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Should I mention that I have a Bipolar disorder in my statement of purpose?
Should I mention that I have Bipolar disorder in my statement of purpose and ask my lecturers to mention it in their letters of recommendation(I am doubtful that they will) ?
Bipolar disorder was a critical roadblock in my academic life man. When I was having maniac episode I was like "I am God, I don't need to study, I can clear this test without studying" or it just felt like I am overdosing on caffeine, I couldn't focus. When I was feeling depressed, I was just too withdrawn to study, I was almost suicidal. Either way, I was too emotional to do anything !
The aggregate GPA of my undergrad courses is 3.216 and the simple average of my last 4 semesters GPA is 3.106. It was in the last two years that I was diagnosed with bipolar disorder. I tell you its not easy managing meds and life. Most psychiatrists in India are idiots. Some of these psychiatrists even diagnosed me with adult ADD :| Its because of these drugs and incompetency of my shrinks that I feel my GPA dropped. Should I mention that too, cause in US I would even have access to better shrinks than here ..
My GRE score is 322/340. I honestly feel I could have got a much better GPA and GRE score without this disorder man. I even got highest grades in all my practical exams too.

First, as a basis see: http://academia.stackexchange.com/questions/324/how-do-you-get-a-bad-transcript-past-ph-d-admissions In short, reducing this to a less complex issue. The advice there is excellent for that, anyway. The real divergence is the medical issue being cited as the cause for the grades, and how to address this. It's possible that it's best to put it behind the veil of non-specified "medical issues that went undiagnosed". The bottom-line will likely be stressing that the grades are not an accurate reflection of your potential/qualifications, and not so much about the past.

Hey will I run into risk if I say I have medical issues ? Like people could think, this person has health issues so there is a very good chance that he will perform badly here if admitted.
Also I can't control what my lects put in their LOR, should I ask them to put this behind a veil incase they do put it in the LOR ?

Well, the main issue is framing. If it comes off as "I have a chronic condition which will make me unlikely to do well in your program", then that's going to go badly . If it's "I had a problem in the past due to a medical issue that was not in my control, but I've addressed it now" and you make a convincing case that you've moved beyond and can function and succeed, then you've got a chance to make something work. That things will be hard for you is absolutely true and my heart goes out to you - but I can't see how the potential for explanation could outweigh the risk of stigma. That said...

You absolutely must talk with the people who will write letters for you and make sure you get on the same page. If they know of your struggles and how hard you worked to overcome many medical issues (countless others don't ever graduate or even live to tell the tale, so give yourself due credit!), work with them to frame it how you decide to handle it in your letter. If you just say "medical issues" and decide that's good, they need to not 'out' you (and in the US that would a huge no-no for a professor without a release form signed), but whatever you decide it should coordinate.

Your letter and your recommendation letters should tell a cohesive, mutually supporting story. If you say "I'm much better now and looking to the future" and they say "they have struggled with their condition and I hope you won't count their present medical issues against them" that's not good. They need to match up, regardless of how you decide to handle it.

Thanks a lot sir :) Thanks for the empathy :) I can't tell you how rare that is these days :) I didn't get what you said here sir.
"If you just say "medical issues" and decide that's good, they need to not 'out' you (and in the US that would a huge no-no for a professor without a release form signed)"

@BrianDHall can you form your comments into an answer. I think they are far better than the answers currently provided on this page.

I would not put it in the statement of purpose as it is a forward looking document (what do you want to study, what qualifications do you have, why study at X university, etc.).
If you must include it, then the diversity statement is a good place.
That being said, I would recommend that you do not include it. You can mention that you “struggled with some health/personal issues” in college but are now prepared for university, but you do not need to give details beyond that. This is your health privacy at stake. You should talk to your letter writers to make sure they know they should  not disclose your personal history without your permission.
Once you are accepted, you can inquire about student health services and reasonable accommodation for your needs.

What's a "diversity statement"? There was no such thing on my grad school applications.

I had never heard of it either, but Google is helpful.  Here is one explanation: http://theadvancededit.com/admissions/should-i-write-a-diversity-statement/ (the writing there makes me cringe a bit, but it covers the ground).


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The registrar's office requested me to raise the cap of my courses
I work for a small private college and today I received an e-mail from the registrar's office requesting me to raise the cap of two courses that I will be teaching in the spring since there are a few students on the waitlist. This e-mail was also copied to my department chair, who has not responded yet. If I say "yes" to this request, this would mean that I will need to work more without getting any compensation. Also, the quality of my courses may suffer as a result of raised caps. I do not think the college has any written rules or policies regarding this specific situation.
My Questions:

In this case, do I have the right to decline the request, or should I always be submissive to such requests?
Is it appropriate to negotiate with the college to "conditionally" raise the cap, such as requesting a bit more pay for teaching an additional number of students?

Another point: My college likes to raise the cap to allow students on the waitlist to take the desired courses. To me, this practice defeats the purpose of having a cap in the first place.
Edit
Initially, the registrar's office requested an increase in the cap of my courses by 20%. I respectfully declined the request, articulating my concerns. Surprisingly, this matter was brought to the attention of the academic dean by an unidentified source, not from the registrar's office. Subsequently, the dean unilaterally raised the cap by 10% without seeking my input or consultation. While I am not entirely satisfied with this resolution, it appears that my ability to influence the decision is limited. I find myself in a situation where I reluctantly accept the imposed changes.

How did your discussion with the department chair go?

@Aruralreader, he mentioned that if I refuse to raise the cap, he will support me.

Is your position ordinarily considered "full time"?

@BryanKrause, yes, I am a full-time tenured faculty.

Of course the college wants students to get the courses they need to graduate in 4 years. If the course was not full would you accept lower pay?

@JonCuster, no. My understanding of the cap being N means I am willing to teach no more than N (instead of exactly N) students in this course.

Is the course required for major/graduation? Making a student pay for an extra semester because they can’t get into your course is not a good thing.

Yes, this course is required. There are currently ten students in total on the waitlist. Yes, they paid their tuition. Instead of raising the cap, another solution would be offering another session of the same course. But I am not sure if the college is willing to consider this option as it means more expense for the college.

Admitting 10 extra students to a lecture course beyond a cap of, say, 50, would increase your workload, but perhaps not by an unreasonable amount. Doubling the size of a 10 student seminar would be unreasonable.

Instead of a financial compensation, you may ask for an extra teaching assistant to decrease your work load.

What exactly would increase the workload? Do the students submit essays at the end? Is there a seminar-like examination? Is it a written test that you would need to grade 10 extra copies of? If it's a written test at the end try to get a teaching assistant for help with grading the test.

What is the financial situation at the college are there already cutbacks or is the reserve flush with invested cash, regular donors and so on. You might say okay let's raise by half. Or is the increase deemed necessary because these students are clamoring to be in your course.

Why do you have a cap? There are hard caps and soft ones. "We ordered reagents based on 20 people and cannot get more in time" is a pretty clear signal that raising cap isn't really doable. On the other hand, "there are 20 chairs in this classroom right now" means that you need to sacrifice some student comfort but you can get 24 students in the class just fine.

Who set the cap in the first place?  Why?  What is the purpose of the cap?  How high is the cap and how much do they want to increase it?

@ZizyArcher At a small liberal arts college that's maybe less likely, but a lot of caps I see are based on the fact that for safety reasons it's not allowed to have more students in the lecture halls than permanently installed seating, but that's for lecture halls in the range of 300 to 500 seats. Using a second lecture hall with a live stream costs a lot more (usually someone other than the lecturer is present and makes sure the live stream works) so it's only done if the second one is reasonably full too.

"the cap being N" - how was N set?  Are there specific factors that make it a hard cap (capacity of lecture room etc) or was it more a guideline?  How many extra do they want you to take - 1 or 2 is different than 10 or 15.

If this results in an increase in your workload, it could be reasonable to request an according increase in pay. Or otherwise, it may be possible to reduce another part of your workload. I can imagine a lot of options here. But we do not know what options are applicable here, and we do not know your preferences nor your registrars preferences. This really seems like something to discuss with your department chair, and not a good fit for this forum.

@deep64blue, they hoped to increase the total cap of the two groups from 60 to 72. (20% increase)

Policies vary from place to place and even across different departments or colleges within the same university. I was at one point a department chair and handled various similar situations to what you are describing, and the precise details of the situation matter a lot. At my department the cap on the number of students can in some cases be a rather fictitious number (basically a placeholder that means almost nothing) that is easy to raise without any administrative implications - in such a scenario probably our administrative staff would make the change without consulting the instructor. In other cases raising the cap would amount to having the instructor do a teaching overload, which meant that they did not have to agree to do it. The precise rank of the instructor would also make a difference, since the employment of lecturers for example is governed by a collective bargaining agreement, whereas that of tenure-track faculty is governed by different rules and policies.
Bottom line, we can't say what the policies (and/or unwritten norms, which can also be a factor) are at your institution. However, if they phrased it as a request you can simply assume that you have discretion over the issue, and if you don't find the request reasonable, you can just say no and see if they'll push back.
However, I would caution you against asking for more compensation. While my experience is not with small schools, it seems to me that as a tenured faculty you shouldn't expect to have your salary adjusted on the basis of small details regarding the amount of work you do, which could reasonably vary quite a lot from semester to semester and from year to year. No department would appreciate having to deal with this level of pettiness from a tenured faculty member. What might make more sense is to ask for compensation not in the form of money but in the form of relief from some other work duties, such as service on a committee or other administrative work, if you feel (and can make the case to the chair) that that would be a fair bargain and prevent you from taking on an unreasonably high workload. Such a request might be declined, but it's unlikely it will be perceived negatively.
Finally, if we're talking about raising the cap by a few extra students, again it seems petty to quibble over such things. In that case you might as well say yes and profit from the good will you will be generating, which you are likely to be rewarded for at some unpredictable time in the future when you are the one who needs a favor.

It may be more appropriate to raise the salary issue in the course of ordinary performance reviews/promotion reviews/etc; flexibility and having taught more students than expected are enumerable examples of job performance.

I cannot thank you enough for providing such a detailed and extremely helpful answer! I admire your kindness in helping me!

One semester, in one of my big lecture classes, supposedly capped at 125, the registrar put 135 students in my class.  This wasn't a problem until the 6th week when I gave my first test and everyone showed up.   I had 10 more students than functional seats.  So I had the TA take 10 of them into the hall where they sat on the floor and wrote the test.  My complaints fell on deaf ears.  But one of the students called the Fire Marshall and suddenly ears were opened.  There's an occupancy limit for lecture halls and the Fire Marshall is no one to mess with.

@BryanKrause Serious question - do you guys have actual performance reviews with actual salary implications?

@xLeitix Yes; faculty can make a case for raises based on merit or equity. There's also the promotion calendar. My impression is that the review itself is mostly a formality (I am academic staff, not faculty) and I'm sure it depends on department but if faculty want to make a case for a salary adjustment that's the time to do it.

@A.R.  The registrar has the number of seats in the computer.  The keyword is "functional."  At a school where the football coach makes $8M a year, I don't think there's any excuse for having 10% of all the seats in all lecture halls broken.  As in the seat is missing or the writing surface is missing or a spring is sticking out of the seat.  But that's the state of affairs.  Or at least they could inventory and update the computer.  Anyway, yes, I didn't bother to count the seats because they were supposed to be counted.

When faced with requests to increase enrollment I usually agree, as long as the department ensures that I receive the teaching support I need. So - more TAs, graders, resources etc.
I think that flatly refusing is not reasonable. However, if you have concerns, absolutely raise them.
Make it about the students: You can say that your class is the size it is so as to ensure good learning outcomes, that you need additional support (be specific on that point), or perhaps even a co-instructor.
Whether you can ask for extra pay really depends on your contract. In my R1 university I can’t ask for extra pay if more students enroll, but there’s a standard ratio of students to teaching staff we need to maintain, so more students means more instructors. My contract does not say anything about maximum class sizes, just the number of courses I have to teach. What does yours say? If it says nothing then there’s very little you can do I believe.

Thank you for your answer! My contract does not say anything about the number of students either.

Don't forget room size, too...

@BryanKrause, when they raise the cap, they will find another room for this course.

@Zuriel That's good, but I would certainly double check that it's the case; when I was a student it was quite common that this did not happen in overenrolled courses and that sometimes administration thought that some students would drop a course and didn't have any solution when they didn't.

@Zuriel You are assuming a level of coordination and rationality that likely does not exist.

Generally speaking, course sizes are capped for a few primary reasons:

To control the teacher-to-student ratio.  I think that it is fairly widely believed / known that the fewer students in a class leads to better outcomes.  Thus class sizes are capped in order to improve these teacher-to-student ratios.

To limit teaching load. At a lot of institutions, contracts specify that an instructor will teach a fixed amount of "load".[1]

Because classroom space is limited.  The fire marshal (or local equivalent) limits the number of people that can be in a room at any one time, as cramming too many people into a room leads to safety problems.  Capping a course is done for these safety reasons.[2]

To ensure that last-minute registrants who need the course can get in.  There are some classes which fulfill university or departmental requirements, which tend to "fill up" quickly.  While more senior students typically get to register early, they sometimes forget or otherwise fail to register on time.  Colleges will often set class size caps a bit low in such high-demand classes in order to ensure that they can slot in a graduating senior at the last minute.

When you are being asked to raise the cap for a class, you should consider why that cap exists, and who established that cap.  Is it a cap imposed by facilities to meet fire code?  a departmental cap to avoid overloading a faculty?  or did you establish the cap to ensure that you have a number of students which you are capable of effectively teaching?
You should also consider why the registrar is asking for the cap to be raised.  Is there a particular student who really needs to get into the class?  or a cohort of students who got stuck without a class when another section closed due to low enrollment?  or is there just more demand than expected?
These things should weigh into your decision (and, ultimately, it should be your decision, as the instructor).
For myself, I generally try to say "Yes" to requests to enroll one or two students beyond the cap.  For one thing, I know that a large number of students are likely to drop in the first week or two (I teach math; many of my students are less prepared than they think they are, and bail when they learn that they actually have to turn in homework).  I also think that it reflects well on me to be a team player, and demonstrate that I'm willing to help out the department / division / college when the need arises.
What I wouldn't do is make a fuss about compensation.  I get paid a salary to teach classes.  To an extent, I don't have to, because my contract ensures that I will be compensated appropriately—but I think that if a contract is silent on overload pay (and I really would recommend that you look into that), I don't think that you win points by asking for a pay bump.  It comes across as kind of petty.
What you might ask for is a load reduction in the following semester, or a reduction in committee work, or some other mild perk in recognition  of the extra work you are taking on by admitting more students into the class.  However, even in this case, if you are only admitting one or two extra students, this may still come across as a bit petty.

[1] For example, my contract specifies that I will carry 16 load points every semester.  I earn 1 load point for one Carnegie hour of contact time in a lecture, 0.7 load points for one Carnegie hour of lab time (not that I teach any lab classes, but means that a one credit, three hour lab is loaded at 2.1 points), etc.  But these load computations assume a class with something like 25 or fewer students (I don't remember the exact number).  For every student over that set number, I accrue additional load points.  If I go over 18 load points, I earn an extra prorated bit of salary.  So course caps exist to keep faculty from going into "overload".
[2]  While working on my masters degree, I taught several sections of precalculus, with each section capped at a different, seemingly arbitrary number.  Upon investigation, I learned that these caps were exactly tied to the capacity of the rooms in which these classes were scheduled to be taught.

If the cap is because of a limited classroom size (your reason #3), then the faculty member wouldn't be asked to increase it. At any reasonable university in the US, the administrative staff would be aware of the physical capacity of the room and would know it's forbidden to increase the class cap beyond that number. What the administrators would likely do in such a case is contact the registrar's office (or equivalent office in charge of physical classroom space allocation) and ask to be allocated a bigger classroom, probably before or in parallel with asking for the instructor's consent.

@DanRomik (1) The cap may be set because of capacity issues, but institutions will often set the cap at a few seats below the MAX capacity so that they can squeeze a few extra people in.  But this often leads to a classroom that feels cramped (or, in one case, when a chair had gone missing, no place for a student to sit).  (2) The first part of the post is really just to outline the reasons that the caps exist in the first place.  Room capacity is a big one at a lot of institutions.

(3) I intentionally tired to avoid giving a prescriptive answer, and merely tried to suggest the things that one might consider when deciding whether or not to add more students.  And it is possible for a registrar to mess up and fill a room beyond capacity (if, for example, it is not the norm at an institution to cap classes because of room capacity, but there happen to be a couple of smaller classrooms with hard caps).

Generally speaking, I would anticipate that these decisions are a matter for the department to make.  I would recommend that you have this conversation with your department chair.  The specifics will vary from institution to institution, so it is hard to give detailed recommendations.
If you are concerned that the enrollment increase will have a significant impact on your workload, then I would suggest you let your department chair know about your concerns.  If you prefer to not increase enrollment, I would suggest you let your department chair know that as well, and ask them to support you in declining the request.  Then ask your department chair what they'd like you to do, and follow their instructions.
In any reasonably operating institution, assuming you have been a reasonable citizen of your department and a reasonable team player, I would expect that a department chair would want to try to accommodate your preferences; and if there is some overriding reason why that's not feasible, I would expect them to share that with you as well.  I think approaching this from the perspective of sharing your perspectives and then asking your chair what they want you to do will help set an appropriate tone for that conversation, as they are the boss and decision-maker for these purposes.
It would be reasonable and routine to ask your chair whether the department will provide additional resources, particularly TAs and/or graders.  It is institution-dependent on how these are allocated.  Normally, a significant increase in course size can increase workload, so it is reasonable to ask that the resources provided match the new enrollment size, and if it's not possible to provide resources that are customary in your department for a class of the adjusted size, then it would be reasonable to let your department chair that you are not comfortable expanding the course without those resources.  This doesn't mean you should necessarily expect to receive extra resources, if the resources you're already receiving are customary and routine for classes of the updated size, but it might mean that.  Only you and your chair will know the policies and norms for allocation of resources to courses.
If you're still not sure how to proceed, find a senior faculty member in your department who you trust and who is familiar with the department's practices, and ask them for their advice and input before you talk to the department chair.  They will know what is customary for the culture of your department.  Different departments might have different expectations, and only someone in your organization will know what that might be.

This answer attempts to address something I don't think is adequately covered in the other answers (to date). It is a supplement, I think.
My inclination, personally, is to agree to such requests and I have done so in a couple of instances that increased the number of students by 25%. In one case I was given extra (experienced) help for grading and in another just an apology that extra help couldn't be arranged as no one else was able to do it. But it was a temporary thing, not something that occurred regularly.
But the reason for this answer is that the needs of the students and their overall programs needs to be taken in to account, not just the needs and desires of the individual faculty member. If the course is an elective for which other possibilities exist it is easy to say no and hard to apply pressure from above.
But if the course is one in the major that is required and important for other later things, then saying no might disrupt the education of some students (see below). For example, a course in a sequence might be important to most students. Likewise an upper level required course might not have options for students about to graduate. All this is especially true if the course isn't scheduled for another year. In such cases, you might just need to "grin & bear it". You might, in some cases, need to adjust the pedagogy to make it possible, but that is generally a possibility in any case.

In an oversubscribed course it might be possible for the registrar or department head to select out a few students who don't really need the course at the moment. For example, some non-majors take some courses, but have other opportunities for electives. And, some courses don't require others as prerequisites, so a student schedule might be rearranged without loss to them.
It might also be possible to negotiate with the head that you drop off of some committee that takes time and effort so that it doesn't impact your research too much. Liberal arts colleges tend to be heavy on the service requirement, so this might be especially open to you.
If you were the department head I'd have some additional suggestions and you might consider raising them. One option is to split the course into two sections. Perhaps you teach both and someone else covers some other part of your teaching load, or someone else teaches the new section. For a course scheduled annually it might be possible (or not) to schedule the course in the following term and rearrange student schedules so that no one is adversely affected.
Another, somewhat odd, arrangement, is to factor out the few very best students and have them take the course as an independent study. You might be able to manage them separately with minimal guidance, perhaps by have them as a collaborative learning team that reports to you and you push along. I'm assuming small numbers, of course.

I'll also suggest with others that requesting salary increase is probably a non starter, and that speaking with colleagues is worth the effort.
Hmmm. Maybe the dean can find you a bit of travel money for the following year if you say yes now, they might hesitate to say no later (yes, a bit devious - sorry).

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Is it a good idea to name some mathematical objects after my thesis advisor?
I am doing my Ph.D. thesis in mathematics. I am wondering if it is a good idea to name some mathematical objects after my thesis advisor. The two objects I have in my mind are:

A representation, whose existence and faithfulness is a main result of my thesis. This representation has not be studied before and thus unnamed.
A collection of subgroups of a certain group, which have been studied by others but with no specific name assigned to those subgroups.

I did not ask this question directly to my thesis advisor since I believe that out of humility he would decline this request. Have asked this question to a mathematics professor from another university, who personally knows my advisor well and he says that it was a very good idea. But he was somewhat drunk when answering my question and I am wondering if I should take his answer seriously.
Edit: The representation I have mentioned is similar but different from a classical representation, which is named after the mathematician Emil Artin. In this case, should I still call it "Artin's representation", or "(my advisor's surname)'s representation", or leave it unnamed?

You could for instance call the representation $\rho$.

If you need a name for a representation which is similar but not quite like an Artin representation, you can reflect that in a proper name, which contains "Artin" and an adjective describing the change.

Is it possible for you to talk to that other professor again, when he's sober?

@DavidWallace Not easily... He lives in a different town which is a few hours flight away. It seems that the advice I get from here is more reliable than his personal opinion.

Well, there's this new-fangled thing called the telephone that might be useful in a case such as this.

Yes, @DavidWallace, but if the majority here agrees that it is better not to use my advisor's name, I will just forget the suggestion of the other professor.

Honestly, I think two factors - the fact that the other professor knows your advisor personally, and that the other professor works in the same field - make that professor much better qualified to answer the question than a bunch of semi-anonymous internet people whose qualifications you can never be sure of.  At the very least, he might give you some things to think about - reasons why naming something after your advisor is a good idea, or reasons why it isn't.  I don't see the harm in at least talking to him.

I see! Thanks @DavidWallace for reminding me this!

FYI, Buchberger named Groebner bases after his thesis advisor, in his thesis. But the concept was not very closely related to something already named after another person.

It sound as though your advisor was not the first to study/define/use these objects, but rather you just want to name them something, and think it might be nice to name them in honor of your advisor.  Please don't do this.  You'll only contribute to Stigler's law of eponymy, confuse people, embarrass your advisor and/or offend whoever was the first to study these objects.
Bear in mind two things: (i) Not every random object deserves a special name.  (ii) When you name objects, name them in a descriptive and evocative way, that will make using the terms intuitive and non-confusing (as a corollary, it also shouldn't conflict with other notation).  Many people don't even like the idea of name any mathematical objects after people, though it's common practice.
Now that naming them after your advisor is out of the way, you should feel free to consult your advisor on naming these things.

+1. Mathematical objects are not like beetles or asteroids; we don't name them after people just to generically honor them. If a mathematical object takes on the name of a person, it's because there is a consensus in the community that this person deserves the credit for introducing the object.  It's not a decision that the discoverer, or even early practitioners, get to make.

Thanks for the advice! For the representation that I mentioned, theoretically I am the first one to study it in my Ph.D. thesis and my advisor has helped me a lot in the study. In fact, some key ideas in the proof of its very existence are from my advisor. In this case, since it is unnamed anyway, should I name it after my advisor?

Zuriel, no, the proper thing to do is credit him with suitable acknowledgements in your thesis/paper.  And it's typical that advisors help students with key ideas.

However, it's possible that his name could get associated with it later by someone else.  I recently wrote a paper about a conjecture in someone's thesis paper.  He did not name the conjecture after his advisor, but it was clear the advisor had this conjecture in mind first, so I named the conjecture after both of them, even though the advisor's name was not the paper where it was first stated.  (I checked with the advisor first (his student is no longer in academia), whom I know, to make sure this was okay.)

@Zuriel: As I said, I agree that you should not. Make it clear in the paper what his role was in inventing the objects, and choose a descriptive name, but leave it to posterity to  decide if they are interesting enough to name after someone, and if so who. Like I said, this is not up to you. (The "interesting enough" criterion is significant too: having something trivial or uninteresting named after you is an extremely dubious honor, and you are not in the best position to judge this.)

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Is concentration an extremely important working habit?
I study mathematics and by "working" in the title, I mean researching and serious reading on my field (reading difficult papers, books, etc.) I believe the answer for other fields would be similar.
Am I right in saying that concentration is an extremely important working habit? I definitely feel that my working habit needs improvement: I stop working and check email/facebook, read news/forums, or even play a few blitz chess games from time to time. I believe that it is very distracting and that my efficiency is low. I also listen to music but this is probably less distracting and sometimes may even be helpful.
Is it right to say that an ideal working habit is that

Be completely immersed in working, avoid all possible distractions, refrain from visiting any irrelevant web sites, turn off mobile phone and email notification. Work for a few hours until reaching a planned milestone, or when the body forcing a stop (micturition, hunger, low energy level, etc.)?

What's your question? I don't see anything beyond "concentration is important, isn't it?" But that's not even a meaningful question, and somewhat banal. So what is your question? What aspect of academia are you asking about, as per the [help/on-topic]? To help get to the bottom of this: what would you do with an answer? Why is it important to you to ask this? In what ways does this represent an actual problem that you have faced?

@EnergyNumbers, I need some expert opinion on my working habits and I am basically asking how important concentration is: is it absolutely essential? How can one be more concentrated while working? I have listed a few plans such as refrain from visiting any irrelevant web sites, turn off mobile phone and email notification; would appreciate if someone would comment or add something on it.

That's rather broad: there's a whole Stack Exchange devoted to [productivity.se]

@EnergyNumbers thanks! I was not aware of it. I assume that the working habits of mathematicians, scientists would be different from those who are in other fields such as athletes or businessperson; that's why I ask it here. Not sure if my question will be considered as off-topic.

As a mathematician, this is a very personal matter. Some people work 9-17; some have very irregular working times. Some have a habit of always going to the office to work, to help mentally separate 'work' and 'time off'; some work from home when they have no teaching or administrative tasks to do. Some people listen to music, some don't. Some check their Facebook at work, some don't. Some work in long streaks, some prefer to have a quick pause every half an hour or so.
Do whatever works for you. At this point in your career, you have been a student for at least 12 years; you should know yourself and be able to evaluate your productivity objectively.
This is even more true for a mathematician: mathematics is mostly a mental endeavour, and it is easy to start thinking about your work in your head when you are engaged in other activities, such as walking, driving or showering.
Sometimes your best ideas will come when you are not actively working/studying. Of course, you can't do everything like this, but the important ideas often strike at improbable times.
If you are a student starting out with maths, the only advice that I can give you is plan ahead, and recognize when you are going to be late if you don't increase your productivity. Many students can't tell when it's the moment to really turn off your Facebook and start studying until it's too late. Poor midterms should be taken as a big warning sign.

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Accused of cheating by proctor due to information on scrap sheet
Sorry if this is a bit long. I took a final for an intro elective (I'm a college senior), a pretty easy A- GPA booster class (average before this final was 90+).
I have learning disorders so I get to take the exam in a private room. Shortly into the exam, I asked to take a bathroom break and grabbed tissue from the washroom. Then I went back into the exam room and continued, got carried away and started doodling on one of the tissue papers. I believe I wrote about three words on the sheet before the proctor came by and asked why I had unauthorized "notes". I explained that these weren't notes and just me doodling. He asked why I didn't doodle on my scrap and I said I was using my one scrap sheet for actual calculations and didn't want to run out of space on it. He said ok but that we would need to go to the head proctor and report it just in case, and if she was fine with it I could keep writing. He gave me back the papers and we got up to head out to her office.
Once out of the exam rooms, he said on a second thought to give him the papers instead and he wanted to hand them to her. I said no, sorry, I can't do that, we are already heading there, whats the big deal with me holding them? He said something about protocol, but I told him I didn't feel comfortable with handing him my papers.
He then tried to grab them from me, which was when I ran into the bathroom because I felt like he was trying to attack me (been raped before - guess I got triggered). He goes into the bathroom with me still trying to grab my papers. I ran out telling him to get another proctor because I am feeling harassed and uncomfortable, so I went into the next washroom and he followed me in there. I had a panic attack, and ran out again trying to get as far away from him as possible, that was when he called a female proctor who sat with me the entire time in the hallways till they brought a counselor. Now he claims that I cheated with unauthorized notes and I have to go to a meeting with the dean.
Also they are bringing as evidence my scrap sheet because I had previously been given the same exam but couldn't complete it due to being sick (I memorized a keyword from each question wanting to see (also kind of hoping)  if they would administer the exact same exam and matched the old questions to the new ones). I don't see how that has anything to do with the three words I wrote on the other sheet.

What is your question?

Basically how do I prove that I did in fact memorize the questions? They sent me my scrap sheet where i matched version 1 to version 2 so even if I match it again they'll say that I already saw it from the evidence file and memorized it then.

If I were the Dean, I would ask you this question: "Why did you grab tissue from the washroom?".

I had a runny nose, and they saw me with the tissue.

If you memorized the questions, just write them down or match them again in the presence of the dean, should be the fastest way to prove that.

Are there any witnesses to the part where he tried to grab your sheets and you ran away? Someone who could testify if the proctor's behavior was out of line?

Matching them again wont work because they already gave me my scrap as evidence and will say that I looked at that.

There should be witnesses to the fact that he followed me into the washroom on two different occasions and that I had a panic attack because of his behaviour.

I think one important question is the story he is telling. Is he openly lying about his actions or what happened, or does he just have a different interpretation of things than you do?

I have no idea what story he is telling. But I also dont know what he cold be telling that would justify following me in the washroom, there were two other proctors that happened to be absent the whole time till I ran out of the washroom trying to get away from him. But they had to get a counsellor because I had a major panic attack - i've been sexually abused before, being trapped like that was very triggering. However, I dont want my state to be seen as a reason for cheating or something.

Well, he thought you were cheating and hiding evidence, and when he tried to get a hold of it you suddenly ran to get rid of said evidence. I can understand why he would follow you and try to stop you under these assumptions, so I think it would be best to talk things out instead of assuming evil intentions from his side. In the best case, this is just one big misunderstanding that can be sorted out. Either way, it doesn't seem to fit the Q&A style of this page, as there is no concrete question we could answer here.

I wasnt planning on suing him or anything. Just worried that he would try to justify his actions in some way hat would cause me to look bad. I admit that when I left the first exam I was really hoping to get the same questions as I had looked them over, but there was no way of knowing for sure that I would, and my main motivation for memorizing stuff from the exam was to figure out if they did in fact recycle questions and possibly use that to my advantage next time. However, I did not do anything against the honour code on cheating.

Does your school allow you to bring a lawyer or other counsel to the hearing? If so, I strongly suggest you do so -- even assuming everything you say is accurate, there are enough pieces that do not add up that simply explaining the above may not be sufficient; counsel can advise on the best way to proceed.

I'm going with my counsellor. She was called when I had a panic attack after what happened with the male proctor and she helped me set up my counselling and doctors appointments and get back on sleeping and depression pills. The proctors actions have really opened up old scars. I don't know of any lawyers to call on such short notice, the meeting is tomorrow. I have booked a meeting with the ombudsman for after the deans meeting if it is needed.

I'm sorry, but it looks like it will be impossible to prove your innocence under these conditions.  You refused to follow the instructions of the proctor because you "didn't feel comfortable with handing him [your] papers" (which is not a sufficient explanation), and later failed to control your emotions and ran into the washroom as if you were trying to get rid of some evidence.

He went in there with me though, so he watched me the whole time till someone else showed up.

Also he was the one that initially told me to take them myself, if he had taken them when he first asked me to go with him, I wouldnt have them on me in the first place. I should add that I write my exams in an exam centre due to having an anxiet disorder, I dont do well with sudden change like that. I panicked which is why I was hesistant

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Processing Submissions on arXiv
My submission has been processing for two days now, is this normal? I know that submissions might get the tag [on hold] and take a long time, but arXiv says that if this does not happen, submissions tend to stay in the "processing" phase for a relatively short time. My question is whether two days classifies as a "relatively short time" and, if so, how long does a submission usually take to process? If it does not classify as a relatively short time, who should I go to to ask for help?

My guess is that the time in processing status follows a roughly bimodal distribution. The first peak is when everything goes well, and certainly occurs before even a day has passed. The second, presumably broader, peak depends on how long it takes the automatic processing system to fail, and someone to have a look at it. I don't know where this second peak is located, but the point is that I expect there to be two "normals", depending on whether your submission had technical issues or not. Personally, I'd feel justified in contacting arXiv after three days or so.


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Uploading preprints of old Elsevier papers to arXiv, and updating arXiv preprints by newer versions
Let's say that my first scientific paper was published in 2010 in one of the Elsevier mathematical journals. At that time I didn't care about uploading a preprint of the paper to arXiv which I now regret. Is it ok to upload the paper to arXiv today? Do I break my license agreement with Elsevier by doing this? Is it appropriate?
Also, let's say that I uploaded a preprint of another paper to arXiv 6 months ago and at the same time I submitted the paper to one of the Elsevier journals. I was asked by the Elsevier reviewer to make a revision of the paper. I made the revision and the paper was accepted for a publication. Is it ok to replace the original preprint on arXiv by the latest version of the paper which will be published by the Elsevier journal?
Finally, assuming that the answer to the previous question is affirmative. Is it ok to replace an original preprint of yet another paper by its latest version even if the paper was published three years ago (but I never replaced the original preprint by any newer version)?

Hi, I added 'Elsevier' to your title since the question mainly seems to be about their preprint policy. Hope that's ok with you.

Yes, it should be okay -- see the 2013 version of their license policy at https://web-beta.archive.org/web/20131022235944/http://www.elsevier.com/about/open-access/oa-and-elsevier/oa-license-policy . It lets you do the same even for other people's papers (cf. http://www.cip.ifi.lmu.de/~grinberg/algebra/dkr1978.pdf ).

This is covered on the Elsevier website. Some key points:

An accepted manuscript is the manuscript of an article that has been accepted for publication and which typically includes author-incorporated changes suggested during submission, peer review, and editor-author communications. They do not include other publisher value-added contributions such as copy-editing, formatting, technical enhancements and (if relevant) pagination.

and

Authors can update their preprints on arXiv or RePEc with their accepted manuscript.

and

Preprints should not be added to or enhanced in any way in order to appear more like, or to substitute for, the final versions of articles.


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Use of QR codes in academic publications
Modern academic publishing is based to a large extent on the use of the Internet, and many of us consult articles or even books mostly in PDF format rather than hard copy. URL links to both reference material, and data sets or complementary material the author makes available to the reader are becoming commonplace, and are easily accessed from within a document that is consulted in electronic form.
However, in some cases the document can only be accessed in paper, which makes following a URL awkward. Examples of this could be some editions of books available only in paper form, or CVs (as discussed in this question on SE: Is it advisable to have many hyperlinks in an academic CV?).
In similar circumstances, both the manufacturing industries and the marketing sector tend to use QR codes that are easily scannable from a mobile device, such as this one containing the URL of Academia on SE:

To date, I have personally never seen the use of QR codes in academia.
My question is therefore: what major factors make the use of this technology less likely to become commonplace in academic publishing - or more likely, as the case may be?
Edit: thanks to a comment below, my attention has been brought to some scientific books by Elsevier and O'Reilly that do contain QR-codes to enrich content with online material. In both cases, the field were Computer Science and Technology in Medicine.

This is a comment as maybe I'm an outlier, but I'd find typing academia.stackexchange.com into a browser many times more convenient than using a smartphone with the appropriate app (my smartphone, new about two years ago, has no native QR reader and almost no space for new apps) to scan it. Not to mention I can easily write down the URL, and remember it.

@dbmag9 This may be true in many cases. But what about this one (from my thesis): http://ark.intel.com/products/33082/Intel-Xeon-Processor-E5440-12M-Cache-283-GHz-1333-MHz-FSB

I have seen academic books (e.g. by Springer) that feature a QR code on the cover, and another one at the end of each chapter, that links to the electronic article. Also, finding QR codes on posters presented during conferences, or even on slides, has become pretty much commonplace in my field (that doesn't mean everyone uses QR codes, just that I have frequently seen them used on almost every conference I have recently been to).

@O.R.Mapper Interesting, thanks. There are none in books I own, probably because they were originally published some years ago.

To add to my previous comment: This blogpost shows an example of a conference where QR codes were used in 2012. (Other than that, I'm confused by the blogpost. The author claims it is a medical conference, but it actually seems to be a CS one, on social media. Weird.)

@O.R.Mapper I'm also in CS; have just found codes in some O'Reilly (recent) editions. So it may be more common in some fields than others.

http://shouldiuseaqrcode.com/images/flowchart.jpg

@O.R.Mapper. That blogbost quite clearly describes a medical conference. The first talk mentioned was "Pilot Project of Personal Digital Assistants Use by Ethiopian Emergency Medicine Residents" and the second was "Accuracy of the iPod Touch for Detecting Self-Paced & Prescribed Physical Activity". Okay, it looks like it was a "use of tech in medicine" conference.

@TRiG: True. I got confused because the conference was called "Med 2.0", but the subtitle is "World Congress on Social Media, Mobile Apps, Internet / Web 2.0". On the other hand, when looking closely, I realized that there is an even longer form of that subtitle that adds "in Health, Medicine and Biomedical Research".

In my field it's increasingly frequent to see QR-codes on academic posters at conferences. They usually link to a downloadable version of the poster that replaces the handwritten email list that used to be pinned by each poster to request copies.
In one of the last one I made, I included QR-codes that linked to little GIF animations of my results. People could scan and watch the animation (finite elements models, motion measurements etc.) on their cell phone.
Their advantages in academic articles however is less evident, as most articles are read online and can include clickable links. Note also that journal article have an archival function and it's generally discouraged to publish links that might go obsolete. It's necessary to include all the information in the article itself or rely on the journal's own archival of external material. Hence, I believe, QR-codes are not useful in the context of published articles.

Had not thought of conference posters, good one.

+1 for use on posters. That seems like the one place where it would be more convenient to whip out my phone. I can then save the resulting link for later reading on a device with a real screen. :)

In one of the last one I made, I included QR-codes that linked to little GIF animations - how many people actually scanned these? I see QR codes on posters occasionally, but I rarely see anyone actually scan them.

@ff524 I guess that sums up my motivation for asking this question; QR seems to be used quite a lot in certain situations (even aircraft boarding passes), but does not seem to have caught on in academia. Most people present at a conference will know how to use QR, but may not have the reflex to actually do it in this context.

Re usefulness of QR codes on published material, lots of people (like me) prefer to print a PDF rather than read it on the screen. The QR code might come in handy in this context IMO.

@ff524 I got about 5 to 10 hits per link excluding my own and to ones of my colleagues.

I think this is a matter of convention and necessity.  As you already point out, most documents are online.  If something is online or in pdf form, having a QR code that is scanned with a phone is a waste of space, as the user can just click on the link instead.
In the case you are describing, I find it rare that any document would be only available in paper form, if it was made at any time since the invention of the QR codes existence (which it would need to be in order to have one).
The question also seems to be a rare situation.  You are saying a new document is published, but it is only available in paper, but it contains other information that needs to be seen online.  It is hard to imagine a document which is in paper, that contains some valuable data that needs to be viewed on an electronic system, in which the time saved from scanning a QR code on a phone and dealing with a phone screen outweighs the use of a tiny url or permalink typed into a computer.

Indeed, I agree with most of your comments. This question was in fact inspired by the discussion about the question on CVs that is referenced, where the committee evaluating candidates' CV would often have immediate access only to a printout of the same. Perhaps some manuals are also still published in paper form, to avoid or at least hinder issues with illegal distribution of PDF copies.

@ALANWARD  Right, but the issue (currently) with QR codes in that context is the device.  If they committee is on a desktop, or looking at a monitor with a projector shared, how will they scan the code onto the computer, and I for one do not enjoy serious reading on my phone.

"do not enjoy serious reading on my phone" - neither do I :-/ . There are QR code converters for computers, such as the qtqr software for Linux. However, the question as originally stated concerns more printed material than a projected electronic version. Granted, this is -as dbmag states in a comment- a bit of an outlier situation.

Worth mentioning that there's a tinyurl-like scheme already used for almost all research publications -- the DOI (Digital Object Identifier)

@BenVoigt Yes, perhaps QR could be a good way of scanning DOIs from paper support into a computer to access the content on-line. As for electronic supports, I would guess most of us do the now traditional Copy+Paste. ;-)

@user1938107 Although your answer sums up nicely some of my own feelings on the subject, I will be accepting Cape Code's answer due to the poster twist that I had not thought of. My thanks to both.


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Role of textbook reading for a PhD student
When I start reading a research paper in my research area, I flooded with a lot of new words, techniques etc.. In the majority of cases, I start reading the relevant textbooks for expertise in order to understand the research paper well, instead of going to research papers again. I am not sure whether it will work, but gives it confidence in the topics under research.
It is well known that textbook reading may take lot of time and energy. Continuity can also be an important factor while comprehending a textbook.
At least in my university, studying research papers is much encouraged by experts or professors. And supervisors, known to me, suggest textbooks to read very rarely. I am not sure about the practices of other countries.

What is the role of textbook reading for a PhD researcher?
Is it underrated? Why do some supervisors ask for reading research papers only, and don't give explicit priority to textbook reading?
Do PhD students of top universities has habit of reading textbooks?

Use all tools at hand as you find use for them. Textbooks fill certain niches.

@Aruralreader Why do supervisors then does not tell it explicitly? But tells about reading research papers? Does it happens only in developing countries?

Earlier today, I answered an email from a prospective student who asked for suggestions of things to read in my area. My answer listed just textbooks.  On the other hand, by the time you're doing independent research, you'll very probably need lots of background knowledge that isn't (yet) covered in textbooks, so you'll have to read the relevant papers.

My advice @hanugm: Your career is in YOUR hands. Don’t imagine your instructors to be your educational parents, they are helpful guides, imperfect and human, that’s all. The ball is in your court. Learn what you can and, most importantly, understand your field with any and all resources available to you. I wish you best in your future endeavors!

One thing I have found quite useful when textbooks are scant are certain PHD theses, which are often written with less knowledge assumed than the average paper. Reading the introductory sections of a relevant thesis can be helpful background.

There are some very good textbooks which are worth reading, but it really depends on the book and how much thought has gone into it.  I get the impression that some textbooks are just dumping grounds for a bunch of minor results and lemmas which an academic has found along the way, and which they then tie up with exposition into a long narrative.

I suggest training yourself to read textbooks. I didn't need to in high school and usually didn't need to in college. By the time I started grad school, I wasn't used to reading textbooks except as occasional references. I really wish I had trained myself to read them earlier.

One of the things that I feel gets scrambled a bit in math/compsci pedagogy (which I'm inferring OP works in) is you need to get to a point where you can read/scan a math book a not do exercises, which take up way too much time. That sets you at a point where you can reasonably transition to reading journal papers (which obviously don't have any exercises). YMMV.

Although I use textbooks to an extent, these days lecture notes provided by professors from universities around the world are a lot more useful to me.

I am probably not a great role model regarding this, but I read something like 100 papers in 3 months when I started my PhD research, and after than I was only reading whatever papers and books that were necessary to solve some specific problem.

I am an established academic and I read textbooks.  I read introductory texts when moving into new areas, and more targeted texts as reference material.  I also watch YouTube videos - if someone else has taken the time to put information in a context that is easy for me to absorb why not use it?
What you should be considering is what you will get out of the text.  Textbooks are usually great for general background information or to overview a field.  They can also be helpful to learn specific techniques.  Sometimes, there'll be a text that perfectly introduces what you need, and does it well.  When that's the case - use it.
As a newer researcher you need to make sure that you are reading in a structured and organised way, not just randomly trying to absorb everything and equating reading with advancement.  Sometimes textbooks are useful.  Other times they are not. Just make sure you are reading with purpose.

Reading whole text books takes a lot of time and should only happen in cases were the book covers your PhD topic or closer field to a large part. Beside that, I would limit reading selected sections or maybe chapters, to understand common knowledge.
Usually text books teach you common results most researchers would agree on. They try to be comprehensive and teach the reader. Papers discuss new approaches and ideas, which might turn out to be insufficient or plain wrong. Over the time the idea of a paper might be embedded in a larger context or be viewed from a different angle, which might make it easier to understand.
You have to do both as a PhD student:

you have to get the common knowledge, that should happen in your Bachelor or Master studies. There your read text books. As a PhD student you should know the terms and common knowledge and read less text books.
you have to understand the current research in your field and compare your own work this the work of others. For that you read papers. In most cases, you don't have to understand every detail, but you should get the idea. Maybe you have to learn to skip understanding these details. Only papers that are very close to your work, you have to understand bit by bit - because you have to explain what distinguishes your work and why your approach is worth investigating.

A really well-written book or monograph can reduce the time required to get the core content from up to a dozen or more research papers.
A deep research paper can have ideas hidden in it which even the experts (and sometimes authors!) have missed.

One of the ways one succeeds in research is by finding ideas which others have missed. Such insights are unlikely to be found if one follows a well-laid out development such as is often seen in textbooks.
On the other hand, there are many forests worth of research papers. You could easily miss the trees if you spend all your time in them!
An approach that has been useful personally (for mathematical topics) is to make notes on assumptions while reading research papers and go back to those notes if one looses the track completely. The assumptions could then be followed up through textbooks. Similarly, while reading texts, it can be quicker to avoid reading "line-by-line" and fix "rough" arguments on one's own. If a sufficiently wide gap in one's understanding is detected, one can go back and read the relevant section in detail.

This depends very much on what you're trying to learn, but you should never rule out the right textbook (or any other tool you can use to acquire knowledge, for that matter).
In quite a few cases, if you're brand new to a field you may not even be able to follow research articles until you've hit the textbooks.  If for no other reason, in early papers in a field notation hasn't even been settled upon.  Newer papers will tend to use consistent notation, but probably wouldn't provide definitions for the unfamiliar.
Also, some stuff you need to learn to round out your education and help you communicate with those adjacent to your space.  I did my PhD in a systems neuroscience area, and was woefully inadequate in neuroanatomy at some point.  It would have been a huge waste of time to learn neuroanatomy from the literature when there are dozens of good textbooks -- and I used the textbooks.  I may not have the understanding of a practitioner in the field, and my knowledge isn't nuanced, but I'm not a neuroanatomist -- I'm a neuroscientist that needs familiarity with neuroanatomy.

There are many different qualities of textbooks, after all! :)
Many are exactly imitations of older (not necessarily good, but successful) books, perhaps with better graphics, or some other superficial changes.
Some have resonated with for-profit publishers' ideologies, and are heavily promoted.
Etc.
Even among those which aim to serve their subject, there is often a tendency to be toooo encyclopedic, which has some virtues (for reference purposes), but does certainly heavily mask story lines.
And, yes, sometimes there are monographs ... which can be exactly what you need, if they hit your interests, or can be completely orthogonal to your goals.
It is highly non-trivial to gauge the quality of a book without looking through it in some detail (not to mention having an idea about the relative competence of the author). So, for myself, I've bought (out of my own pocket, supposedly from my clothing budget... :) thousands of books, most of which are high-end textbooks. I've looked through every one, searching for potentially amazing ideas that were previously unknown to me...
EDIT: Likewise, I certainly do also look through a great many on-line preprints for the same reasons...
Yes, some expense, and one of my activities is to try to replace some ridiculously expensive textbooks by my own lecture notes, in several subjects.
But/and both for my own purposes and for purposes of competent exposition, I do need to know whether I'm missing something... especially in fields where I supposedly am expert. :)
True, not everyone can skim through books or large papers quickly. So a strategy that requires that may be infeasible for some. I'd hesitate to "excuse" it, though, as though not doing so were essentially irrelevant.
Yes, I do essentially require my own research students to read most of my own notes, as opposed to explicitly requiring reading of "official textbooks", but this is less forgiving than it might sound, since my own notes do cover quite a bit. And, my people seem to be inclined to look at the standard textbooks in any case.
(This is in math, at an R1 state school in the U.S.)

I rather suspect this is very much down to the subject being researched. As someone who has a Ph.D in Chemistry I would have said that 90% of my research needs came from published papers and monographs as they were probably the most relevant source. Chemistry textbooks would give you a valuable insight into the fundamentals of an area but research would be far more up-to-date.


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Proper salutation in email for requesting a resource
Suppose I read a research paper and write an email to the authors, requesting some resource or asking a doubt. I know the email address and author's name from research paper.
What is the proper salutation? Is it proper to use "Dear sir" or not? What are the other alternatives to salute?

@hanugm One piece of advice, if writing to someone outside India, I'd avoid the word "doubt". In American English, "I have a doubt about your paper" might be understood to mean "I think your paper is wrong". https://www.merriam-webster.com/dictionary/doubt

Per this meta discussion, I have changed the duplicate target to a better match.

Dear sir reads as an Indian english address to me. I don't know whether it would be the preferred address in an Indian academia context, but it sounds a little odd in an international context.
If you want to be formal and are writing to US or UK people, then the form of address is "highest title - lastname". This could take the form of "Dear Prof Smith and Dr Doe". In the US, everyone from assistant professor upwards is addressed as "Prof", whereas lecturers, senior lecturers and readers at UK universities are addressed at "Dr".
If you are addressing people in Germany or Austria, the formal way is to list all titles + last name. So here the typical form is "Dear Prof Dr Schmitt". If you were to write in German, you'd add in a "Herr" or "Frau" as well, so "Sehr geehrte Frau Prof Dr Schmitt".
The many countries not mentioned here will also have their own customs. However, given that academia is a very international endeavour, and given the US cultural dominance in international stuff, no reasonable person will be offended by a "Dear Prof X"/"Dear Dr X" address.

Very good answer, great context. I'd just like to add that all your proposed forms of address (in English) have an added benefit of not having to guess at the recipient's gender. Though most often there should be no need to guess as more and more Universities request staff maintains profiles with pictures, so it's usually easy to find that info.

I would, in German always Adress unkown people with "Sehr geehrte/r Prof. X" and then see what they reply. In subsequent emails I always adress them however they adressed me. "Liebe/r" seems to me informal and I would only use this for someone I have already spoken to. I ave encountered too many German academics which were really insisting on such formality at  least in the first email.

@JennyH Good point, I've corrected the German address. These days I'd probably just write in English anyway, as I prefer the gender-neutral options.

Regarding Austria: Yes, it is customary to list all titles on door plates or on the envelope when writing a formal letter, but the address is usually just "Sehr geehrte(r) {highest title} {last name}". I can't remember ever having been addressed in a mail as "Sehr geehrter Herr Dipl.Ing. Dr.techn. X Y, Bakk.techn.".

Look up who the corresponding author is, if it's a co-authored paper. This is usually indicated in a footnote. If it's a single-authored paper, use the name and title of the single author. Let's say the name and title are Dr. Jane Doe. Then the proper salutation is simply:

Dear Dr. Doe,

Generally, if you're unsure, you can never go wrong with Dear Prof. Dr. Surname. If that person is not a Prof., no problem, they'll correct you if needed.
I would only use Dear Sir, if I was unsure to whom (person-wise) my e-mail is addressed, for example, if I'm contacting an organization.

"Prof. Dr."  Only if they speak German.

Some recipients might be offended, but there is no rule or set of rules for salutations in e-mails. In theory, "Hi…" is as good as anything.
To be most polite, you would follow the same etiquette laid down for "real" letters on paper, which is best expressed in full editions of Chambers Dictionary and Debrett's Correct Form, backed up by Burke's Peerage.
Be careful using "Dear sir" which is insulting without a capital "S" or if the recipient isn't a man and lazy if the excuse for not using a particular name was that you were writing to a company.

Dear Prof. X
Even if I suspect the person is a grad student I use the above. (And others did to me when I was.) Hard for anyone to be offended, and you don’t need to be overthink it. Some may find it overly deferential but few will find it insufficiently so. “Dear Sir” is worse as it presumes a gender. “Dear Dr” is worse as in some (European) countries you risk demoting someone. “Hi Firstname” or “Hi” or “Good morning” risk being seen as insufficiently polite by people who get upset about this kind of thing.
Sometimes I write to people I know in their role as editors, etc. Then I will sometimes use “Dear Prof. Lastname, Dear Firstname”. Someone did the same to me today. I wasn’t offended by the additional formality.
As someone whose name is frequently mis-spelled I urge you to double check it before hitting send.

Nowadays I almost never use salutations in an email and just start straight in with my message. I see email as different from formal paper written correspondence and I believe  that many recipients see it different also.
Just as in Stack Exchange, I treat salutations, greetings and signature blocks as pure fluff that get in the way of the communication. However, others may have a different view.
I am, however, quite careful to ensure the leading sentence is polite, and explains the purpose of my query. Something like would be the very first line of my message:

I am interested in your paper "...." and am wondering if you would be able to answer a brief question ....

I always try and make the subject line clear as well, knowing some sort email by seeing sender and subject before reading the contents.
So my answer is remove the salutation, and it avoids the whole question of getting it wrong!

Well, you may treat them as pure fluff, but many other people would consider an email from a stranger starting directly with "I need your data set" to be rather impolite. And given that OP explicitly wants to be polite ...

I often use a no-heading and no-or-minimal-signature email with people within my organisation that I work with (usually when I know they're expecting the email) but it sounds a bit too bold for cold emailing somebody.

Related: https://www.nohello.com/.

@TrangOul Not sure how that is relevant here, since adding a salutation in an email followed by the actual content below it is very different from just sending a hello and waiting for a reply.


text:
Citing a math theorem with errors
Suppose author X writes a paper, and in this paper, they prove a result that is a very small part of their paper. However, the result has a mistake. Based on personal judgement, it appears the mistake is an innocent mistake that does not disrupt the intellectual flow of the paper. i.e. it is very reasonable to believe the author X had the ability themselves to get the proof right. In fact, it may have been simply a typo. Nonetheless, it is unarguably incorrect.
Author Y comes along and builds other results off of the (corrected) ideas by author X. Author Y wants to (for good reason) cite author X, as their results would not have been obtained without author X.
What is the correct way to do this in a paper? The way I see it, there are 2 possible actions for author Y:

Pretend like author X didn't make a mistake at all and give them full authority on their theorem.
Say something like ... "the results are based off the ideas by author X" but don't give as much of a "these are author X's results" flavor. Author Y then after mentioning author X, proves the theorem themselves.

Action 2) seems to be the most reasonable in the sense that it is intellectual honest and doesn't shame author X for no reason. However, is it considered plagiarism to be somewhat vague about what author X did?
Thank you.
EDIT: I realize another option is to allow author X to correct their mistake and then do action 1. But with how slowly paper publishing occurs, this seems unjustly detrimental to author Y so I don't consider it a real option.

Inform author X of the typo/error so they can proceed and publish an errata or whatever they feel is appropriate. Independently of this: I suggest to go as in option 1), maybe including a footnote indicating that there is a small inaccuracy in the printed statement in author X's work, and that the statement you are giving is the correct/intended version.

@AndrésE.Caicedo do you disagree with Robert Columbia re 'We provide a corrected proof in Appendix A.' or otherwise?

Given the situation as you describe it, in particular that there is evidence that the author could have corrected the presumably-small mistake themselves, I'd recommend that you quote the true assertion, and/while noting, literally, that there is an easily correctible error or typo in the proof as written.
Catching typos is important, but is not "research", of course. And, yes, once typos or silly mis-statements are pointed out, many authors can repair them without hesitation. So I myself generally consider "paper X" to be "paper X with all trivial typos and obvious blunders corrected". (Still, yes, sometimes the boundary of this is not clear...)
In particular, yes, I give credit to authors for obtaining a result who've slightly messed up the argument, both for observing what is true, and for at least approximating the proof.

My advisor did precisely this in one of his papers.  He cited the earlier paper for a particular result and added a footnote, which pointed out the easily correctable error in the older paper.

To add to this, mathematical typos are pretty common, and when they're "obvious" they're probably only worth pointing out if they're in a statement of a result, rather than a proof, as a note to people who might look at the paper without reading it carefully.

I've seen all sorts of ways of addressing this issue, some more questionable than others. In a recent paper, the authors solve what they call a conjecture of so-and-so. They also describe some issues with a potential attempt to prove the conjecture. If you go to so-and-so's paper, you see that there is no conjecture, instead the result is stated as a theorem, and a proof is given. The "issues with a potential attempt" actually describe the mistake in the published proof.

Thank you for the advice. All of the answers seem very reasonable!

You may want to phrase it carefully, just in case that either you are mistaken or the author is sensible about this. Maybe you can write something like "We obtain the same result as in [1] but with a different multiplicative constant" instead of "We obtain the same result as in [1] but they messed up the scaling factor". Then the reader knows your result and the author can have a look at the difference, but you did not accuse anyone.

paul garrett, do you disagree with Robert Columbia re 'We provide a corrected proof in Appendix A.' or otherwise?

@BCLC, providing a corrected proof, if the errors are not completely trivial, can be worthwhile, in my opinion, as it really does carry out the execution of the expected corrections, rather than merely claim that "corrections exist". :) Some referees would want such an appendix to be cut, but nevermind.

@paulgarrett thanks!

paul garrett, please help here: Re-citing a math theorem with errors

I believe that paul garrett is pretty much correct here, but here's a way you can incorporate this into your paper:

Smith and Jones (1995) found that the area under the rhomboid apparatus was upper-bounded by the third order discriminant. While their final result is valid, a minor flaw was found in their proof. We provide a corrected proof in Appendix A. Given the established upper bound, we now show that the lower bound is negatively correlated to the complex derivative under the hyperspace gradient....

This approach gives your reader the "best of both worlds". You acknowledge the source upon which you build your own findings, acknowledge the minor flaw in that source, and provide a proof that your reader can rely on.

Robert Columbia, please help here: Re-citing a math theorem with errors

2) Say something like ... "the results are based off the ideas by author X" but don't give as much of a "these are author X's results" flavor. Author Y then after mentioning author X, proves the theorem themselves.

You’re missing the forest for the trees here. The result is author X’s result. A small mistake that anyone can correct cannot reasonably be said to change that fact. It would be rather small minded of you in such a situation to try to give the impression that author X does not deserve 100% of the credit but that someone like you had to come along and “prove the theorem themselves”. Depending on your precise phrasing, it can even come across as intellectually dishonest and/or insecure.
The best thing that you can do to serve both author X and your readers is give author X full credit for the result, while at the same time pointing out that their proof contained a small error (and as I said there is no inconsistency between saying those two things), and then explaining, in as much details as you feel is needed, how the error can be corrected.