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Is a PhD degree from a European university considered equally valuable as one from the US?
I earned my PhD in continental Europe. Except going to a few conferences outside Europe, my network, collaborations and events were all in Europe so I was pretty much living in a European bubble. I am still here, but now that I am in a faculty position I started collaborating with people from everywhere and travel quite a lot outside Europe. As much as I try to avoid generalizing and I am aware that much is field dependent, there are some things I noticed about the general perception of European PhD degrees (and this can probably be extended to universities in general) outside Europe:

Students from Asia (especially from China and Korea) I met said that they prefer going to the US for a PhD, and Europe is only a second option because of less prestige.
When I was considering applying to positions in the US, a few people told me informally that I don't have good chances as those who apply with PhD degrees from US universities, without even considering my CV.

But my experience is conflicting and makes me confused:

I visited a few universities in the US, and noticed that people doing a PhD are treated as students rather than as employees, financially they struggle and most of them have to work on stuff other than research (taking courses, teaching). Frankly the whole system looks miserable to me. In many European countries they would be employed with a decent salary and benefits, focus only on research, have a better travel support, among other benefits. If one was given the choice between the two, I don't understand why anyone would go to the US to do a PhD instead of Europe (no hard feelings) and consider it a better option.
Judging from job applications I get from fresh PhD graduates around the world, on average those with a PhD from the US are not better than others (I am aware that this might be biased because good PhD graduates in the US often prefer staying there).
American PhD theses I have seen are not as good as those from Europe. For example, in the Netherlands most PhD students must publish a few journal papers before they graduate (some have 4-5, and this doesn't include conference papers). The theses are usually of high quality, and are even published as books. Looking at recent PhD theses at elite US universities like Stanford, Harvard, Berkeley and MIT, I cannot help but consider them less good and with less contribution.

This will likely strongly depend on the field, but in general I find that the average PhD experience, student wellbeing and quality of work in Europe is no worse than in the US, if not better. Yet, people worldwide seem to favor US degrees.
Is a PhD degree from a European university considered equally valuable as one from the US?
If not, why is there this gap and lower perception of PhD degrees from Europe?

Depends, my friend who graduated from Jena scored really good job. Other still struggle. Some British are regarded as Ivy league and there are increasing number of US going in Nordic countries for postdoc. They score good assistant professor possition in US after postdocs there. STEM field is flexible. However humanities and social science is very rigid

I think most important thing you need to get job in academia is opportunity. If you are at correct time, in correct place with correct people, you can get job no matter from where you did your PhD. In addition to that, local politics plays very important role in employment options. So if you have PhD from US, you are likely to have more connections in US than if you have one from Europe (and vice versa of course).

I think this has little to do with the quality of the title and the graduated person but it is instead linked to other aspects of general political and economical power, as well the prestige of certain institutions. For the rest I agree with you. At least going back twenty years, a period in which I was in contact with students from everywhere and, beside their own qualities, the preparation was that of high school for imprint. Moreover I have read on an ACS magazine that PhD students struggle even with health insurance in the US. Obviously I could have chosen a PhD in US, but at MIT or so.

In American lit programs, dissertations tend to be argumentative. In Spain, more bibliographical. Broadly speaking, each side sees the other's dissertations and feels they are lower quality due to different expectations. Dunno if that holds up for other countries/fields, but I also would caution the broad labels. Furthermore, PhD/dissertation culture can change. It used to be in Portugal you would work on a dissertation for well over a decade, but now the government has put in a strict shorter time limit that has necessarily reduced the scope and complexity that dissertations can have.

Does this answer your question? Why are US PhDs different from European PhDs?

Europe is not a country.

There's a pretty huge variation in (objective) quality of Ph.D.'s in the same University, with the same supervisor even. And pretty huge variation in perceived quality on top of that. So whatever is any objective or perceived difference in "average reputation", conditioned on U.S. vs Europe, it is less than the variance inside those populations.
What is true, I think, is that people love making value judgements based on perceived ranking of institution and (inside the field) on the advisor. The very top universities in the world, though of course there is not universal agreement what they are, have pretty global name recognition. But once you go below that top tier, awareness of who's who gets a lot less outside of home continent, overall and in many disciplines. Being in North America, I'm likely to know what's 2nd tier vs 3rd tier around here (and I mean that without criticism of either one), while I won't have a clue between 2 Italian universities, for instance. I expect someone there will have a firm opinion about that, but much less clue about University of [U.S. State #1] vs University of [U.S. State #2]. This will result in a "reversion to the mean" bias in my impression of candidates from far away, unless I take the time to look into their specific situation. And since we're all trying to hire "the top", reversion to the mean bias is a negative bias in this instance.
Finally, it's worth noting that the conditions for study at U.S. Universities actually vary widely. Yes, you are more a student than an employee. But (this is 20 yrs ago) I got paid a very decent living stipend in return for teaching 3 hrs a week, rest research; others might have much higher and precarious teaching loads and a less good stipend; and in some fields you pay high tuition and scrape together a living from non-University sources. So I don't think you can generalize meaningfully.

In mathematics a European PhD seems to be more valuable than the US degree as far as the research potential is concerned. The US degree gives you a noticeable advantage when it comes to the consideration of your teaching record in the US. For some reason the American students are viewed as "special" (though after 20+ years of work in the US I failed to figure out what exactly is so special about them: they cheat just as much as we did in Russia, they are just as susceptible to brainwashing as we were (though the content of the brainwashing is different) and they have about the same abilities and levels of motivation on average and in the extremes). So, if you have a US PhD, this usually means that you have a couple of years on your American teaching record as a TA and that is often highly valued nowadays whether justifiably or not.
Another advantage of the US degree (if you want to work in the US) is that you automatically get some connections (through your advisor, conference attendances, seminar talks, etc.) so you are not a total stranger never heard of before when it comes to the job search and, under the usual situation when you are one of several OK candidates in the pool but not a superstar, this gives you a higher chance to get selected not in the first round, but in the second or the third (once I cannot get somebody from the top of the list, I'd rather vote for someone familiar to me than for a grey horse when there is no big difference in credentials).
The US system may look miserable or great depending on the university, your adviser, and the source of funding. If your adviser values you highly and can throw some money from his or her grant into the game, you may have a really great life. If not and you are at some teaching-oriented college, expect to be treated as a cheap work force.
That is (my impression of) the US situation. If you want to end up in some other country, listen to what people from that country say.

I would say, from what I understand, the answer depends on who is doing the valuation. I have seen people claiming certain school/countries has a bias towards phds from the US. I have also heard that it was better to do your PhD in US if you want to stay in US afterwards and it was better to do your PhD in Europe if you want to stay in Europe. It is hard for me to elaborate further without expressing opinions. I think there is some truth to American Universities being more prestigious. They are much more name recognized for one reason or the other. My impression is that American Universities were significantly better as there had been huge brain drains to US and good educational acts such as the G.I. bill while Europe and other potential contenders were recovering from the WW2 and other political instabilities. Also, I would say this is a passing trend. contemporary US politics seem to go in the direction that

makes much harder for underprivilaged Americans to get decent education
makes it very hard for successful foreigners to come into their system
less welcoming for academics to stay (let it be xenophobia or let it be widespread misinformation on factual topics such as climate science or medicine)
makes harder for American Universities to compete fairly with foreign ones on graduate admission

I think what you are observing is "the heart of academia" shifting from US to Europe. European graduate programs are, I think, much better. To my experience, they are free and easy to apply, they do not require meaningless paperwork (for admission), they usually offer good benefits (healthcare, maternity benefits etc.) and many more things that you have listed. There are also some issues with the European system that still make America more of a "hot spot" when it comes to applications. The biggest example is that European system usually only gives stipends to PhD applications (and PhD programs require masters degrees) whereas the American Universities usually offer a way to earn money (even though it is seriously underpaid with little benefits). People who wish to apply abroad after their bachelors can not apply the European programs unless they have sufficent external funding for a masters first. It seems like there are some German innitives dealing with this issue (DAAD, Berlin Mathematical School etc.).
In short, I believe the American Universities and their PhD programs were far better. Hence they have a huge name recognition and prestige attached to their names. However, I think currently they are equal to sub-par with European programs and they are overvalued with very few exceptions. It usually takes a few generations for peoples' perceptions to change. I think overtime, with this trend, American Universities and their PhD programs will be valued more according to their actual quality (at least by foreigners). But in the meantime we have overvalued schools/programs living off their former success. You may also check this answer for my opinion on the subject with expilict examples.

@artificial_moonlet yes but even if the charges exist they are waived for EEA (European Economical Area) citizens.

I'll add my 2 cents and address this point of yours, which the other answers have not really talked about yet.

Students from Asia (especially from China and Korea) I met said that they prefer going to the US for a PhD, and Europe is only a second option because of less prestige.

There are more "big name" and "elite" universities in the US (and the UK) than Europe.  In continental Europe, basically the only places with an "elite" ring to their name are ETH Zurich, ENS, and the Max Planck institutes.  Compare that with all the Ivy League universities, Stanford, MIT, Caltech, Berkeley, etc.  The US also has a huge list of mid-level universities like UCLA, UIUC, Duke, Northwestern, etc. that also outrank pretty much anywhere in (continental) Europe, as far as global name recognition is concerned.  Obviously, this does not reflect that research is better in the US than in Europe, but for various historical reasons we are in this situation where essentially all the "elite" universities in the world are clustered in the US (and the rest of the anglosphere)

In much of the developing world (and even in the more wealthy parts of East Asia), the US is very much still seen as the land of opportunity, to an extent that is perhaps hard for Europeans to understand.  The US is seen as the place to go, if you are talented and ambitious and seek to advance your career.  Canada, Australia, or the UK, would be seen as the next best option.   If you go to Europe, you would be seen as someone who wanted to go to a western country/ a developed country, but couldn't make it to the US.  I am not saying that this view is correct, but that is the way things are.

I think you are sadly misinformed about the quality of European institutions.

@Buffy In case I wasn't clear enough:  these are NOT my own opinions.  I am merely stating what many people in Asia think, in an effort to answer the OP's question.

I got my Ph.D. from a small university in Northern Ontario (Canada).  I have been working in the private sector and know very little about getting into academia.
To the best of my understanding, your likelihood of success is determined by the quality of your publication record.  Then the pedigree of your education comes second.
I've found there is always one-up manship that goes on between Europe and the US - and not just on the basis of academics.  European patents are purportedly harder to get than those in the US.


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What should I do about students' grammar mistakes?
I teach mathematics at the university level. While I do not expect anyone to speak and write perfectly all the time, I do feel that students who emerge from college should not be regularly misspelling words and using poor grammar. So when a student sends me an email using such constructions as "Me and X met" rather than "X and I met," I feel it's almost a duty of mine to correct them, yet I usually refrain, because I don't think the student would understand my pedagogical intent and would instead label me as the grammar police, especially since I am a mathematics instructor. Is there any way I can help students develop better writing skills without becoming despised?

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You can post a statement at the start of class saying that you may on occasion provide feedback to grammar or phrasing mistakes even in such mundane exchanges as email simply as a way to improve the clarity or professional tone (versus colloquial tone) that a students should have as they move forward in their career.
You can generate a "learning toolbox" folder, create a document of "Some Common Best Practices in Communication", and make this available to the students.
You can incorporate grammar and phrasing as grading assessments, leaning on the statement that being able to communicate the approach and results from mathematical analysis with clarity and professionalism is an outcome for the entire math program (and therefore becomes a part of your course).
Whatever path you decide to take, you must be clear to the students when you are making any statements about their grammar and phrasing whether your statements are requirements that the students must correspondingly follow because they are part of your assessment (grading) metrics. By example, the default statement that you might need to repeat a few times throughout the class could be "Unless I say otherwise, any comments that I may make back to you about your grammar or phrasing are simply to help you appreciate how you could communicate in a clearer, more professional manner". Alternatively, should you decide to grade grammar and phrasing in some manner, do so fairly against all the outcomes that your course should provide, do so with at least implicit blessings from a quorum of your department colleagues, and do so using standards that students can access before you start the assessments. This avoids the undue perception that you are unfair or capricious, grading too harshly for grammar and phrasing as only a small part of the course outcomes, being the only faculty member who cares about such things, or using standards that no one else uses.

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Setting expectations in advance is good advice here and for any topic.

The document of best practices could also contain frequently made misstakes and you could add errors you encounter in emails and asinements on the fly

You should continue to refrain from correcting your students' conversational English.  For the reasons you identified, correcting their speech or an informal email is unlikely to lead to a good outcome because it's so personal.  There's a good chance they'll experience it as insulting and intrusive, they won't change, and it certainly won't help your relationship with the student.
But you are free to red pen your students' written assignments with corrections, meaning that if you want to work on improving your students' formal language skills, even a math teacher is free to give essay assignments, e.g., "Tell me your career goals and why you're taking this class."

Agree with this. Also for this specific question, OP put a debatable construction as an example ("me and X" vs "X and I"), where it is not universally agreed that one is better than the other in the context of an e-mail to instructor (especially as an undergrad). If the example OP gave was more like misspelling ("We can proof this theorem"), I would agree with occasional correction, since it interferes with comprehension. But with the given example, I won't suggest even occasional correction, so +1 to this answer. To be clear, when writing paper together, ofc it's fine to correct grammars.

I agree that conversational English (colloquial language) is often best left alone to take its own path. One can sometimes politely go "sideways" by giving return statements with the proper phrasing, e.g. "With regard to your request for an appointment, the graduate student and I will be glad to meet you at ...".

You can proof a theorem by covering it with a damp towel and putting it in an oven set to 85℉ (302½K), or just leave the oven lamp on with the door closed, until volume is doubled.

Actually, it is not clear to me at all why improving someone's writing should be insulting. Of course, some students might get it wrong, I agree. But I would love if people correct my speech as often as possible so that I can progress, but unfortunately most of the people don't do exactly for the reason you stated - they think that I will be insulted.

@Mihail Criticizing someone's writing need not be insulting if the assignment is set up as an exercise in "professional communication" where more formal standards apply.  But I would not criticize their informal email.

@Araucaria it's Gagauz. Why?

@Araucaria well, I don't think so. Nobody is perfect no matter native or second language. So it won't bother me if people fix me in informal talk, because in the future that will help me to be more professional in formal talks.
But let's agree that both of us will be happy, if I never point on your grammatical errors, and on the other hand, I will try to encourage people around me to point on my errors because I believe that prescriptivism makes the text comprehension more smooth and thus makes life easier.

English is not like mathematics in that there is typically not a universally accepted prescription of what is right and what is wrong. In particular, what is considered "right" is highly dependend on social and geographical background. Even things that you have been taught as being unequivocally wrong might be considered perfectly fine in different social or geographical circles.
So unless you plan on doing an extreme deep dive in different dialects of English, what you will end up doing by systematically correcting your students' English is imposing your personal view of what is right and wrong. Doing so can significantly impact the confidence of students speaking/writing English that would be perfectly fine in their social/geographical/cultural background.
Since you are a mathematics instructor and (presumably) do not have formal training in the pedagogy of langauge, you should probably refrain from "correcting" your students' English.

Arguably the essence of mathematics is the use of formal language, and so possibly the mathematics instructor is most sensitive and best situated to attend to such issues.

@DanielR.Collins Arguable the essence of mathematics is the use of formal language, and so possibly the mathematics instructor is the worst situated to attend to issues of natural language.

Of all things, spelling: dependent and language. Too small for me to edit.

Also, part of any proper mathematical education is to learn the sociolect of mathematicians. English that is perfectly fine in students' own social circles may not be fine in the general mathematical social circle. They should learn this at some point, preferably before it has serious consequences.

@Servaes No, mathematicians need to learn how diversify their sociolect. It is exactly this type of exclusionary attitude that is causing problems in diversifying academic circles.

@mmeent This is not something particular to mathematicians; most (if not all) academic circles have their own sociolects. The same is true for industry. Or really, almost any social circle for that matter.

Yes and not accepting people that don’t use it is a problem everywhere.

Ask them whether they want this feedback.

Is there any way I can help students develop better writing skills without becoming despised?

Yes: change careers and become an English professor.
But if that seems like too drastic a step... consider that people who make English mistakes1 fall into two groups:
The first group is people who aren't particularly interested in improving their English2, and who will not welcome advice on doing so. That may be simply because they don't see the value in getting beyond "can be understood", or it may be for more considered reasons; there is a great deal of politics and history tied up in the question of which varieties of English are considered legitimate "varieties" and which are viewed as "incorrect". Even well-meant "corrections" can easily come across as patronising or worse.3
The second group is people who do want to improve, and who welcome advice on how to do so. Many, but by no means all, are non-native speakers.
Both these groups are large. There are enough in the first group that if you make a habit of giving unsolicited advice, a great deal of it will be wasted effort. There are enough in the second group that you could devote your entire life to helping them without ever running out.
That being the case, if you want to volunteer English help to people, it makes sense to focus on the latter group where your efforts will be productive and appreciated.
So ask them whether they want to be helped. At the beginning of the term, you could let your students know that you're willing to provide feedback on written English to those who want it, explaining your pedagogical intent and why you feel this might be worthwhile, and then see who asks for it.
If you don't get enough interest from your own class, well, there are academic editing services who will pay for somebody willing to provide that kind of advice in technical writing. (Some don't pay very well, but since you're looking at doing this for free anyway...)
I sympathise with your position. I used to be the guy who offered unsolicited English correction to everybody, whether they wanted it or not. I eventually realised that it was largely unpleasant for my associates to be getting advice they hadn't asked for, and I also discovered that a side job in academic editing was a great way to get paid and thanked for correcting people. So now I expend my energies in that direction, and everybody is happier for it.

For which, read "make English mistakes" as "do not follow the version of English that I consider to be authoritative".

For which, read "improving their English" as "changing it to more closely resemble my preferred version of English".

For instance, there are far more people who speak Indian English than Australian English. But many who acknowledge Australian English as its own variety would view the quirks of Indian English as "errors".

There are two ways to approach language: prescriptively and descriptively. You are leaning very strongly towards prescriptivism, while most linguists are much more on the side of descriptivism these days. There's always a balance to be found between the two in real life, though.
Prescriptivism is the belief that there is a right way to use a language. Descriptivism is the belief that the way people use a language is the right way, and that all you can do is describe that way. In a way, prescriptivism is like treating the way that language is used as people doing math (they can definitely do things very wrong) and descriptivism is treating them as the math itself, where if you see a conclusion that collides with your world view (assuming the math was applied correctly) you adjust your world view.
There is definitely some room for prescriptivism: learning a language is definitely based on it. And when the meaning of the statement is becoming unclear, there might be a place for it too. Some languages also have things that are very hard for language learners, but native speakers are very consistent about it (e.g. when to use "de" or "het" in Dutch) and in some environments, some prescriptivism might justified.
I don't think prescriptivism has much of a place in a Math class, except in places where the meaning is becoming unclear.
So yeah, especially, for something like "Me and X met", you should continue refraining commenting on it. Or perhaps better: don't just hold back commenting but see it as learning about how language is evolving.

While I respect the opinions of those of you expressing a disdain for prescriptivism, I personally believe that education and discourse would benefit from a return to it.

Excuse me while I expand on what this actually means:

While I respect the opinions of those of you expressing a disdain for teaching made-up rules by rote and rigidly enforcing them, I personally believe that education and discourse would benefit from a return to teaching made-up rules by rote and rigidly enforcing them.

That's all prescriptivist grammar is: made-up rules, which must be learned by rote because there is no logical reason to prefer them over any other rule. Each prescriptivist rule was made up arbitrarily, typically by one person who lived hundreds of years ago, typically a man with high enough social status that enough other people accepted his personal preferences as authoritative wisdom.
So the reason you might think it's wrong to begin a sentence with a conjunction, split an infinitive, or end a sentence with a preposition, is because some long-dead guy preferred it that way so he made up a rule saying you had to write and speak like that. And he wouldn't have had to make up the rule if people were already following it, so all of these rules represented active campaigns to change how other people speak and write, so that it conformed to the rule-inventors' preferences.
Try this: invent your own grammatical rule. How about "never use a semicolon after an adjective" or "each noun in a list must have its own article"? Now imagine yourself teaching your new rule to your students and enforcing your rule when your students email you. Would it be reasonable for you to do this? Surely not, because it is not a teacher's role to impose their own personal preferences on their students. But then what makes it any more reasonable for you to impose the personal preferences of some guy who died 100 years ago? His preferences are no more rational or less arbitrary than yours.
Now suppose all of that hasn't convinced you that prescriptivism isn't beneficial to your students' learning. But how about this: your students are smart enough to know that your grammatical rules don't make any sense, and perhaps they'll think the rest of what you're teaching is just as dubious.

You seem to be saying that all grammatical rules are pointless and arbitrary. But many grammatical rules do make sense, and are agreed on by practically everyone.

@toby544 I'm saying that all prescriptivist grammatical rules are arbitrary. There is also such a thing as descriptivist grammar, which also has rules, but the purpose of those rules is to describe the way language is used rather than to prescribe usage (and specifically, to prescribe a different usage than what is actually used, otherwise the rules would not have been invented).

@kaya3 the grammatical rules might be arbitrary, but having a common ground helps us to have a more smooth and fast reading and concentrate on the semantics of a text rather than on a form.

@kaya3  I think your argument has many holes. "Try this: invent your own grammatical rule ... But then what makes it any more reasonable for you to impose the personal preferences of some guy who died 100 years ago? His preferences are no more rational or less arbitrary than yours." In some cases prescriptivist rules are irrational and arbitrary, but in some cases they are sensible and logical for preserving clarity and common understanding. Also ridiculing them because they were written down or decided by men rather than women is a very weak argument.

@toby544 All prescriptivist rules are arbitrary. Just because something makes sense and follows logically from some premise does not mean it is not arbitrary. It is still completely arbitrary which premises you choose and which arguments you choose to make from them (vs. which you choose to give up on, as OP says about "thou" as opposed to "you"). Here the arbitrary premise is that "me" is an object of a verb, and the logic is that therefore it shouldn't be used in the subject position as in "me and X went". But it's obviously arbitrary to say "me" can only be an object.

You can arbitrarily choose instead the rule that says "me" is allowed to be a subject when it is joined by a conjunction, such as "and". If you then prescribe that rule, you are doing so just as arbitrarily. However, if you are willing to get off your high horse and accept that grammatical rules are only useful insofar as they describe what sounds right or wrong to people who speak the language, then it's not arbitrary to say the "except when joined by a conjunction" rule is better than the other one - it more accurately describes how English is used by people who speak English.

As for "ridiculing them because they were written down or decided by men", you are making an unwarranted leap. I ridiculed them, and I pointed out that they were mostly invented by (privileged) men. The latter is not the reason that prescriptivism is ridiculous. Did you genuinely read my answer and think that I would say that prescriptivist rules invented by socially-disadvantaged women are sensible? Because I honestly can't believe you would infer that from a good-faith reading.

I once read the thesis written by a coworker, in the degree program for Computer Science or something similar to that.  It was full of typos, spelling errors, and grammatical errors, and I found that to be detrimental to the reading of the paper.  Her professor had the policy of "this isn't an English class."  But, that doesn't mean you shouldn't do basic proofreading!  How do I know you don't have similar errors in the math or code expressions?  It gives a rather poor impression, tainting any assessment based on the work being reported on.
I think you need to explain that language varies with the context, and writing up results constitutes a more formal context than spoken conversation.  Even then there is a range of contexts:  spelling mistakes on a hand-written exam can be overlooked, but a typewritten term paper should have been checked before handing it in.
The issue is: does the student consider a quick email to be an informal context that can use colloquial language similar to speaking in person?  Then would a correction be useful because the writer actually doesn't know, or would it be annoying because the writer does know how to use a more formal mode, but was simply not using it here?
Whether it would be fruitful to point out such mistakes in email depends on how well you know the specific student.  Noting it on their work, on the other hand, is appropriate, and they should be prepped with an introduction that their results should be documented in a more formal tone.

I am French and obsessional about the correctness of my beloved language. I make lots of efforts to write and speak properly and suffer when reading emails and listening to some people speaking (including on the national radio).
I am also a father of two children. One of them is like me: grandiose language skills :). The other one is the destroyer of the future of French: not only he communicates as if he was taxed on the nr of lttrs, but in a sentence of eight words he manages to fit nine errors (slightly exaggerating).
Both had the same education, same schools, same everything. Both are very good at maths and sports.
The older one will have an easier life, the younger will suffer because of how he will be perceived - despite all my efforts to improve his French.
So what should you do? Nothing. It would especially be a pity if you marked based on their language abilities, some people just do not get it.

Just do it occasionally, not every time. If someone has terrible grammar then just correct one mistake, not all of them.
Tell them when you first meet them that you think writing skills are important, so you might occasionally correct grammatical mistakes, and you hope they find it useful. You could tell them the second sentence of your question, which puts it very clearly.

Some of the other answers look more thoughtful than mine, so don't take my advice without reading them. Overall, some advice might be suitable in one country but not in another. For example, in some countries, a mathematics instructor may not be free to give assignments that are not about mathematics.

In a properly functioning university, every academic in every field is a member of the grammar police
The pedagogical intent of correcting grammar mistakes is self-evident --- it is to teach and assess proper grammar.  It is perfectly appropriate (and generally desirable) to correct grammar in any field of tertiary instruction, including mathematics and other STEM subjects.  As to whether you choose to do this in activites outside the scope of your own courses (e.g., in emails from students, etc.) that is a matter for your own discretion.  I tend to agree that it is a duty of academics to instruct students outside the scope of coursework, including giving instruction in soft-skills, spelling, grammar, etc.  In any case, in a properly functioning university, every academic in every field should be a member of the grammar police.
As a secondary matter, I think you need to reconsider unreasonable fears about how you will be perceived by your students.  You are there to be their teacher, not their buddy.  Properly functioning universities do not "let the inmates run the asylum".  Students receive instruction from experts who know more than them, and if they "despise" receiving feedback on the quality of their work from said experts, then they are in the wrong place, and are free to refrain from pursuing tertiary education.
With regard to the specific issue of correcting grammar in student emails, I don't have a strong view either way.  It is legitimate to give students instruction on their grammar in this context if you wish, and it may assist them in learning to craft more professional emails.  That is a useful skill for the student to take into the professional world after graduation.  On the other hand, you might decide that this is going beyond the scope of the intruction you want to give, or you might decide that you want email communication to be a forum where students needn't worry about these issues.  Either approach is legitimate and it is within your academic discretion.

By this same claim, the English department should feel free to give instruction on mathematics without paying any mind on whether it's hypercorrect or contradicts the information from professors who actually know what they are talking about. And both should feel free to instruct on electronics and the safe use of medications and the practice of law.
As a pedagogue, if you fail to stick to your own lane, you risk damaging the good work of people who know what they're talking about, and damaging your students grades in subjects other than yours.

The kinds of spelling and grammatical problems one encounters in undergraduate work do not require expert knowledge.  They are simple things that are well within the abilities of any literate mathematician to correct.  By the same token, while an academic in the English department might have difficulties with various areas of mathematical instruction, they could certainly correct basic arithmetic errors.

@DewiMorgan Are you suggesting that English departments are concerned only with grammar and spelling? That's rather insulting at best. Most functioning adults have mastered spelling and grammar; it's not that hard. Just as most functioning adults have mastered basic arithmetic; addition and multiplication aren't that hard either. It doesn't take a PhD in Modernist American Poetry to know whether to use their or they're, just as it doesn't take a PhD in Algebraic Geometry to know how to compute the weighted average of a few numbers.

@Araucaria I derived that from their attempted analogy with mathematics; certainly a mathematics department is concerned only (mostly?) with mathematics. Their comparison suggests that conversely, an English department is concerned only (mostly?) with grammar.

Also, from the discussion under the accepted answer (by Jeffrey J Weimer), it is clear that OP understands the difference between grammar and register, and explicitly distinguishes them (whereas user kaya3 there seems confused by the distinction).

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How long should it take to write a calculus III final exam?
Between inventing problems, agonizing over making sure material is adequately covered and that the problems are reasonable and sufficiently different from the practice exams, and then making a second version, it's taking me upwards of 20 hours total. (I'm just estimating. Didn't get out my stopwatch.) Is this reasonable, or am I abnormal?

what is calculus III?

You can ask questions like these at Mathematics Educators Stack Exchange.

This seems extremely long to me. Maybe some of the methods I discuss in this Mathematics Educators Stack Exchange answer could help, especially copying/pasting similar previous quiz and test questions as discussed in the first two paragraphs of the "2nd post" section and briefly in the "Major tests" paragraph of the "1st post" section.

Take as long as you need to write the exam, but time how long it takes you to undertake it
For creating a new exam from scratch, that doesn't sound unreasonable to me.  Crafting new mathematical problems and solutions from scratch is time-consuming and so is crafting a new exam.  If I recall correctly, I would say I've also taken that long to craft a final exam before.
You should bear in mind that the time taken to construct new questions and form these into an overall exam with adequate coverage varies wildly depending on how much practice one has had and how many times one has taught a course before.  Usually it takes a substantial amount of time to craft initial problems and exams for a course but then this get easier and faster each subsequent time you teach the course.  If you repeatedly teach the same course you may get to the point where you can write a new exam in 2-3 hours instead of 20 hours.  In any case, it really doesn't matter --- being a professional means that we take as long as we need to do our jobs properly, and if it takes a long time then it takes a long time.
In regard to concerns about timing, I'd stress that it's not very important how long it takes you to write the exam but it is important how long it takes you to undertake the exam.  After you have finished writing the exam, give yourself a few days to forget it and then time yourself taking the exam as if you were a student seeing it for the first time.  (Even if you've given yourself a few days you will need to artificially "forget" it as you work through it so that you don't work too fast.  Make yourself go over the thinking time you would have needed if you didn't just write these questions a couple of days ago.)  As a general rule-of-thumb, for an undergraduate course the lecturer should be able to complete the exam in about one-third of the allowable time, and in a graduate course the lecturer should be able to complete the exam in about one-half of the allowable time.  If you are taking longer than that to undertake your own exams then it is an indicator that the allowable time for the exam is too short.

That aspect of the question appears to me to be answered in the first sentence.

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How to deal with blinding when the new paper is a continuation of one's own prior research?
I wrote a paper (P1) which went through peer review and got published. The paper introduced a new graphical user interface (GUI) primitive.
I then wrote P2, which extends P1, turning it into a new class of UI, which had no analogs at the time of writing (and maybe still doesn't, but the window of opportunity is shrinking).
P2 is not just a thin layer on top of P1, it comes with substantial enhancements that are the result of our "lessons learned from P1" analysis + new ideas.
P2 stands on its own, and it refers to P1 as if it were written by other people, per conference requirements. P2 also provides a short intro about P1, such that someone unfamiliar with P1 can still get the picture. It also provides comparisons to analogs of P1, explaining how our approach differs and arguing that our approach is better.
The set of P1 analogs consists of ~5 papers. One is a preprint, 3 are just providing their designs but not including any usability evaluation details at all, or deferring that to future work. This leaves us with one good alternative, which we were not aware of at the time work on P2 started. However, we did refer to this alternative in our related work section and compared it to our own product (there are some ideological differences in our approaches).
P2 explains that we chose to base our work on P1, because at the time of writing P1 was the only artifact of its kind that has gone through formal usability tests and provides detailed results of their evaluation process. Of course, the fundamental underlying reason is that P2 is the continuation of our previous work on P1.
P2 has been submitted for peer review, and a reviewer rejected it, one of the reasons being "it only considers one paper [referring to P1] containing a very similar design".
What is the right way to explain why P2 is built on top of P1 without compromising anonymity?
p.s. note that the reviewer in question seems to have forgotten about the section where we compare P1 to alternatives. It could be that that section is not convincing enough, not well-written - but in that case the reviewer would have said "it is not convincing enough" rather than "only considers one paper". The review is otherwise thorough, I cannot say that I have the impression the reviewer hasn't read the paper fully.

I think the reviewer is suggesting that you should either cite more P1-like papers or that the step from P1 to P2 is too small to warrant a separate publication. Which of the two (or maybe both) may be more clear from the context, hard to judge based on one sentence. Your suggestion to state something like: "It is only based on P1 because we are the authors of P1" probably does not address the reviewer's concerns.

I think you are going in the wrong direction, by trying to hide that you are the author of P1. I think you should have openly acknowledged that you are continuing your prior work and just remove your name from the reference (possibly providing a nameless copy as supplementary material).

@mlk That's a delicate suggestion, especially since the reviewers might be aware of P1 and it's author -- I think there's a chance that this strategy could lead to a desk rejection.

@ralien The reviewer's concerns are (1) you only considered one prior paper, (2) the design from P1 is too similar to P2. Pointing out that you authored P1 does not remove any of these concerns. For (1), you either need to include more papers or better explain why one paper is sufficient. For (2), you need to better explain how P2 improves on P1. There's also a chance that P2 is in fact not a significant enough improvement of P1, and you cannot publish it as is.

@mlk - the conference rules explicitly say authors should cite their prior work this way.

@Louic, the problem is that it is a relatively new area of research. The set of P1 analogs has ~4 items, of which only 1 (besides P1) has conducted a user validation study and published detailed results (the others were just "here's our artifact, user validation is a future step"). This analog didn't exist at the time we started work on P2.

@ralien then that is what you can tell the reviewer.

A lot of these comments should be answers. But write the paper the way you think it should be written and let the editor worry about blinding. That is their job, not yours. But @lighthousekeeper, seems to have something valuable to say here.

@Buffy Thanks! I guess that instead of answering the question, I'm questioning the premise, hence the comment.

@lighthousekeeper, I recognize you didn't answer, but I have the same concerns and wanted to emphasize them to the OP.

@lighthousekeeper, you raise valid points, however I believe that is not the case. I updated the text of the question accordingly. The pool of other papers to consider boils down to one candidate, which was covered in our text. The delta between P1 and P2 is non-trivial, it wouldn't stand on its own otherwise.

@ralien if it's covered in the text maybe it's to easy to overlook. State at a prominent location, maybe in the introduction, that only two relevant papers exist. Regarding the non-trivial delta, the reviewer seems to have a different impression than you. In both cases I still don't see that it's an issue with blinding.


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Stuck without progress working on thesis - worried about failure
I am a student of Indian origin. I am Studying Mechanical Engineering in a local university in north of Germany.
I am writing my thesis in a company. My task is to optimize the throughput of the line. I tried to apply 2-3 concepts on optimization to the output of the line, but my all efforts been in vain. Now I am looking at my computer screen the whole day everyday, hopping hopelessly from one research paper to another but finding nothing. I have only 2 months before my final presentation in front of the company's manager. And in it I have to prove to them that giving me this topic for my thesis was not a waste of around 1500€/month.
I am not able to sleep. For the last 15 days I haven't gone out for shopping or anything. Eating just a little bit of food only one time. Talking to no one, my family or friends. Just sitting all day in front of the screen trying to find some kind of breakthrough. I think i am going into depression.  I am afraid that i will fail this thesis.
I don't know what to do? How to do? Who to ask for help regarding my thesis and topic. I am constantly worried about what if i fail. What will happen. Should I have to go back to India without completing my Master's.
Update 28.09.2020:
Thanks a lot. I have passed my Thesis as well as my masters with satisfactory Noten(Grade). Over all 2.5 Noten for my Master Degree and 2.5(average of Report and Presentation) . Once thanks a lot this wonderful community who gave me the ideas and support in my difficult time.

I hope you prevail. I've been this worried in school and eventually everything will be better and it will all be behind you. I am sorry that you are struggling with so much stress.

Rather than deprive yourself of food and sleep, I would suggest having a good meal, getting some sleep, and try talking to other people.  The reason theses are traditionally done at universities and not done through the mail is that talking to your advisor, professors, and fellow students is considered important for making progress.  Explain your failed solutions to them.  It will definitely be less depressing than going over failed solutions by yourself.

Once a problem is in my head, I find that if I take a break when I'm stuck, do something totally unrelated and think about other things, especially a light leisure activity, often my subconscious will still be processing the problem and I will spontaneously arrive at a solution. Take a long walk, read a fiction book, take a long hot shower, play a moderately difficult video game, get your mind off the problem with a soft distraction for a few hours. And most importantly do something you enjoy to get your mind out of this hopeless state! Its hard to generate ideas when you feel hopeless.

Document the failed attempts you made and try to be as general and thorough as possible to close as many doors as possible. Not every problem has a solution. You will have something written down, will not be staring at a screen for no reason (you will be staring at a screen for a reason) and maybe along the way get the luck and the reward.

Remember: Documenting negative results is also important because it stops people from wasting time, money, and effort on them in the future.

If it can help, I think the first thing I would do in your position is an analysis of the production line timing, to understand how and where time is spent and how it can be recovered. Even if you never come up with an improvement at all, the analysis itself will be really useful in the future. Good luck and take care of yourself, you can do it!

You negative results are incredibly useful information to this company because it tells them that the next time they investigate optimising, they don't need to consider the options you've already tested. That saves them time and money that they can rather spend on other options that may give them the results they would like. So you haven't wasted anything - yes it's awesome to be able to say "I solved this problem", but being able to say "this problem cannot be solved by methods X, Y, Z" is just as valuable, if not more!

But why are you not talking to your supervisor? That is what the supervisor is for.

I'd tackle the problem from the other side. Please, take care of your health and mental well-being. My feeling is that having basic things cared for also helps the research. And yes, talking with your supervisor helps. But taking a break might help even more and is much easier accessible.

Try going for a long walk. Remember your brain is a blood powered machine, and the mere act of walking and getting outside forces you to think of other things, and will maybe help you sleep. Don't be ashamed that you have not made progress yet, (although as others have said documenting your failed attempts is very useful, and a probable indicator that those Germans have their line pretty well optimized already) and be prepared to ask anyone you come across at your work, or any other contacts for help .. which you have already done to some extent by asking here. Some problems are hard, Strength

Your post makes me concerned you are showing signs of burnout. If that is the case, you should seek professional help before it gets worse. Remember: mental health is real health.

you are not suppose to make a breakthrough as a master (or equivalent) student. In your thesis, you will describe your problem, describe potential solutions and your reasons for them, then you try those solutions and report that they didn't work. Done, you are done now. Good job.

Having worked with master's students in an applied research lab, I am fairly confident that you are not expected to come up with a solution that will dramatically change the production process and lead to great profits. Your stipend is not contingent on your work delivering monetary returns; research doesn't work like that.
You are engaged by them to apply your skills, use your time and energy to contribute to their problem. The magnitude of that contribution and its ultimate impact on the company could vary wildly. So steer yourself out of both extreme expectations (that you will fail completely, vs you will create a revolution through your work) and put in your honest, best efforts. Be systematic and document everything. What you see as a negative result or failure now could be a positive confirmation to a more experienced researcher at some time in the future. Don't worry too much about the ultimate outcome, but don't procrastinate either. Keep executing chunks of work, and once again, document everything.
Remember, you justify your stipend through your efforts, not through the outcomes.

I completely agree with this. My master's research failed to produce successful results (i.e. we were trying to create an improved algorithm and failed), and my thesis was still considered a success by my committee.

Your work has not been in vain.
What you have shown to the company are those methods which don't offer improvement, now, they can continue looking at other methods.
While you have had a limited time to look at a few methods, you should write those up and then consider suggesting other avenues that they could continue after you finish. That should sort your thesis issues...

Exactly.  I can't count how many times in meetings people will chime in with 20 different ideas about how to improve a process.  If you can show them concrete data from six of them showing the changes that were made and what the result was, then that instantly gives you a headstart for the next round of experimentation.  It really is extremely useful to have well documented and well tested experiments, even when they produce a null result.

Expectations
First of all, it is important to be clear precisely what the expectations of this project are. If you are a master's student working alone on such a project, there should be no expectation of positive results, especially since you seem to indicate that you have only been working on it for a short amount of time. A Ph.D. might be a different matter, but then you would work on research for many years before writing a thesis.
It sounds to me that you have set a particular bar of expectation for yourself that you feel you are not reaching. Reevaluate if that expectation is reasonable, firstly for yourself, and second by the official standards which you are being held to.
Communication
In such situations, having communication and people to talk to is important. You should certainly be discussing the situation with a supervisor, but do not cut off contact with friends and family and jeopardize your mental health, which will do nothing good for you. You are less likely to make any breakthrough if you are starving yourself and not talking to anyone. Discuss what you are working with someone, anyone, whether they understand it or not, and discuss other things as well! Relaxing can help a lot. Take breaks, go for walks, meditate, whatever helps you to calm yourself and clear your head.
You may be suffering from impostor syndrome
I think you underestimate what you have accomplished and your future achievement potential. There is no reason to give up when you have already put in so much effort. If you genuinely feel that your current position is due to lack of effort, then that's something you can change going forward, but it doesn't sound like that's the case. You've put in the effort, and null results are results, don't dismiss them!
Do not worry about the money
Consider that any entry-level engineer with a Bachelor's degree at your company probably makes at least twice what you are being paid. No reasonable person would consider that they had wasted money paying someone minimum wage to do research on how to improve their production line for a few months, even if they didn't produce a positive result (and no one can expect a single master's student to produce significant result in a few months of work).

+1 for "entry-level engineer[...] makes at least 3-4 times what you are being paid". Also keep in mind that new engineers are often expected to take some time learning and training  before they're "operational", i.e. before they are expected to know what to do next and have little supervision, delivering anything might a whole year depending on area and company processes.

Am entry level engineer in Germany absolutely doesn't earn 3-4 times €1500. 2 times is more likely, before taxes.

Start writing up now what you have. Describe (properly) the results of the 2-3 concepts. The next student doesnt have to repeat them then. If you finish the first (complete) draft and you have time, try to come up with hypothesis why these concept failed. If you even have more time, do numerical experiment to check this hypothesis. Add this to the thesis. Depending on you supervisor send him the individual drafts.
Submit your thesis. You will most likely only fail if you do not submit.
You also have a supervisor at university, s/he is usually the person to ask for advice.

Okay thank you. I am going to write my Professor at the University for advice. I will be needing some help from his side. Supervisor at the company is showing no Interest at all right now. Its like he had left his hope upon me. He is result oriented rather than effort oriented. But now i am not going to go by his strategy. I will do the simulation. Do experiments on it and will complete my thesis. Also i am going to write what problems i faced when implementing the method what i was supposed to implement. Thank you. I love this forum. You all have raised my spirit and hopes.

When you write the email it might also be best to ask for a personal meeting (you seeing your uni supervisor) to discuss these things.

My dad works at a technical university and he often complains that supervisors from companies do not support their students properly; even excellent students struggle with company-led theses. Stop putting any hope into your supervisor and get as much help as you can from the Professor. I like this piece of advice: imagine that your thesis will be read by the next student working on the same problem. That will help you put in enough detail. Fellow students and friends might agree to read individual chapters of your thesis in exchange for reading a chapter or two of theirs and give you feedback.

From personal experience working with people from many other cultures, I know that in some Asian cultures the idea of "failing to complete a task that you have been promised to do" is taken much more seriously than it is in Europe.
As a personal anecdote, a co-worker had arranged vacation time to make a religious pilgrimage. The group were scheduled to depart at 2am. At 11 pm (three hours before departure) the co-worker turned up in the office, attempting to complete some task he had been given before he left!
By pure good luck, there were some senior employees in the office at that hour of the night, having a conference call with a customer in a time zone 8 hours different. The guy was told in no uncertain terms to stop working and go and catch his plane, but he was reluctant to do that until somebody else said they would take full personal responsibility for any consequences of the work not being finished.
To most westerners such a story might seem like pure fiction, but I was there when it happened.
You will not achieve anything by "not going out for shopping, talking to no one, and barely eating" for 15 days - except that you might end up as a medical emergency case because of self neglect. You have made an honest attempt at solving the problem, and you have some results, even though they are negative. That is as much as anyone in the West would reasonably expect from a student writing a thesis.
Put your effort into making a good report of what you have actually done, and the things that you would have liked to do but found too difficult. That will almost certainly be enough for your thesis to be accepted. The risk of lying in a hospital bed and not submitting anything at all is just not worth taking!

1500 euros/month is not a big deal for the companies, they do not expect you to offer them breakthrough solutions.
Negative results are results, report them if you have. That is research
Frame your suggestions as hypothesis and try to critically analyse them. Those optimization methods you mentioned try to address how they can enhance their production and bla bla.
Write the literature review about those papers you are reading and that by itself can be good study and great chunk of your MSC thesis.

Thats a good idea. Thank you for your input. I really appreciate it. So i will write which papers i have referred. Why i felt like that this paper can be useful for this particular problem. What was the reason that i wasn't able to accomplish my problem with th method or concept mentioned.

From your description it is difficult to understand your research question.  How about a little more detail so that the community can help you brainstorm ideas?
Aside from that, you are suffering from tunnel-vision and defeatist mentality.  You are so focused on failing you have become unable to gain traction.  You need to take a few days rest, then come back to the table and try to think about your problem from a new angle. I have found it is useful to read research papers from a different but related topic. Sometimes that reveals new avenues for inquiry.

Thank you for your reply. My topic is find the optimal size of buffer in between station or nos of pallets in the line by considering failures and cycle time of the station. As an conclusion i need to find a mathematical way to optimize tha line so that the throughput or final output of production line increase and implementing the results in simulation software.

This could easily be a simulation study. Vary all the parameters you have to measure. Maybe you’re already optimal. Start by quantifying what you know. An equation that captures current efficiency

I have already done it. But according to discription of my thesis i need to find some kind of mathematical way to do it. There are ways to do it. But they are too complicated to understand. If i will do this by simulation there wont be many things to write about. Is there anyway that i can deregister my thesis and find a new topic start from the scratch. My supervisor is not showing any more interest as before in my thesis. I told him 2months back that this is getting too complicated for me to understand and i won't be able to complete it. Please allow me to give resignation but he said no.

No offense but this attitude suggests you are either not interested in the problem or not interested in a higher degree. ‘It’s too complicated’ isn’t something academic minded students say. ‘It’s not interesting’ is another matter. And, your advisor may seem disinterested as a reaction to your disinterest.

No offense taken. I am here to understand my situation. I love simulation and production line. My academic is also in same area and that's why i have chosen this topic. But for the amount of time i had. In my opinion was to vast or i can be wrong. I have tried multiple methods but due to lack of data or no one to clear my doubt. I wasn't able to implement the methods. He is disinterested in my topic, there was a little bit misunderstanding between us regarding the deadline of registration of my thesis in university. I register it after 2 months of starting and it should be done within 1month.

Look, I am Master student in a very similar field, Aeronautical engineering in Spain, I was going through the very same thing like a month and half ago, and with the help of my mum I realized that sometimes, health and wellness are way more important than academic results.
Professional help will also help you getting over it, a healthy diet, taking care of the relationships and a bit of exercise are essential to maintain your mind clean.
Aside from that, those dealing with students like us expect from us realistic results, this means that they do not expect you to improve drastically the performance of whatever you are dealing with in just few months, but they are rather interested in seeing how you have fought against the problem, and how you have learn from it.
Good luck, hope you recover from this, recognising you might be entering into a depression stage or having anxiety problems is the very first step towards a full recovery.

I can't talk to my mum or dad openly about my current mental situation. They will be worried I am about 10K Kms away from my hometown. But I have started doing meditation and had gone for walk it fells great. Thanks. About my thesi. I currently have blurry vision how will it look like. I will tell my supervisor about it. Lets see what happens and what he comments on it. Thank you for your valuable advice.

If i will do this by simulation there wont be many things to write about.

What we have there is the real problem, your attitude.
If you cared about the subject, rather than only about getting the degree, you'd see many interesting things.
For instance, try a sensitivity analysis. For each factor in your simulation, keep the others fixed and run simulations with that one factor slightly larger and slightly smaller. For some factors, the final result will hardly change, while for other factors the final result will change a lot. That tells you which factors are worth further investigation and which are worth ignoring.
If the only thing you give your employers is a ranking of how important each factor is, they got their money's worth.
But that's just one example.  There really will be "many things to write about".

this is getting too complicated for me to understand

How the universe works is too complicated for anyone to understand.
Yet, despite concentrating on only a few of the most easy aspects of the problem, Einstein is generally not thought of as a failure.
Everything that's complicated is made up of many non-complicated things.
Find some aspects that by themselves are relatively simple and study them, ignoring the rest for now.
Even if you don't complete it yourself, the parts that you have analyzed will help your successors to understand how the simple parts fit together to form the complicated whole.

From the OP's comments, it seems that interest is not the issue attitude is not the problem

Thank you very much. I think i will be going with the simulation. Its model is almost ready it will be completed within two days and then i will start using the method of experimenting and function of  Genetic algorithm which is provided by plant simulation. Thank you so much for the clarification. I think i can know think straight and see my thesis in order. Thank you once again.

The feedback I give below is rooted in my own experience, going through all years of school and employment - when I was always expected to provide something.

I am not able to sleep. For the last 15 days I haven't gone out for shopping or anything. Eating just a little bit of food only one time. Talking to no one, my family or friends.

Well, that is the perfect recipe for disaster. How do you expect your brain to function properly (even, better than properly, since you are trying to do a highly intensive task) without caring for it? Go ahead and eat nutritious food, have good rest, do some exercise, and then things will definitely improve.

Just sitting all day in front of the screen trying to find some kind of breakthrough.

With a under-nutritioned, not rested brain? No way.
Moreover, a thesis (regardless of the level) implies research, and research means that you can (and sometimes MUST) cooperate with other people. Go ahead an talk with anyone who might be able to give you some idea. Even terrible ideas can turn into genius ideas.
Corollary: if you have no benefit of staying in front of the computer, do something more beneficial. Even sleeping is better then torturing yourself uselessly.

I think i am going into depression. I am afraid that i will fail this thesis.

As I said, good food, rest, exercise... It will go away.

I don't know what to do? How to do? Who to ask for help regarding my thesis and topic.

The thesis is not something that you do in a toilet and you must be alone.
A thesis has at least one coordinator (provided by the university).
In your case, there are two coordinators, the other one being assigned by the company.
Each of them will provide you with support according to their area of experience / expertise. Even if they do not push or pull you about the work you do, be PROACTIVE and go talk to them. Tell them about your results until now. Tell them about the problems encountered. Ask for help. Ask to be assigned to other specialists which might have good feedback which you can use.

I am constantly worried about what if i fail. What will happen. Should I have to go back to India without completing my Master's.

Leave the worries until after the final exam passes. How can your brain think about the work you need to do, if you keep it busy with analyzing ways of failure?

Bottom line:

provide the best conditions to your brain to function at maximum capacity;
remove from mind all negative stuff (worries, fears, negative emotions...); they will appear independent of your will, but when you become aware of this, push them out
again;
be proactive and be in regular contact with your supervisors;
be proactive and seek help / information / ideas from anyone who might be able to provide them;

My own case: I am able to ignore all the negative stress before a serious endeavor (exam, delivery of project, preparation for some bigger activity...) - even to the point where I feel too "free". However, once the event passes entirely and the really final results are in, my brain suddenly releases all the energy and the feelings and everything which I ignored previously. Physically I become weak for a few seconds / minutes. On rare occasions, I needed to sit for a minute, to recover.
That works excellent for me, and I would never want to change that. Even though the feeling of weakness is not something to be proud of, it allows me to really concentrate on the task and deliver maximum performance.

Thank you very much. I have started taking care of me. Going for a small walk and doing meditation. I have this things in my schedule.
I am introvert kind of guy, not proud about it. But will ask my supervisor in company to guide me to the person that can help. But the problem is that i got only two months left. Now starting with the new methodology will be difficult.
I will complete my thesis but i am not sure that i will able to satisfy my University and my supervisor. I will get less grades and unsatisfied. But the way i have done my work i deserve that.

You started to change for the better. That is great. At your own pace (you can choose it yourself) keep improving. I wish you luck. Talk to the professor too, he might have some good advice for you.

This is not your fault. It seems like you had a bad supervisor at the company since a supervisor should meet up with you often to discuss your problems and your progress. He should guide you towards a successful thesis.
Now, first of all, talk to your thesis supervisors and tell them about your concerns. You should have one supervisor in the company and one supervisor at your university and you can ask both for help.
I want to add that here in Germany, people rarely fail their thesis. Not because everyone writes a great thesis on great results, but because the threshold of passing is very low. Not only results, but also effort is recognized, therefore:
Get the formal aspects of your thesis right: e.g. no spelling mistakes, good looking images, proper citing, good literature summary, polish your presentation...
If you do that, you will not fail. For the master thesis, negative results are totally acceptable.
Therefore, for your thesis and for the presentation:

summarize the literature
show the methods you have tried, show that they did not lead to an improvement
make educated guesses about why it did not lead to an improvement
if you have an idea, explain what else could be tried in the future

Maybe the company will not hire you, but you will definitely not fail your thesis.

Should I have to go back to India without completing my Master's.

If you really do fail, maybe because of the limited time left to write the thesis, then that is also not a problem at all. You lost some months, but you can just try again with another topic.

If you do not submit you will fail. (but this is basically the only way).

Posting my concerns over here was the best thing I had thought in last 2 months. I think my line is already efficient. But there is always a possibility of optimization.
I will surely write and complete my thesis on time. I will complete my first draft of the thesis till end of this month. I will be more focus on the points you have mentioned above and try to write properly and neatly.  also my colleagues told me that writing is more important than the positive results.  I still got two months and i will do it. No more procrastination.

I think you're focusing on the wrong facet.  Instead of worrying, "How do I optimize their process," think, "What makes an optimum process?" - and then relate that to the existing model.  If it turns out that the optimum way of doing something is what the company is already doing, that's great!.  It's not a failure if the company is already doing the right thing!
Instead of focusing on "But I didn't change anything!", focus on "How can I help identify why things are optimal?"  Because it's entirely possible their configuration isn't due to extremely studious effort, but a bit of trial-and-error.  It's entirely possible that you will give them immense benefit in laying out why their current setup is optimal - they might think it's good simply because they haven't been able to identify anything better, not because they've done rigorous analysis.  And, well, I can guarantee you: no factory line remains unchanging over the long haul - they have to adapt, improve, and reorganize.  Processes change.  Requirements change.  Etc.  So being able relay why it's currently ideal might help them keep that efficiency after a change down the road.
If I were in your shoes, the next path I'd start poking down is their line history.  Did the current setup emerge due to methodical analysis?  Was there trial and error?  You may be able to give a great deal of value in being able to say, "The current line is actually extremely efficient - there aren't a lot of gains to be had.  However, one thing I noticed is that the road to get to the current setup seemed to systemically have a problem with neglect of transport and transit times.  These three areas were shuffled around quite a bit, trying to decrease the time moving parts around the factory, but if that was analyzed up front, it might have helped back when the reorg was required."
(For what it's worth: I worked awhile as a IT Dev in a Tire Manufacturing Plant, and was semi-involved in efficiency evaluations.  So I actually have a bit of experience on this front.  The plant liked it when someone said, "You can shave 15 seconds off the total build time if you toggle the location of these two presses."  They loved it when someone said, "Well, there's a systematic mistake XYZ you're making with this - you can shave 15 seconds off the time if you toggle the location of these presses, and the next time you're shuffling the line, you'll get the same savings if you keep in mind XYZ.")

Thank you Kevin. I will ask my supervisor for line change history in my next meeting with him. Changing postion of the machine can help. I will surely try this in my simulation. Lets see if i can get some postive result.

Thanks a lot. I have passed my Thesis as well as my masters with satisfactory Noten(Grade). Over all 2.5 Noten for my Master Degree and 2.5(average of Report and Presentation) . Once thanks a lot this wonderful community who gave me the ideas and support in my difficult time.


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Uploading adapted research code with missing licence
I adapted some code from a public GitHub repository for a paper, and I have to upload my code to make my work reproducible. I cite the work for which the repository was created in the paper and added comments with a link to the repository in my code wherever I adapted code from it.
The repository includes a readme that states: "If this code was useful, please cite...", but they seem to have forgotten to provide a license.
I assume that this means that it was illegal to even adapt and use the code.
I contacted the authors to ask them to upload a license, but I need to upload my code tomorrow because of paper deadline.
What to do? I assume the risk is very low here because the intent of the authors is clearly to provide the code to the scientific community. They just forgot to add the MIT license. Is it common to just ignore such little legal issues in science?

As a developer, I would open an Issue on Github asking them to add license information.

@BernhardDöbler scientist often don't maintain their code repositories they created for papers. Also this question was about a situation with time constraint. Opening an issues was the first thing I tried, but I did not expect a quick answer

While I agree that the risk is small unless the copyright is held by a corporation, I don't agree that one should make assumptions about unstated author intent. Copyright reserves certain things to holders even when they don't state it. One of the reserved rights is the right to make adaptations and translations.
I can't guess how "common" such assumptions are. I'm pretty strict myself in affirming the rights of holders. If a right isn't granted, it is, in my view, wrong to assume you have it.  I hope that is the general view.
There intent may not have been to allow adaptations. Don't just assume that it is.
You may be able to meet your paper deadline without uploading your code until you have an actual affirmative statement from the original authors. Papers take time to get published.

Thanks for your opinion, but I mean this would already imply that it was illegal to adapt it? Not only to upload it afterward. So my paper is built on illegal code? I think probably many of the 79 papers that cite the work adapted the code, too.

Anyway they just added a license =)


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Publish more in less cited journals, or publish less in more cited journals?
Grad student just getting started here, this question popped in my head this morning when stumbling across a former colleague that has already published a lot but in journals with low h-indexes.
Generally, is it better to publish more articles in journals that are cited less often/have a smaller reputation, or publish less in higher impact journals?
Bonus question : does the answer changes if considering early-career scientists vs later stages?

Publishing in top-tier venues is better than publishing in lower-tier venues. Is that what you wanted to know? Perhaps not: high h-indexes don't necessarily correspond to top-tier venues. Regarding early-career scientists, top-tier venues (should) only accept top-tier work, which isn't typically produced by early-career scientists, hence, such scientists will target lower-tier venues

Oh I thought h-index was an indicator of top/low-tier venues. Just getting started in evaluated journal reputation (and this is outside the scope of this question of course).
I understand that early-career scientists won't publish in the highest impact journals, but then should they aim to publish more in lesser-impact journals or publish less in higher-impact journals then?

"high h-indexes don't necessarily correspond to top-tier venues," but they are an indicator. Regarding "more in lesser-impact journals [vs.] less in higher-impact journals then," it isn't that straightforward: You'll surely do the best you can, some of your results won't be as prestigious as you hoped, some won't be as prestigious but were really interesting to you, others will be better than you hoped, ...

In many cases, it matters more how much your work is cited than how much other papers in the journals where you publish are cited.

Actually, high impact journals get that way from the quality of the papers in them, not the other way around. So, I'd suggest that you look at it a bit differently.
Write as much as you can based on your research. Make the papers as high quality as you are able, with new and interesting results.
Publish them in the "best" journals that will accept them, but "best" means the most appropriate for the subject matter as much as anything.
If you get rejected somewhere, revise and send the paper out again, perhaps to a less prestigious journal.
Over time you will have a "mixed" portfolio. But you will have a good portfolio if you keep at it.
Keep a lot of irons in the fire. You will probably spend the bulk of your effort at one project at a time, but keep notes on other ideas that arise along the way and outline new potential publications as you have the time. If you get stuck on your main project, pick up one of the others.
No, the answer doesn't change. In fact it is the way to get, successfully, to the later stage.

Oh I get the "suggesting to look at it differently" : publishing more in low-impact journals or less in high-impact journals is not "equivalent" - i.e. not a (conscious) choice a researcher has to do, is that it? Work quality would dictate what journals you can publish to, and work volume would dictate the amount of articles you publish? I was kind of relating this (false) dilemma to "is it better to aim for quality or quantity" but I guess that was a wrong way of looking at things according to your answer, because it isn't a choice the researcher will have to do in the first place.

Started as a comment but got too long:
To be practical, I would aim your first papers at "decent" subspecialty journals.  Not Science/Nature (covering all of science).  Not journals covering all of a field (e.g. Journal of American Chemical Society, Physical Review, JAMA).  But the next level down (e.g. Inorganic Chemistry).  They are not hard to get into if you (A) do classic, good, science and (B) write it up clearly and honestly.  [Of course if you discover phlogiston, do a press release and send it to Science.]
In general, the mags from ACS or APS are "decent".  But you will also learn equivalent from Elsevier, Wiley, etc in your specialty.  However, the commercial publishers tend to saturate the waterfront, so avoid their lowest impact journals, new launchings, etc. unless you have no other option.
Usually you can't save up work and then have a better package that (thus) makes it into a higher ranked journal.  Note: sometimes you might be able to self review a campaign of work.  But even in that case, you would be better off having published earlier in the more specialized journals.


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What is the best way to see if my students understood?
What are the methods you use to check if your students really understood the material you presented them with?

What have you tried? What has your research shown so far?

Why is it tagged 'research-process'? Are you interested in teaching or in research about teaching?

This question is much too broad.  The answer is "Assessment" but again that is very broad.

And, give some hint about the field in question.

In theory this is exactly what exams are supposed to do. In practice, that's a different story.

The first thing you need to do is decide what you mean by "understand."

‘Bloom’s Taxonomy’ is a useful tool for classroom educators. Benjamin Bloom creates the taxonomy, which was later revised by Lorin Anderson.
His taxonomy helps educators develop critical thinking and higher order cognitive abilities in students. It provides a framework, or organisation, for classifying classroom lesson objectives.
Bloom’s Taxonomy states that, from the lowest level of cognitive rigour to the highest, a student is required to:

Remember
Understand
Apply
Analyse
Evaluate
and, Create

Changes to the Model:
The term ‘Remember’ was previously known as ‘Knowledge’; ‘Understand’ also replaced ‘Comprehension’; and, lastly, the order of ‘Create’ and ‘Evaluate’ was switched.
Bloom’s Taxonomy is actually a hierarchy, where students must first master the lower levels before mastering the higher levels. The levels represent a shift from simple and concrete thinking to more abstract and complex modes of thinking.
Tables of descriptive verbs have been made available to help educators plan lessons. These tables have been aligned to Bloom’s levels of Taxonomy.

‘Remember’ can be described as to: Arrange, Describe, Order, Name or Memorise terms.
‘Understand’: Explain, Summarise, Paraphrase, Discuss
‘Apply’: Choose, Modify, Discover, Diagram, Show
‘Analyse’: Break down, Calculate, Model, Subdivide, Infer
‘Evaluate’: Critique, Judge
‘Create’: Generate, Plan, Produce

If students are able to apply their understanding and analyse, evaluate or synthesise something from it, this is evidence that they have understood what they have been taught.
Whereas, if they were only to memorise something, this would not show understanding.