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Is changing some words plagiarism?
I'm looking for a clear, definitive answer to the following question: Is taking someone else's writing, and changing some of the words, inherently plagiarism?
I find resources that describe plagiarism are usually a bit vague around this issue. For example, one commonly-quoted book says this (Pechenik, 2001, p. 10):

Don’t plagiarize.  Express your own thoughts in your own words...
Note, too, that simply changing a few words here and there, or
changing the order of a few words in a sentence or paragraph, is still
plagiarism.  Plagiarism is one of the most serious crimes in academia.

Or this likewise from the IEEE Publications: Identifying Plagiarism page:

... we should be able to agree that changing only a few words or
phrases or only rearranging the original sentence order of another
author's work will be defined as plagiarism.

Now, the fact that these sources each refer to changing or moving "a few words" leaves open the question of whether changing or moving more words, or many words, would possibly be not-plagiarism. Is there any threshold at which changing words becomes not-plagiarism? Possibly all of them?
The practical concern I have is that recently I've gotten a high frequency of students I've caught for plagiarizing in my courses (around half) saying something like, "Ah yes, when I took that file I didn't change enough of the words because I was rushed for time. I'm sorry, next time I'll change more of the words."
Ultimately I'm wondering if the best response to that is, "That would still be plagiarism [even if you changed all of the words]!", or if the response needs to be something different and more complex.  (I find that for such students with possible language problems, more complicated responses are likely to be disregarded, so I'm looking for a minimalist communication in these situations.)
The best answer will not go into discussions of practical issues of detecting plagiarism. A reference to some authoritative source on this issue would be a value-add.
It may be helpful to note that "plagiarism" is emphasized here because it's central to my institutions' (and others') academic integrity definitions and enforcement mechanisms. In our case, "Copying another person’s actual words or images..." is the primary (but not the only) example of what counts as plagiarism.

Unfortunately, I think that many students are often actually taught that copying and plagiarism are the same thing. Also, don't expect students to grok plagiarism (or anything else) as if it were a genetic trait of humans.

Note that the tag [tag:students] has been deprecated.  See https://academia.meta.stackexchange.com/q/5066/75368

For the specific context of responding to that student, I'd respond with: "It's not about changing words, it's about the contribution you put into this project/paper/course. I don't want your biggest contribution to be simply changing words. This course is about ____, so you can contribute synthesis or novel idea about this course, but not about knowing how to paraphrase."

Do not use the term "plagiarism" in a teaching context at all. As many answers below point out, plagiarism is using ideas without attribution, which is completely irrelevant in a teaching situation: it is customary to use ideas taught in the course or written in a textbook without attribution. (Imagine having to attribute all "ideas" in a solution to a standard math homework/exam problem.) What's more, few lecturers/textbooks care about proper attribution in the first place.

What you are forbidding/discouraging is not "plagiarism", but specific ways of working on assignments: copying from elsewhere verbatim, paraphrasing from elsewhere, etc. E.g. I advise students that they are allowed to read any sources, but that they should close them as soon as they start writing the assignment.

@Kostya_I: Unfortunately, that is pretty much the opposite of our institution's (and others') definition of plagiarism, and central use of that term in its academic-integrity policy and enforcement mechanisms. I've added that detail to the question at this time.

@DanielR.Collins, what I mean is that two very different terms are conflated here. A "plagiarism" in the research context is a use of ideas without attribution. This is obviously not the same "plagiarism" as the one that the students can be punished for, simply because this covers a lot of what the students are expected to do. E.g., most math homeworks and exam papers have no "References" section at all, yet their content is supposed to be based on someone else's ideas. It would be better to have two separate terms.

What exactly is the course about? (there is a big difference between e.g. mathematics and social sciences).

I guess it boils down to something simple: if you didn't write it, then it's plagiarism. And that includes copying and changing bits inside.

You could force them to sit in a room with nothing but a pencil and some paper to complete the exercise.  Then you are assured they can't copy or plagiarize.  This is a bit of a pain, so maybe only do this once or twice per course, say, at the midpoint and then at the end.  Give these exercises a heavy grade weighting - in excess of 50% of the course grade.  Now, even if they cheat all year, they still can't pass.  If they elect to shoot themselves in the foot they're only harming themselves.  The adult world will punish them severely enough for dishonesty afterwards.

Depends on what you do with it. 2. Depends on what you disclose. 3. Depends on how much is "some". ... but basically, if you don't mention the text's original author, then yes.

Plagiarism is about correct attribution of significant authorship.

It sounds (based on a reply to an answer below) as if they're reproducing someone else's answer to a question they were supposed to figure out themselves.  If so, this has little to do with scholarly attribution AFAICS. They cheated by looking up an answer; this was unfair as they're trying to get academic credit for skills they don't (yet) have; "changing the words" in this context is a form of lying. If this kind of direct appeal to their moral compass / personal pride doesn't work, what @J said is probably the only solution that will.

@J... As one who is/was saddled with what is called an eidetic memory, I would have easily written, verbatim, any answers to a test. No book opened, no notes. I was helped immensely by a particular English teacher in high school how to study and rewrite, in my own words, what was needed, expressly to avoid plagiarism. At the time, it was easier said than done, and convincing her student (me) it was worthwhile, was one of her fondest achievements.

The clear, definitive answer to your question

Is taking someone else's writing, and changing some of the words,
inherently plagiarism?

Is YES, and you need to go no further than a dictionary.

the practice of taking someone else's work or ideas and passing them
off as one's own.

The moment your students (or anyone, for that matter) tries to solve a writing task by looking for what someone else has written and then trying to include it in their work as their own, it becomes plagiarism no matter how many words they can change; it's the action of putting/trying to put someone else's work into theirs what constitutes it.
The thing is, the rest of the body of your question shifts it to both "how can I tell my students/make them understand that what they do is plagiarism?" and "am I wrong by assuming that what my students are doing is plagiarism?".
The latter is easier to answer: no, you're not wrong. The former, though, is a bit trickier.
Your students already believe that plagiarism is about what can be detected as such, and not what they're intending to do. This probably isn't on purpose - they might not be "evil" students, merely misled. You need to make them understand that their offense is not "not changing enough words", it is "thinking of taking the writing of someone else without proper acknowledgment".
Maybe you can make it clear by establishing it with a simple "do/don't" rule:

DO: write your own thoughts and conclusions, and use citations from other authors or written material to support them.
DON'T: take the writing of other authors/material and put it in your work as yours, neither by copying it as is nor by changing or paraphrasing it.

I'm marking this as the accepted answer, because it's the best-supported and highest-upvoted response that was able to answer the question with a definitive polar (yes-or-no) assessment. If there was a future or modified answer that could likewise provide a polar response (whether yes or no), then I'd be open to switching it at that time.

Is taking someone else's writing, and changing some of the words, inherently plagiarism?

The most concise, clear answer I can think of is the following: Disallowing plagiarism is about protecting ideas, not words; however, the way something is written is often a (protected) idea. The writing's structure and organization, the details that are included or excluded, the transitions, the figures, the references -- all of this may be protected intellectual property, and none of this is addressed by simply substituting some words for others.
Hence, students are wrong when they believe that all they have to do is "change a few of the words" -- even if one does not steal the words, they are still stealing the writing, which is much more than just word choice. The most egregious form of this is when someone copies an entire document and then goes through line by line making trivial changes to the wording. This is absolutely plagiarism: using different words does not change the fact that they are still stealing the writing. (On the other hand, detecting plagiarism is much harder when these substitutions are made...and many students honestly believe that plagiarism is defined by what TurnItIn can detect).
So I'd love to say the answer to your question is an unambiguous "yes" -- but consider this sentence:

Elementary particles comprise quarks, leptons, and bosons.

Many students mistakenly believe that they need to make some trivial modification to this sentence to avoid plagiarism. But this sentence contains no "novel ideas" -- certainly not in the content, but not really in the writing either; there are only so many reasonable ways in which one can state this fact. Indeed, it is likely others have published this exact sentence before. Hence, taking this sentence without attribution (with or without having changed some of the words) would probably not be inherently plagiarism. But this is a slippery and ill-defined slope: while this seven-word sentence is probably not complex enough for "plagiarism" to be possible, other sentences (particularly longer ones) certainly are.
Finally, we should note that schoolwork presents some unique challenges for avoiding plagiarism. In most nonfiction work, there are four types of information: (1) well-established facts, (2) primary sources, (3) secondary sources, and (4) our novel contribution. Usually, an essay will have most or all of these -- #4 is the reason for writing the essay at all, #1 and #2 are important because our work doesn't exist in a vacuum, and occasionally #3 is helpful. Many schoolwork assignments, however, only have #3 -- there is already some writing in a secondary source that single-handedly meets our requirements. And so the student's job is just to rewrite the existing essay but somehow to make major enough changes so that it becomes original work. This is a subtle distinction that doesn't have much in common with the real world -- no wonder students are confused.

it is likely others have published this exact sentence before --- I expected this, and more specifically I expected that a google search would show this, but curiously a google search right now doesn't show this: "Elementary particles comprise quarks, leptons, and bosons" -- "No results found for "Elementary particles comprise quarks, leptons, and bosons.". Results for Elementary particles comprise quarks, leptons, and bosons. (without quotes):" Your answer should show up soon, however.

haha, I was going to check...I guess the 3! possible combinations may have made it less likely.

Actually, linguistics tells us that aside from formulas, any sentence of more than a few words is vanishingly unlikely to have been said before :) But, of course, the trivial / non-semantic variations aside, that sentence is very likely.

Your boldfaced passage leaves me very confused ("Plagiarism is about protecting ideas, not words"). My institution's (CUNY) formal policy defines plagiarism primarily as this: "Copying another person’s actual words...". A secondary bullet point refers to the taking-ideas issue. (Link) In your estimation, is the primary CUNY definition simply wrong?

The policy you quote states: "Plagiarism is the act of presenting another person’s ideas, research or writing as your own." This is consistent with my bold passage -- plagiarism protects ideas, and both "research" and "writing" count as ideas. "Words" by themselves may or may not count as ideas -- some words (like poetry) certainly are, while others (like the quark sentence) probably are not. The key point is that plagiarism is much broader than just taking the "actual words" (though I agree that stealing the actual words is the most egregious, and most detectable, form of plagiarism).

I disagree with your example. If the student happened to come up with that exact sentence on their own, it wouldn't be plagiarism. If they copied-and-pasted, it would be. The correct thing would be to either copy it in quotation marks and give attribution for the quote, or restate fully in their own words (this is slightly different than copying the sentence and changing some words) and also give attribution for the idea.

Sorry, I disagree on both counts. Using quotation marks for my quark sentence above would be very strange (at least among mature authors, maybe not students). There is no need to cite "common knowledge." And, I would argue that an essay is either plagiariarized or it isn't; making it dependent on the author's thought process is a losing battle. That said: I agree that these boundaries are blurry; even if copying the quark sentence above is okay, copying three such sentences in rapid succession is much more dubious, and the line is not always clear.

What about citations? Adding a citation allows you to use someone else's "content" -- but it does not entitle you to steal their writing -- But quoting and citing isn't stealing. I often tell my students, the easiest way to avoid plagiarism is to quote and cite. (Of course, a paper that is 90% quotation is not a sufficient contribution, but that's beside the point.)

@cag51: I still see those as contradictory. You say plagiarism is not about protecting words. My school's policy says it is about protecting words (writing), among other things. I see that in other institutions' policies, as well. Unlikely this will be the selected answer in its current form, as it doesn't seem to interface with real-world academic integrity policies in a useful way.

@DanielR.Collins I see this answer as aligned to your university policy. Remember that the definition and the enforcement can take different forms. In this case, the definition of plagiarism is about protecting ideas, but the enforcement manifests as checking the similarity of word use, since that's what's enforceable. In the face of a plagiarism accusation due to a student writing similar words as another, it is not an automatic case of plagiarism, but it should be investigated, whether the similarity in word usage counts as plagiarism or not, by checking how the student came up with them.

So, to quote Josh Part's answer that you liked: "Your students already believe that plagiarism is about what can be detected as such, and not what they're intending to do." That is also the essence of this answer. What can be detected (word similarity, copying) is what your students are thinking about, but plagiarism is not simply about what can be detected, it is also about the intent (here is where "protecting ideas, not words" comes in. Words can be detected, ideas not so simple, need investigation).

I object to the terms "intellectual property" and "protection" used here. Disallowing plagiarism isn't about protecting property, it's about ensuring academic integrity. Plagiarism is bad because passing off someone's ideas as your own is bad - but using someone's ideas (which would still be wrong, in the property analogy) is actively encouraged.

Sorry about my literal-mindedness, but I just have to say that your assertion that the sentence 'Elementary particles comprise quarks, leptons, and bosons' contains no "novel ideas" made me laugh uncontrollably. I know it's not what you meant to imply, but the sheer amount of human effort and ingenuity that was required to even define each of those concepts (let alone the standard model as a whole) is so staggering that I can't think of a less appropriate example sentence.

@MassimoOrtolano: Re: antiplagiarism - there is a reading of cag51's sentence that does make sense: The existence of plagiarism as a concept is about is about protecting ideas, not words.  Plagiarism always has negative connotations, unlike copying in general which includes things like making a backup of your photos.  So the whole idea of defining what plagiarism is, and having a name for the concept, is about protecting ideas.  Admittedly it requires some mental gymnastics. :P

@cag51 I still think copying someone else's words without attribution is always plagiarism, regardless of whether the words express common knowledge.

Students sometimes believe or claim to believe that plagiarism is some highly technical, perplexing concept. While it is important to clarify what plagiarism is and is not to the student, in an actual discussion with a student who believes that they should have "changed more words", I find it helpful to start from an ethical principle that the student will find it much more difficult to misunderstand or claim to misunderstand, namely to give credit where credit is due.
Here is a concrete suggestion. One can get the conversation going by asking whether the student found it helpful to have the relevant passage as a starting point. Make the distinction between using general ideas found in some text and using an actual passage in some book or article as a starting point for one's own writing. This way of putting it makes the number of words they changed irrelevant. Even if they change every single word, the point is whether or not the specific writing in the source passage was substantially used in the writing process, whatever the end result of this process.
If they answer negatively, you can express skepticism about their answer, since they did in fact actively choose to use it as a starting point for their own writing. If they did find the work that the author of the original passage helpful in composing their own writing, you can ask them whether they believe that the original author is due some credit for that. Whatever they answer, explain that owe some credit to the original author. Then you can get into a discussion of what plagiarism is or is not, but I believe that grounding it in a familiar ethical principle will help. (Confession: I myself find it useful to think in terms of fair vs. unfair use instead of plagiarism vs. not plagiarism, and to use the term "plagiarism" primarily when ill intent is clear.)
Another approach if they say that they will "change more words" next time is to paraphrase this back to them as: I will change more words so that I can avoid citing source X. Then ask them why they wish to avoid citing source X.
If you want to wax philosophical, you can then explain that science only works as a cumulative enterprise which encourages people to stand on the shoulders of giants and ordinary mortals alike. This cannot work unless it is a win–win situation for the people involved. Other people's work allows you to see further and write better, and conversely, they benefit from having their share in your work acknowledged.
(The point raised by Massimo Ortolano is also important to get across to the student.)
Edit: the other answers focus on using other people's ideas, which is justified but potentially a bit nebulous. You can also choose to focus on using other people's work instead, which I find a bit more concrete in this case: they are building on the work that some other person has already put into composing the passage in question.

These kinds of "give credit" and "use citations properly" suggestions seem very tangential to the kinds of cases I'm dealing with. The kinds of assignments I'm dealing with are fairly short (one-page) scientific problem-solving, and looking up and copying answers to them is entirely outside the scope of the assignment. I find students don't think plagiarism is a perplexing concept; they are confident it involves changing more words in a submitted answer. Unlikely this will be the selected answer.

@DanielR.Collins You might want to clarify that in your question. I think the question with that clarification is less about plagiarism and more about bad assignments and/or plain old cheating. Even a third grader can be expected to show work for "2*12=24" without copying someone else's, even though the visible outcome is probably exactly the same as if they had copied.

Fair enough, this is not the kind of assignment that I had in mind when writing the answer.

@DanielR.Collins Adam is correct about what plagiarism is, but that doesn't mean that plagiarism is the only problem an assignment could have. If a student copied an entire book for an assignment, and cited it properly, they have not plagiarized. They arguably also have not done the assignment, since they weren't the ones who wrote the answer, so you'd probably be justified in giving them a zero grade. But there wouldn't be grounds to bring them in front of an academic misconduct board, since there was no dishonesty.

Looking at this definition of Oxford University, plagiarism is using other people's ideas without acknowledging them. Under this definition, even if you were to change all the words, or rewriting the whole thing in your own words, you would still commit plagiarism, as long as you don't give credit to the original source where you took the idea from.

Admittedly, the linked page says "work or ideas" -- not just ideas alone. The first two bullet-point cases under Forms of Plagiarism are (1) "Verbatim (word for word) quotation...", and (2) "Cutting and pasting from the Internet..." This is the same priority seen in my institution's policy, too.

@DanielHatton that's precisely why this concise answer is so important. What the students seem to be worried about is not so much what plagiarism is but what gets them caught.

Relativity was not my idea, but when I talk or write about it, I do not want to keep having to cite the many men that made it possible.

You changed a very important word when quoting that definition: "Plagiarism is presenting someone else’s work or ideas as your own." Not using but presenting as your own. This is paramount. There are many ways to use other people's ideas, work and research and most of them are not only OK but very desirable. Presenting as if it was your own is the problem.

Changing a few words is the worst form of plagiarism. It's basically proof the student knew it was wrong and is trying to hide it (I saw it most often with students copying from a friend's assignment, but same idea). "I'm sorry I didn't change more words" is really shorthand for "I know this class doesn't matter and you don't care. Let me go and I'll cheat better next time so you can pretend everything is fine".
There are two reasons we care about plagiarism. One is so our graduates don't do it. A few years ago an influencer (Rachel Hollis) posted "still...I RISE" without saying it was from Maya Angelou's "And still I rise". She got ripped a new one and never recovered. And she changed almost half of it! If you have to write an original article and start by rewriting someone else's, people go nuts. Here's one about a fired student reporter from my Alma Mater "Tibbs ran an editorial that was about to be published through a plagiarism checker: 71 percent." Strangely, the article doesn't mention whether 29% changes were enough -- apparently copying with any number of changes is fireable plagiarism. Huh.
The other reason we care about plagiarism is that the assignments are meant to show what you know. Being able to turn it into your own words is the proof you understood something. If you just use an internet search and a thesaurus (also on the internet), that proves nothing, so is worth 0 points, and is also lying. "I wrote this" means you thought of all the words.
For dealing with it, one fun thing is to talk to other students. I've found that most fully understand doing your own work vs. copying. And they get seriously angry if they think someone is getting away with messing up the curve and the school's reputation by cheating. Getting a faceful of "tell me you're not going to fall for their bullsh*t and let them pass" may be helpful. For a real earful, also tell the student "but they changed a lot of the words".

"It's basically proof the student knew it was wrong and is trying to hide it" Or they honestly didn't understand what "plagiarism" means.

Yes, this is a form of plagiarism called close copying.

+1, appreciate the concise answer.

Regardless of whether it is plagiarism, think about the context: if a student does this in an assessment then all they are demonstrating is the ability to use a thesaurus. Assuming the goal is not to assess the student's ability to use a thesaurus, any coursework demonstrating only that ability deserves a very low mark.
This follows regardless of whether you call it "plagiarism". That matters if you are deciding whether to put the student through the institution's procedure for academic misconduct. I would do this if the student failed to cite the source they had mangled, and not if they had cited it properly. But either way, "work" done this way gets a very low mark because it deserves one.
What I tell students is this:

The ideas are supposed to go from the textbook (or whatever other source) into your head, and from your head into your coursework. If the ideas are going straight from the textbook into your coursework, without going via your head, then you are missing the point.

The problem is not that the work they submitted is "too similar" to the source material, it's that the process by which they are working does not and cannot lead to useful, meaningful learning. That is true whether or not the process is called "plagiarism", so I'll leave that question to the philosophers.

My university tends to focus on the aspect of things being misleading (poor referencing not being an offence). The most important thing to do is ensure that you have a good assignment with marking criteria that focus on understanding. The easiest way is often to ask students to apply their knowledge on a specific (novel) case. That should also solve chatgpt issues.

I don't think there can be a clear definition.  The point is whether "changing a few words here and there" meets the learning objectives of the assignment.  If not, then it is trying to pass off the the content of the passage that does meet the learning objectives as being their own work and ought to be viewed as plagiarism.
Using a thesaurus or grammar checker to paraphrase the passage probably does not demonstrate any understanding of the topic in addition to the choice of passage.  So being able to choose a suitable passage is all that the student deserves marks for (which probably isn't very much).  What value have they added by paraphrasing?  What understanding have they demonstrated?

Separate from the academic grade-credit issues, we also need to think about how this interfaces with the school's mechanisms for academic-integrity enforcement actions around plagiarism. So I think the emphasis here is at best half of the issue.

I think this is a useful answer in explaining it to a student though in a way they can understand. Why is plagiarism bad in a university assignment? Well firstly, it is bad because in the "real world" passing off someone else's ideas as your own is one of the worst kinds of misconduct, but also 2) because if you copy someone elses work, you don't demonstrate understanding (an academic, rather than disciplinary issue), but it you change the words, you are trying to hide you lack of understanding (a disciplinary issue).

@IanSudbery exactly, I suspect some plagiarism cases are because the student has come from an educational culture where paraphrasing wikipedia etc. achieves good marks, and they don't realise that they are not meeting the learning aims, or that there is anything wrong with it.

First, at the end of the day, in a course setting, plagiarism—or the acceptable level thereof—is what the professor decides it to be.
But I think that instead of concentrating on the amount of words changed, the key point that needs to be addressed with the students is another: if you have to read and change the words to write your essay, it means that you didn't understand the concepts enough to make use of them and, consequently, to pass the exam.

"First, at the end of the day, in a course setting, plagiarism—or the acceptable level thereof—is what the professor decides it to be." No, it's not Plagiarism isn't just an academic issue, it's a disciplinary one.

@Acccumulation Yes, but it's the professor who decides whether to trigger a disciplinary action or not, according to their judgment. So, it's what the professor decides it to be.

If they aren't using a standard definition, their charge will not be upheld, and making charges based on idiosyncratic definitions is misconduct.

@Acccumulation I'm not speaking of idiosyncratic definitions.

The key concept of plagiarism is presenting someone else's work as your own. Deception is central to it. If you copy a passage verbatim, that's not plagiarism if you openly declare it to be a quote. It might be copyright violation, and handing in a paper that consists of nothing but direct quotes is unlikely to receive much credit, but it's not plagiarism.
Where it gets confusing is that if you're a student, obviously you're not doing your own primary research. If you write that most of Napoleon's troops in the Russian invasion died, then (unless you're in a really advance program, maybe) nobody's going to come away thinking that you pored through historical record calculating how many the initial and final troop numbers were. Obviously, you looked up someone else's work. So using general facts from other people isn't deceptive (but that doesn't mean you shouldn't cite them!).
Using other people's wording, on the other hand, is deceptive. And "using" doesn't mean just copying verbatim, it also means taking that wording as a basis. Changing someone's words around is different from writing something de novo, and presenting the former as the latter is deceptive. Taking the dailies from a movie and editing them into a new cut doesn't make you a director. That's not a perfect analogy, though, because there's a clear line between actually shooting scenes versus using someone else's scenes (and, actually, re-editing a movie is a creative act, it just doesn't constitute "making a movie"), but there isn't such a bright line between "moving someone's words around" and "writing something new".
As to the language issue, while you should make accommodations for language difficulties, ultimately this is your student's responsibility. It's your student's responsibility to learn what plagiarism is, failing that it's their responsibility to learn enough English to understand an explanation of what plagiarism is, and failing that it's their responsibility to find someone who can translate the explanation. It's not acceptable that "more complicated responses are likely to be disregarded", and if they have such a cavalier attitude towards core academic concepts such as plagiarism, they have to live with the consequences. They don't get to dodge disciplinary repercussions just because "this is hard to read".

Types of Plagiarism
It often helps to break down plagiarism into different types. That's what Harvard does, for example, breaking it down into six kinds. A lot of other universities use the same or similar categories. The beginning of the course is the best time to (re-)explain what plagiarism is (ideally quoting your school's own policies) to hopefully prevent it before it happens.
If a student points out they didn't use the exact same words as the original author, you can point out that they are referring to only a single type of plagiarism (usually called verbatim plagiarism). The type of plagiarism you're seeing where they "didn't change enough words" is called either inadequate paraphrase (the wording is too similar) or uncited paraphrase (paraphrased without citation), or both.
The key is that it's not plagiarism if they paraphrased completely (changing enough of the words and wording) and cited their source. And if they did both but they weren't allowed to consult with sources, that's a violation of academic integrity (but not plagiarism).

The last para about citing sources seems odd. The problem was that an original assignment was copied, right? That makes it sound like they could include: "This assignment was copied from [link] and you can see I made 15% cosmetic changes", and get an A (or maybe a B with a note about better places to copy from?)

@OwenReynolds "15% cosmetic changes" still sounds like inadequate paraphrase. The last sentence of my answer was intended to address points like solo assignments that use other students' work (similar was mentioned in another answer) or anything where the student used sources that weren't allowed (e.g. quoting the internet when only the textbook was allowed during a test).

Yes.
As a student, many institutions provide access to plagiarism checkers, which highlight text that may be dubious.
I used a small paperback version called APA: the Easy Way, my father had once shown me a similar compact Chicago Style Manual.
Here is a link to Worldcat's list of libraries around Washington DC that have a copy of the first one:
https://www.worldcat.org/title/apa-the-easy-way/oclc/1183823482&referer=brief_results
These work, but you need to read and refer to them.
As a teacher, see if your institution offers a plagiarism checker (turnitin, for example https://www.youtube.com/channel/UCG9mtsMkQaDDq3PSxa5zMEA). These allow you to show students exactly how to check themselves and are worth some class time to teach them what's expected, what's accepted, and what isn't.
They also lighten the load for submissions, grading and (in the case of the one I mentioned above) designing assessments.

The easiest thing to tell your students is this:

If you use someone else's work, cite them. If you don't, you're committing plagiarism.

When this issue comes up in undergraduate work, it almost inevitably comes down to intellectual laziness. The student in not focused on school; s'he wants to slide through to a passing grade with minimal thought and effort, because s'he has other concerns: social life and dating, activism, emotional issues or anxiety, etc. These other concerns are natural and important — we all go through a lot of crap in that age-range — but part of the job is encouraging students to learn focus and balance. You're not doing them any favors by being overly lenient.
If I were in your shoes, I'd look them in the eye and tell them that I understand (because I really do), but that the behavior isn't acceptable. They need to step up. I'd give them a choice between a zero on the assignment, or a chance to rewrite the paper in a way that convinces me they understand the material. And I'd let them know I'd be reading the revised paper extra carefully. If you can find a way to break the myopic fixation on grades and get them to focus on acquiring knowledge, this problem should solve itself.

From my experience, this is taught by high school teachers because they, themselves, do not understand plagiarism; at least, in the US. I wouldn't blame the students as they were never taught what any of this means: they were taught they have to produce the work required, and if they don't produce the work required, they cannot continue and will fail the class and are not given any sort of out or alternative path.
This is a version of Goodhart's Law ("When a measure becomes a target, it ceases to be a good measure") in effect; so many words are required in that assignment, where they come from doesn't really matter. On top of this, they are taught that referencing anybody's work (while simultaneously teaching them how to cite work and what citing means) is wrong: if you cite too many works, teachers will happily shave points off your grade as if you had done something wrong.
Sometimes an argument is complex and requires citing a lot of previous work, and all your core contribution is providing the glue for a bunch of cites. In science, this could be the form of a meta-study and all you did was pull your conclusions out of a wider body of work that no single cited paper represents, and it's entirely possible your paper just concludes that multiple papers agree and reinforce each other and finding that out was your contribution to science because no one else ever wrote this.
Citing other people's work is not plagiarism, citing other people's work and paraphrasing it (without changing the meaning) is not plagiarism. Copying it verbatim without cite is plagiarism, paraphrasing without citing and without adding anything meaningful to the new version is plagiarism. This is commonly not taught to students, so don't blame them, just try to teach them.

To answer the titular question: absolutely yes.
Now when it is dealt with, the bigger issue at hand is that students don't understand your expectations and the reasoning behind them.
Make sure they understand what materials they are supposed to use for their assignments, how and why. Similar to how students doubted the need to not use the calculator for arithmetic in school, they now might be doubting the need to calculate something else by hand when Wolfram or Maple exist. To the similar tune, if they looked it up online and there is the exact solution to their problem, why not just use it? Are they to pretend they never saw it?
To me, the perfect approach is when they either already know from your material or find in someone else's work the approximation to an answer and have to fill in the gaps, and if the problem is purely technical, doing calculations by hand is helpful but only if they are your focus as a teacher, and some people struggle more than others with those; you might need to consider accommodating them as well. If taking prior work is fine by you long as the proper attribution is given (after all, someone has to teach students to work with literature!), state that explicitly. Unfortunately, school focuses on "no cheating/copying" in a way that leads students to the "just don't get caught" mentality you seek to get rid of.
So meet the students where they are, consider what skills you deem important for them to develop, and sit down with them so that they explain their solutions to you.
As an exercise, you might even ask them to explain some relatively trivial fact so that they know the difference between common knowledge, where the attribution is not needed, and deriving works.

It is not a question of proportion, or how many words: plagiarism is a qualitative assessment.  It is largely a question is claiming as own the idea of someone else.
Clearly direct copying without attribution is plagiarism, but consider the following examples.
During a final exam, two students Charlie and Bob make the same sequence of conceptual errors on a question where they are asked to evaluate the ground state energy of a molecule (for instance).  One or both of Charlie and Bob could be guilty of plagiarism even if the texts explaining the calculations are largely different.
As another example, suppose Bob somehow accesses the work in progress of Charlie, and decides to redo this work on his own without acknowledging the source of the work as Charlie’s.  Even if Bob’s paper is significantly different in language and structure from Charlie’s, Bob can still be accused of plagiarism.
In the examples above, one can argue that the ideas were improperly claimed to be that of one person (say Bob) whereas in fact they are Charlie’s idea.

I'm confused by the first example - if Charlie and Bob answer the question independently, it's not plagiarism if they use the same line of reasoning, or even if they write the exact same words by chance alone. If Charlie and Bob never see each other's paper (and I don't see why they would in an exam setting), it's impossible for them to plagiarize. Of course, proving that would be difficult given identical incorrect answers.

@NuclearHoagie yes.  I would better have said that in this instance once can rightly suspect plagiarism, and differences in wording would likely not make up for the low probability of independently making the same sequence of errors.

Let's look at from a different perspective. What would it look like to not plagiarise a source. You would discuss how the ideas and information from the source applies to your specific problem (or topic). So at the very least you synthesise the source with your own essay topic. This might involve a bit of paraphrasing (or quotation in even less cases) but only in so far as you explain the ideas in order to then relate them to your own.
Of course there are cases where you need factual information, in which case a simple quotation may be best. At university level that should not earn many marks though (only demonstrating the skill to summarise)

You seem to have forgotten to mention citation.

I tend to avoid the word citation as it tends to be confusing: ie it is not clear whether quotation is meant or merely referencing (discussing the source without providing a quote). Students tend to massively overquote because they are told to cite their sources.


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Does every professor need to do research?
I wonder if there are some professors only focusing on teaching or management but no research. I think this may be feasible.

I am an Associate Teaching Professor.  My duties include no research.  I teach twice as many classes as my colleagues.
A position as a teaching-track faculty member is not uncommon in US universities.  But, it isn't common either.  My department has about 4% of its faculty on the teaching-track.
Very feasible.

In the Netherlands you can have a "buitengewoon hoogleraar", who has a professor position of typically one day a week and another position somewhere else. Often this is an external entity like a company, but this has also been used to give a professor title (but not the pay) to someone who does the managent of some institute.

At my UK university we have a few academic staff whose job title is "Teaching Fellow". These are postdoctoral positions. They spend all of term time teaching, with the chance to work on some of their own research over the summer.

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Does TA application usually have training and interview?
First I thought every university would interview and train their TAs somehow. But I just get to know that my university doesn't have that, at least for marker and lab tutor. Is it the way the most universities do? How could they know the applicants are qualified enough?
I am in Canada and my field is electrical engineering.

What is your field? which country? - Like in Germany, normally if you got a scholarship to TA position they will consider the first 3 months as test, then they will prolong the contract with indication of your tasks and training plan.

@Krebto I am in Canada, many graduate TAs only do the job for a single term(4 months)

Some universities and programs assume you will figure out how to be a TA on your own. Some (perhaps even most) universities also assume faculty will figure out how to teach on their own, so perhaps it isn't surprising.

I have never heard of a university in Canada in science or engineering that train their TAs. It is just assumed that you know how to do the job...

In my experience (US, biological sciences), TA training is uncommon or nonexistent, except for having prior experience teaching the same course. Interviews for TAs are more common, but certainly not required, and less likely if the TA is from the same department as the course. Depending on the size of the course, "TA meetings" may be more common where TAs meet (perhaps with the course instructor) to standardize lessons/grading, establish learning goals, etc, but I would not call this "training."

@BryanKrause How they guarantee that the applicants are qualified for TAs?

Nothing is ever guaranteed, regardless of interview style or training. They may ask for a resume or course history. Mostly, they assume if you are a graduate student in (field) you are qualified to TA a course for (field). Most TA positions also aren't entirely free of supervision: especially if it is just a grader TA position, probably the instructor is creating the answer key. The best few students in a lab course are probably qualified to tutor a typical lab.

@BryanKrause Make sense. A friend of mine, who was a marker, told me that the instructor let the TAs to do the marking scheme by their own for the assignments. I mean even the weight of each question was decided by TAs. I think that maybe a little too much rights.

You're right it's a nutty system, but that's how it is.... When you are a department administrator, I hope you will do things differently! In the meantime, you'll have to do your own training by talking to more experienced TAs. The best way to learn to be a fair and efficient grader is to work alongside an experience grader. Friday afternoon is a good target time. An experienced grader will be more likely to agree to a tandem grading session if you bring dinner.

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How much would writing a thesis help for a person's career in industry(not in academia)?
There are many people who pursue a thesis-based master's degree but do not want to pursue academia after graduation. If people just want to have a good job, is thesis writing helpful to them? My major is electrical engineering.

Could you be more specific about your question? The value of completing a written thesis likely varies by field and position, even in industry.

I can think of two reasons you might want to write a thesis.

If you would inherently enjoy the challenge.
If digging in and writing up specialized knowledge in a particular topic might be related to your future work on the job.

Either of these would be a good reason -- you don't need both.

Actually having a Ph.D. can be seen as a disadvantage in industry. I have met this attitude from a couple of employers / potential employers. They see you as an academic, and not wanting to do real work.
I think it would be less of an issue with big employers, but certainly smaller ones, at can be an issue. It may be worst in my case, as I spent a number of years as a post-doc at university.
If you don't want to do academic work after university, and just want a good job, I'd personally suggest the case for doing one is rather weak.
Others experience may be different, but I personally think the main thing you get out of a Ph.D. is the ability to do research properly. That is a transferable skill. My Ph.D is Medical Physics, but I work in a completely unrelated field (I'm director of Kirkby Microwave Ltd, developing vector network analyzer calibration kits) The skill of doing research I learned during the Ph.D. are very relevant to the products I develop, and hope to develop, despite they have nothing to do with what I actually did during my Ph.D.
If you go into industry after 3 years spent studying for a Ph.D, you will probably find your manager does not have one, and is earning more than you!
I can't recall where I read it, but there was an analysis somewhere of what it costs to do a Ph.D. If you consider a "good job" one where you gets lots of money, you will probably find the loss of income for those 3 years is significant and you may never make it up in your lifetime.

The question is about writing a thesis as part of one's master's degree, not about doing a PhD.

Oops - my error.


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Generally, what kind of non-academic misconduct can make a student get expelled?
We all know a student is expelled because he committed something extremely bad. But how is extremely bad? Must the student commit a crime or something? Unfortunately, university policies do not give details of that.
(In America and Canada)

This will be highly dependent on country and university. E.g. having sexual intercourse in the lavatories of a christian university in the US might get you expelled but will have no consequences in a regular german university. I therefore vote to close.

Many relevant Q&A on here, this is but one : https://academia.stackexchange.com/q/28966/72855

Likewise, reporting that you were a victim of sexual assault will get you expelled from BYU, but in other places, people might investigate the crime.

As an undergraduate, I served on the disciplinary hearing board for a large private secular university in the United States. I saw the full spectrum of cases that came before the board, from minor infractions to severe violations of university policy (and the law).
In my experience, the university was reluctant to fully expel someone. Minor infractions typically resulted in some form of mandatory training and/or disciplinary probation. Repeated minor infractions might result in a short suspension. For most severe policy violations (e.g., assault), the university preferred to hand out lengthy (1-2 year) suspensions rather than permanently expelling the student. Obviously, I'm sure that many students chose not to return after this setback.
The exception to this was sexual assault cases, which provoked a more unequivocal response from the university. Expulsion was certainly on the table for cases where a student was determined to have committed sexual assault. At the very least, the perpetrator would be suspended as long as the victim remained on campus, to ensure that the victim did not have to interact with the perpetrator. Inevitably, Title IX requirements and liability concerns shape both the hearing process and the outcome for sexual assault cases. This type of scrutiny was generally absent from other cases.
I can think of one other case where the hearing board recommended expulsion for a student. In that case, the student dealt tens of thousands of dollars of hard drugs to an undercover police officer over many months. The student was arrested and the university subsequently began an internal hearing process.
The standards and process may differ for other types of universities, but generally I got the sense that my experience was representative of other large secular universities in the United States.

Good answer! Can you please add an explanation of "Title" IX"?

Can the university do anything to a student who has not yet graduated but already finished the degree and left the university?

@problemofficer Title IX is a federal law in the United States that ensures gender equality in universities. It is probably best known for improving women’s sports offerings, although recently it has played a large role in addressing sexual assault and sexual harassment on campus. The Wikipedia page for “Title IX” explains it better than I can.

@Rapidturtle I’m not sure that I understand your situation but the outcome will depend on the location and type of university that you’re attending. It will also depend on the nature of the infraction. If I had to guess, I would say that the university would probably be reluctant to pursue it if you’re no longer a presence on campus.

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Masters application with bad 1st year transcript
When I started the course I had a very negative attitude and did not participate or even bother trying to pass. I am not proud to say that I failed multiple subjects in my first year of degree.
In my second year I came to realize that this is the opportunity I have been given and actually started working really hard on pushing my CGPA up. I have successful done so bringing it up to 3.25 out of 4.0 from a low of 1.9. Once I started actually trying I found that I do have a passion and would love to pursue a master.
I am worried that I stand no chance because of that first year record. My question is do I stand a chance to get in a masters program and what do you think would help strengthen my application.

Schools do like to see that students have improved overtime so you do have that going for you. I would say the answer to your question depends on the type of program you want to get into. I can only speak from research university experience but I have seen people with not great GPAs (around 3.3) get into even PHD programs if they have enough research experience (i.e. posters, papers, lab manager experience, etc.)

Yes, there is a certain amount of "forgiveness" for first year grades, because a lot of students have trouble making the transition to college.

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Is it appropriate to include dollar amounts for awards granted when applying to a math PHD?
This question includes REU (research experience for undegraduates) grant, travel grants, or prizes awarded. I've seen a friend's CV and he seemed to do this. I was wondering if this is to be expected or if one should refrain from posting the amount awarded.
Perhaps it is worth mentioning that participation in an REU (and the support received) does not really belong in a "grants, honors, and awards" section, or at least that is my impression.
There is a similar question on this website, but I'm asking specifically about  applying for graduate school and what is culturally accepted among the mathematics community in the United States

I'm not in math, so just a comment. But yes, I usually see dollar values (I have them on my CV, and no, I would be surprised to see an REU in such a section, but I also never had one so idk. Maybe better to have two questions

@AzorAhai I'm in math, and I don't usually see dollar amounts on students' CVs.

This seems like the kind of thing which would vary between geographical cultures as well as subject cultures, so it might be worth editing the question to state the geographical culture of interest.

@PeterTaylor agreed. Edited the last sentence

It is entirely your choice -- doesn't hurt, but not necessary either.
Readers of grad school applications generally have a decent idea of how much REU or travel grants (a couple of thousand dollars) and how much departmental awards are worth (a few hundred dollars, typically). So not stating a number is not a big deal. Stating a number also doesn't hurt: if it's within the range a reader would expect, then there is no harm done, space is cheap; if the dollar amount is surprisingly large -- say, a $5,000 award for your work, then that's useful knowledge and should have been on your CV indeed.

That is fair, I meant to mention that as well: all standard amounts of money (save maybe one such grant.) thanks


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How should one present research done in a CV to a graduate program in mathematics?
This is a question about how to best convey research done to an admissions committee for graduate school.
I have basically two combating philosophies, both may be wrong:

state the "official name" of a paper that is either in preparation, published, or on the arXiv. Follow this with collaborators and perhaps the year you worked on the project.
State the field " Number Theory," state collaborators, and give a brief description of what we accomplished: "We classified classically integral quadratic forms that fail to represent at most two positive integers." Then give where the article was published and its name.

I guess for communication purposes, I like the latter, but I've never seen this done. That being said, I also have some research that is niche enough that the title will not be well-understood by a general audience of mathematicians.
Secondly, I don't like the first since it creates an asymmetry if I want to mention that I am currently doing research on my CV. I guess I can expand on my research experiences in a personal statement, but I figured that a brief description here is helpful.
I guess I want to convey the type of research I've done, since it is a bit diverse (not that much, but pretty broad) so I just wanted to know if there is a good way to proceed.
I think that option (1) is more professional, but also not helpful as it might as well say "I did X number of research projects, and this is their status."

It doesn't really matter where you describe the research, as long as you do describe it. The admissions committee will want to see your description, and they will find it.

There are some general ideas about what is "standard" to include in CVs, but they only go so far: you still have some leeway on what to include and how to include it.
It is fine to give a brief description (e.g. the abstract) of your works on your CV.  You should certainly also include all of your collaborators!  Either way, you should take some space in your "personal statement" (a bit of a misnomer -- it should be a "professional statement," not e.g. a narrative about how you came to love mathematics) to describe this work.
Finally, for what it's worth -- I was familiar with your paper on quadratic forms, and I just looked back at it again.  I wouldn't quite describe it as "analytic number theory."  It has some analytic number theory, some computational number theory and some, well, quadratic form theory (that's on the algebraic side of number theory but I wouldn't quite describe it as "algebraic number theory").

Hi Pete! It's good to hear from you. If it's analytic/computational/algebraic then that just sounds like number theory to me, so I'll leave it maybe there fore safety. Thanks for the correction. I will then provide a brief description, and hope that this is okay. Is there a standard way to indicate which collaborators are professors (or graduate student supervisors)?

Although I suppose I gave a bad example for (2) since the name of the article somehow tells exactly what it is about. I was being lazy because it was the easiest to describe :).

I agree: just "number theory" sounds best.  I would suggest listing all coauthors in (presumably alphabetical) order and leaving further discussion of their roles for your personal statement.


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What are some career options for Math PhDs who want to work in non-Western countries (e.g. Southeast Asia, Central Asia, Africa)?
I am about to enter a PhD program, and I am very interested in learning about opportunities that allow me to go abroad after I finish. During my undergraduate career, I studied in China for a year, and I really enjoyed the environment of learning new languages and living in a different culture.
Specifically, I want to know about some of the challenges that one might have in looking for university or research positions in non-Western countries, and subsequently, how one might transition back to the United States after having spent a considerable amount of time abroad (5+ years). I have felt that math is a universal topic, and many universities abroad (especially in Asian and central Asian countries) would have faculty positions for English speaking PhDs to move there. However, I don't have any information to justify these beliefs.
I'm not as concerned about salary or ending up at a prestigious research university. I really enjoy teaching and working with students, and I enjoy math enough that any position that would allow me to continue working in mathematics and with students would be acceptable. Am I entirely off base in hoping to find positions abroad? What are some challenges that I might not have considered?
EDIT: I should have clarified. I am an American student beginning a program in the United States. In that context, then, what are things that an American PhD should be aware of when looking for opportunities in non-Western countries, such as those in Southeast Asia, Central Asia, Africa, etc.?

Somewhat related: http://academia.stackexchange.com/q/2689/948

Abroad is relative.

Here where I live, a better question would be "are there reasonable career options for math phds who don't want to work abroad?"

I've edited the question to make it more specific to what I was intending to ask. Thank you for the feedback!

This answer is mostly for Asia.
Yes, there are programs in at least Japan and Korea (that I am aware of) for American Ph.D to find a job, including professorship.
I think the largest difference/challenge you will face is that many times, being a student and working in Asian countries such as China, Japan, Korea, is very different.  In general, the faculty, students, local businesses, etc. are happy to accommodate students spending some time in their region, learning their language, and living.  Systems are in place for this and the universities most often actively encourage it.
Meetings
As a professor it can be (but not always) different.  Unless you learn the language fluently before you go, think about your new colleagues and how they will feel, being required to speak to you in a language other than their own.  Not necessarily about the weather, but more importantly (what I noticed) is in faculty meetings, budget decisions, etc.  In this case, you can easily be the only person not able to understand, which leaves two options: you are left out of the meetings or everyone else is forced to speak your language (if they can).
You mention not caring about prestige, but I would caution you that many 'bad' universities have a lower chance of faculty being comfortable in English.
Administration
Beyond faculty, which may or may not speak English, you still will have administration to deal with.  Do you assume your contract will be in English? While some online university systems are in English, I have seen many parts that are not, such as the email system in English, but the login systems or vacation registration is not.
Culture
Of course, you need to think about culture.  The idea of Asian culture may allure you, but remember it is not always what it seems (just as people going to America find out).  In at least Japan and Korea, Impact Factor is the largest measure of performance, and you must follow it.  Be ready to change your work style if it does not fit into the way you are evaluated.
Resources
You can check https://www.higheredjobs.com/international/  for international job postings.

A supplement to @user1938107's excellent answer about Asia. There are some future career issues you need to think about before you come to Asia to work.
The first one is tenure.  Many Asian countries offer only visiting professorships to western scholars. Those visiting professors do get higher salary than local people. But, most of them are not permanent positions. In other words, you'll need to look for another job somewhere else after a few years when the contract expires.
Another issue is sabbatical leave. Because you are a visiting professor, you don't get sabbatical leave. You are free to go anywhere in the world, but there is no guarantee that you'll get the same position when you come back.


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How can I obtain an academic reference, if I have been out of college for a very long time?
I have completed my Master's degree 25+ years ago, and I decided to go back to college to further my education with a Doctorate degree. I fulfill all the requirements, except for the need to provide 2 academic references.
How should I proceed to obtain the references? Should I hunt down my former professors in their retirement and hope they retain their faint memories of me?

I suggest contacting the admissions office and checking that they're really interested in academic references in your case. The generic requirements are probably aimed at applicants who have been in education more recently than you. Try to get referees that can vouch for your critical thinking and problem solving, and if you have been working in a similar area to the doctorate you should ask referees that can vouch for your subject area knowledge.

@Alexandros I just wanted to emphasize the fact that they are really old. They were already old back then.

You can use the "edit" button if you would like to rephrase.  (Registering your account will help make sure you don't lose this ability.)

@DeniseRadi I've edited to remove the age joke while hopefully preserving the idea.

Your situation now is very similar to my situation in 2001. I got all my references from colleagues who knew my recent work. Fortunately, I had been doing research-like work, except in an environment where it lead to product and patents, rather than papers.
The professor who supervised my master's degree project was still working, and I could have contacted him, but I felt that my recent work was more relevant than a project I had finished in 1975.
I made sure one of my references was academically well-connected, although working in industry at the time. The other two were a software engineering manager and a computer hardware engineering manager who could write about my range of knowledge as well as my research potential.

Agreed.  They are more likely interested in hearing from someone who knows what you have been doing recently, rather than from someone who knew you only 25 years ago.

I was recently in a similar situation.  Although my time away from academia was somewhat shorter than yours (10-15 years), and even though some of my professors were still active in research, I did not think they would be in a position to write a strong recommendation letter.  "I vaguely remember this student from 15 years ago, and she got A, so she must have done alright," is not the sort of recommendation you want.
My solution, which has worked out well for me, was to spend a year taking graduate level courses at a local university.  In addition to taking the classes, I went out of my way to introduce myself to the professors at the outset and explain my situation. I was able to get involved (in rather minor roles) in two research projects, one each semester.  This allowed the professors to write much stronger letters than I could have gotten from professors of 15 years ago.  It also had the benefit of improving my applications with recent, relevant coursework and research.  Even if you have all of the requirements, some recent academic experiences may be valuable, depending on your field.  "Fulfilling all the requirements" and having a strong application are not quite the same thing.
Of course, this may not be applicable to you.  It is a full year, at least, without funding.  It requires a nearby university at which you can get involved with classes and research.  It delays your starting time by at least another year.  These are all drawbacks, and may be more or less burdensome depending on your situation.

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How to reply to a potential PhD supervisor who asks if I have my own funding?
I have a Master in Computer Science and I am applying to some Canadian Universities for a PhD...
After contacting to a supervisor, I got a positive reply, however he asked me:
"Do you have your own funding to support your PhD study?
What and how should I reply? On one hand having some financial support is quite vital to me, but on the other hand I don't want to lose this opportunity (I may work in order to support some of the costs!)

Just answer the question? If you have another source of funding, tell him; if not, tell him that. What are you asking us, exactly?

A non-academic job is not funding.

There may not even be an opportunity to lose. Getting financial support is "vital" to you, and the question sort of indicates that the prof. is not able or willing to provide financial support. What do you expect to gain from not answering truthfully?

If you don't have funding, the professor is your best bet to get it; he can either pay you directly, or point you which grants to apply for, and help you to do it.

Just answer the question honestly.
If you have your own funding, say so.
If you do not have your own funding, say so.
If you do have your own funding, there is really no problem.
If you don't have your own funding, it may be possible to arrange some for you.

If you don't have funding yet but have an idea where you could potentially acquire some (scholarships etc.), say so. Professors like candidates that think for themselves. It makes them hope the candidate is similarly self-motivated in research.

Your own funding doesn't mean your lifetime savings, it means a fellowship or scholarship you have won.

You should just give a clear and honest answer to the question. In fact, in this case, you have no option but to be honest. If you do not have funding and say that you have or can arrange for some funding, you will be in a problem later. On the other hand, if you are honest, the professor might guide you on where you can procure funding. I can understand your apprehensions of losing on the opportunity, but if that is the worst case scenario, you will have to accept it. If neither you nor the professor has funds for the project, the "opportunity" that you are talking of will anyways not be successful.

Depending on where you are in the world, this may less be a real question of finances and more a question of intellectual freedom and general freedom to pursue relevant research in the track.
With own funding, there are no responsibilities to third parties and the stresses involved - and there are no possible conflicts of interests regarding the subjects one can research.
It also frees up the timetable, as most provided funding has a limited period for which it will be provided. If one were to tack on another year of research for the benefit of the degree and the field it is much easier to do so with their own funding.


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How to recruit participants for online experiments?
We are currently doing a study where we thought it might be smart to try out the possibilities of recruiting participants from the Internet. I was thinking it might be best to ask more experienced members, where would be the best kinds of places to publicize the experiment, and what strategies they would recommend to this?

Do you mean "publish" as in publish a paper about the experiment, or "publish" as in publicize the link so people visit it, or what? Please clarify.

Thanks a lot, point well taken. I did mean this in the sense of publicize, I now see how poorly phrased it was for academia. The problem I would say is still rather general: The internet offers a potentially infinite pool of participants to take a part in our experiments with close to no costs in the form of people surfing the web. It seems worth a thought how best to reach these audiences for attentive participants, who follow the instructions and make an effort. We'll continue to look into this. Thanks for the corrections though, and sorry for spamminess.

Ok, since you have clarified we were able to reopen the question. Hopefully this can get answers now.

If it's truly considered an "experiment", there may be limitations on where/how you can publicize it. What's the nature of the study? For example, if you're asking health-related questions, if it's some type of mental health survey, etc.. Even if it's just a "simple" survey, there still may still be policies and regulations that you'll need to follow. In some cases your only option might be to follow your institutions procedures for recruiting/publicizing your type of study -- That can still be done via internet, just within the institutions' system for publicizing & recruiting participants.

One approach that has become popular amongst many social and cognitive scientists is the use of Amazon Mechanical Turk, which is an internet piecework marketplace.  Many people have used this for recruiting study participants, and IRBs have been quite receptive to its use.
Designing studies for Mechanical Turk is challenging, and presents different issues than designing for in-person studies.  A number of online resources exist that discuss the advantages and challenges (e.g., this blog, this paper, and this website).  Mechanical Turk also poses sampling issues---as has been noted, however, typical recruitment methods also end up getting almost exclusively WIERD participants, so it's unclear how much of an issue that actually is.


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Special character from an arXiv paper title displayed incorrectly in Google Scholar
Recently I uploaded a paper to arxiv.org, the title contains the letter (α), I wrote it in latex form $\alpha$ in the website, it recognize it and it is displayed correctly, but when the paper is indexed in Google scholar, it appears as $\alpha$ in the title, any idea how can I fix this?
arxiv Link
Google Scholar Link

I doubt that you can fix it.  But I wouldn't worry too much; I think readers in technical fields are used to issues like this, and will not have any trouble parsing your title.

This should be posted at Tex.SE

@fileunderwater: I don't think so: it's basically a question about Google Scholar, not about TeX.

@fileunderwater - First question to ask before migrating: "Is this on-topic here?" If "yes", then no migration necessary, even if it's more on-topic elsewhere.

Do you mind linking to the paper in question? It might be difficult to know how to fix it otherwise..

Your target audience won't even notice - they compile it when they look it. It's like the the old joke that no one notices if you put two "the"s next to each other in a sentence, like I just did.

I suspect that Google Scholar is getting the page title from the metadata of the arXiv page, which has the following title metadata (look at the HTML page source in your browser to see it):

[1509.00976] In-Band $\alpha$-Duplex Scheme for Cellular Networks: A Stochastic Geometry Approach

The good news is, you can edit how your own papers appear in Google Scholar.

Create a Google Scholar account if you don't already have one. Then sign in to your account.
Click on "My Library."
Then click on the paper in question, click on "Edit," make your changes, and hit "Save."

Thank you, I didn't know that I can edit the title.


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MSc Dissertation Tables & Figures Errors submitted
I submitted my dissertation yesterday, one day before the due date.
Upon reading back through the dissertation, I noticed quite an error in my methods and discussion.
Unfortunately, due to adding a number of extra tables in my methods which in turn automatically were updated, I now have elements of my methods which is referring to the wrong table.
This also occurs in my discussion.
Example: "As shown in table 1 a p-value of....".
When in fact that is actually number as table 2.
I have a couple of hours so I could resubmit but I'd be cutting it very tight. Do you think I will lose many marks because of this?
I estimate referring to the wrong table occurs 6-8 times between methods and discussion but some references are on the same page so are clearly seen.
I emailed the lecturer but I haven't heard back along with a fixed copy.
Thanks for any help

Pretty much everybody has had a story like that. Honestly this is “small potatoes.” A reviewer might comment on it, but no rational reviewer is going to say “This was an A thesis, but you had the wrong internal cross-references, so you only get a C.”
However, I would caution others that if it’s caught before the final required submission deadline, you can at least try to send the corrected version to the faculty reviewers as an email. The worst that can happen is they’ll ignore it.

I would go ahead and have it corrected and prepared ready - if they then say "submit a corrected version now or by 4pm" then you have it ready.
However, if they say have it corrected for final submission in 2 weeks then you are still ready.

It's final submission today. I have emailed him a corrected copy and I am waiting to hear if he wants it resubmitted via hard copy. Does cross referencing cost much in terms of marking?


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Should I include interviewees in my dissertation acknowledgement?
Background: I am writing a MSc dissertation in a technology/business-related topic.  I interviewed 15 people for about an hour each.  Each interviewee was given a choice of anonymity (e.g. tech-sector employee), organisation only (e.g. Microsoft employee) or named (Joe Bloggs of Microsoft).  Most went for named; although in the final version of the text when I referred to interviews I just used organisations (mostly for presentational reasons).
Question: Is it considered polite to include the interviewees in the acknowledgements (clearly just those happy to be named)?  If I did so I would probably email first to check they were happy (and I'd got their name/title right!); although might be overthinking this...
Edit: I have written consent from each participant regarding the use of the information they have provided.

I would think that it is probably enough to recognize them as a group: Thanks to the fifteen people whose ... enables this research. You might want to name the companies, provided that there was some cost (monetary or otherwise) to the companies.
Alternatively you might, at the end, without connecting any individual to their responses, thank them by name, maybe obfuscated: J. Doakes, M. Jones and thirteen others who prefer not to be named.
Likewise, if the positions held by the respondents is essential you might list that with or without names, even if it is just summarized: Three executive vice-presidents, one chairman of the board, and ... (That isn't the same thing as individual acknowledgement, of course, but informs your readers.)
My reasoning is that you probably don't want readers of your thesis to contact your responders, more to avoid them being bothered than for any other reason.
If the research requires that a name or other identifying information be associated with a response then you need explicit permission. You likely need to retain the written permission.
I'll also note that there are laws in various places that speak to issues like this. In the US, most universities have an office of research that will give you very detailed information about research, especially research involving human subjects. It may be the same elsewhere. In the US, see an officer of the IRB (Institutional Review Board) at the university. Your research may be covered or not. I suspect that for simple interviews it won't be covered, but you should check.

To my point of view, an interview is also a (weak) kind of a source to be cited, so I would add each interview as a literature reference by giving the date, content ("Interview on Topic X") and the information the People allowed you to use (might be "anonymous, Person from industry X" to "Peter Parker, CEO of Spiderman agency"). I would make a subsection in the references section showing "here are the interviews" and the list them.
While I was working in acadmica, I asked all my students to do so.

Thankfully for me, my university provides advice on this matter: they recommend referring to interviews within the text, as opposed to in bibliography, as they are "non-recoverable."  They give less advice on the protocol of acknowledgements, so I'll go with @Buffy 's advice above!


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Arbitrary units or unitless plot to protect data?
My question is about naming semi-arbitrary units in a (conference) paper.
I am writing a paper and, in accordance with advice from my mentor, I need to remove exact data and parameters from most of the paper because some of it is sensitive information. Ideally, I would like to preserve the shape of the plots but make the units arbitrary.
Note that this doesn't in any way interfere with understanding the results. The exact same procedure can be used regardless of the exact parameter value (literally the slope of a line), but we aren't allowed to publish that value.
In one case, I was plotting two curves on the same plot showing the difference in performance between two actuators. I normalized both curves, but then they more or less overlapped, which made the graphic uninteresting and a bit confusing. So, I normalized one plot and then did some relative scaling / biasing of the data to preserve the overall shape somewhat proportionally.
What would I call that? Normalized data? Arbitrary units? Unitless? Should I just make a note that the scale has been adjusted to preserve the shape?
In another case I have two sets of linear fitted data and I am having a similar issue on how to display and label these things, because the units will be rather arbitrary but it won't be quite normalized.
Thank you for your time.

I'm confused - were the curves not overlapping originally, but became overlapping after normalization? If so you presumably normalized them separately, which would produce that behavior by design, or the scale's off. Standard procedure for arbitrary units is to divide all data by some reference value (e.g. the normalization constant for one of the curves). Individual scaling only serves to confuse things. But for your purposes, why not plot the difference (in real, normalized, or arbitrary units) instead of dealing with two curves?

Yes, you are correct. My approach isn't good and I wasn't sure what the standard was. That would be a good idea. Thank you.

If the parameter doesn’t matter, why don’t you regenerate all data with a different non-secret parameter?

The data is a measurement of the position of an actuator vs the drive voltage. I cannot regenerate it. The actual value is of interest to those theoretically applying the simulation to the project at hand, but for anyone using the technique, it could be a different value that accords with their particular system. Normalization seems like the way to go.

You are not the first to publish papers based on sensitive information - check other papers published .. I know of 4 projects  that have been classed as “secret” and they were passed but not made public...

How can the units on a plot possibly reveal sensitive information? What are you measuring in, "number of dates Josh had last year"?

Again, I don't make the rules buddy. Use your imagination.

@Trusly It happens. I remember at least one unitless graph from early in my career, because I was working with people who didn't want to release details of the material properties of the thing I was evaluating. I'm not convinced the secrecy was necessary, but it wasn't my opinion that counted on that one.

If that paper is submitted to IEEE Transactions on Microwave Theory and Techniques (and judging by comments, this journal should be a decent enough fit for the purpose of this discussion), you would have to provide the measurement results. The journal guidelines explicitly ask for it and no arbitrary units or unitless plots will suffice.
Reproducibilty of the research is very important. And obfuscating the data certainly goes against it. If this plot & experiment itself is crucial for the paper – and you are not allowed by any means to disclose the parameters required to reproduce your experiment – you don't have a paper. Which might be sad, but that's not "the science" and "scientific process" fault, but ITAR (if that's the case) and yours, by (un)willingly accepting their terms.
One might judge that this is a conference paper, not a full journal one. But I, personally, prefer to have very similar standards for both conference & journal papers – and a lot of conferences have a similar (if not better) review process.

Thank you for providing the link! This is indeed for a conference paper, not a journal paper. It's for AIAA. I will check their guidelines.

On reproducibility, one thing is that the work is about a simulation, not an experiment, per se. The hardware parameter doesn't effect the functioning of the simulation, which is the focus of the paper -- it's a detail about the system we are modeling.


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Getting a job and quitting PhD at university in UK
I am going to be straightforward in here. I am currently doing PhD at university in UK within the field of power electronics. However my previous background was related to general Energy Engineering (i had some modules in electrical engineering, however majority was related to thermodynamics, heat transfer, some chemistry, fuels, combustion), thus I had a lot problems in adjusting to the topic (systems modelling, Matlab Simulink, signal processing) and I am still not feeling confident in this field. But straight after graduation I did not have many options and one of my module leaders told me about available PhD position at the same university, where I did my master. I started by the end of November 2017. I participated in a few, very professional progress meetings and all the time I felt lack of confidence in power electronics' field. Thus it was full (extremely) of stress. Since then relations with my supervisor become very cold, however I got some friendships with my office colleagues (but I have a lot of problems talking about my research project being aware that I can easily make a mistake and say sth stupid). Suddenly (like 3 months) ago I noticed Graduate Scheme job offer in the building close to department and I made an application. It's not a typical job as the 'company' is on the campus and project is research-based but with normal salary. I was rejected after assessment day, but suddenly (yesterday) i got an offer. They asked me whether I am still interested, I said yes - waiting for formal contract etc.
I am aware that many people regret decision about withdrawing from their PhDs as it become difficult to come back. But this job is not a typical office one, it's in the lab with manufacturing, processing etc. and even description said that can lead to PhD. What would you do? I am ware that some tough decision will be in front of me - asking university to withdraw me from PhD program, but I know that I will not get better offer than this, maybe ever. Other question - how long time before I have to inform university about withdrawal?

you have way too many personal details in this question, are you not concerned about privacy?

Please don't vandalize your own posts.

In addition to @ΈρικΚωνσταντόπουλος's comment: if you use a SE site then you should be aware that (a) we discourage self-deletion for the purposes of concealment (b) users with sufficiently high reputation can still see deleted questions and answers. So if you didn't want to disclose so much, it would be better not to write all the details in the first place. That said, I think your original question had nothing that would cause me personally to have a bad impression

You say "no one needs to know about my PhD drop as my official graduation took place in 2018" but surely your CV would indicate that your Master's finished in 2017.
Anyway: I can't advise you on whether it is a good idea or not to drop your PhD for industry, since that is a very personal decision. However, I would note that in most UK universities that I know of (and almost certainly in a Russell Group university), the first year of a PhD has a kind of "probationary" status, at the end of which a student would be upgraded to "confirmed" status if all parties are satisfied with the student's progress. Therefore, withdrawing/transferring within the first 10-12 months is a bit easier and less problematic than doing it after 12 months; if the people in your department are sufficiently mature and professional, then they should accept that you have genuine reasons for your change of path.
You also ask how long you have to inform the university of your withdrawal. I would say that you should talk to someone ASAP - if you are not confident doing this with your supervisor, you should try to find the "Postgraduate Tutor" or similar person for your department, or even approach someone in the Faculty of Science. They can advise about practical matters such as terminating your registration as a student - universities nowadays have to be more machine-like in dealing with changes of registration.
BTW, you don't specify if there would be any issues about e.g. immigration status. I am assuming that there are no such issues, since the people who offered you the job should have discussed this with you; but if you are on any kind of visa or study permit then withdrawing from the PhD would affect this, and you would need to talk with the prospective employers about what to do.


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Switching from PhD to MRes, taking a Leave of Absence, or dropping out of PhD due to mental health
If a similar question has been asked before, then I'm sorry; it's just that so far I haven't found much here or elsewhere related to the specifics of my situation. Maybe I'm not using the right key words. Also, I'm posting anonymously because I don't want my university to know (yet) that I'm considering these options.
I'm a first year MPhD student at an English university and I'm considering either switching to the Master's degree or taking a Leave of Absence, all due to my mental health, if not dropping out entirely.
I've had First Episode Psychosis for a couple of years but it's under the control of risperidone, a drug that might be making me feel sleepy. It's either that or I've developed depression, since for the last six months I've felt fatigue, having lie-ins until midday and hours of naps in the afternoon most days, so I'm ridiculously behind on my studies. I've been referred to a psychiatrist (again) and I've been getting therapy via the university.
I absolutely adore Mathematics and I've wanted to do a PhD in it now for over a decade. Thus it's strange that it's gotten like this. I came in strong, having prepared for such a long time, but around January of 2018 my mental health started to decline.
I'm fully funded by a scholarship that was awarded competitively by dint of my academic background (but it's not ESPRC). This makes me feel extra guilty that I'm not doing enough.
My supervisor said recently that I should be doing at least five hours a day but I rarely do over an hour.

What should I do?

I know my health should be my number one concern.
I don't know whether I'm able to take a Leave of Absence with my funding situation.
Switching to the Master's degree is an option that might take the pressure off, meaning I'd get an MRes and graduate in 2019 instead. To be honest I kind of want to do that, since then I could apply for a PhD elsewhere; it's not that I don't enjoy the research project - because I do - it's that the topic was a compromise to start with: I wanted to do algebraic X but ended up doing combinatorial X.
I've had better PhD offers in the past, really, like from The University of St. Andrews, but I missed out on them because I'd had a panic attack during my very last exam, meaning I had to resit it the next year and they were ESPRC funded - they couldn't defer. I might get a stronger offer the next time round.
Then again, I might not get any . . .
I'm scared for my future. If I switch course or drop out, it might result in a bad reference and, in turn, an inability to get onto another PhD programme.

Could I reuse my 2016 MMath degree references in the event of a bad reference from my current university?

I don't think I can stick to the full PhD programme. I doubt I could make the confirmation from MPhD status to PhD status following my next supervisory panel meeting, even, especially if things continue with my sense of fatigue.
Please help.

My goal is to become an academic.

Update: I have taken a Leave of Absence.

This somewhat depends on your longer term goals. You don't need a doctorate to do mathematics, though it helps to have access to other mathematicians. Take care of your health without closing out those goals if at all possible.

@Buffy My goal is to become an academic.

What is an MPhD? I'm not familiar

It's a temporary position before being enrolled onto the PhD programme, @AzorAhai.

Have you been able to get advice from someone in your department about the possibility of intercalating? This might provide a period of recuperation during which you can try to evaluate your options - and it may still be the case that after this period you choose not to return to your PhD

Wishing you all the best. Hope that time allows for some healing.

It is possible that your issues are entirely due to stress alone, or possibly stress combined with burnout. I can't diagnose anything, of course, but stress itself is a killer. Even without other issues you are wise to reduce the stress to manageable levels.
I think that keeping on as you have been will likely be damaging. If your advisor is a sensitive enough person, the place to start would be with him/her. If you are otherwise happy with your situation (as it sounds like you are not) you might be able to stretch out your studies, depending on the project. It might not be unless your project is relatively independent of other things going on in a research group, however. But to do this will require being forthcoming to your advisor and you need to judge whether that is reasonable.
If you can take a Master's without prejudicing the future you might have the best situation, given what you say about not being so happy with your current project. Solve the stress problems, apply elsewhere and start anew. It will take you additional time, of course, but a fresh start with a fresh faculty can be empowering. You will leave some baggage behind. I did this for a different reason and it made a world of difference. A leave of absence may put you back where you are or not, depending on too many factors to deal with here (funding, baggage, ...).
But the bottom line is to take care of yourself and secondarily try not to close out your dreams. You can't know the future, but you can do what you can to maximize your place in it.

This is a good answer overall, but I just want to point out that "if you are otherwise happy with your situation (as it sounds like you are not) you might be able to stretch out your studies, depending on the project" might not be feasible within the UK system. Many universities have a rule of the form "PhD students must submit within 48 months of starting the program(me)" and although there are possibilities for stopping the clock (intercalation) this requires formal interruption of the program(me)

@YemonChoi. Thanks for the clarification. You can't argue with the law, though it seems overly rigid to force actual humans into such a rule. I understand the thinking behind it, of course. This closes off some options for the OP.

@YemonChoi, yes. It is something that requires buy-in and not resistance from the faculty involved. Some will be willing. Some not. Some will be bound by external constraints of the funding or the nature of the research. Very complex, but the OP should have a handle on the local situation.

Sorry, I should have said, when I referred to "faculty" in my now-deleted comment, I meant the Faculty of XYZ who are the organisational level above the department. E.g. my department in LU has to play by the rules imposed by the Faculty of Science and Technology, who are to some extent our bosses. So what I meant is that while it may be possible to go over time, the Faculty of XYZ see this as missing a deadline and might take some action against the Department, e.g. withholding funding or putting pressure on the Head of Department

There's a very clear difference between the three options that you've listed- depending on your long-term goals, the right option should be easy to determine.
If you still want to ultimately complete the Ph.D. program but know that because of your health you simply can't be successful as a student now, then you should try to take a leave of absence for however long it takes you to recover your health. It's a bad idea to try to work through your current problems- you might do so poorly in your studies that you'll be asked to leave the program.
If you've changed your goal and decided that you'd like towards a master's degree, and if you think that you can be successful in the master's program without taking a leave of absence, then you should ask to switch to the master's program.  If you don't think you can be successful as a master's student right now, then you might ask for a leave of absence first.
If you've come to the conclusion that completing a graduate degree isn't one of your long-term goals, then simply withdrawing from your graduate program is probably the appropriate path.
Of course you may not be sure what your long-term goals are.  Figuring this out while dealing with a serious mental health issue is very difficult.  Requesting a leave of absence might provide you with the time you need to figure that out.
You should certainly find out what the consequences of a leave of absence would be for your scholarship.  You'll need to discuss that with the scholarship sponsor.

Note that the UK MRes is not really a separate programme to the PhD; the work involved is the same, the duration is simply shorter. It is usually awarded in cases where, at the progress review at the end of the first year, the candidate is either not up to the required standard for a PhD or themselves choose to leave (maybe they aren't enjoying it, want to go to industry etc).

@astronat I thought that was the MPhil? In my own institution/department, the MRes seems to be the name given to the first year of an integrated 1+3 PhD programme. Although looking online it seems that different institutions use the terms in different ways