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Should I use equations in a research statement for faculty positions?
I'm writing a research statement for a faculty position. I've divided the statement into small sections discussing past, current work, and future directions. I'm wondering if people often do use equations in the statement about their research?
The research is on machine learning (ML). The target is a mathematics department with an ML opening.

You are asking the wrong question. The right question you should be asking yourself is "How do I best explain what I want to say, to the audience I have identified for the thing I'm writing". You will notice that I'm saying this not with regard to a research statement as part of an application, but in general: This is the advice you should consider for everything you write: Identify who your audience is, what they know, what they want to get out of what you are writing for them, and then use that insight to decide how you should write.
As for the specific question: Yes, research statements addressed to math departments typically use formulas. That's because that audience is clearly capable to understand these formulas, and will want to see enough detail that it is worth stating them in concise, mathematical notation.

Thanks. Since you are in the math department, how many pages do they usually write? Is 7 pages too much?

In my institution's current job ad, we suggest 3-5 pages for a research statement. By the way, it sounds like you might want to apply for this particular opening…!

@GregMartin wrong link?

3-5 pages sounds like a reasonable number.

I am applying to Ph.D. programs in Optimization/ML this year, and my advisor suggested that I should "put formulas in my research statement to show people the work I have done". However, I find it hard to do in practice since for formulas to make sense you need to define some notations first, which takes a lot of words. Additionally, I cannot explain my research in a sentence if the readers are not familiar with the background, and using words allows me to gross over some details. I wonder if I should still use equations at the cost of conciseness to please the admission committee?

Sorry, the correct link is https://www.mathjobs.org/jobs/list/20980

"Identify who your audience is, what they know, what they want to get out of what you are writing for them, and then use that insight to decide how you should write." If your audience is the whole department, then you're right that you need to define notation. If your audience is that part of the department that does things related to what you do, then maybe not. In any case, the other universal truth also applies: "Talk to your adviser about it."


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How should I address my two supervisors (one man, one woman) in an email?
I am currently doing a PhD. My professor, which is my first supervisor, is a man. My second supervisor is a woman and works for my first supervisor. The etiquette and the courtesy, at least in my country, requires to greet the female first, e.g.:

Dear Dr. Female,
Dear Prof. Dr. Male,

This sounds wrong to me, since my professor is my main supervisor. Can I greet my professor first without violating etiquette?
My PhD position is located in Germany; my research field is mathematics and I write everything in English.

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Hierarchy beats Gender in Germany
In a professional context in Germany, hierarchy beats gender, at least according to the Knigge, which is an etiquette guide of nontrivial influence. This goes as far as to be gender-blind. Only rank is important.
So you would address the highest ranking person first, in this case, your professor.

Seems reasonable. I will stick with that, thanks.

This answer is correct (+1), but I would like to add that it is likely that your professors will not notice or care who is mentioned first. Of course this depends on the professor(s) in question. Germany can be a little strict sometimes and it doesn't hurt to err on the side of caution (hence +1), but most people I met (including many Germans) would not care at all.

TIL that there is a canonical ordering by gender in German Ansprache?

@TheoreticalMinimum: Some care, others don't. Thus, assuming equal rank, greeting the woman first is the only safe choice if your goal is not to offend anyone.

@darijgrinberg, "Sehr geehrte Herren und Damen" just sounds wrong.

@o.m.: I know, but I never thought to apply the logic when addressing people by their names.

@darijgrinberg: it is rarely needed in practice because it only acts as tie-breaker where importance in the given context is not sufficient. And even there, on the scale of politeness it is only a comparatively small thing - all other things being equal noone will be upset, but you may use it so as to not need to think about the order. Whereas Fr. Prof. Dr. med. h.c. mult. Heinz may be visibly upset if you greet her OA Dr. med. Müller first: importance beats gender every single time.

@o.m. well, better “Sehr geehrte Herren und Damen” than “Sehr geehrte Damen und Herren, liebe Neger”!

This may sound flippant but I’m being 100% serious:
You’re doing a PhD in STEM and addressing your supervisors. The customary form of address is “Hi” or, if you have a very formal relationship with your supervisors, “Hello”; not “Dear Prof. Dr. X” — even in the traditionally hierarchical German system.
Starting an email to your supervisor with “Dear Prof. Dr. X” is distinctly weird and risks coming across as off-putting. If you’re not on first-name terms with your supervisors, simply leave off the name entirely from the salutation (i.e. write just “Hello”, not “Hello Xavier”).

I think "Hi" or "Hello" is far to informal, given the type of question the OP has (if the OP had an informal relation with their supervisors they wouldn't ask it).  I'd only switch to that if I'm on a first-name basis.  Otherwise, I'd much rather prefer "Dear. Mr. X" than "Hi Prof. X" in level of politeness - the latter feels oddly impolite (including, and in particular, in German, which is not the question here).
I also think that your classification of "Hello" as a "very formal" address is rather odd.

@user151413 I (strongly) disagree. OP also said all communication is in English. “Hello” is a completely acceptable, neutral email greeting even when you don’t know the interlocutors at all; it’s fine even in a fairly formal context. Once you know the interlocutor, it’s more than fine. — As for calling your supervisor “Prof. Dr.”, that should probably be addressed in a separate question but in OP’s professional context (PhD in STEM in Germany in English) it’s also very unusual, and if I had to guess I’d say that OP is committing a minor social faux-pas doing so.

@user151413 I disagree. English is English. What parts are you referring to?

@user91988 I disagree. English is not English. There is a local context. In Germany, I would consider "Hi Prof. X" informal. Not from a student writing from the US, but from a student who has been in Germany for a while.  Just as I would find a student who does not know which part of the name is first or last name inappropriate, if they have been around for a while - things might be different in their culture (or english culture, whatever that would even be), but this does not mean you should not try to learn the local standards.

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Although I like this answer – 1. in Germany it's really not that universal to be per du with PhD supervisors. Many professors indeed put all their ≥master students on a “hallo Firstname” basis, but they tend to make this explicit – my master supervisor asked me if I was ok with that. Others do still prefer to stick to the traditional forms.

2. There's at least nothing wrong or weird with using a formal style, even if the professor doesn't care about it. Here in Norway, “hei Firstname” is very much the standard and everybody knows it, yet some of my fellow PhD students (one I have in mind is from Pakistan) apperently aren't comfortable with that and will write something like “dear Prof. Firstname” (in a group chat). I do find this somewhat odd myself, but certainly wouldn't say there's anything wrong with preferring a “polite/professional” mode of conversation, regardless if you're the supervisor or student.

In addition to @PhilYardman's point (which is correct) you also need to consider how directly your email addresses whom. This beats both hierarchy and gender: the importance in the style link in @PhilYardman's answer is evaluated in the context of the email.

The ones who are primarily addressed (To) come first and are always greeted.
So, if you primarily write to your secondary supervisor and "only" keep your supervisor informed of this, the greeting starts with "Dear Dr. Second-Supervisor"

Those who are only informed (CC):

I name them, but usually put that greeting into parentheses. This reminds everyone that more people are reading this email, while also signalling that the ones in parentesis are only notified.
It would also be acceptable to not include them in the greeting.

If there are further people on BCC, they are not named (that would defeat the purpose of BCC), but you may use a generic greeting - depending on the context and content anywhere between "Dear all" and "Sehr geehrte Damen und Herren" [Dear Madam or Sir - but the German version is in plural], or a group address (Say, "Dear supervisors")

I'd adapt the level of formality  ("Sehr geehrter Herr Prof. Dr. med. mult. Supervisor" - "Sehr geehrter Herr Prof. Supervisor" - "Lieber Prof. Supervisor" - "Lieber Herr Supervisor" - "Lieber Vorname") to the customs at your institute and to the likes of your supervisors. This varies a lot between fields, institutes and people...
"Prof. Dr." sounds too formal to me for the STEM fields I work with - but e.g. in the medical field it is AFAIK quite common (and there the position in the hospital would be attached as well "Chefarzt Dr. med.").

I think that these are some useful additional hints, thanks.

To me, "Sehr geehrte Damen und Herren" is more what I would use if I don't know who reads this email (similar to "To whom it may concern") - it would be not something I would use to address a set of known people.

+1 On bcc, you can name people (without defeating the purpose) when the intention is to include them just once, e.g., to thank them for the introduction. (By all means edit to include, if you like.)

@user151413: In this case, while I know who gets the email, one important intention of blind copy is to keep privacy of the readers in BCC. That being said, it is often possible to address them in a more direct fashion. Which is what I often prefer to do. E.g. "Dear study participants". However, that is rather informal - if a more formal address is appropriate, "Sehr geehrte Damen und Herren" is IMHO the way to go.

@TheoreticalMinimum: SgDH is entirely appropriate if you do not know who and how many are addressed. Including the special case of only one person happening to be addressed. You here are all people involved, i.e. it is appropriate even if I know, but the recipients could be multiple people of different gender and the recipients do not know each other. It is not appropriate to use plural if everyone involved knows there is only at most one person of each gender, and it is not appropriate to include a gender that cannot possibly be in the "audience". Sehr geehrte Damen is entirely appropriat

for a formal greeting of a female-only group. It will sound old wannabe playboy only if it is not female-only but a group that may comprise other genders as well (for all I or the recipients know) but is guessed by the wannabe playboy to contain females only, ignoring, say, male elementary school teachers. This is still in the context of BCC addresses where recipients know less about each other than in other contexts. But I think we're getting off-topic/quite down the rabbit-hole.

@TheoreticalMinimum: ah, ok - of course. Yes I misunderstood you. As for Sehr geehrte Damen, as a woman I can only say that do not see anything per se inappropriate with it (nor with Sehr geehrte Herren in the opposite case). Neither pronounced by men nor by women. I'd draw the line of inappropriate where it is only estimated/guessed/expected (as oppoesed to known) that noone of the other gender is addressed. Tone/intent may play a role as well. Of course, deliberate mis-addressing is entirely inappropriate.

Let us continue this discussion in chat.

Concerning your examples, note that in the German Anrede, "Professor" ist always spelled out (in contrast to "Dr."), e. g. "Sehr geehrter Herr Professor X", but "Sehr geehrter Herr Dr. X").

Adapting the level of formality is good, but as a German native I would never use the combination 'Lieber Prof' or any 'Liebe/r' plus last name/Sie Form. From formal to informal: Sehr geehrter Prof Last Name, Hallo Prof Last Name, Hallo First Name, Lieber First Name. The last being very informal, I would not really use that in a professional context. So Lieber First Name is ok if you want to ask the prof to drink a beer after work but not if you ask him to proof read your draft.

@quarague: (also native German) I meet the combination of Liebe/r + Lastname quite a lot in situations where Sehr geehrte/r is too formal since one knows each other, but the question of first names never came up. BTW, I'd put Liebe/r Herr/Frau/Prof/Dr. Lastname as less formal than Sehr geehrte/r Herr/Frau/Prof/Dr Lastname, but as more formal than Hallo Herr/Frau/Prof/Dr Lastname. However, it may be that Liebe/r is the old-fashioned version of new-fashioned Hallo. Where I have been, the scientific staff below professor was always on first name basis. (Above it varied - I'm on perfectly friendly

last name terms with some of "my" professors and institute directors, on first name basis with others.) Also with  technicians, workshop folk and administration this varied on a case to case basis. I'd still say that a PhD student should not assume they're on a first name basis with a technician who has more years of professional experience than the student is old. In my experience there's a non-negligible fraction of such staff that prefers rather formal ways - and I have seen students/scientific staff who were very condescending. I'd avoid Hallo whereever such sensitivities could lurk.

The etiquette and the courtesy, at least in my country, requires to greet the female first

This answer will be a little bit on the philosophical side (probably too much so for some people’s taste), but I’d like to suggest another way of thinking about the question. Instead of asking what is tantamount to “how can I best conform to what my society expects of me in email greetings?”, you can turn the dilemma around and ask “how can I help dismantle antiquated social norms that assign different genders to predetermined roles, and push society ever so slightly in the direction of being more rational and fair?” In other words, put the focus not on being the best follower, but on being the best leader. Granted, the particular social norm in question is a harmless one, but the point is that it’s part of a larger pattern of gender-aware (or outright sexist) norms which are not all harmless.
If you like the idea of looking at things that way, just write the greeting in the way that seems most logical to you based on the content of your email and your relationships with the two co-advisors.
Of course, the specific dilemma in your question is so trivial that it doesn’t really provide much of an opportunity to be a leader. Whatever you do in this specific situation, I doubt anyone will even notice it, let alone know to interpret your behavior as a conscious attempt at shifting social norms (although if they happen to ask you about it, you can certainly explain the thinking that went into your decision). But I’m mainly suggesting this as a mindset to adopt in similar situations that you may encounter in the future, some of which may be more consequential. In other words, the current situation can be used as a kind of training or practice opportunity to get into the habit of challenging stupid social norms — particularly in a low-stakes environment where no matter what you do, it’s almost certain that nothing bad will happen.

I didn't downvote, but I suspect the downvote is due to some people (and cultures) viewing this as not all that trivial. As for me, if it's more than two people, I usually use "All,". If it's two people and I'm not especially concerned, then it'll be alphabetical by whatever I used (if only first names, then alphabetical by first names) and I make sure names in the "To" window are in the same order. If I'm concerned, then I might use something like "X (and also Y)," and put Y in the 'cc' send window and write the email as if I'm talking to X, where X is the primary person for the email.

@DaveLRenfro I was fully expecting some downvotes (precisely for the reason you mentioned), so I’m not troubled by it. Indeed, if there’s a culture that thinks it matters a lot that the woman’s name comes first in an email greeting, all the more reason to challenge this outdated belief.

I haven't downvoted either, but as I wrote in this meta answer trying to dismantle antiquated social norms may cause issues when one has to deal with old timers. Know your enemy first ;-)

@MassimoOrtolano good point. Well, all the Germans I know are pretty sensible people, so I assume my advice is mostly harmless in this particular situation. In others, yes, of course breaking norms may come with a cost and one should take that into account when making decisions.

In a professional context, it is often acceptable and actually useful to address correspondents using their functional title. In this case I think it would certainly be acceptable to use

 Dear Supervisors,

It sidesteps the issue of order and immediately makes it clear in what capacity you address them. This would of course not be appropriate in the context, e.g., of a course that you are assisting with which may have nothing to do with them being your (research) supervisors.

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Teach in a university with a master degree
I don't know if here is the best place to ask that but I'm finishing my master degree in pure mathematics and I would like to travel and know another countries before enter into a doctorate school. In my country with a master degree you can teach in a private university or even in a public university with tenure in small villages or in public universities with 2-years contract in bigger cities.
I would like to know if in your own home country is easy to work in a temporary job as a "professor" or be a permanent professor with tenure in smaller areas with a master degree.
Remark
I know that is impossible to teach pure mathematics with only a master degree, but there are a lot of faculties of civil and food engineer, actuarial sciences, computer sciences, etc... which have logic, calculus, linear algebra, etc... courses, i.e., simpler courses with doesn't necessarily need a PHD professor to teach it.
Thanks a lot

When you say in your home country are you trying to get information on every country or are there some specific countries you are interested in?

@earthling I'm trying to get information on every country as possible :)

In the United States, a master's degree typically qualifies you to teach at the junior college or community college level, and also to teach as a lecturer at the university level.  However, you should know that in mathematics there is substantially less supply of these jobs than there is demand for them.  That is, they are hard to find and don't pay very well.

this is true even in small towns? for example, in my country, in a small town, It just opened right now be a "professor" with tenure with just bachelor.

If I've understood your question correctly, you are asking if you can work with your master's degree as an instructor in mathematics while you are touring the world before beginning a doctoral program.
If that is indeed the case, the answer is maybe, although it would be very difficult to accomplish.
The reason for this is that you would likely have to surmount visa issues, which can make it difficult for foreign nationals to gain employment in another country. You'd probably have to line up the position before you traveled, which would complicate things even further.
However, another thing to keep in mind is that in most universities, the math courses are taught out of the math department—including "service" courses taught for other departments, such as CS, engineering, and physical science. Even in these cases, first priority likely goes to faculty, existing teaching staff, and graduate students within the department. Only if there remains a need for additional teaching staff will they be likely to offer you a contract. And, as Stirling points out, they're unlikely to pay very well. (But then again, I suppose this is just a means of supporting yourself during your travels, in which case this might not be such a bad deal.)

not necessarily, For example, in Europe the countries are very near to each other, I can be in a particular place and from that place I can travel in the weekends.

Even in small towns is difficult? for example, in my country, in a small town, It just opened right now be a "professor" with tenure with just bachelor.

"not necessarily, For example, in Europe the countries are very near to each other": Yes, but first you have to get a job in one of those countries, and this needs to be done in advance. You will almost certainly not be able to just show up in Europe and look for jobs.

"Even in small towns is difficult?" If those countries are in most industrialized nations, and most of the ones in Europe, yes. Again, the job hunt will be made more difficult because you're a foreigner, and therefore will have to go through more hurdles. (In most of Europe, for instance, an employer would likely have to show that you have "unique capabilities" that can't be found in the EU.)

I'm not concern with this, I have other means to get a visa. Another possibility is do a PHD out there.

Fine, but the basic answer is that in most Western countries, a tenured position nowadays requires a PhD. Getting around this in most countries simply isn't an option.

The way you're saying that gives me an impression that even with a PHD I would not have easily even a non-tenured professor position.

In many countries, yes, that's true. You can be a lecturer, but not a professor. (A professor is normally expected to advise graduate students who will receive PhD's!)

Do you know which countries I can easily be a lecturer with a PhD? Thank you for your clarifications.

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What can academics and students do to reduce racism in academia?
I am a postdoc at a university in the UK. Before I came here, a friend warned me that racism is common in the UK. True enough, during my first few months here, I have already received a couple of racist gestures and jeers, including one instance inside the university campus, possibly from a student.
What I would like to ask is this: what part can we play, as academics and students, to reduce such instances of racism in the academic settings?

I come from Indonesia, and being Chinese, racism has been a part of my life. I have seen signs of improvement, but when I grew up, I still remember how it was. I am not complaining about UK, although I must admit that during my study in Norway, I experienced hardly any instances of racism or discrimination whatsoever. I am not asking which country is the worst. I share my experience just to show that it is real. I am not asking how to cope with racism, either. I am asking if there is anything I can do, or we can do, as academic community, to reduce instances of racism in academia, to make it a better environment for an increasingly international academic population. I am citing UK, because that's where I am now; it could have been another country. But wherever I am, I have a part to play in making it a better place.

Is this a case of boat programming ? I.e is there any reason that academia is special and different from other workplaces with regards to racism ?

@Suresh I think there are issues that are particular to universities. See my answer below.

It's not that racism is common in the UK, it's that we have the freedom to complain about it that it seems so prevalent.  Coming from Indonesia you should read this: http://en.wikipedia.org/wiki/Discrimination_against_Chinese_Indonesians and understand that the UK is a free, diverse and forward thinking nation and a university by definition is full of educated people. If educated people from a free, diverse forward thinking country have racist tendencies then I wonder how racism in Indonesian universities is? How many black lecturers were there in your university? I had many in my university..

@Aaron I am sure you are right that UK universities are not markedly more racist than in many other countries. However I don't think that was the question or even a suggestion in any of the answers/comments.  The question as I read it was about an absolute level of racism. In relation to your specific question, of the UK's 18,510 university professors, 85 are black according to the Guardian newspaper.  This figure on its own does not tell me anything about university level racism however.

Professors and lecturers are two totally different things, but anyway.. 85 goes into 18,500 around 200 times, which means for every black professor there are 200 non black professors. This includes Arab, Indian, Chinese and every other classification. While in a completely fair society 200 would be more like 50 (as for every black person there are 50 non black persons) there are many other factors to consider such as cultural differences. I wonder out of those 85 how many are African descent as apposed to Caribbean descent? I'm guessing 90% African at least...

@Aaron, I agree. It is worse in Indonesia, and it is well-known. I grew up with it. The first paragraph is just to share my experience, but perhaps I should have jumped straight into the main question.

@Adipro, I have looked at your university page and some of your work and to be completely honest, you are a real credit to our country (and the human race in general) and I for one am very very very happy that you have come here. Anyone who negatively discriminates against you because of your race is not worth your time. I understand it's tough, an extra obstacle in your way but such is life my friend.

@Aaron I think around 3% of the UK population are officially termed Black or Black British. That would be about 555 professors.  However as I said, you can't deduce anything about university level racism from this simple figure.

@Lembik That classification puts a Somalian, Jamaican and Aboriginal Australian in the same set. These three sets of people could not be more different unless you removed some pigment from their skin. I am talking about afro-carribean black people. And as I said, I would be willing to bet my house that 90% of those black professors are of African as apposed to Caribbean or any other descent.

As Aaron rightly pointed out, UK isn't especially racist, at least not more than most of the other countries. I tend to think that bigger the city in which the university is located, the less is the overall prevalence of racism.
That being said, I am sorry to hear you encountered racism in your profession. I do think that the advice by @Shion is a valuable one, and "Do onto others 20% better than you would have them do unto you to account for the subjective error" should be your modus operandi.

If, however, you find the prejudice by a particular person unbearable, and you have solid evidence of racism, don't hesitate to escalate the matters to your or his/her superiors.

I am not white, but I was born and raised in the UK. Studying computer science I suffered from not being able to understand some of my lecturers accents as brilliant as they were. If I could click my fingers and that guys accent disappeared would I have done it? Yes. Alternatively we could have just hired a native speaker. This is not about race, but about understanding. If a white English lecturer used to whisper all the time, I would want to replace him also.

@Watto, how would that modus operandi translate into a practical situation?

Adipro, what Watto means is (collectively as Indonesians)  treat those people well enough that you will force them to change their opinion of your race.

Could you give some examples, @Aaron?

Examples of how to treat people well??? If you need to ask for examples, I would have to question whether it's due to your race that you are experiencing adversity...

@Aaron, yes, I suppose it is.

@Aaron, to be more clear, let's say someone insulted me because of my race while I was walking home. What I could do, for example, is to stop, approach him, and invite him for tea at home. But how would I know if this person was going to insult me, that I could have done him good in advance? I would say that "Do unto others as you would have them do unto you" is a general command, while "Love your enemies, do good to those who hate you, bless those who curse you, pray for those who abuse you" would be more appropriate in this context.

How come no one discusses the racism of affirmative action, especially against Asians? I can't speak for UK, but there is certainly a lot of that in academia in the United States, especially against Asians.

One of the forms of racism that UK universities suffer from is that they use unfiltered student opinion to inform hiring as well as evaluation of academics.  Academics with foreign accents or unfamiliar (or particularly formal) appearances that the students don't like then suffer.
Interestingly this form of racism is widely understood and largely eliminated in the retail sector where no one would be allowed to choose the race of an employee based on the preferences of their customers.  It is also a form of racism we could easily eliminate from academia if we honestly faced up to it.

I think the point of my answer has been slightly lost (see comments below). The point is that the students are not asked "Can you understand what the academic says clearly?". They are merely asked to rate the academic using a number and are not required to give any reasoning. This hides any prejudices they have and allows the hiring/evaluation committee to use racial preferences without having explicitly to admit they are doing it. The committee just says "They got low student evaluation scores".

Academics with foreign accents I think that a line needs to be drawn here between racism and objective concerns. I, for example, had an opportunity to listen to a middle-eastern researcher affiliated with a UK University at a conference. I literally have NO words to describe how horrible his accent was. If he wasn't reading his power point presentation word for word, I would have absolutely no idea what he was talking about. I wouldn't be able to attend his lectures if he were my teacher.

@AndrejaKo In my experience it's not that the students literally can't hear the words, it's that they don't like the accent. But actually it is more that they don't feel the academic is the sort of person they would want to go to the pub with.  I also think you are on very thin (legal and moral) ice if you allow discrimination based on how familiar a particular accent is to the students.  Can you imagine not hiring someone with an Afro-Caribbean accent in a shop because some of the white customers find some of the words he or she says confusing at first?

Yes, I can. The worker in the shop should be capable of communicating with the customers efficiently. Some accent would be OK in my opinion, but if customers can't understand the worker, what's the point of having a worker? That's why I said that a line needs to be drawn. I can't say that it is easy to make objective criteria for the levels of acceptable accents and I also can't say that the cases you may be thinking of aren't just racism pure and simple. I just want to point out that there could be real problems which should not be dismissed because they can be classified as racism.

Also related video.

I agree with @AndrejaKo that this is more blurry. I studied at UK university where 50% of staff and 2/3 of students (including me) were from outside UK or other English-speaking country (continental Europe, Middle East, Far East etc.) as far as I remember. There was one professor though whose accent no one could understand (even after half of year of lectures). (Just to be clear I don't deny that there might be some cases when it's just a dismissal of 'funny' accents).

@MaciejPiechotka I agree that if someone's accent is so strong he/she cannot be understood that is a real problem. However I have never seen that. What I have seen is people with foreign accents and unfamiliar manners (for example always wearing a suit and tie and being very formal) being given low ratings by students and then those ratings being used in hiring decisions or evaluations.

As @AndrejaKo says, accent can certainly be a concern (how frequent of a concern it is or should be is a different matter entirely). My freshman year of university in the US saddled me with a calculus professor with a particularly thick Hungarian accent, which was very difficult for me to understand (and from what I could tell, my peers had difficulty, too). Combined with a soft voice and illegible handwriting, there was no reason for me to attend the lectures save to find out what the homework would be... which required understanding his accent and/or handwriting. (I dropped that class.)

Andre is right. I've worked with many foreigners who have such bad accents they're next to impossible to communicate with verbally (and more often than not have writing styles that need several iterations of question and answer to understand what they're writing). In an environment where precise and exact communications are crucial that's a severe handicap. It'd be racist to assume everyone with a certain skin colour has that handicap, but can you really blame people whose experience with 150 of such people has been uniform to be wary of the 151st?

<> And the reverse is true as well. I'd expect people in say India to have trouble understanding my accent and take that into account when considering me for a position where verbal communications with locals is essential.

@Lembik: What would you suggest as possible ways to eliminate this form of racism which you have observed?

@adipro  Universities should treat student evaluation the way a commercial firm would treat customer feedback.  That is they can consider specific detailed comments from students that are relevant to the academic's professional abilities but should understand that using raw numerical scores is fraught with difficulties and should generally be avoided.   In all cases, they should apply their own professional judgement.

Recognize that you may or may not have an implicit bias, and examine your own actions accordingly. This also goes for sexism. For example, rather than simply assuming "I'm not a racist!", sit down with something like the list of invited speakers for a conference and genuinely ask "Did we include people of color? Did we include women? Were they more than tokens?"
Like all things in academia, reducing bias benefits from rigorous, systematic thought.

It is really unobvious how to implement this in a lot of fields.  Assuming that the speakers are chosen because of a) their relevance b) the quality of their recent work and c) their availability, I am not really sure what steps you, as a conference organiser, could take in practice to have more people of color or women (for example) that wouldn't be tokenism.  Also, there are many academic fields where women are in the majority so the whole basis seems slightly off.

First clue they're not a token: They were chosen because they were chosen, not because 'Oh crap, we need a minority'. Also, you'd be astonished how many academic fields where women are the majority don't see that reflected in panels, senior researchers, chairs etc. Just because its "unobvious" doesn't mean you, as an individual, cannot sit down and make a considered effort.

I should say "Oh crap, we need a minority" is absolutely standard in UK universities and explicitly built into our internal quota systems for committees and the like.  You appear to be firmly against quotas which is a perfectly reasonably point of view but many are in favour of them.

To avoid tokenism, you need to make sure you include a diverse pool of people from the beginning of the process.  That is, don't wait until you've made a list of people to invite and then check whether it needs tweaking to be reasonably diverse.  Start with a long list of people to consider inviting and make sure that list is reasonably diverse before you start narrowing it down.  (If it isn't already, then you've just found evidence of implicit bias in one of its most stubborn forms - the blind spot.)

Sitting down and ticking boxes "50% women, check. 10% blacks, check. 10% Chinese, check. 10% Indians, check" is in itself racist as well as tokenist. You're explicitly setting targets for minimum numbers of specific groups irrespective of their credentials, excluding better qualified members of other groups based on skin colour or sex. And THAT created resentment towards the very people you want to "be more inclusive for to prevent racism". If I'd see my application rejected in favour of someone from another race with worse credentials simply because of his skin colour, I'd be angry...

@jwenting Where did I suggest there was a checkbox, or indeed target percentages? Self reflection, and if you discover you have invited no X asking why perhaps that is, is not the boogyman you're making it out to be.

@Fomite you're still thinking along "we must have X% of this or that group or we're racist" lines, which is the wrong way to go about it. Consider this scenario I've seen myself: a university department gets 100 student applications, ALL whites. Companies trying to hire those students are by law required to hire 10% blacks. They're of course unable to do so because there aren't any blacks, yet they get fined hundreds of thousands and named as "racist companies" in the press for their "refusal to hire minorities".

@jwenting: Fomite is not proposing "not enough X = racist", but rather "did we fairly consider X?"  If the answer in good conscience is yes, we fairly considered X, then job well done. But given well-documented implicit biases in academia, refusing to even ask the question is unjust.

@JeffE IMO if you have to ask the question, there's already something wrong... The matter should never come up, people having been selected solely on merit by general principle. Thus if you have to ask the question whether you've invited enough blacks (for example) you're already acting on correct premises, as the race of the invitees should be utterly irrelevant. And yes, I do realise that racial quotas for such things are very common.

@jwenting You're denying the existence of implicit bias, which is well documented.  Again, the question is not "Did we invite enough blacks?" but rather "Did we fairly consider the black applicants?"

@JeffE I don't deny it exists. You're however denying the equally real fact of life that quotas exist, and that such questions usually come down to "did we invite enough blacks/indians/women/whatever" rather than "did we pass up a qualified candidate because of his/her skin colour/race/religion/sex". 2 different questions, but often morphed into one with the more insidious one masking and overruling the other.

@jwenting I'm sorry you have such short-sighted colleagues. Please don't assume the same of mine.

@JeffE Your very reasonable point is rather harmed by the existence of quotas where really the question is precisely "Did we invite enough people of type X?".

@Lembik I refer you to the original question.

@JeffE  I apologise if I have misunderstood which part of the original question I am being point to but... for maximum clarity, is your view that quotas are themselves racist?

@Lembik My view is that merely enforcing quotas, instead of actually attempting to address fairness, is unjust and ultimately self-defeating. See http://en.wikipedia.org/wiki/Goodhart's_law .

Do unto others as you would have them do unto you
I believe that this is really the only thing that is in your control.
As the popular song goes, "Everybody's a Little Racist". :D
You cannot change minds of people forcefully but you can only change the way in which you behave.
Having said this, I don't think that I have faced any instance of racism inside the ivory tower in the US. Socially, yes. Academically, no.

Would you please add some examples of changing the way in which we behave?

There are many things we can do, here are some that I have been doing as a foreign student in the US and now an edcuator. And hopefully it would help sparking some more new thoughts.
Aim for promoting diversity, NOT eliminating racism
Politically, you will have a lot more buy-in in organizing a "diversity week" than an "anti-racism week." Racism is not something we can eradicate because it stems from the sense of superiority and difference in power, which will always exist in various degree. And in a personal level, given the same race/ethnicity, one person may think a certain treatment is totally fine while the other one may show a strong sign of being offended because the treatment promotes racism. You cannot win.
In most cases, the more one tries very hard not to be a "racist," the more difficult situations one can get into. A fun example: an African American colleague of mine went to watch 12 Years a Slave with her husband and after the movie ended, a white couple came up and said, sorrowfully, "You people really had it hard, didn't you?" I found that attitude of "We had treated your ancestors so badly that now I am going to make up for it," a bit of, well, racist.
Instead, promote diversity. Diversity is less "silo," it incorporates many other aspects like religions, sexual orientations, races, ethnicities, etc. What's more, it gives us some goal to achieve, something to build instead of some infinite amount of pests to destroy. This new goal will certainly improve your mental health and open up a lot more possibilities in improving the situation.
Promote critical thinking
Embrace critical thinking in both study and teaching. A lot of racism-related phenomena wouldn't pass the most fundamental critical evaluations. Equipping students with this invaluable skill will help them dissect the situation with higher clarity and certainty. Racism itself is very biasing, to the extent that it's nearly hilarious. For instance, if a member of Purple race commits an atrocious crime, the members of Green race tend to attribute the blame to the whole Purple race. While among the Purple race they tend to attribute the blame to the very criminal as a "bad seed," outlier, or isolated incidence. A simple thinking exercise on situations like this one opens up discussion among students quite well.
An additional benefit of being able to critically think on your feet is that you can instantly downgrade an intense racism argument to a logic-based, evidence-based discussion, pointing out the pitfall in their thought process rather than pointing out that they are a racist.
Know your history well, and be ready to listen to other's history
I found myself somehow have become the go-to person when someone has questions about my country. It is, to some degree, a polymorphic racism. Just because some girl is born in Japan doesn't mean she can dance like a geisha, just because some guy is from China doesn't mean he can recite all the characters in the Romance of the Three Kingdoms. However, I do take this consultant role seriously, and try my best to be an ambassador. I tell them the good, the bad, and the disgusting, no reservation.
Don't check your identity tags too soon
This is somewhat similar to that poor answer with like 10 down votes. Sorry to say that but I do agree with that answer to a certain extent. I have never sorted out a clear list of identities for myself. It's not like I am in denial, my identities are always somewhere but I don't tend to flaunt them right at the beginning of an interaction. I feel that in a lot of the times, conflicts happen because we decided that the action or treatment has clashed with our identity a little bit too soon: You said something against penguins, and I am a penguin, so I have to be upset now and punch you in the face. I would, instead, opt for understanding where they come from first. If the situation is non-hostile, I would proceed to explain (with critical thinking and evidence) that it's not always the case, and move on. You can correct the information, you can never correct a person's attitude, they have to do that bit by themselves.
Find an optimal environment
Lastly, it's important that you are promoting diversity in a place that you feel reasonably tolerable and accepting. This whole process of achieving understanding is going to be very long, and it's not worth risking your happiness or even life just because you want to make a statement in a hostile place. In conclusion, don't cave in, be present and remind others of our existence. They don't need to like us, but they do need to know we are here to stay, with a strong will.

+1 for Know your history well. (Plus one for the rest as well, but I can't upvote twice!)

also should be added, fight white supremacy?

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


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Recommended rejection of a paper, but invited to review the paper again
I was recently asked to review a paper, and ended up recommending a rejection of the paper. The journal has, apparently, asked the authors to revise their paper, and the journal has come back to me asking me to review the revised paper. There is, however, no option offered for me to decline. I will likely recommend rejection again as I see that the main problem with the paper is still not addressed. What should I do in this case? Should I write to the journal that I am not willing to review this paper again, or should I go ahead with the review and recommend rejection for the second time? Since I need to provide my comments to the authors again, what should I write while still being constructive? This was my first time recommending a rejection.

It's probably good that you were re-invited to review the paper. It'd be worse to have someone who doesn't see your objection review the paper on the second round and weaken your confidence in the review process!

This has happened to me a couple times. As Peter Jansson has pointed out, what probably happened is that, while you recommended rejection, reviewers 2 and 3 said "it's actually publishable if the authors solve such-and-such problems". This is the kind of situation where a sympathetic editor will make a "revise and resubmit" decision.
In this particular case, you have it easy. Just write a very short review along the lines of "in my first review, I recommended rejection of this article because of [problem that made you recommend rejection]. As the authors have not addressed this problem, I'm regrettably forced to maintain my previous evaluation".
[FWIW, one of the times I reviewed a paper like this, the journal actually ended up publishing the paper in question, with the problematic section still exactly as it was  when I reviewed and rejected it. Go figure]

I am actually able to see the other reviewer's recommendation, which was major revision. But yes, I understand that the editor is free to make his decision.

The suggested comment is helpful, but would you write the same comment to the authors as to the editors? It does sound hard for the authors.

You can pretty up the comment a little: "In my first review, I wrote the following about the paper ... , which I viewed as grounds for rejection. In this version of the paper in X, Y, and Z, my concerns were not addressed. As such, I cannot recommend this paper for publication." Note that as part of the review process most journals require authors to submit a "response to reviewer comments" letter, so you should also check that to see what their justification for leaving the changes in are. In direct answer to your question, I would not refuse unless you're super busy & can't turn in a review.

That the paper was not rejected probably depends on the second (or more) reviewers comments. I would consider it normal to ask if reviewers wish to review the paper again. That you were still asked may be a mistake, most electronic systems would require you to make a decision on that point. There may also be a flaw since a rejected paper would not need a second review and the paper was not rejected based on your suggestion. One can only speculate. I would consider it only fair to write to the editors and state that you are not interested in re-reviewing the manuscript. You could state that your impression is that a similar result would be likely were you to do the job. But, honestly, why you decline the review is no-ones business and you should have been asked before being faced with the task.

Do you not think that a brief review along the lines suggested by Koldito in his answer (posted a few hours after yours) is a better option than just refusing to re-review?

Whether you want to review or not is a personal question. If you have the time and want to provide information to the editors, that is of course gratefully received by the editors. But, there is no better or worse way as see it. Just because you get a request you have no obligation to put more work into it. Most people will, in my experience, provide more than a "No thanks" in a reply.

OK. It's just that, in this case, the reviewer has already put in enough effort to conclude that the paper should be rejected, so the only work remaining to do is to write the one-sentence review, "I recommend the paper be rejected because the reasons I previously gave for rejecting have not been addressed." That seems to be no more effort than declining to re-review.


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Can I cite a manuscript in term paper
I am doing a term paper on the subject of minimum spanning trees algorithms,
I need to cite "Shortest connection networks and some generalization" paper for the prim's algorithm made by Prim, after searching I found a manuscript of the paper.
My question is, can I cite the paper? is this allowed in the citing formats?

If you use the information, you must cite the source. End of story. If by manuscript you mean a pre-print, the final peer-reviewed article will carry more weight so you should access the published article if you can.

(You should cite Jarník's earlier paper describing the same algorithm as well. See also this PhD thesis, which includes a detailed literature survey.)

Like many others you should cite: R. C. Prim, “Shortest connection networks and some generalization,” Bell System Technical Journal, 36: 1389-1401, 1957.

Of course you can cite unpublished manuscripts; this is regularly done in academia. However, the important issue is that you must appropriately indicate that it is an unpublished manuscript, and cite (if possible) where the manuscript was found. This will allow for due consideration of the work in context.


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How do I convert my PhD dissertation so that it can be published as a book?
I have just completed a PhD by research, which I think has some merits in being available as a book (This is, of course, my personal opinion). The research cuts across several fields (e.g. sociology, public policy).
I am wondering what I need to do to take the next step.
In particular:

How do you turn an academic piece like the dissertation (which is written for the examiners) into a book (which is for the general public)?
How do I find publishers who specialise in my field?

Have you asked your advisor about this ? Much like "Don't walk. Run", this could serve as a generic answer for so many questions here :)

What are your goals for publishing. Do you want to make money? Do you want it to count towards tenure? Do you want it to educate the general public? Promote your research?

I want to promote my research to (1) make it widely available and (2) to get some kudos for my CV. Unsure how these two goals could be reconciled.

I mean, a PhD dissertation is written for the examiners (with detailed referencing) but a book to educate the public has a more relaxed and reader-friendly style (i.e. less referencing details etc.).

@JaveerBaker if you start your comments with an @, like I did here, the person will receive a notification. I would say that books for the public don't have a more relaxed referencing style, they just have less detail that needs to be referenced.

There's something wrong if you "write the thesis for the examiners". The aim of thesis is a good thesis, not a good feeling of the examiners. They should be good enough to recognize this. Good theses are written as more general works, proving general knowledge, many references etc., they do not aim to solely present the student's results.

I would second @Suresh's suggestion to consult with your advisor. But their ability to give you useful suggestions depend on whether he/she has experience publishing books (not all professors have books, as many stick to editing books of invited chapter, contributing their papers as chapters, or publishing in journals). If little luck with your advisor, chat with your other committee members. You might want to first check their lists of publications (on CVs) to see if they have any books (series monographs also count). So, do some homework and then consult some faculty you know for advice.

Why do you want the book?

For prestige?: publishers who contact you, don't do any review and charge high prices will only increase your prestige to those that don't know them (and these are probably not those you want to impress).
For dissemination?: why not just put the pdf available (as was already recommended)?. Those who are interested will find it, those who are not will probably not buy a PhD thesis
For money?: I doubt you will really make much out of it.

My recommendation: put it as a pdf on your website / your school's dissertation repository. If you see that lot's of people download it, consider an improved version as book.

In many disciplines (especially the humanities), it is still obligatory to publish a monograph in order to get a PhD. Although, there is shift to cumulated PhD theses with articles in peer-reviewed journals, sociology, at least in Continental Europe, still values monographs.

These questions are very important and I suggest they be considered. In my field, a book published by a shady publisher would only make you look worse as an academic.

-1 In my field it is very uncommon not to have one's PhD thesis transformed into and published as a book. It is also quite important to have the book published by a highly-regarded publisher.

Your first question is quite tricky (to answer and to do). It depends on what you mean by "the public". A version for academics needs little change from a thesis. For students you need to consider how to highlight what can be learnt from your work. For the general general public,  you'll have to start thinking about rewriting perhaps quite a bit, keeping your language accessible and building a narrative. As I am in a different field, perhaps some or all of this is already a part of your thesis.
The second question is simpler, who publishes the books that you read for your thesis?

If your university does not require you to publish your dissertation as a book, I would be very reluctant to invest the time needed to get your dissertation published. I would put the PDF of your dissertation on your own website, making it available to everyone who wants to look at it. I would spend the time needed to rewrite your book on writing more peer reviewed articles. Either by publishing chapters from your dissertation, or by doing new research. I think publications are more important than a book, especially for someone like you who still has only a few publications.

As a partial answer, Springer used to publish (theoretically) outstanding PhD thesis in Mathematics in its 'Lecture notes in Mathematics' as research monograph. However I do not know how many of the published volumes are Phd thesis.  Definitely a (math) thesis requires a lot of polishing and rewriting before publishing.


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What, if any, roads are open to graduate schools for athletes with borderline grades?
My understanding is that colleges with sports programs will admit students with "low end" but not "off the charts low" grades if the respective sports teams want them. By this, I mean grades just above the "cut-off" for admissions, without having to make a special case or allowance for the athlete.
Suppose a certified athlete tried to get into a graduate program with similarly minimum grades. To take an example, suppose the Yankees shortstop Derek Jeter retired, went to college, and got something like a 3.3 GPA which is the cut-off for certain graduate school programs.
What constituencies (if any) might such a graduate applicant have (e.g. celebrity value)? Or are "athlete" slots open only to undergraduates?

Do you row to a world-class standard? If so, Oxford or Cambridge would seem to be a good bet.

@aeismail why not grades tag?

@EnthusiasticStudent: Because the question isn't asking about what to do about the grades. It's asking about how being an athlete can help with master's admissions (to compensate for a weak academic record). You could ask the same question with someone who has a strong academic record, and therefore the grades aren't the dominant factor.

@EnergyNumbers: Are you referring to a Rhodes Scholarship? I hadn't thought about it from that angle but that seems like a valid answer.

I'll answer based on the U.S. (which is where these issues are most relevant, I believe).
There is no special consideration for athletes in graduate admissions.  Undergraduate admissions are handled by admissions officers who often use all sorts of non-academic criteria, and recruiting athletes to play for the university is a specific goal at many universities.  However, graduate admissions is done by departmental committees made up of faculty, and the non-academic criteria that play an important role for undergraduates (well roundedness, extracurricular activities, athletics, etc.) are irrelevant.  If anything, a continued desire to participate extensively in high-level athletics could be considered a disadvantage, since it would take time away from academics.
If Derek Jeter wanted to go to graduate school, I'm sure some faculty would be impressed by his fame, but they would also be careful and skeptical in evaluating his qualifications.  In any case, there certainly wouldn't be a special admissions slot designated for an athlete.

+1. You might find a special scholarship in some places after being admitted, but getting admitted is a matter of convincing them you can hack it academically. You might consider trying again after you can point to some years of real-world professional experience in that field, so you can argue that those grades are no longer an accurate representation of your skills and focus.

To add to Anonymous Mathematician's answer (i.e. no special treatment), I would add that the major reason to recruit athletes at the undergraduate level is you want them to play for you, in intercollegiate sports.  The National Collegiate Athletic Association (NCAA) is the governing body for US college sports, and their rules would normally exclude graduate students from playing.
The NCAA eligibility rules are complex, but a general principle (as I understand it) is that each athlete may only play intercollegiate sports for at most four years in their life.  Moreover, all four of those years must normally come within 5 years of first enrolling in college (as an undergraduate).  A college athlete applying to graduate school would almost certainly have used up their eligibility and would not be able to play for the graduate institution; perhaps for a year at most.  Thus the institution would have no real interest in recruiting them for athletic reasons, since they wouldn't be able to play on the intercollegiate teams.
For Derek Jeter, there's another reason he couldn't play: there is an amateurism requirement, and anyone who has played a sport professionally would likely be ineligible under that clause.  Indeed, athletic programs have suffered severe penalties merely for letting their athletes talk to agents.

In the case of Derek Jeter, I wasn't thinking of his playing. But I thought that there might be some "celebrity" value in admitting him. Apparently not.

@TomAu: My point is that such an admission could be based only on celebrity value, not on any potential athletic contributions.  You could ask the more general question as to whether celebrity is an asset in graduate admissions.  But I think that most departments are very sensitive about their academic reputations and don't want to be perceived as compromising them, which might be the case if they admitted a less-than-qualified student for non-academic reasons.

I would imagine a powerhouse school would make all sorts of accommodations for a star althele who was still eligible. That said, I would think they would try and recruit them into an undergraduate program, but if it took offering someone a PhD, even without them having any undergrad education, I bet they would do it.

@StrongBad: I'm skeptical.  There are lots of powerhouse schools and lots of star athletes every year, and I've never heard of one being admitted into a graduate program without an undergrad degree.

@NateEldredge but those really desirable star athletes don't even bother graduating since they turn pro after 2 or 3 years. If it is not men's football or basketball it is not powerhouse since the team is not making millions for your school.

As a partially parallel case, Imperial College readmitted Brian May to complete his PhD in astrophysics after a 30 year gap.  They might not have done that for someone less famous.


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Teaching classmates who don't put much effort in
I'm not sure where to ask this so I thought I'd ask you here.
I'm in my 3rd year at university doing maths and some of the modules are a bit tricky. I know this and I know the way that I need to work in order to understand the material and pass the exams well. Due to this, I try and spend  a lot of time learning the theory (and recently its been through loads of questions on here). However, what I noticed with some of my friends is that they don't put in the same amount of effort as me (quality wise).
Let's take the example on semidirect products. A lot of us have been struggling with constructing SDP's, however I've tried very hard to learn the theory on them and what the answer's are looking for and what the methods I need to do (and why I'm doing them) to try and learn how to construct them. A lot of that has been on Math.SE but I've been referring to online PDF's and lecture notes as well. Now, my friends know that I put this in and try and learn it and so I can do the work properly, so I think they're trying to take advantage of that.
Today I showed one person how to do a question regarding compositions on Möbius transforms and they just refused to think for themselves. I said "think about it, because I'm not going to tell you what the answer is" and they still wouldn't think (just kept saying "I don't know"), so I didn't tell them the answer. Eventually, after some BIG hints, they got what to do. Now I've noticed people are relying on me to tell them how to construct SDP's (as this is a main question in the exam). From my history, you can see that I've struggled a lot with this and I think I'm close to solving this problem now, but at the same time I can tell that my friends aren't going to learn it themselves. Mentally they've given up and so won't even bother learning it.
My question is this: Should I tell them the answer, when (it is when and not if because I WILL get it!) I figure out how to do it?
I feel bad because obviously I don't want to lie and say "I don't know how to do it" or mess up their exam, but at the same time, I feel like they had the exact same time as me to do this, and the same resources (online, books, notes, ask the lecturer, etc.) yet they still didn't do it. So it's their own fault. Plus, the time it'd take me to teach and explain it to them, I could spend that couple of hours doing my own work. Other examples, revise another module, etc.
What should I do? Do you academics have any tips?
I'm sure you feel like this sometimes when people ask questions on here clearly without thinking about and just expect you to answer it.

This is not an instructor.  This is a student talking about working with his fellow students.  Edited title to maybe make this a bit more clear since most of the answers seem to have missed this point.

In my experience, undergraduate students are a lot like children. They will be as lazy as you allow them to be. They will resist learning. They will resist doing the work and putting in the time. It's human nature...and it is something we, as teachers, must get the students to change.
Were I in your shoes, I would make it clear how to do something (as any teacher should) but I would certainly NOT do the work for them. If they keep saying "I don't know" then you should tell them "It's OK. Not everybody gets it their first time. Perhaps you get it when you take this class for a second time." I usually see my students' eyes open a bit on this one as they see that you are being so compassionate and understanding while still being refused to be manipulated. They also get the clear understanding that they will fail if they don't do the work.
We need to help students. That includes helping them to not be so lazy.

Are you sure about but I would certainly do the work for them?

Thanks...forgot the very important word NOT. I've edited my answer accordingly.

Undergraduate students ARE children. anyone under 30 is really still a child.

No, undergraduates are adults. The people you're thinking of that resist learning and hard work are called humans.

I've run into this situation far too many times.  You're right to be frustrated, and you shouldn't have to devote your precious time to endeavors that bring you no benefit.
Be honest and say something like "I'd really like to help you, but I just don't have the time.  If you'd like, I can share with you the resources that helped me understand it, but I have enough on my plate already."

If you have found certain resources useful in your quest to teach yourself then create a zip file containing the most useful to pass out to anyone who asks you for help. This is YOUR qualification and if you feel that you need to spend more time on your own studies in order to get the grade you deserve then don't waste that time spoon feeding others that are unlikely to be a part of your life 2 days after graduation.
Your facility should have some form of online discussion forum so if you really feel responsible for the outcome of your cohorts exam then create a potted version of your findings on there so that everyone can benefit and you can just direct any people with further queries there - the added bonus to this is that your tutor may well add some clarification to what you write so if you have misunderstood something you also gain from doing this.

+1 for "spoon feeding others that are unlikely to be a part of your life 2 days after graduation".

So I was just going through all my old SE stuff and your "unlikely to be a part of your life 2 days after graduation" is a pretty funny comment. Out of all the people I was referring to in this question, there is not a single one I still speak to, after three years of living, working a learning together at uni. Crazy huh

I do agree partially with Paul, when he says that you can feel frustrated and you shouldn't feel forced to answer every question for them.
Although, I've noticed to be able to explain something, you need to understand them quite well. Even some times, you are forced to attack a problem from different point of views depending on who asks, since the same explanation won't be convincing to everyone. By doing so, you might make a new link between different part of the material, and increase your own understanding. In my experience, helping other students has almost always a net benefice and is a really good way to improve yourself.
Also, as you continue, having only the answer will not get you much further and especially in math where concepts build upon each others, you will have a net advantage over all the others.

I suggest repressing the natural urge of "They don't deserve this, I put in the work. They didn't, I deserve this." as while it may feel good, it won't get you anywhere. You might like to keep enjoying the fact that you have shown you are a hard working independent learner, to feel satisfaction (that you deserve).
Look at if from a Advantages and Costs of teaching
Advantages:

Teaching is a fantastic way to cement your knowledge. (Many say it is the best way.)
This gains you friends, or at least positive acquaintances. These people become your colleges, and industry contacts once you graduate.
Gaining a reputation as a self-less helpful person, can open up doors to you.
Teaching is a valuable life skill, that will help you rise through your chosen career
Improving the quality and reputation of your institution. Obviously this is only a small step, but a journey of a thousand miles begins that way. If it becomes known that "Graduates from X, really know there stuff." then you have increased the value of your degree, wrt getting jobs etc.

Costs:

Time (this is a big one)
Boredom, repeating stuff over an over, one you have completely got it, gets you no where.
Grade Scaling: If your university scales the final grade, so that only your position relative to class average matters, letting other people fail will improve your score (by driving the average down). However you really have to cripple someone (or many people) especially in larger classes, to see any really benefit. It's a pretty cold strategy.

Actions:
Look at the costs vs benefits, and be honest with your fellows, if it is not to your benefit to help them .

if you don't have time, tell them (that you don't have time).
If you have got bord, tell them you can't keep going over the same stuff, you've move on the other things.
If you are a harsh enough person to be motivated by Grade Scaling, tell them "We're in direct competition, helping you is only hindering myself."

"Teaching is a fantastic way to cement your knowledge."  I totally agree here.  But he is complaining that his coeds are not interested in getting taught.  They just want the answers.  If he tried figuring out how to arrive at the answers more easily, it would help him as well.  But a mere game of withholding answers and finally telling them is just a waste of his time.  They don't learn anything, he doesn't learn anything.

I never mentioned anything about withholding answers and finally telling them. (Indeed I do not address anything to do with telling them answers, only todo with teaching them. As what you said is obvious). Perhaps that comment was meant to be on another post?

Ahh you did you misinterpret "if you don't have time, tell them?" I will edit to clarify.

Students who don't put much effort in, do so usually because the material does not interest them. If you can make the material interesting enough to get them excited about it, they will begin to put in more effort.
And to answer your question, should you tell them the answer? In most cases, no, you should not. No one learns by being told the answer. People only learn by coming to an answer using their own mind.
On the other hand, if YOU don't know the answer, then you should first find the answer yourself, and THEN still don't tell them the answer but use the fact you now know the answer to help them reach the same conclusion (without telling them the answer).


text:
I got an offer from my dream graduate school days after starting grad school somewhere else. What should I do?
I have been offered a PhD in a European country which I have accepted and I started attending (my first month). However, just few days after starting here, I got another offer (from a different country) with a subject that interests me more (honestly, it's my dream research topic since UG school).
Internally, deep inside me, I want to leave and pursue my dreams and the things I am more passionate about. However, I feel very bad and selfish to do this. The supervisor at the first institution struggled to get me the funding and to get me rolled in without hustle and this kills me morally.
I accepted the first offer because the second one was still too far and I wasn't given enough time from the first institution to wait for an offer from the second one (the subject is also the closest among all others to my interests).
My engagement with the first institution is still on the trial period, in which case I can cancel and leave without any problem.
I don't really know what to do now. I have good relationships with my current supervisor, and he has faith in me. I also have great relationships with the research team. I just don't have enough courage to tell them such a shocking decision.
I want to get some advice, from a career point of view (should I pursue my dream research topic or not?), is it morally acceptable to do such a thing in my case? And what are the possible implications on my current supervisor and the first institution (impact on funding, impact on his reputation, etc.)? What are the possible problems I could face from a legal and administrative point of view?
In case I am advised to leave, what is the best and the least hurting way to tell the first institution and the supervisor? Should I do it face to face or only by email? How will I return back their material without showing my face?
And the last question, what could be the possible reaction of my supervisor?

You should be selfish.  But also be sure you consider the quality of supervision as well as the research topic.

I am not experienced in the world of academia, but I agree that you should follow your heart. But you should also do your utmost to do the right thing, and that entails sitting down face-to-face with your current supervisor (and anyone else relevant) and explaining to them why you are doing this. They will be disappointed and unhappy but, unless they are a robot, they will understand and honestly wish you the best.

@IanKemp I agree with the sitting down face to face and doing the right thing, but I disagree with the robot. The robot will be rational and understand. It's the humans that may react erratically. :-)

The only thing I would add is that likely "they" (the department) gave you a short time to decide precisely to create this situation. By ensuring that you had to take a decision about them before you had all the responses from other schools, you're encouraged to do the "safe thing." For better or worse your advisor probably did not do this, but your institution did, with the intent of (possibly) getting students who might have otherwise gone to "better" schools. Whether that impacts your "moral" considerations is really up to you.

Are all other things equal, or not? If this was in the world of commerce, rather than Academia, would you hesitate to jump ship?

What are the possible problems I could face from a legal and administrative point of view? - I'm confused.  You earlier said this was a trial period and you could leave without any problem.

I would tentatively suggest discussing the situation with Dream Supervisor before making any moves. They are going to find out eventually, and I think it's better addressed sooner than later. Once trust is lost, it's hard to get back. Plus, depending on circumstances, there may be alternative solutions, e.g. a jointly-supervised PhD.

Have you signed a contract for entering the PhD process? In my university in Germany, this contract asks if you have already previously signed this agreement, and starting a second PhD might be more problematic, as you would have to justify why the first PhD was stopped.

For what it's worth, I would stick with the current PhD place and try to turn it into something good. The grass can usually be made green wherever you are - most things are what you make of them anyway. It's usually best in life to stick to the commitments you've made and have your word mean something - that will generally count for more long-term than any particular career choice at the time. And @RobbieGoodwin, I don't think it makes a difference whether this is academia or commerce - same argument.

Visiting the other group would be my first step.

Having the image of an opportunity jumper is not great either...

Academia is a small world and bad news travels fast. If you do go to Dream School, bear in mind you might have to work harder to earn their trust.

In general, you should go to the dream school.  But before doing so, you should also evaluate your feelings about the dream school and see if they are based on reality, or just a fantasy.  Sometimes people have dreams that don't have much connection to reality.  Will it really make a difference in your life if you go to the dream school?

To be honest, you will not be spared the moral decision. There will be a number of angry and/or unhappy people if you leave, there is no way around that.
The core question is: do you know the other supervisor? Will you be happy with them? Is the added value of the other topic/institution so much more than your current that this difficult and costly decision is worth it?
Because, yes, you will burn bridges. You have now to evaluate whether it is worth it. Do not look just at the institution, but also at the topic and supervisor. They are your key factors.
Should you find out it's not the right thing for you after all, that first institution is closed to you. I do not expect them to want to take you back; it would be unbelievably magnanimous (and lucky, namely that they would have a position and would re-offer it to you) from them to do it - and risky, too.
That being said, keep in mind that, they may be unhappy, but it is your life and your future at stake here.
In the end, nobody can make this decision for you. May your decision be the right one for you.

Thanks, I think all what you've said is fair. There is a complete story behind the second PhD and I've known the supervisor for some time. By enthusiastically reading research papers in our common area of interest (while I was doing masters), I randomly read one of his and contacted him just to comment on few things but ended up keeping contact (which proves why I am more into that second PhD). The research topic is tailored and the institution is internationally recognized.

@Noah Ok, so that point's cleared. Now you have to evaluate whether the added value is sufficient to compensate for the downsides. Of course, you could be lucky and, like Jerlich says, the current team will not hold it against you. Here, it is more likely that an experienced supervisor will may take it more lightly than a younger one, but also an older one can find his inner vindicativeness. It should figure in your considerations. As I say, this is your life, so it should not automatically mean that you should not take the opportunity - just be aware of the cost and whether it's worth it.

This is a great answer; you should allow yourself to be a bit selfish. Ask the reverse question: If your current supervisor was offered their dream faculty position at another university, would they turn it down because their PhD student wanted them to stay. Very unlikely. You may burn bridges, but your own career and happiness are perfectly valid moral counterweights to the offense or inconvenience you may cause your current boss.

To add a personal anecdote to D Greenwood's reverse question, the precise thing happened to me, my supervisor left to a new institution for a dream job shortly after we both started. There was obviously a lot things that needed fixing at the time, but we managed. 5 years down the track it's still a thing I'll bring up occasionally, because, lets be honest, it's an unusual thing to happen, but it's all water under the bridge now, and I've never felt any ill will towards him because he handled it very professionally.

@Phill That happened to a friend of mine. They were able to follow the prof to his far away new uni. Before the PhD could be completed, the prof went to a $$$ job in industry. On the other hand, 57.2% of students drop out for various reasons.

Go to the Dream University
This quote from your question says it all.

Internally, deep inside me, I want to leave and pursue my dreams and
the things I am more passionate about. However, I feel very bad and
selfish to do this.

In this case your dream is achievable. Follow it. Everyone else will be OK. Your supervisor will probably get another student and even if he doesn't he'll have forgotten all about you in a year or so.
In contrast if you don't go then passing up this opportunity will eat at you. Whenever things are hard at OK University you'll be imagining "What if I went to Dream University?". You will also start to resent your OK University supervisor. You've given up a dream to avoid inconveniencing him. How can anyone be grateful enough for that? You only make this level of sacrifice for your immediate dependant family (wife and kids.)
Accept the offer in writing with Dream University, get conformation in writing, make sure that you are in. Then tell everyone at OK university what's happening. Use email for the administrators, and tell your OK university supervisor face to face. They'll all be disappointed, but they'll be OK. They'll probably understand.

It might be nice to add to this answer (which I like the best) a remark reminding the OP of what they themselves said: "My engagement with the first institution is still on the trial period, in which case I can cancel and leave without any problem."

If you have just started the first PhD, I don't think there will be that much anger towards you. At this point there has not been a substantial financial, advisory or intellectual commitment to you. You are not abandoning a project midway through its completion.
Of course, it depends on the PI of lab you are leaving. Maybe they had another student that they could have taken instead of you and your leaving will cost them a spot. If they are a senior person with a big group, your departure will have minimal impact on them. If they are a junior person building up their group they may have more invested in you and feel more animosity. I personally would not begrudge you. If your current advisor is a good person you can just ask them for their advice.

I agree. He could just ask his current supervisor. If he is going to be mad, he can just leave to "dream institution". Other responses could be: "ok, go we know it is a better place and you deserve it". Or he can say "it is entirely upon you, it is your decision" - in this case the current supervisor will be maybe suspicious in the long time.

From a career perspective, it doesn’t matter if one is your dream and the other is not. What matters is:

What is the future of each individual field?
How many publications does a PhD student in each group churn out during his/her PhD, what is the quality? There can be orders of magnitude in differences in quality
How is the general funding? If you need expensive equipment, can you get it?
To how many conferences do students typically go?
And if you are not staying in academia (most likely) what are the job prospects in each field?

That is all from a career point of view (which your question asks). From a work perspective, the 'mood' culture of a group is more important. I also think is it a good idea to follow one's dreams (if you did enough due diligence to see if the reality in the field matches approximately what your dream is; example: like I find biophysics extremely interesting, but the daily work would be standing in a lab, which I can only bear for like once a week, it is too dull for me).

I was in a very similar position as a PhD student (although I hadn't actually started a PhD when I made my choice.) I chose not to go to the dream university. I went for the one with the better quality supervision.
Who knows, I might never even have achieved a PhD if I had gone to my dream university? I will never know because I didn't choose to go there.
This was 17 years ago already. I have always regretted my choice and I will regret it for the rest of my life. I advise you to quit and go to the dream university. Good luck!

Nice to hear people admitting regret and using it to help others.

'My engagement with the first institution is still on the trial period, in which case I can cancel and leave without any problem.'
That answers your question.  There's a trial period.  Use it.
Now, man up.  Talk to your supervisor.  Just possibly he'll surprise you with 'Oh, THAT'S what you wanted to work on?  You can do that here!'    OK, probably not :-) But anyway, be honest.  A reputation for making hard-headed decisions won't hurt your career.  A reputation for unexplained unreliability might.

Reading through comments and answers I think I have a different opinion. First I have to say I commend your moral values and your consideration.
Now, in response to your question, I think leaving the current position is in gray area in terms of morality. After all you wrote a motivation letter and had an interview before getting the position, in which typically people express desire and commitment to the team and project. If situation is horrible in your current position, the answer would be easy but if it is good enough, after getting into the new place you might not be happy(er). I mean, if the supervisor is good, if the team is good and if the university is good enough, I say the outcome mostly rests on your effort. As they say, the grass isn't greener on the other side. It's green where you water it ;)
Now, basically research is driven by enthusiasm and your current supervisor knows that. So, if you discuss with them that your level enthusiasm and endurance is affected simply because you got into this dilemma, they probably find it good for their research team that you leave.
Now my suggestion are in two scenarios:

You decide to stay

You can keep connection with the other (with more prestige) university by:

A. Trying to shift the research so that you can find a overlap
between you research and theirs (if possible, idk)
Getting a research visit position to that university under
supervision of the other prof.
Making your PhD a double-degree (if the rules of both universities
allow, that is totally doable and usually both  university will be
happy)
Making publications together with the other professor
Doing post-doc or second PhD after this one in that university

You decide to leave

Lets be honest, your leave will incur and inevitable damage (though small luckily because you are leaving early). Now, I have a few suggestion:

Discuss with your current supervisor that you know if you choose to stay you will not be resilient in research and motivate as before simply because the thought of other position will eat away you moral, so this is good choice for them as well

Offer small compensation for the money they have spend on you (for example you can say give back saving from your salary so far, the money is not important here, this serves as token of gratitude)

Offer (and seriously follow-up after you left) a collaboration with the current team. If your work load is manageable you can still contribute slightly to the work of previous institute (e.g. reviewing the works, brainstorming, etc.)

After you've left, contact and ask if there is something in their research that you could involve and even better ask if they accept your research visit there.

I think if you do those at least you do not end up burning the bridge completely and also you have taken part of damage and responsibility of your decisions.

I really like the answer. I was also wondering if you could find any common research topics and then try to collaborate with the research group (e.g. interning at the other group for X months doing a publication) and then later on trying to go for a postdoc there (might be carreer-wise even better because the post-doc really decides the further path maybe even more than the PhD). So try to see if any synergy could help you for  a collaboration. But if you still feel that is not enough leave---with all the consequences.

I picked some quotes about decision-making from  a huge list. Here are some that I think might apply to you.
“If you do not change direction, you may end up where you are heading”
― Siddhārtha Gautama
“People will always have opinions about your decision because they're not courageous enough to take action on their opinion.”
― Steve Maraboli
“Sometimes you make the right decision, sometimes you make the decision right.”
― Phillip C. McGraw
“The decision is your own voice. An opinion is the echo of someone else's voice.”
― Amit Kalantri, Wealth of Words
“If you have to choose between any two, first choose time to think.”
― Mohith Agadi
“When you decide who you want to be you'll know what to do.”
― Richie Norton
“A wise man makes his own decisions. An ignorant man follows public opinion.”
― Grantland Rice
“Those who refused to create the kind of life they want for themselves will
end up living their lives for others, and such can only earn them little
joy or many sorrow.”
― Bamigboye Olurotimi
“Those who believe in their brainpower and find a way to utilize it fully often end up making valuable contributions to the world.”
― Dr Prem Jagyasi
My answer
Toss a coin. If you like the answer, go for it! If you don't like the answer, continue tossing the coin until you get an answer you like.

It's possible to keep tossing the coin forever without getting the answer you like :)

@Stuart Golodetz  - I challenge you to prove this by experiment!

Even if I was allowed to bias the coin to always fall one way, I don't think taking you up on that would be a good idea ;)

Remember, the education is about YOU and the product of the education is your abilities and your knowledge.
The educational institutions getting money, professors and other staff being employed, etc, etc... are all secondary effects.
Do whatever is better for you. You are the only one to decide what is better for you. It is you holding the greatest stake.

But this is about sunk cost.

I would take some time to carefully think about it if you can. A good supervision is also important and it can make you really enjoy what you are doing. It depends also on what kind of person you are. I am the one who needs and wishes to be inspired and the topic is really important, but not the only thing to consider. You will interact with people and you have to enjoy the working style of that department. But if you conclude that the other option is a better choice for yourself, than go for it. That´s your career.

Unless you are going to seriously hurt someone in the process, go follow your dream. You will be dead for ever in a few decades.

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