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Can a honours supervisors be called a Project Leader?
I am completing my undergraduate honours.
To do some of my experiments I am considering applying for some supercomputer time.
I would be applying to a external organistation who manages supercomputer for research in this state.
It funded by a partnership of universities (including my own) and the state and national government.
One of the conditions on the application is that the listed "Project Leader" be a non-student member of a university.
Can I (after talking to my supervisor), fill out the paperwork, listing him as "Project Leader"?
Even if his (direct) contributions are minimal, I would still be going to him for advice regularly, so he would be providing leadership on the project.
On the other hand, I would be the person doing all the interactions with the people from the supercomputing organisation.

I assume you have asked your supervisor about that? You certainly cannot book supercomputer time on his name without asking him first, right?

I explictly said "After speaking to him." in the question.

Yes, this is a fairly standard description of a supervisors role in undergraduate research projects. Typically supervisor, despite potentially limited input, are responsible for the research conduct of their students. This might include booking of resources (e.g., labs or super computer time) and ethical approval for research that involves human and animal testing.


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Appreciation email after interview
I had a virtual interview with  a hiring committee in a university for a faculty position.  Do I need to send an email of appreciation after that? If so, to whom I should send? Can I send one email to all interviewer in one email? or it must be separate emails?

If you met with them as a committee, then I would send a quick email to the committee chair. It can be very minimal, thanking them for their time and expressing your continued interest in the position.
Probably not totally necessary, but can signal interest, which is occasionally useful if you are perceived as a candidate who may have lots of competing interviews and offers. It reiterates you are serious about their particular opportunity.

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Forgotten Documents in Grad School Applications
I am applying for grad schools in the US for mathematics PhD programs.
I studied in Ireland and as a result, was asked to upload English translations of all documents.
My degree certificates are in Latin. I have only just realised this now, and it's a week past the submission date for the schools I applied for.
I have ordered an English translation, and intend to send this on when I receive it.
Is this something that can affect the outcome of an application? If so, is there anything I could do to improve the situation?

Is there a reason you cannot ask the program?

Also, could you do something differently if somebody says it can affect the outcome?

I think that if someone is interested in you, they will ask for translations at a later point. Also, as suggested, why not ask them via email?

If the institutions you're applying to are anything like mine, none of the mathematicians evaluating your application will care about a late translation. The only possible problem that I can see is that a clerical worker might not pass your application on to the math department until the translation arrives. Then the mathematicians will sigh, say something like "Bureaucracy strikes again!" and consider your application along with the others as if nothing had happened.

You should contact the institution(s), apologize for misunderstanding requirements and offer to send the proper documents when available. Mention that you have requested them. Ask if there is anything else you can do and whether this will affect your application.
It is impossible to say what will happen but it is all you can do at the moment. I suspect that it can be resolved, but can't guarantee it.

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Who chooses the number of reviewers in a submitted journal?
The question is very simple: Who chooses the number of reviewers that will peer-review a submitted paper on a journal (for Round 1)? Also, if there are more than 2 reviewers (2 I believe is the mainstream), does this show something about the quality of the journal? Does it show something else/more that I don't "see" right now?

Please answer my update, if you can...Thanks...

You should make a new question, posts on SE are supposed to contain only one question. But I can tell you that it depends on the journal. Sometimes you have access to all reports immediately, but for others you only see them when the authors submit their revision.

Please keep your posts focused on a single question, and especially don't add additional questions after receiving answers. Also, the added question has been addressed before: In peer-review, is it common for a reviewer to be shown and asked to comment on other reviewers' reports?, Does a reviewer get to know comments from previous reviewers?

Ok ok! No problem, I opened new question...

The handling editor of the paper does this. In some cases this is the journal editor (or one of them), in many cases this is the associate editor nominated by the main editor. It could also be a Special Issue guest editor.
Note that this is a random process. Although some journals officially require three reviewers (or even more), it is always hard to predict how many reviewers will agree to review and then actually do the work, and the "journal quality" is probably only a small factor in this.
So a journal in which regularly two reviews are collected, can occasionally have three or even more just because the handling editor asked more people having in mind that one or more may drop out (and then it doesn't happen). Or further reviewers are invited because a received report is not very informative.
Also an editor of a journal that aims for three or more reviewers may decide to be happy with two if at a certain point in time two reports are in and there is reason to believe that all further invited reviewers have dropped out so that going for three would add substantial waiting time; or if the two reports available give a clear picture already. An editor may even decide that a single review already "kills" the paper making a convincing and strong case against it.
In principle you could think that a "three (or more) reviewer policy" is better for a journal quality-wise, but of course this may also lead to delays, and may often not be consistently applied. So I wouldn't necessarily assume that really good journals will always provide three or more reports.

Note that the journal itself, likely through an "editorial board" sets a policy for the desired number of reviews. As this post explains it isn't always possible to adhere strictly to that policy, both because of the nature of reviewers and the nature of papers.


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Is it appropriate to invite a reviewer to collaborate on the paper they reviewed?
My manuscript underwent peer review at a big journal. The manuscript was revised but ultimately rejected due to language issues, even though the reviewers acknowledged the study was of good quality.
I am wondering whether it would be appropriate to write an email to the reviewers, or in my case, the editor (since the review was single-blind), to inquire if they would be interested in collaborating with me to improve the paper?

The answer to the question in the title is yes, but the problem with your proposed course of action is that helping you fix languages issues in a manuscript does not entitle them to be co-authors.

I see no problem with this --- in fact, I think there are often situations where the reviewers would make good coauthors if they are interested in the paper.  You should note that reviewers may be quite senior in the field in some cases and may be uninterested in acting as coauthors, but it is worth a try.

If the reviewer(s) did not disclose their identity, it is already a sign they do not want to be pursued further about the paper under discussion.
My advice is to read again carefully their review and take their message literally: do a thorough review of the language/style in the writing of your study, the material is of good quality, but it is poorly communicated.
The reviewers are expert in the field, they may have interest in supporting and cooperating towards expansion of the scientific knowledge.
However, they clearly do not see a need to improve the scientific quality of your work, so they are unlikely to contribute.
If you nonetheless contact the editor, take into account that the editor may have good reasons to shield their pool of experts from authors interactions, at least but not at last to avoid undue influence (authors may be well known influential professors and reviewers may be temp postdoc on a thin line...).

In most blind reviewing systems that I know of, professional ethics FORBID reviewers from disclosing their identities (to prevent the author from trying to influence them). So, I do not agree that anything the reviewers say would suggest anything positive or negative about their openness to such collaboration.

@Tripartio In most blind review system I am familiar with, the reviewers have the right to anonimity. It is not an obligation. Reviewers can renounce to this right anytime they want, and they sometimes do, after final decision (like in this case).

I guess we operate in different academic communities. But I think my view here is probably more prevalent (e.g., see the accepted answer here: https://academia.stackexchange.com/questions/14358/in-single-blind-peer-review-can-you-reveal-your-identity-without-the-editors-c). Regardless, I doubt that it is very common in practice that reviewers would take the time to sign their names even after peer review is over, even if it were considered acceptable. I am genuinely curious: is that actually a common practice in your discipline?

@Tripartio "sometimes", I never said it is common. But it is a possibility. And one that is given by the reviewers to the authors. If the reviewer wants to show an opening to collaborate/discuss in person, they provide their identity at the final review.


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Recommendations regarding publishing 'folklore' results in math
I've recently obtained some results which I have not found in the literature explicitly. Namely they are hinted in certain published literature, but very shortly and not in a very constructive sense.
After consulting with several people with experience in academia, I was told that it is frowned upon to publish these results more explicitly. I therefore decided to not write these results out properly.
Following this experience I was wondering whether there is a requirement when working on new projects to verify whether certain results are 'folklore'? Should one consult with an expert in the field before trying to publish results? Is it frowned upon to write something out explicitly, while trying to extensively discuss the result, and upload it to the Arxiv?
I should mention that some of my obtained results seemed not known by people in the field in my working group. I also wished I could refer to some of these properties in related topics.

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I don't think this is a problem per se, but you need to have a good reason for doing so.  For example, if your paper uses folklore result X in some interesting way, then it is perfectly sensible to say "although X is well known, we were unable to find a proof in the literature and provide one for completeness".
However, writing a paper that just says "we provide a proof of the folklore result X" is a waste of time: if it's a folklore result, that means other people know how to prove it but don't think it's worth publishing on its own.

"if it's a folklore result, that means other people know how to prove it but don't think it's worth publishing on its own." ─ This reminds me of the joke about two economists who walk past a $20 bill on the ground, one saying to the other: it must be fake, or somebody would have picked it up by now.

"that means other people know how to prove it" You forgot to add a quantifier some before the adjective "other". Sometimes that "some" is just one and occasionally that one is dead already or, in more optimistic scenario, does not remember the proof. So I would say "explain in your papers everything that you cannot quickly find a good and accessible reference for". Wasting your time is irrelevant. Spare the time of the readers, or don't communicate at all.

@fedja If it's just one person then it's not "folklore", it's "an unpublished result of X".

He-he. That is only for the first few years. Then, if it really starts circulating around, almost nobody knows about $X$ any more than you know the exact source of any particular rumor on social media. All you can say is "I got it from Agnes" (if you remember that old Tom Lehrer song).

+1 for the first paragraph. The second paragraph is fine too, but I hate this reality of academic culture—it's sloppy science (not to mention even experts are often inaccurate about what they can easily prove).

I'd argue it's important to call out any folklore relied on in this way, as it doesn't mean anyone knows how to prove it: just that they think someone once did. How many hundred thousand people died of covid because of the folklore belief among epidemiologists that particle sizes larger than 5 microns would fall to earth rapidly and not be contagious except through contact? (see: https://medium.com/history-of-women/the-woman-who-helped-debunk-a-fatal-covid-19-misconception-a5679b96eb5d).

Like Greg, I agree with the first paragraph; however I rather strongly disagree with the second (at least as a general rule).  I remember an big folklore result for 30+ years in my field in my area that many people "cited" but I'm not sure anyone ever knew the full details of how to prove it (and the authors got lazy).

I gently disagree with some of the views expressed in this thread. If a result is "folklore", that already goes to show that it is natural and relevant, others wouldn't have thought about the question before. Moreover, not everyone roams the common rooms of the seven departments where this folklore knowledge is passed on from person to person, so there is genuine value in writing such knowledge down. It also makes it available as a reference - and if this is a question it comes up often, then it is useful to have the result advertised in its own paper, rather than being hidden in a paper that uses the result along the way. And finally, only when this folklore "result" and its proof are written down do we, the mathematical community, get the chance to scrutinise it. Did a crucial assumption get omitted? Does the proof method apply more broadly? Isn't there an easier argument that also proves [well-known lemma with an intricate proof in the literature]? So in my view, there can be great value in writing down folklore "knowledge".
However, the above is just my personal opinion, which is not a consensus in the community, and maybe not even a majority view. There is certainly a good chance that a paper proving such a folklore result will get lukewarm referee reports at best. It is unlikely to get published in a very selective journal (and these days, more journals than you might think would consider themselves to be very selective). As a matter of career advice, I would nudge a junior mathematician to spend their time on work seen as original and innovative. Do you think you have a clean proof of a result that you and others may use later and that will only take you a short time to write up in detail? Go for it. Is it tangential to your work, and it'd take you months to finish the paper? Maybe focus on your main project instead.

We have additional information here that experienced people in academia who are aware of the specific results have suggested it's not worth it for this specific example; so, it seems they already got some outside advice to focus on something else.

Well, I don't understand how publishing these results could ever be "frowned upon" (unless the author learned much of the argument from others). So I probably disagree with some of this advice. We also learn that the original poster wants to use them, and that some people in his working group are unaware of them. I agree we lack context, but I doubt I would conclude that it would be improper to publish these results if I had all context.

I'd go further and say that such "folklore" unpublished results should be frowned upon. Let's see the proof and talk about it. Sometimes mistakes survive for a long time since nobody cares to re-do the work. If a result is of enough importance to be cited, and has not been published, then either it's a wrong result, or it should be out there damnit :)

What is "folklore"?
First, because there appears to be some confusion in the comments, I think it is important to give some context.  In contrast to other areas in academia, mathematical results can be proven to be true.  Mathematics is not particularly empirical—we don't experiment or interview research subjects.  A well-formed statement in mathematics is either true, or it is not (whether or not it can be proved one way or another question entirely... thanks, Gödel).
Published results in mathematics typically consist of one or more mathematical statements ("theorems"), along with whatever argumentation is required in order to prove that those statements are true (within whatever system of axioms and logical reasoning has been adopted for that publication).  There are no "negative results", nor ethnographies, nor partial experimental results.
In this context, the culture of mathematics values novel results (i.e. statements which have never been proved before) or, barring that, novel methods (i.e. lines of argumentation which have never been used before).  Proving an incremental result with standard techniques is typically not considered interesting, and will typically not merit publication.
In this setting, the term "folklore" has a fairly specific (if somewhat ambiguous or non-rigorous) meaning.  The "folklore" of mathematics consists of results which are believed to be true, but which no one has bothered to fully flesh out or publish.  Generally speaking, these are results that experts agree are true, and it is very possible that some of these experts have taken the time to walk through a proof, but haven't published, either because they seem too trivial or too tedious to bother with.
"Folklore" is not necessarily "common knowledge", nor is it necessarily "low-hanging fruit", though it can have connotations of either (or both).  More typically, "folklore" consists of results which are assumed to be true, but which aren't particularly novel and/or appear to be amenable to standard techniques—these things typically don't rise to the level of "interesting enough to publish".  These are results which are communicated primarily through word-of-mouth (e.g. from advisor to student, or within a particular working group), but which aren't published (for whatever reason).
For reference, there is a pretty good discussion of mathematical folklore on nLab (nLab is a kind of mathematical "wiki"—it is a collectively edited collection of articles which is meant to serve as a kind of "lab notebook" for mathematical reasearch—the article on "folklore" roughly reflects what (a select group of) mathematicians think about the topic).
Is it "ethical" to publish folklore?
Assuming that one has a proof of some folkloric result, there is nothing unethical about publishing that result.  Indeed, I would argue that it is probably a Good Thing™ to publish these results, if for no other reason to have it written down for the sake of peer review (both in the context of having a committee of experts vet the result, and in the context of having more eyes in the community to spot bugs).
Is is a Good Idea™ to publish folklore?
*shrugs*
Ideally, if an old result is being used to prove a new result, then a proof of the old result should either be cited (if it exists in some other paper or text) or explicitly given as part of the exposition leading to the proof of the new result.  If part of proving a new result includes allusions to the "folklore" of a field, then note that it is a folkloric result, give a proof, and move on.
It is also, in my opinion, reasonable to put forward a paper which seeks to do nothing more than prove a result from the folklore, though there are things to consider when going down this path.
From a CV / career standpoint, it very much depends on how advanced the author is:

For a student, I would think that attempting to publish a folkloric result can only be a good thing.  Because of a perceived lack of novelty, it is unlikely that such a result will go into a "good" journal, but students (undergraduates and graduate students alike) typically have very few publications, and any publication is going to look good.

There is also nothing wrong with a late-career researcher publishing such results.  They have nothing to lose (e.g. they have tenure and are not looking for further career advancement), and are potentially adding to the published record.  Why not?

However, for an early career researcher, one should carefully consider the opportunity cost in pursuing folkloric results.  Is it a good use of your time to write a paper that is probably only ever going to get into a C+/B- journal?  or would it be better to work on something that is going to go into a better journal?  There is also a chance that publishing this kind of result will just look like CV padding, but this is going to depend very much on whoever is reading over that CV.

From the point of view of recording human knowledge, I think that there are many good reasons to go ahead and publish folkloric results:

These results are sometimes wrong.  If someone manages to prove that something in the folklore is wrong, then it needs to be recorded, particularly if many other results depend on the incorrect folkloric assumptions.  Moreover, I would imagine that someone who can disprove a result in the folklore would have a huge leg up on the job market.

Even if the results are not wrong, they may be very niche.  An outsider, not immersed in the culture of a particular sub-sub-sub-sub-field might not know the folklore, and might waste time on something which is already "known" (imagine the physician who reinvents calculus, but with something known only to a small number of specialists).  It is helpful for the dissemination of knowledge to publish these things, even if it is not a huge career boost.

Many specialist fields in mathematics are opaque to students.  It is helpful to publish the folklore if for no other reason than to make the barrier to entry that much lower.  Publishing the results means that students can learn the material, which makes it easier for new researchers to enter the field.

Overall, my preference is that these results get proper peer review and publication.  They are likely not to go into particularly prestigious journals, but I think that it is valuable to make folklore explicit—a "shadow repository" of folkloric knowledge is kind of antithetical to the ideals of academia—it makes knowledge less accessible and circumvents peer review.  I am on the side of "publish".

Why do you write "Good Thing" and "Good Idea" with capitals and a "TM" up there? (I have a suspicion why you do it but (a) I'm not 100% sure and (b) if it's nothing more than what I believe it is, I recommend to remove it, because it doesn't serve your answer but can potentially confuse, particularly non-native speakers.)

@ChristianHennig It is both a bit of a joke (a small nod in the general direction of Martha Stewart), which is meant to indicate a little more strongly that these are opinions, and that they are put forward in a light-hearted manner.  They are kind of important to the tone that I am trying to convey, hence my preference is to leave them alone.

too tedious to bother with Ah, the famous "I didn't bother with it" notation on the margin? "Too tedious to bother with" screams "publish or shut up" to me :)

@Kubahasn'tforgottenMonica  Possibly, bit it is also possible that the proof is a long and tedious, but otherwise routine computation.  And it may be that someone once tried to get it published, but the reviewers responded with "there's nothing novel here".  That doesn't mean that folk shouldn't try to get these things into the literature, only that the culture (both of mathematics, and of academia more broadly) can make it difficult.

Some math journals do not mind publishing new proofs of old results and proofs of "folklore theorems"; one of the best (in my opinion) is "L'Enseignement Mathématique". The quality of papers they publish tends to be quite high.
In agreement with other answers: Publishing proofs of "folklore theorems" is a valuable service to the community but is easier said than done. It is easier to accomplish if a "folklore theorem" is needed for a proof of another result in your paper. Then you can try to publish a proof as a part of a paper (possibly, as an appendix). Another option is to publish such proofs as a part of a book. I have done both several times.

A mathematician Olivia Caramello [complained][1] of people saying that a lot of what she wrote was "folklore". I am not in a position to decide who was right or wrong in the dispute, but what she wrote about it looks interesting and relevant.
EDIT (1/5/2024): I forgot that I recently read an article that also seems "interesting and relevant" :-) : Synthese, Volume 197, pages 3875–3904, (2020) (see also the [preprint][2]).
Abstract:
We investigate how epistemic injustice can manifest itself in mathematical practices.

We do this as both a social epistemological and virtue-theoretic
investigation of mathematical practices. We delineate the concept both
positively—we show that a certain type of folk theorem can be a source
of epistemic injustice in mathematics—and negatively by exploring
cases where the obstacles to participation in a mathematical practice
do not amount to epistemic injustice. Having explored what epistemic
injustice in mathematics can amount to, we use the concept to
highlight a potential danger of intellectual enculturation.

They also discuss the "Caramello case". I don't want to provide long quotes here.
[1]: https://www.oliviacaramello.com/Unification/InitiativeOfClarificationResults.html
[2]: http://philsci-archive.pitt.edu/15133/1/Epistemic%20Injustice%20in%20Mathematics%20%28to%20appear%29.pdf

Upvoted. One sentence that attracted my attention: "It is clearly unfair to pretend that a young researcher presents his/her results, which he/she had discovered on his/her own without being told about them by anyone, as non-original on the grounds that “experts knew them but never wrote them down (or publicly communicated them)”."

It's not rare in applied mathematics to use results from pretty advanced branches of abstract mathematics, but since applied mathematicians are not "experts" in these advanced branches, I suspect there's a bunch of "folklore results" that have never been written down even though they could be pretty useful. Arguing that some results don't need to be written down because "experts know them" is gate-keeping and elitist, and borders on obscurantism.

I agree. A statement without a peer-reviewed proof is a conjecture, no matter how simple or folklore it may be.

@SpencerKraisler: Not necessarily. For instance, you will not find a proof of the statement 1234 * 5678= 7006652 a peer-reviewed literature. Nevertheless, it is not a conjecture, but a routine calculation which nobody in a right mind will be verifying in a refereed paper.

In math, insight is king. If you publish "interesting" proofs of such theorems and those proofs give general insight into a class of important problems, then they are worth the effort of publication. If the proofs are pedestrian, then the opposite would be true.
But it is the reviewers and editors of reputable journals that can make the judgement about the value of this (or any) work. If it has the necessary aspects of novelty and importance then they might want to publish it. But you have to contribute something to the literature.
It is possible, of course, that some "well known facts" in math are actually wrong. It doesn't happen too often, but it can. What is "obvious" might actually be incorrect. Only an exploration can guarantee correctness. But even then, pedestrian work may not be publishable.

I don't think there's an ethical problem here. Of course any publication of this kind would need to acknowledge that this is implied in the literature already, and justify giving a proof by lack of availability and use for the community. As a reviewer I'd ask myself whether I could prove it myself in an hour or so if I had to, and whether I can find any publication where enough is said that a reader just needs to connect the elements in a straightforward fashion to arrive at the proof. In these cases I don't think it'd be worth a journal publication, although it could still make a worthwhile addition to a textbook that uses the result or provides the tools, and this thing can be given as example.


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Should I enquire about a newly announced PhD position while waiting the outcome of a previous application with the same PI?
I am considering pursuing my PhD with a particular PI who had a studentship available in their lab focusing on antibody drug conjugates (ADCs), and I applied for it, but received no answer yet. Recently, I discovered that the same PI has another position available in the broader field of therapeutics, which also comes with international funding. Both projects align with my goals. Should I take the initiative to email the PI and inquire about the second opportunity, or is this a risky move at this point

As a tip, please make sure your username is not your real name if you are concerned about what you are saying and, as a second tip, please work proofread your writing (such as punctuation). Also, I see no harm in setting a conversation (such as Zoom or phone call) to discuss positions with this professor.

Showing interest on both positions should not hurt your chances of getting a position with the PI, it seems natural that you would be willing to work in either projects.
I would consider contacting the PI depending on the call deadline and the expected date to have an answer from your first application. For example, if the evaluation in the previous call is not finished before the deadline for the second position you can let the PI know that you will apply for the new position as well. On the other hand, if you receive a rejection letter from the first application you could also contact to understand if they encourage you to apply again or not.


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Graduate Certificate After Masters
I have a Masters Degree from the UK and I would like to apply for a graduate Certificate studies in a field completely different from my Masters degree in Canada.
Would there be an issue in processing the study permit to Canada?

Is this a question about immigration? Or visas?

Note to readers that a Graduate Certificate program is a non-degree professional skills advancement program offered in many places and in many fields (web search). It normally requires a few courses beyond the bachelors degree.

And a Canadian Study Permit is a limited term residence permit for study in Canada.


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What should I do if I receive an email asking for minor corrections in a manuscript, with no reviewer comments?
I have received a mail yesterday saying that I should do some minor corrections in my manuscript, but there are no reviewer comments included. How should I proceed in this case?

I'm not sure what you mean by "same.thing" are you referring to another question?

contact the editor

What should you do?  Be happy!  Your paper was not desk-rejected! ... It is not the responsibility of paper referees to find errors in your paper: that is your responsibility.

@GEdgar It would be still nice to have a pointer what to look at. There could be a remark such as an exemplary number of grammar errors and stating that there are more.

@GEdgar Even if the referees approve the manuscript as it is, OP should have received their comments stating that. If it got minor revision the authors should be made aware of what led to this outcome and what they should fix.

Why the downvotes?

@DavidRaveh they are "legacy" downvotes, look at the edit history and you will understand.

There are two obvious things that might have happened here. Neither are things to worry about.

The reviewer comments are on an online manuscript management portal. You need to log in, probably to the same place to submitted the manuscript and check there.

The editor simply forgot to attach the comments. People forget to include attachments all the time.

Having double checked you definitely haven't missed the comments on an online portal, I'd simply write a polite email to the editor in question, thanking them for their time handling the manuscript, saying you are more than happy to make the corrections, but that you can't find the reviewer comments anywhere and could they please point you in the correct direction.

2b. The editor did not notice that the reviewer wrote their report in the box titled "Comments to the editor" instead of the one titled "Comments to the author". As a result the reviewer's comments are not automatically appended to the email.


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How to establish a collaboration with other researcher?
As a Ph.D. student, I am curious about how collaborations among researchers are established. To me, it seems like it is a very informal process: someone proposes an idea(while in a lunch discussion, for example) and the other person tries to give some advice. Eventually, the first person will return with some results and the process will continue till they get both involved in the topic. Is this standard in academia? Is there any other way of establishing collaboration?

very very informal process

It is generally good to be explicit about your expectations. You don't want to end up in a situation where one person thinks it is her/his project and the other person has a well deserved place in the "thank you section", while the other person thinks she/he deserves to be a co-author. Such a conflict is really bad for everybody involved.
So when I propose a collaboration or someone comes to me with a proposal, I will discuss co-authorship from the beginning. This makes the discussion less informal than you suggest in the question.
It may still happen (and it has happened to me) that someone comes for advise, and I give that advise under the assumption that I am not a co-author, and the original author is so happy with the advise that I end up being "upgraded" as author.
Similarly, but more tricky, it may happen that I am "downgraded" when my contribution is not significant enough to warrant authorship. Maybe because I did not invest enough time in it, or the sub-problem I am supposed to tackle turned out to be less relevant to the entire project than originally expected. The tricky part is that ideally the downgraded person has to agree otherwise we are in a conflict of the type we were trying to avoid.

Yes, usually it is an informal process. However, it implies the researchers to know each other work. That is why conferences are good to promote new collaborations: you have the opportunity to know more about other works through the seminars and then you have the social component (beer/poster sessions, coffee breaks and conference dinner) in order to facilitate the approach. The first objective is to find a common ground where the two researchers could work together complementing each other research.
As a Ph.D student you are stimulated to take Short-Term Scientific Missions(1) (STSM) in other labs, which is excellent to effectively establish and maturate a new collaboration. In addition, you start to open new perspectives for a possible postdoc position.
There are other possible approaches, such as inviting a professor to visit your lab, but I think that the best suitable for a PhD student is the formula conferences+STSM.

1 - A STSM could have a duration of a couple of weeks up to several months. If you are based on a European Union country you may be able to ask for financial support through the COST project (European Cooperation in Science & Technology).

I started several collaborations with other researchers as a PhD student.
All cases were "accidental" — i.e. I met my collaborators at a conference or seminar and found their talk interesting. The content of their talk was somewhat related to some part of my PhD thesis and I went to talk to them afterwards, asking a question and wondering if their approach to the subject could also work in the case I'm working with (or solve a particular problem I was working on).
I usually thought about their talk more in the weeks after and eventually contacted them by email, asking if they would be interested in working on some particular project together. (I guess their positive reply would be the official start date for the collaboration.)
Note that I was not head-hunting for collaborators — I wasn't trying to pick the most relevant talk, try to ask a meaningful question and relate their response back to my area of expertise — so I don't think the above would work as a manual How to Win Collaborators and Influence People¹.
However, attending talks and interacting with other researchers is certainly something you can try to do more, even if you are someone who is naturally held back / introvert (I am). (Actually, none of the collaborations were started during a social event such as a lunch discussion. If you have a question, my advice would be not to put it aside and wait for the "right" informal setting.)
¹ I haven't read the book I'm alluding to, I just find the title memorable.

The only collaboration that wasn't initiated by myself was with my advisor and his coauthor. My advisor had asked me to read over a preprint of his, where he and his coauthor were stuck for some time. I happened to be able to solve their problem.
Being approached as a PhD student about collaboration is naturally a rather rare case, as for most researchers PhD students of colleagues are not really the go-to expert — apart from your advisor not many people will know in what area you are trained and your advisor is more likely to have more expertise than you.

I had intended to write this as a comment, but I already passed the character limit. But I guess it can count as an answer.
Well, if you stick to formalities you might end up not having so much opportunities. Having good enough knowledge and opportunities coincide on informalities. Systems which are strictly formal aren't really realistic. Malcolm Gladwell actually talked about jobs and job hunting. I remember he said something along the lines of "60% of the job hiring in the US were based on informal connections". I think the same applies to Academia. The physicists and mathematicians who brought a lot to the world often had lots of informal communication.

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What to do after finding a mistake in my published paper?
I have published a paper from my PhD work early in this year and now I find an unintentional mistake in my paper. This mistake was made in a figure where in the Y-axis I have showed expression of one molecule in cells (which can vary) in 10 to the power 3 scale instead of 10 to the power 2. The discussion about that figure does not change at all due to this mistake.
Moreover, in another figure where I compare the expression of that molecule is correct. Now, I have completed my defense and will submit my PhD thesis with this mistake. My professor is very harsh and I can not tell him about this mistake.
Though it does not change anything in that specific figure and final conclusion of my result, I just can not sit calmly. Is this mistake destroy all my efforts that I have done last 4 years?

Hi. This question is related to yours, you may find the answers useful: https://academia.stackexchange.com/questions/110965/how-does-an-erratum-on-ones-own-paper-affect-ones-career-as-a-researcher

https://academia.stackexchange.com/questions/68707/how-common-is-it-for-submitted-papers-to-have-minor-errors related

As Ethan said in an ideal situation you could notify your PI, make this simple correction and move on BUT we do not live in an ideal world. You said your PI is "harsh". I can't quantify that but if you think this mistake would postpone or derail you completing the program then I would suggest sitting on it until you have all of your signatures and are ready to graduate. The mistake doesn't change any of your results, made it past your PI and peer review it is not worth the headache while you are approaching completion. You can contact the journal at a later date to submit a corrected figure. At that time you may have to get your co-authors to approve the change or the editor could just accept it. Congrats on the paper and graduation. Welcome to academia!

Take a deep  breath. This is not the kind of mistake that can destroy four years of work.
The journal may have a way to provide a correction if the paper is available on line.
If you had found the mistake only after your degree was final that would be all the answer you need. Since you noticed after publication but before you are finished, the natural thing to do would be to ask your professor. Any reasonable one would accept it as an honest error. I can't address what your advisor would do if you told him about the error. In my opinion he is partly responsible - he should have carefully reviewed your submission.

Thank you for your kind suggestion.


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Is it better to do a bachelors in general Computer Science or in a subfield focused degree?
I'm in a dilemma between whether to do bachelors in general Computer Science or a specialization in it. These specializations include Artificial intelligence, Cyber security, Data Science, and Software Engineering.
From what I've heard, it's better to do a general CS degree in order to form a strong basis, but I'm also hearing it's better to do specialization as the industry is getting oversaturated and it's better to have specialized knowledge.
I'd really like the insight of someone who has a good idea about the industry. If it helps I have profound interest in Artificial Intelligence; but I'm swayed away from a bachelors in AI for the aforementioned reasons.
An elaborate explanation is appreciated.

‘Is it better …?’ What does better look like to you? Do you have a goal in mind?

A bachelor’s degree isn’t particularly specialized regardless of what you call it.

I don't have a concrete goal in mind; I just want to be financially stable in the future while also pursuing my interests. I've familiarized myself with machine learning stuff, but I'm unsure if I can make it a career goal considering the volatility of the industry and whether there will be a demand for what I do

If there's a way for you to work through a few summer internships, you might end up with a bit better insight into some of the opportunities in industry. And in the meantime, learn to code, nonstop.

Where is it possible to do a "specialized" CS degree at the bachelor's level in those subfields? General CS seems pretty necessary in all of them.

@Buffy, these kind of specialized degrees [which I don't think are a good idea] exist in Australia for example. Maybe England as well, though I am not sure.

The best condition of the tech industry can only be described as changing, in the last 10 years many trends have came and gone. The only way to build a successful career in the industry is to have experience in the field. The best advice I can give is don't run after degrees. Get a basic degree in computer science and develop your skill set and adapt the ever changing nature of the industry.


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How does one do PhD?
I'm currently a PhD Candidate in Theoretical Physics.
After getting into the program, I realized that studying and being able to teach Physics is one thing and doing research is another. My adviser is giving me problems and I'm working on them.

how does he know that such a work doesn't already exist?
how does he know the problem in the first place?
how do you search for problems to work in so that I may do the same thinking as him?
When I am working on a theoretical question/problem, I catch myself wondering, is this work really going to help others? If not, which is generally the case, what am I doing?
When do I know, if the paper I'm working on is worth publishing?

Welcome to Academia.SE! You are asking a lot questions and, as such, your question is way too broad. Some of the questions you ask probably have already an answer here, try the search function or look at the list of related questions on the right of the page. Then, if after this search you still have questions, try to ask them separately, so that we can answer them.

The short answer to most of your queries is: Systematic Literature Review

Maybe we should change the title to 'how to research' :)

Simply put, the answer for most of your questions is: experience.
Advisors are usually people that are working on a specific field/domain for a while. They know the other people who work on this field as well (from conferences), and their work (from doing bibliographical reviews for each written paper).
In my experience, while it is indeed interesting to work on stuff that have a direct world application, that is not strictly necessary. Pure science is still science and you never know what people will be able to do with your research in the future.

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Switching university for PhD but staying in the same city
I am currently a graduate student in mathematics at the University of Montreal. I also did my undergraduate studies there.
I know it is often frowned upon to do all your graduate studies at the same university. I have read online it is often better to go somewhere else for your PhD.
How far does one have to go for the PhD studies?
In Montreal, there are three other universities (McGill, Concordia, UQAM) and I was wondering if just switching university (while staying in the same city) is sufficient in academia. Will it be frowned upon?

I don't know where it's "frowned upon" to do all your graduate studies at the same universities, but I know of people that stay with the same institution from their first day in undergrad to their PhD. If you feel the need to move, then that's fine. But if you already like your current university climate, I would stay.

@SeanRoberson See this answer and this one for some insight into the "frowned upon" aspect of getting multiple degrees from the same institution.

It's worthwhile to consider the reasons for going to a different university.  Different scholars have different opinions about their subject.  Even in a subject that is 'objective', different scholars have different opinions about which parts of the subject are 'important' or which types of methods are more 'elegant' than others.  Scholars in the same department tend to have similar opinions because, even if they start out with different opinions, over time they adjust their opinions through discussion and their opinions converge.  (continued)

Hence someone who has all their education at the same university is at serious risk of getting a one-sided view of their subject, with the opinions held by their professors implicitly assumed to be true without even the idea that different opinions on these matters are even possible.  What's important is that one goes some place where prevailing opinions are different.  Other universities in the same city are probably okay, but not if the departments collaborate a lot or if one department dominates all the others.  (continued)

A university far away might be problematic if most of its professors are graduates of your current university or vice versa (or both are dominated by graduates of the same third university).

I stayed at the same university for Bachelors, Masters and PhD. Even in the same group where I did my masters. So far, it does not hurt at all. If I would not want to move for personal reasons, I would be definitely thinking about staying here. Here I have an academic network (that I will try to not lose contact with when moving) and collaborators. At the place I plan to move to unfortunately, I will have nothing at the start.

@skymningen From what I have heard it is difficult.to find a good post doc if you have stayed in the same university for all your studies.

@skymningen - It is often a good idea to diversify.  It is not always necessary.  But to answer your question, if you're going into a good program in the same city, it seems to me that you would probably still reap the benefits of the diversification factor.


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Is US experience usually required for TT jobs?
Update/follow up: Can this have something to do with the specific rank? I mean, does it make sense to require this for the rank of Assistant professor for some reason?
Link for the posting: http://cra.org/job/umass_lowell-assistantassociate-professor-computer-science-2-positions/

I was checking some postings from cra.org, and found this remark:

For appointment at the rank of Assistant Professor, by the time of appointment, applicants must either have a PhD degree from a US university, or have at least one year as a post-doctoral researcher in a US university or US research lab.

However, I didn't find that in other postings. Is this unusual or so common that isn't usually spelled out?

This is the first time I've ever seen such a requirement.

This is a bizarre requirement that I have never seen and sounds unwise to me, except maybe for a position requiring specific U.S.-centric expertise, e.g. a search for a law school faculty member specializing in U.S. constitutional law (even then, requiring a U.S. PhD/postdoc sounds to me like the wrong way to ensure that the candidate possesses the relevant expertise). And no, I do not see why it should matter that this is an Assistant Professor position.
Based on my experience with bizarre/illogical rules at organizations, I'm guessing that what happened is that the department that is requiring this at one time had a really bad experience hiring someone without a U.S. background, and after that someone there decided to make sure that that particular mistake would not be repeated, no matter how many good opportunities that would mean missing out on.
Note that while I think this is a silly requirement, at many U.S. universities a tenure-track candidate who has no U.S. teaching experience could reasonably be considered by some people to be less competitive than another candidate who possesses such experience, all other things being equal. But this judgment call does not require a special rule, since being well qualified to teach to the standards of the university is already a requirement of the job.

I found the job ad. It is for computer science TT job. You can confirm it by reading the Minimum Qualification section.

@scaaahu yes, I guessed it was for a CS job since that is OP's field, but tried to answer the question in the generality in which it was posted.

Prior experience working in a particular country is a sufficiently specialized requirement that it cannot be "implicitly assumed." Such requirements should appear in every such position to which it applies. (Personally, I have only seen such requirements posted for positions outside the US, with the requirement being one or more years abroad, not specifically in the US.)


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Reference for use of name@math.univ.edu for mathematics department email addresses?
I have noticed that many mathematics departments (a little over half of the public and private Group I departments) follow the name@math.univ.edu format. Does anyone know of a reference to a discussion in Notices of the American Mathematical Society or elsewhere about this common practice?

May we know why you are interested in this?

An administrator at my university is trying to change us away from the common format. I am trying to collect information about it for my department since it has many people upset. I also seem to recall reading briefly about the format somewhere; it might have been in the Notices. It would be nice to be able to make a reasoned appeal to the administrator, and more information would be helpful.

Surely the biggest point against changing everyone's email address is exactly that: it's a change, of which you now have to inform everyone who might think they know your email address.

This is not specific to math but just the straightforward way to assign e-mail adresses and domains respectively.

What is the proposed change? If it is from "john.doe@math.univ.edu" to something like "john.h.doe@univ.edu" (a change which one of my research collaborators experienced), point out to the administrator that there will be a greater likelihood of confusion. My collaborator often gets emails intended for a colleague in another department. No real harm done (yet), but some of these emails contain confidential student details etc. and so there could (in theory) be grounds for a lawsuit. Mention of potential lawsuits might scare the administrator off :)

Senex-- yes that is exactly the sort of change the administrator has in mind.

Just find a bunch of published journal articles that contain old email addresses, and show them to your administration. It is too late to change any email addresses now, as the old ones have already appeared in hundreds of journal articles which are available not only online but also on paper in university libraries throughout the world. (Of course they can provide new email addresses that work in parallel with the old ones.)

@Jukka Suomela: people routinely move from one institution to another, and their old email addresses stop working. So there is no real expectations for the emails listed in journal articles to work for very long after the articles are published. And, for emails within the same school, they could easily handle the transition internally with no lost mail. So this argument is not likely to be very convincing if the administration has done their homework.

I don't have a reference about this. The split in email addresses is often because mathematics departments were among the early adopters of computing. I don't know whether this applies to your own institution, but it applies to several I have been at, of different sizes from 5,000 to 50,000 students.
When computing technology began to be available, mathematics departments were among the first adopters. Computers and mathematics go together. At quite a few schools, the computer science department is still part of the department of mathematics; at others, the two departments started together (when the math department began to hire computer scientists), and split apart later.
In the period before PCs became ubiquitous in the 1990s, mathematics departments often found funds (often via grants) to operate computer labs, web servers, and email servers on their own. At this time, especially in the 1980s, university-wide computing services were often quite primitive, and often consisted of terminal servers instead of PCs.
Over time, as computing became ubiquitous, universities hired their own IT staff, and began to run their own web servers and email. This is how, at several institutions I have been at, I had two different email addresses (one for the university and one for the math department) and two web pages (same split)
Now that email and web servers are viewed as a basic service that the university provides to faculty, it is more difficult for mathematics departments to justify having their independent systems. Administrators correctly look at the separation as an inefficiency, asking why the department can't use the same system as everyone else.
In my opinion, math departments that want to continue to have separate systems will need to present a very strong case for why the separate systems are necessary, beyond the historical developments that led to the separate systems coming into existence. As email and web services become more and more of a staple commodity, this argument gets more and more difficult.

Who said anything about a separate system? It is just a subdomain.

At the schools I've been at that have a sub domain for math emails, it is because a separate mail server was used for the subdomain. The sub domain can have its own MX record in DNS. Yes, it would be possible to point the sub domain to the same server that handles the main domain, subject to a few implementation issues.


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How to overcome a much earlier academic dismissal from undergraduate program in graduate admissions?
I am an international student from Korea and I have a very serious question while I am preparing for graduate school admissions.
I graduated from two years college with 2.8 GPA. After that, I went to a 4 year institution but got dismissed within three semesters due to insufficient GPA. (I was taking more than 18 credits hours because of my greed and exhausted). After the dismissal experience, I went to another 4 years institution without transferring the classes that I took from the 2nd school bur 1st school and graduated from there with 3.87 GPA. In total, I spent two years in two years college, three semesters in the 2nd institution, and 2 years in the third institution.
Now, after some teaching experience while and after my undergraduate degree, I decided to continue and develop my academic career in order for more experience and more effective teaching in a graduate school.
My question is that as I alluded to above, I have a dismissal record from my past school, and this makes me quite scared. What can I do to be wise on my application regarding this fact?
(Please, don't say that I must lie or hide my record because I don't want to take that risk, also that was part of myself and moment that I could learn a lot.)

American perspective:  Your question shows that you made a mistake, but you corrected it.  Your mistake will probably be forgiven if you explain clearly what happened, how you learned from it, and how you will prevent it from occurring again.  Include this as a brief statement in your application letter.


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Effect of bland cover letter for journal submission in biology
I'm not used to writing covering letters for journal submissions, and I believe this is pretty standard in maths. However, I got into a conversation with a friend in biology, who said they expect to write about a page explaining why the paper is so great.
To me this seems an unhelpful practice: a paper should be judged by the quality of the paper, not by the quality of some other document.
We came round to the question:

How would an editor of a biology journal react to a paper submitted with a covering letter that amounted to 'here it is'?

I expect that in most areas the cover letter has a negligible impact. A sentence about why the paper makes a contribution might be warranted, but a page sounds excessive. Perhaps if you include the header, salutation, explanation, valediction, signature it get close to a page!

@Behacad I'm told this is an all-out justification of why the journal should take this paper seriously, not just filling a page with nothing.

It's probably going to depend a lot on what kind you journal you are talking about.  A very selective journal may need a good letter to be convinced that the paper has even a chance of being up to their standards of importance.  A less prestigious journal may not care at all.

For some reason I very much doubt that the cover letter affects my chances of getting accepted into let say, Science or Nature, if I have an excellent paper.

@Behacad I'm afraid you are quite mistaken.  Without a cover letter that convinces the editor of Science of Nature (who is probably not an expert on your topic) that your work is of great importance, they will not even send your manuscript out to be reviewed.

Wow! I had no idea

@Behacad in fact, in Nature only a third of the submitted papers are sent to review (out of those, about a quarter are accepted, which is ~8% from the total submitted papers). So the cover letter is critical.

Of course only a small proportion are reviewed and accepted! But what makes you think that it has to do with the cover letter?

All journals I have come across their guide for authors require a cover letter. Although it's probably partially a remnant of older times, where letters and manuscripts were mailed to the journals, it does have functionality.
The cover letter is a quick way for the editor to decide if it's even worth opening the full article. For this reason, arguments on the novelty, findings, importance, challenges and perspectives of the work should be demonstrated. In practice, it might not be much different than the abstract (different structure of course), but some journals also ask for specific questions to be answered.
It also helps the editor, who might not have the same expertise as the manuscript, to decide whether it's worth sending the manuscript to external reviewers. It also saves him a few hours of work from reading the whole article to understand its value.
It also adds a degree of personal communication between the corresponding author and the editor, rather than being a automated, impersonal submission process.
Finally, I usually add sentences like "all authors have agreed to submit the manuscript in this journal" or "no conflict of interest" etc, which adds a signature under the statements.
In the case a cover letter would only say "here it is", I think the editor would probably drop it in the trash bin, unless:

The title (and the abstract) conveys a subject so important that any editor could not bear not to check it out more thoroughly.
The corresponding author, or one of the co-authors, is a really big name in the field, that (even if the article is not that important) the editor cannot just reject it.

So, in mathematics, maybe just saying "Here is the solution of the problem X" and everyone knows the problem and die to see the solution, then you don't need to add much. But in sciences where a problem doesn't have a name, a more detailed explanation might be required.
Lastly, the manuscript is indeed evaluated by the manuscript itself. However, a good cover letter might make the editor check your submission more thoroughly, out of the tens or hundreds of manuscripts they may receive.
I think of it as the trailer to a movie. If you like Batman and you see Batman on the title, you will check the movie a little more before deciding if it's a crap movie or not. If you see a movie is directed by let's say Spielberg (and you like him), you may do the same. But if you are unsure about the title and you don't know the actors and directors, a trailer might convince you to watch the movie.

Another important point is that in many journals you will get an editor that is not an expert in the field, so even if the editor wanted to evaluate the manuscript itself they couldn't.

@Bitwise Why does a cover letter make the editor any better off than the paper itself? If they can't judge the paper then they should have a referee do so. That's the point of a referee.

@JessicaB still, the editor needs to decide whether to pass the paper to review. In many biological journals this is a major hurdle.

@Bitwise And I'm saying it shouldn't be, if the editor is not in a position to judge the paper to that degree themselves.

@Bitwise Indeed, it's not always easy to have an editor with the same expertise as the submitted manuscripts (as it's not always easy to get reviewers with that expertise). I forgot to mention that. I will add it in the answer.

@JessicaB Because the paper takes a few hours to read (thoroughly). The cover letter takes 5 minutes. They don't decide based on the cover letter whether they accept it or not. They decide whether it should go to the reviewers or not.

@BioGeo Deciding not to send it to reviewers is deciding not to accept it. The introduction ought to be enough to give an editor an idea of whether it is really bad or worth a referee taking a look at.

@JessicaB The introduction no... it just gives the background and you can only understand how well the authors can write. Maybe the abstract can give an idea on the quality of the findings. But again, in a cover letter you can give a wider perspective.

Mathematics and Biology have polar opposite cultures, and much of this is due to what's practical. Some of the top Biology journals receive tens of thousands of manuscript submissions each year. For example, Nature receives 200+ manuscripts each week. They send maybe 30 or so of those out for peer-review. They can't read 200 papers in a week, and likely wouldn't understand them anyway. So they must assess their significance without reading the paper. The cover letter is written so that any reasonably well-educated lay-person can understand why the paper is important, even though the paper itself (even the abstract) maybe too technical. This is actually a somewhat reasonable test to show how important the paper is. It's really hard to sell the importance of an obscure unimportant topic in layman's terms.
As one moves down the food chain of journals (e.g. journals with lower impact factors, that are eventually accepting 25+% of what gets sent to them), the cover letter becomes less important. The journals are less broad, and the editor can assess the importance of the paper from the abstract.
In addition, there is just a culture in mathematics of being slow and methodical about peer-review. Editors actually read the paper. Reviewers will spend a year checking your proofs to make sure they are correct. So the added time it takes the editor to read your paper is epsilon compared to the review process. I'm a mathematical biologist, so I get asked to review both applied math papers and biology papers. The math journals usually give me a deadline of 2-3 months to get my review back, the biology journals usually give me 1-2 weeks. Biologist reviewers aren't repeating your experiments, like mathematicians are checking between the lines of every sentence in your proof [or scowering their brain for counterexamples]. So if in biology it takes 1-2 weeks for the reviewers to get their reports in, the time it would take the editor in chief (EIC) to read every submitted paper would be a significant percentage of the review process, and would really slow things down.
The cover letter is for statements like "We performed the first-ever controlled experiment validating ..." or "We perform the first explicit assessment of the accuracy of method X from paper Y (Y has been cited 1,390 times since 2015, 382 of those citations are from papers in Journal Z [the journal you are submitting to]) and find that 82% of papers in the field are using the method inappropriately."
These are the types of sentences that would be extremely weird to write in a paper or abstract but would be useful information for an editor to have. As the journal becomes more specific, the cover letter is generally more about why the paper fits well in that particular journal, rather than why its the greatest paper on earth (which might be what you'd say if you were submitting to science or nature).
To answer your question about a bland cover letter, like "here it is". While this would likely lead to an immediate rejection at a journal like nature or science or PNAS, at more subject-specific journals it might not end up hurting the paper's chances. The cover letter is to point out things that may not be obvious to the editor in the abstract. Things about citations to papers you are building off of, some more tenuous implications of your work that are too uncertain or controversial to say in the paper, how your paper relates to other papers published by that journal. If you think the importance is clear from the abstract, and you don't have anything additional to add, the cover letter isn't all that important, even in biology. I know several handling editors who say they never read cover letters (although presumably, the EICs do partly to select the appropriate handling editor).

Thanks, that very helpful.


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What are some way to give praise to a professor without resorting to flattery?
In elementary school we are taught to give an apple to your teacher as a sign of appreciation. Obviously it doesn't work anymore in academia.
I wish to maintain a relationship with a professor after his class, so to establish a relationship that maybe worthwhile longer down the road.
What are some of the ways to show appreciation to your university prof. without resorting to excessive (and often empty) flattery or sending him gifts which maybe in violation of university policy and land everyone in trouble.

The goal is to compliment, but I am not sure if it will be received as that. In any case I feel directly complimenting his teaching skill etc. appears too trite. I tend to think of what I am trying to do instead as some sort of micro-praise.

Why do you want to compliment this professor?

Why are you setting out to compliment per se?  That seems like an odd goal unless you are trying to flatter him.

The goal primarily is for maintaining a professional relationship between the prof and I over an rather lengthy period of time. I guess in part I do want him to know that he has had an influence on me, but I don't want to phrase it so it sounds too final i.e. because of all your help and great teaching etc etc now I am at point X

I think this is a classic XY problem. Please edit your question so it asks about your end goal, not just about what you think is the solution to it.

How well do you know the professor?  What is your relationship to him?

Well, an Apple actually might work, but seriously, what is your goal here? Networking? Some concrete goal in the future? Is he such a good teacher that you want to learn more? If you like to work with this person consider asking him whether he looks for student assistants -- and then do a good job. Doing your thesis with this person as supervisor might be another idea. And I always remembered students who were willing to go the extra mile and do really good work in the course.

After I finished my undergraduate degree I wanted to thank those professors who were the most influential to me and my studies over the past years.  In particular, those who wrote all my graduate school letters of recommendations and took the time to help me through the process.  I thought about getting them a gift, but felt it was inappropriate.
What I ended up doing was typing a letter to them which thanked them for all they did to me and provided a specific example in which they were influential to me that helped steer me in the direction I was going.  I then mailed it to the department so they received it unexpectedly.  All of them emailed me to thank me for the nice letter and that it was their pleasure.
This would be a really nice thing to do that isn't flattering and full of praise, but what you actually got from them that was beneficial.
Hope this helps :)

Some institutions have awards for outstanding instructors that students can nominate people to receive. If you believe your instructor was outstanding, you might submit a nomination for a teaching award.

I am first going to point out how the actual application of any answer to this question is very dependent on the culture that you are in, and afterwards, I am going to suggest a few abstract ways how to do this.

As I said, answers to this question will be extremely culture-dependent. Starting with your example of giving an apple to an elementary school teacher, this could be seen as bordering on corruption in some places (especially in elementary school, where it can be surmised that the child did not buy the apple themselves, but was given the apple by their parents and asked to hand it over to their teacher). (Aside from the more practical question, unless you expect to be treated in a special way compared to your classmates, which would leave an extremely sour taste concerning your little apple gift, what the teacher is supposed to do with some 20 (or whatever the size of your class) apples.)
Signs of appreciation, and the degree at which appreciation is expressed, vary a lot between cultures. I grew up in Germany, and seen with a German cultural background, most praise expressed in English-speaking cultures sounds way over the top. Conversely, Germans are often perceived as cold and uncaring by people from English-speaking cultures, as a simple "Thank you for the interesting class." would already be quite a strong praise in German, but is not necessarily perceived as such by native English speakers. (Some of these differences are outlined quite well in an essay that was translated to English by Thorsten S in his answer on Travel SE.) There is even a region in Germany that is especially well-known for that trait, and one of their sayings goes "Absence of ranting is sufficient praise." While it's not actually quite that bad and that somewhat humorous saying should be taken with a grain of salt, it demonstrates well different cultural attitudes toward expressing praise.
The same applies to more material ways of expressing praise. Depending on the culture and circumstances, the way in which a gift (for saying thank you or otherwise) is presented might matter more than the gift itself. To cite just two examples:

In some cultures such as in China, a gift might be simple, but needs to be well-chosen. As pointed out by the graphic linked in a Travel SE question, an apple might be an ok gift, but by no means switch it for a pear.
Wedding gifts in Germany typically involve some money, but the most important aspect (the one that will actually be appreciated and memorized) is that a lot of fantasy and crafting went into them. cf. this, this, or this.

After establishing that the actual contents and wording is very culture-dependent, there might still be some generic suggestions for how to place the statement of appreciation:

At the end of the last lesson, when you see the professor for the last time: If you hope to collaborate with the professor in the future, just talk to the professor and express that you'd be interested taking more classes/participating in projects in the research area of the professor or their department. You can then easily start such a conversation by pointing out that one of your main motivations for that goal is that you found the current class very interesting (or, if the topics do not match a lot, at least that it was very well organized and/or well-taught).
Once you have something specific in mind, such as a project, point out that you found the class very interesting then. You can postpone your praise till that time; being on the professor's "gave praise, but didn't have anything concrete" batch will probably not help a lot, anyway.


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Is "I don't have enough funding" the most popular phrase used as hint for rejection
From communicating with fellow peers, it seems that whenever a professor rejects a student for graduate entrance, he or she will say something along the line of "sorry there isn't enough funding" or "our funding cannot cover a spot for you this year...but feel free to apply again".
This phrase also work its way into graduate interview as well, where the prof would suddenly mention funding questions, and thinks out loud whether he will have enough funding this year to take you.
While all the students failed to get acceptance offer when something along the line of this phrase is uttered...I wonder if there is a pattern in academia (applying for post-doc position, or research) where rejections are treated as lack of funding issues.

While I'm sure this is sometimes used as a gentle way to decline a student, there are also elements of truth to it. Almost everyone who gets an in-person interview at our program would do well if admitted; it IS INDEED our funding that caps the numbers of offers we can make to those students.

It is likely an amalgam of the truth and a gentle let-down. It's a polite way to reject someone, in that it doesn't place the failure in the hands of the applicant. There's nothing you technically did wrong. Nothing you necessarily could have changed. It just didn't work out.
It's also very likely a truthful reason for not accepting a candidate. It's possible that, given a couple more graduate funding spots (getting lucky with a grant, or promised a few TA spots for their students, etc.) that they might accept an additional student, but when those don't work out,  there's nothing for it.

It's not you, it's me.


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Doing Bachelors degree in Maths as distant education for Phd in Mathematics after regular Master's in Optics
I finished my masters in Optics(5 years bachelors+masters together) recently. In the course I had to study subjects like Classical mechanics, Statistical Mechanics,Electrodynamics, Quantum physics and advanced mathematical courses during the first 2 years of the syllabus, just after schooling. These subjects are usually taught in Masters. I even undertaken 2 projects, only to get exposed myself that my ability to do problems are hardly improved during the course it was not how the course was designed. At the end of everything I truly feel that my fundamentals in both physics and mathematics are extremely poor.
It is essential that I improve my maths, I even feel like it is more of my area of interest rather than physics, so I was thinking of switching my field by taking a bachelors degree in pure mathematics(not permissible to directly to get admitted to Master’s in maths
after Master’s in Optics in my country), via distant education as regular classes are possible for me. But mostly I am advised not to do it as I was told doing bachelors degree after my Masters will not be considered in a good way by the admission committee.
The things that I am particularly concerned are:

By the time I finish my Master’s in Mathematics I’ll be 32 and without any prior project experience in the field, so will that adversely affect my chances of getting into a funded PhD program ?
As I am doing or planning to do maths degree as distant education, will it affect getting into a funded PhD program ?
If I could only do my bachelor’s and for some reason I could not do master’s, how will it affect if I try to apply for a PhD program in mathematics or in theoretical physics ?

See it is better to work in theoretical physics with whatever knowledge I have than being stuck by doing mathematics bachelors or masters degree in Mathematics. So that's what I am seriously concerned about as I really don't want to meet a dead end by trying to switch my field.
Or If I am going ahead with this plan, is there any way I can improve my chances of getting into a funded doctoral program in Europe, like taking foreign language or GRE subject ?
Note: I have attached a copy of the email I have sent enquiring my problem to one of my senior. I am truly sorry, Its bit long but I couldn't make it any shorter, atleast reading 1,2 paragraphs would give an idea about what I am confused about.
link

Hi! While I'm only a PhD student and so can't give a full-view answer, I think it is important to note a few things. 1) I read the email you sent and to me it is far too long. Your questions boil down to those you asked here (the rest about your background you could discuss in person). Other parts seem wholly unnecessary and aren't really related to what you would like to know.

In my experience (europe) it is uncommon but not impossible to get 2 bachelors degrees in different subjects. Whether there is funding available depends on the institution - some countries only have central

funding for first-time bachelors students.

Ok, so onto the questions. 1) Age should not be a factor in determining whether you can get a PhD spot. I know plenty of 'older' PhD students

This really depends on the insitution you get the degree from. Jumping into a masters from a reputable university without having the basic maths concepts seems like a difficult ask to me though. In general, PhD funding is in some sense competitive, and so (even though it arguably shouldn't be) the place where you obtain your masters is a factor in determining your strength as a candidate

-3) In Europe it is commonplace to require a masters degree before pursuing a PhD. Other countries vary (e.g. in the US the PhD programme is longer because it essentially also includes 2 years for a masters integrated with it).
Foreign language and GRE scores are nice to have, but my advice would be that if you are serious about maths and decide to take on the degree to concentrate solely on it and learning the basics. There is time after that to sort out applications etc

@TheMathsGeek My first regular masters was from a pretty ok university from people used to go to europe frequently for phd. But the problems are specific to my course. Since it is specialized in Optics I have restrictions to get admitted to mathematics degree in my country, except as distant education.

@TheMathsGeek Regrading Point 1) Are you saying that there is no harm n doing second bachelors in mathematics after master in Optics ?. What if it is as a distant education, how much value it has ?

@TheMathsGeek Point 2) I am not saying to get into a top university without having basics. My doubt was, while doing a second bachelors I will get enough time to strengthen my basics. And after finishing masters in mathematics apply for a phd in the field in europe. But I am worried about me doing my degree as distant education?

@TheMathsGeek Point 3) Distant education, I mean attending classes are not compulsory, from IGNOU, how do I know how much weight it has ?

@TheMathsGeek really sorry for being too broad but I am trying to do a risk analysis here, as I really can't find a similar case anywhere that I am aware of in the internet atleast. And really thanks for your advice.


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Second Bachelors in Maths after Masters in Optics for Theretical Physics Phd
I have completed my Masters(5 year Integrated) in Optics recently with average CGPA. I have couple of projects experiences in Theoretical Physics, but no publications. My masters course had rigorous higher mathematics papers yet I find that I have very little knowledge and experience in doing even the undergraduate math, though I am very much interested in it, may be because my course was designed to give more importance to experimental physics. Thus, I started improving math using online lectures and our mathematics stackexchange forum, and I can feel I am able to gain much more than what I could during the course. But many told me not to take a gap by spending time on maths after masters as it'd affect my chances of a Phd admission, as I am already 26.
So is it a good idea to do a second bachelors degree in Mathematics(distant education) before applying for a Phd in theoretical Physics in Europe/Australia ?
Or is there a better way to compensate the time I spend on improving maths myself ?
Note: The reason I was thinking of doing a bachelor's while improving my math is, that way at least I could show that I was doing something while I was away from academia.

So is it a good idea to do a second bachelors degree in Mathematics(distant education) before applying for a Phd in theoretical Physics in Europe/Australia ?

In general, getting another bachelors degree after getting a masters degree is not seen very favorably.  I understand your though process - show the admissions committee you'll do grade-A work in math.
In reality, it's much more likely to signal to the admissions committee you don't have a clear purpose, and make them wonder why you didn't just switch to a masters in math.  Furthermore, since you already have an advanced degree, they are less likely to be impressed you went back to undergrad and aced another bachelors degree.
The admissions committee is most likely to weight your academic performance doing your masters degree heavily.  If you are truly set on switching fields, I would recommend you get another masters degree in mathematics OR applying for a PhD in mathematics.

In some countries you might not be able to get directly a master's degree in maths after a physics master's. You'll need the undergrad. Unless maybe it is a bad master's, in which case it might not be worthwhile. For a PhD, it never ceases to amaze me how apparently anyone can apply to them without the qualifications needed and get the positions. This is crazy. So yeah, if OP wants to switch to maths then he might have to start from undergrad, maybe third year all the way up. If OP wants to do theoretical physics then the best way is probably a master's in theoretical physics rather than math

I've know several European PhD students that swapped from Physics to Math or Math to Computer Science (or other fields with significant overlap).  Many universities will work with students to figure out how to fill in the gaps.

I think may b u r right. But, undergraduate maths is really necessary for theoretical works, isn't it ?. People often suggest to take mathematical physics paper and 'll be fine with it. But, I feel I should improve math separately, don't know only me have that feeling.

@ss1729 - I've know several PhDs who switch fields from undergrad to grad school.  There is nothing stopping you from getting a second bacholors, but I think you should look at doing a 2nd masters and finding a professor that is sympathetic to your case.

A bachlor's degree is not just a few math courses: it has a lot of other things it comprises of which makes it a 4 year education. Don't get the degree. Just sit in on a few courses, read on your own, and join in the master's courses. End up with a masters if you really need it, but as long as you learn what you need then you can do the PhD.

@ChrisRackauckas - Thanks for pointing out that a BS degree is more than just a few extra courses.  You've also got to consider how long you want to be in school.  4 yr BS + 2 yr MS = 6 years already.  You're time isn't limitless.