute did not concern this kind of 'personal' matter at all. I just conclude that my university which does not have many non-EU students do not feel that they need to provide such information as the guideline (in my answer below) says.

@Karl and who thought the comment was useful, I have tried to learn it. It saddens me again and again how some people just put their personal frustration as comments without any constructive information or empathetic consideration.

There seems to be no legal basis, yet something similar could be found, sort of Code of Conduct originating from the website of Die Österreichische Universitätenkonferenz https://uniko.ac.at/index.php?lang=DE.
My university would be the example of a university that follows the guideline poorly.
For the whole document, please search GUIDELINES for Academic Studies of International Students at Austrian Universities.

"Preferably" means just that...preferably.

@BryanKrause, of course I know that. ;) I guess that's why they actively inform also in English for the need to pay the tuition fee. ¯_(ツ)_/¯


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I found that a method I was hoping to publish is already known. What would be a proper way to retract emails sent to professors asking for help?
Continuation of this post.
Basically, I emailed a publisher and two profs, asking for help on a paper I had written but not submitted. Turns out the method was not as novel as I thought, as an MSE post containing pretty much the same derivation was posted in 2016. Now, I'm trying to figure out how to break the news to them.
Off the top of my head, I considered saying "actually found it's been done before", but not sure how good that sounds. Probably this is as bad as I think it sounds, but any advice making it sound the best?

I've just been re-reading a biography of Alan Turing. One of his first results as an undergraduate was a proof of the Central Limit Theorem (which turned out to have been proved about 10 years earlier).  So you're in good company ...

@BenBolker darnit.  I was just about ready to submit my proof of the Central Limit Theorem.

Did they reply to your initial email?

Yes they had asked me to send the paper in pdf, that's right when I found out about it @NoahSnyder

Ok, then Mark's answer is great.  If they hadn't replied then I would have written an answer saying to just drop it.

Can you explain why "I actually found this has been done before" doesn't sound right to you? That's pretty much what I'd say in an email.

Well, my thinking is that, if I were to inform them that I found something new only to say the next day "ok actually not, it's been done before"... sounds a bit anti-climatic. Alright, then I'll send that

MSE? You mean math stackexchange?

@lalala yeah exactly

https://academia.stackexchange.com/questions/159333/i-found-that-a-method-i-was-hoping-to-publish-is-already-known-what-would-be-a-proper-way-to-retract-emails-sent-to-professors-asking-for-help

Don't worry, we do that all the time (figuring out something has been done/shown before). It actually shows that you do your work.
Maybe give a link to the other solution/work as well in case they are interested (though this is coming from a very different field).

How exactly do I phrase the email assuming that they are at the current stage of asking me the pdf?

Yep!  It happened to me too.  I had a project that needed to compress a large range of numbers to fit in a small space, and I only needed logarithmic accuracy, not linear.  I thought that IEEE 754 was too complicated for what I was doing, and I didn't have a floating-point processor anyway, so I invented my own.  By the time I had solved all the problems though, I had simply re-invented IEEE 754!  (at least I understand it now)

@Buraian Cite the proof you found in your article. Render that as PDF. In your email:  "Professor ____,
I've attached the PDF as requested.
Since we last communicated, I have discovered my approach has already been published. I've cited in my PDF appropriately, and you may find that existing publication at: [URL].
Notwithstanding, are there any improvements you feel could be made to my article?
Thank you for your time! Sincerely, _____"

This is actually excellent - it shows you're doing due diligence and that you're willing to be wrong. I would expect the professors to be legitimately impressed.
I would write something like 1) sorry for the hype the original email included, because 2) I found out it's already been done before and here's the link, and 3) thanks for your time. Who knows, they might say your derivation is publishable anyway.

Well, OP is only so "wrong" considering they seem to have actually found the "right" answer, just a few years after someone else.

This happened to me as well and is absolutely not uncommon in my field (maths). It did not prevent my paper to be published. So I would not worry at all. Actually, this is great because it is very unlikely that you both have exactly the same results so you may even be able to enrich your own results with new light on a similar problem.
You could add a discussion (which can potentially be just a couple of sentences) in the paper that goes along these lines:
" A similar approach was derived indepedently in [?]. However, blabla"
where blabla = some difference in the approach itself, in the observations about this approach, in the applications of this approach or provides a simpler/different proof, etc.

Problem is the actual paper which was prepublished on this was wayyy more extensive than anything I could do/ thought of while writing mine.

It happened to Terrence Tao about a year ago.  Compare the abstract of https://arxiv.org/abs/1908.03795v1 to the abstract of https://arxiv.org/abs/1908.03795v3  to see how he handled it.  Quoting v3, the formula has "appeared in some form or another (albeit often in a lightly disguised form) in over two dozen references, and being independently rediscovered a half-dozen times."

You have done due diligence and are honestly reporting that it has been done. Sad for you, but straightforward to explain.
Say that you unfortunately discovered that the method and proof is already known. You could express regret to have imposed on their time.
On the good side, you have shown that you are trustworthy, honest, thorough and that you have been able to prove something that is true. It's not as good as a paper, but it is definitely not working against you, just the opposite. You have shown yourself to be a professional.

Answering somewhat generally. Having derived the method independently, you're now in the unique position of having all the necessary mental machinery to think deeply about the problem:

Does the preexisting work leave gaps?
Are there extensions to the approach?
Are there alternative routes that would provide the same result. Sometimes it's useful to prove the same thing in many, many ways?
Can you apply the technique to solve some applied problem?
If the problem is computational, can you achieve better performance by substituting some components?
If the problem is algorithmic did the previous authors release the source for their implementation? (If not, were they even doing science?) Venues like JOSS provide a place to get implementations reviewed, even if the method has already been published somewhere.

Don't worry about it.
Results and methods are rediscovered many times over and in many different fields as well.
When you find it out, what you can do is to add some note "I was made aware of this person having previously done somthing similar" and then you cite them in your papers. Quite rarely the formulation is exactly the same so even if you rediscovered something similar or almost the same, maybe you had a different approach leading to the same conclusion.
In many things science the results are not the most important question, but how you get there.
Maybe you derived your method through an algebraic approach while someone else used a statistical techniques to reach the same result or develop the same method. It can be valuable to add both these approaches to the body of knowledge as often in science it is the concepts and approaches rather than results or methods which are very valuable in discovering new things.

Leibnitz and Newton independently developed calculus, so you are in good company.  Just inform others that you independently developed a solution. This happens all the time.

This is not entirely clear. I believe to have read that Leibniz and Newton once met in their earlier years and may have discussed calculus-related ideas. If my memory is right, such a meeting sounds plausible, because it renders acrimony in their battle so much more understandable than if they had discovered it separately in that the contribution of the other side would have been expressly at stake here.

"Just inform others that you independently developed a solution." Then engage in a decades long feud with the person who previously published it.


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Is it common for professors in France/Europe to accept students for PhD positions but ask them to arrange their own funding?
I completed master's of mathematics in Asia in June 2020. I had written to some professors for PhD positions in number theory in December 2019 . One of the professors in France said yes to me but he said that I should look for other sources of funding as his university didn't have PhD funding at that time. So, I began to look for some funding options but I missed applying for a funding opportunity that is open to anyone whose university would be in that region of France. (I came across on it on web at a date after last date).
Then there was a scholarship application from my country and I began applying for it in mid-March of 2020 but for that a confirmation letter from my prospective guide was required that I was selected for the PhD program. When asked for the letter, the professor didn't reply to my emails, but I can understand that happening due to COVID.
So, then I thought that I would apply to Europe again in December and began studying more topics to improve my knowledge and didn't contacted that professor.
My questions:

Is it common in French universities that a professor says yes for PhD but tells the student to look for funding opportunities by himself?

Is it common in European universities that a professor says yes for PhD but tells the student to look for funding opportunities by himself?

Please guide!

What does "December 2019 (last week)" mean?

@DanielR.Collins it means last week of December 2019.

Why do you want to know whether this common? What do you mean by common, 20%, 50%,…? Do you want to know whether there are positions in Europe that are funded and how to find them?

@user2705196 by common I mean atleast 50% .

@user2705196 Regarding your 2nd question  "Do you want to know whether there are positions in Europe that are funded and how to find them?"  If there is some website or some online resourse and you are willing to tell it will be of great help. What I do now is that I go on the website of universitities in which I want to apply, see in  number theory group  that are there profs with which my interest aligns and then I  mail them my CV individually.

Its certainly normal in the UK. Very few universities fund any PhD students themselves (where would they get the money from?). Most students are funded on government scholarships. How these are awarded varies from field to field and I don't know what the norm is in mathematics. In biology they are awarded to centers called Centers for Doctoral Training (CDT/DTPs), which often cover several universities. Each year professors  compete for the right to recruit a student, which they will then advertise for.
Until now, these scholarships have only been open to "home" students (that is British or EU students). Any overseas students have to obtain a scholarship from their own government, or an NGO or charity of some sort, or pay themselves out of pocket. Most profs will take most students who can bring funding/pay their way.
This year things are changing. CDTs/DTPs will now bed allowed to offer up to a third of their scholarships to overseas students. BUT, they will only pay "home" fees, which are generally less than overseas fees. How this difference is handled is varying from Uni to Uni. Some will say that they will charge full overseas fees to overseas students recruited to these scholarships, and the student would have to find the difference (on the order of £10k a year). Other universities are offering to waive the extra overseas fee.

I don't know what "normal" means but I have done it, and I'd expect that it is common practice. There are many universities that admit but don't fund PhD students, or only fund a handful but are open to admit more if they come with their own funding. (I have never worked in France though.)
On the other hand it's not the standard - Europe has many countries and even in a single country there may be big differences between regions and universities (private and public in particular).
Just to give you some stats - I have worked for four universities in Europe. Number 2 and 4 funded most of their PhD students (actually that was the standard way to do a PhD there), although number 2 would admit students who had their own funding, number 1 hired them as research assistants as a standard, meaning that they'd have money but would be expected to work part time for the department, besides of students who came with their own funding (maybe a third up to half of them), number 3 had a few (three or so) funded PhD positions each year but far more PhD students, so the majority was self-funded. Funding regimes change a lot over time though.

I meant common by normal