I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank?

Your question has some issues.  Given some of the questions you have asked on other SE sites in the last few days, I have some reservations about whether your question is being asked in good faith, but taken on its own merits it is a reasonable question so I will try to answer it.

The main issue is that, even in asking this relatively simple question, your writing is far from clear.  If you cannot write clearly in this situation, your chances of writing up a difficult piece of mathematics or theoretical computer science are less than good.  For instance:

  His/Her supervisor(s) accept the work and they published it in a highly known journal and they get rejected.

Laying aside issues of subject/verb agreement and consistency of tense, the entire sentence doesn't make sense: you can't publish a paper and get rejected.

  It breaks what most people believe

I don't know what it means to "break what most people believe".

  or what they have already proven,

What? Are you saying that your proof contradicts other proven results?  Taken literally, that would mean that you have shown mathematics to be inconsistent.  In practice this could only mean that if your result is correct then some previously published work is incorrect.  If that's the case then you need to be very clear about that and explain the flaws in the earlier work.  It distresses me that you don't really seem to believe this but are just throwing it off as loose language.

  i.e., He/She solves the P vs. NP problem or any other well known open problem.

Solving an open problem would not "break what people have already proven"....that's what it means for the problem to be open.  Also saying "P vs. NP problem or any other well known open problem" is a strange bit of coyness: there is no other problem in theoretical computer science (and very few to none in mathematics as a whole) which is "like" P vs. NP.  So it doesn't make sense to give that as an example.  It's like saying "i.e., he found the Holy Grail or some other famous cup".

In other questions you have spoken specifically about having a proof of P vs. NP and then upon questioning have retreated from this.  This sort of vacillation about what you have done is a red flag of "crankiness" that will make professionals wary.

  The reviewers strongly reject his/her work with no justification and they said that the result must be wrong.

Saying that the result must be wrong is not just a justification for rejection, it's the best justification.  No professional reviewer will say something is wrong lightly.  Almost any reviewer who says this will point to at least one specific error.  If they do not, then in practice it almost certainly means that the entire document did not make enough sense to them to be more specific.

  If your advisor accepts the work, the reviewers reject the work without even explain the mistakes (it is the "best" journal in his/her domain) then what he/she must do?

If you submit a paper to the top journal in your field claiming a solution to the top problem in your field, and your paper does not make sense or does not evince even a correct understanding of the problem, then the editors are likely not to want to spend much time in response.  On the other hand, if you are sincerely interested in getting their expertise, it seems reasonable to write back very politely and ask for more specifics about the error.  If your response is in any way argumentative then you risk the editorial staff thinking that you will keep hounding them ad infinitum, and at some point they have to stop replying.  So you should write back saying that you are not considering resubmitting the paper to that journal but for your own progress it would be extremely helpful to know what is wrong with it.  You could also mention that your supervisor found the paper to be correct.

In fact you could be getting more help on this from your supervisor.  If you have really "solved P vs. NP problem or any other well known open problem" and your supervisor believes your solution to be correct, why isn't your supervisor moving heaven and earth to be sure your work is getting the attention it deserves?  That doesn't add up.  The two possible explanations seem to be (i) your supervisor is being too polite with you: s/he does not actually believe that you have solved P vs. NP; and (ii) your advisor's imprimatur does not carry any weight in the community whatsoever.  The latter unfortunately means his/her opinion on the correctness of your work is not worth very much.

A good way to find out whether it's (i), (ii) or -- I do admit that anything is possible! perhaps the top journal in your field is unfairly ignoring your revolutionary work -- is to seek your advisor's help in getting another faculty member to evaluate the work, preferably someone in the department that you can speak to recently.

Finally, you seem to have some real worries that if an unknown person solves a famous problem then it somehow doesn't count.  This is really not the way academia works, provided the unknown person is capable of presenting the work in a way which makes sense to the experts (and if not, what a shame, but what else could one possibly expect?).  Have you heard of the recent example of Yitang Zhang?  Zhang was a non-tenure-track lecturer at the University of New Hampshire when he stunned the mathematical world by proving the existence of bounded prime gaps.  He submitted his work to the top mathematical journal...and by all accounts they accepted it with unusual speed.  In other words, they received a paper from someone they had probably never heard of, looked at it quickly and saw that it was a plausible attack on a huge open problem, and as a result they sprung into action much more rapidly and thoroughly than for most submissions they get.  This is an amazing story, but a true one, and it shows how the community responds to a real situation like this.


Is it better to have no publication than having you as second author?

If the paper is well-written, contributes non-trivial knowledge to a particular field, is peer-reviewed, and you contributed significantly enough to the paper to be listed as an author, you should put your name on it. In the case of fields where pre-prints are common (i.e., it won't be peer-reviewed, at least initially), it is also worthwhile.

What you don't want is to be an author on a poorly written paper. In other words, you should be proud to list a publication on your CV even if it isn't exactly in your primary research area. Especially at this stage in the game, having a few good papers will help your case, even as a second author (and keep in mind that some fields, such as theoretical computer science, should have the authors listed alphabetically and all authors are considered primary).


How to find decent translator for technical jargon for application?

Find a local firm of patent attorneys and ask them what translators they use.

Patent specifications and patent applications are full of technical terminology. Holders of a foreign patent wanting to establish their rights in your country will need their patent translated into your local language. Patent firms routinely use the services of translation firms that specialise in translating technical documents. The translators don't guess at the meaning of specialist terms if they don't know the most appropriate translation --- they will query and check candidate translations.


Is it possible to change paper title after send back from reviewers for revising?

It's normal to change titles during the review process, sometimes reviewers even ask for it explicitly.

If it's causing a problem or confusion, change the title.


Developed technique but was not added as co-author

The proper advice, I think, is to ask for co-authorship on any future papers that use your technique. Point out that you are actually due this for having developed the technique and even more for adapting it to the other students' work. Not for "helping them" adapt it. For adapting it. Nor would I be shy about saying that they made an error in not including you on the recent paper.

They might just offer an acknowledgement and you can decide if that is enough for you. I don't have a recommendation about that, but think that co-authorship is probably more appropriate.

And, if they say no, then your decision about helping is also pretty clear, I think.

I wouldn't make the suggestion quite so strong except that you say the relationship with your advisor is already toxic. You have your own career to think about and your own research goals and needs. You don't need to also do someone else's work without proper attribution.


Finding conferences in subject area (Medical Informatics)

Is this anything like what you're looking for?

Doing some searching of my own, I definitely ran across the problem you mention -- the lists of events in your field are often out of date. So, while there are sites that list conferences by discipline, they might not work very well for you (the one linked above being a tentative exception). This might partially be peculiar to your field, though it does appear in others as well.

However, part of the problem might also lie within search patterns. Hybrid topics are often hard to search successfully due to conflagration of terms, and it seems this remains true for hybrid disciplines.

If you're not already familiar with them, it's definitely a good idea to acquaint yourself with Google's search operators; they can significantly ease your search-related challenges. My favorite is the tilde (~), which when placed before a term includes results with synonyms -- very useful.

Searching like this, I was able to find some individual conferences which seem to have their call for submission still open. (I know little to nothing about your particular field, so if I got these wrong, I apologize):

http://www.imia-medinfo.org/new2/events
http://datamining.conferenceseries.com/call-for-abstracts.php (track
3 on the page)
http://www.kdd.org/kdd2016/calls


After submitting a revised manuscript (moderate revision was requested), what are the steps followed?

You may ask the editor in charge. I.e., send an email to the editor in charge of your manuscript. If you don't know who that is, send an email to the Managing Editor.

However, I don't think there's anything to worry about in this case: the change in status doesn't mean it is going to be rejected. It simply means they got your revision and now (sub-)reviewing it again.


It may help you to understand that much of the value of those notes has been the very act of writing them.  As such, you may find that you have less compunction against throwing them out.

Personally, I maintain an "aging pile" for notes, in which I keep them until they stop feeling relevant.  For some things, that's a week; for others it was a box in my closet and a decade.  You can also remove the physical clutter aspect by scanning and archiving in something with cloud storage: you'll be trading physical clutter for electronic clutter, but I at least find that electronic clutter is much easier to ignore.


How to keep discussions with supervisor on interest?

This is a partial strategy, but I realized it's more an answer than a comment. I'm sure others will have very useful strategies for this all-too-common problem.

You could phrase it as "yes, and..." rather than correcting. "Yes, that's an interesting angle: I thought about that too and then I realized X. So then I [details getting back on track.]" Not saying it'll work, but this may be a way to bring him back with you into the active part of the problem-solving space.

Also, if you can have a one page overview/agenda that previews the path you've taken, that might be easier to get him to follow along with and prevent misconceptions. Also, perhaps have two or three clear questions written at the bottom of the one-page agenda, so he gets a chance to weigh in on something new, and you get a chance to get his clear feedback on something you need to know. (Then email an update with a revised agenda attached, with "Thanks for talking about this! I've added my notes about what we talked about today, for reference.")


Was offered a PhD position, I accepted it but no replies afterwards from the potential supervisors

I don't think you have any reason to worry. Under the current strain and disruption of the pandemic people aren't able to do the things they would normally do. A couple of weeks isn't very long after a deadline as there are probably quite a few administrative tasks that seem to them to be more important to them than reassuring students. The professor in question might have additional issues preventing them from responding in a timely manner (or at all, if they are ill or caring for a family member).

Assume that all is well. You've done what was required of you.

Don't keep hammering, though, as it just makes their workload worse.

On the other hand, you are due an acknowledgement that all is well. A once-a-week email is probably appropriate until you get confirmation.

Note that normal phone numbers aren't being answered at some places. Buildings are locked and people are forbidden to enter, even to retrieve personal effects.

You could, however, keep abreast of any news pertaining to that university by doing web searches. There is a lot of disruption and universities are planning how to finish out this year and finding ways to be flexible for next. Bad things are happening. They could continue to happen.


Is there any ethical issue which prevents me from paying high quality authors monetary compensation, to agree to write papers with me?

I think the other answers are way too nice. As for myself, I have never heard of such a insulting / distorted idea about what a PHD is. Do you want to buy yourself a PHD? There are countless diploma mills for that, so you could hang a useless paper on your wall to claim you have a PHD without doing all the necessary work / research yourself. Do you want to buy yourself an academic career by hiring established professors to write papers for and with you? That is even more insulting. If that was the case, every rich kid could tell his / her dad. "I want a PHD for Christmas. Buy me some high impact authors to write papers with me. Pleaaase..".

It does not work that way. And the fact that you are at the beginning of your PHD and you are even considering this, is even more infuriating for people who have busted their behinds to get a PHD (and some of the people in Academia SE still do to this day). Reconsider why you want a PHD and what you want a PHD for. I am mostly sure you want it for the all the wrong reasons and not because you actually want to do research. In that case, you should probably spare yourself the agony, because without a passion for research your PHD road will be a long, rocky one.

UPDATE: In retrospect, the tone of my answer is pretty hostile. Still, the upvotes showed that my initial reaction to the OP's question also expressed an important part of the Academia SE community. In this sense, my answer might still be useful if it makes the OP reconsider his "thought" of hiring "high-impact" authors to write papers with him, since such an action will probably cause much more damage to him than my "harsh" words.

Moreover, since we had a previous question about "Is it ethical to hire a programmer for ... my CS PHD" and now "Is it ethical to hire high-impact authors ... to write papers with me", I sincerely hope that in the future we do not get any other questions like "Is it ethical to hire a professor to write my PHD thesis if I still do the typesetting in Latex and all spell checking" or "Is it ethical to hire a professor to do my PHD defence, since I will still bring the pizza and the drinks".


Is it okay to typeset someone’s to-be-graded assignment for them?

I think that the best favour you can do to your friend is to teach him how to use LaTeX, so that he can improve the look of his work by himself.

In this way, you won't go against any rule and you'll teach your friend a new skill.


Does a PhD from US carry *more academic value* as compared to one in India even if the research skill set developed is same?

While I was an Indian undergrad in mathematics, I was told similar things by my friends who were doing, or planning to do, their graduation at universities abroad. Specifically, they told me that:

The top universities abroad are better than the top universities in India for graduate education.
Even if I were to be admitted to a good university abroad whose graduate program is comparable to that of an Indian university, the university abroad will be more beneficial for two reasons.

Experiencing a different culture will broaden my perspective significantly, and help in my growth by opening my eyes to more possibilities.
I can build a larger pool of contacts at a university abroad than at an Indian university, and doing so is very important to gain further opportunities in academia.
Somewhat connected to the above points, one can expect more invited talks (and also given by more top researchers) at universities abroad than at Indian universities, and it not only stimulates ones growth by being exposed to diverse topics through such talks, but also gives more opportunities to build contacts with top researchers.

Of course, there is an underlying assumption in all of the above that it is meaningful to speak of the characteristics of "the average Indian university" and "the average university abroad". I preferred to read their advice as saying, "If you compare the opportunities at a university abroad versus an Indian university, assuming that you want to get into those universities and are fairly confident of being able to do so, then it's more likely than not that the university abroad offers the above advantages over the Indian university." Read like this, I think my friends offered a fair assessment of the advantages.
I still chose to pursue my graduate education in India, for the following reasons:

I anticipated that my graduate education would be a difficult time for me, and I would need the support of my family to help me through it. If I were to be abroad, I would have a much more difficult time coping with the stress than if I were in India itself. There seemed to be little point in trading my mental health for more contacts and comparatively better future opportunities; after all, it's not like a graduate education in India dooms my future in academia.
And indeed, my graduate education started off on quite a rocky note, and the support I have received from my family has truly been invaluable.

I anticipated that choosing a guide would not be an easy task. Not everyone who is a good researcher is also a good guide. Not everyone who can be a good guide is specifically a good fit for me. In short, I felt that gambling on my chances of finding the right fit for me at a university abroad is riskier than doing the same at an Indian university: the stakes are lower, the sunk cost (in case I fail to find a good match for me) is also lower, and hence my ability to try again at another institute (in case of failure at one institute) is also higher.
As it happens, I nearly failed my qualifying exams after I secured admission at an Indian university, and nearly signed up with a guide with whom I had spectacular incompatibility issues. Things have sorted themselves out now and I am happy to say that my work is progressing well, at last.

Furthermore, among my friends who pursued their graduate education abroad,  some did struggle with their mental health and returned to India to get support from their family, some did fail to find a suitable guide and were forced to return home and start over in India, and some who pursued their graduate education in India also failed and started over in India. There are also those who succeeded, of course, but I just want to emphasise that it's not such a rare event to face these kind of difficulties that they can be easily neglected from the equation.
In your case, the final decision lies with you, of course. You need to decide how much weight you give to each relevant aspect. For me, the balance weighed in favour of staying back in India. For my friends who were more ambitious and also mentally stronger, the balance fell the other way. Neither path is absolutely right or wrong: you need to measure what is right for you, as best as you can perceive. Good luck!


Want to get back in touch with professor so he won't forget me but don't know what to say

I enjoy it when former students let me know what they are working on and how what they learned in my course is assisting them in their career.

I would suggest an email sharing this information and thanking the professor for teaching such a useful course.


What does it mean if the status of manuscript changed directly from "editor assigned" to "reviews completed"?

It means that the reviewers have completed their work and submitted their reviews. The editor will now make a decision based on her judgment as well as the opinions of the reviewers, and you should expect to hear back from the journal shortly.


You wrote the paper, did the main research, hence your name should go first.

The interns contribution is crucial to this paper, she/he helped a lot, but was not so much involved in the writing process? Name her/him second.

Professor B help a lot with constructing the paper, writing, rewriting, reviewing, etc. Put her/him second to last. Indicate her/him as correspondence author, too.

Since professor A is the main initiator, I assume that the research you did is within his field. He might therefore be also the main correspondence author. He will probably also handle submission and other formalities with the journal. Put him last.

Final Order:
You, Intern C, Professor B,* and Professor A.*

In any way, the person who will handle the submission process, will probably also review this. Don't think too much about the order. In many cases it does not really matter, and most professors do not care too much about this, as they are usually named as correspondence authors anyway.


I wouldn't jump to the conclusion that you'll be rejected.  Many programs use a GRE cutoff, but not all.  Wait and see.

If you don't get into any program that you like, I would suggest that you find something else to do for a year, perhaps back in your home country. Retake the GRE (study more this time), and apply to PhD programs again next year.  It sounds like you'll be a very strong candidate if you can get past the GRE cutoff.  I see no reason to give up.

(Also, are your undergrad professors aware of your situation?  They may have contacts at the graduate programs where you applied, and could suggest to them that they not overlook your application.)


How to ask for a co-supervisor? (master's program etiquette)

No It is not too late. Don't be afraid to talk about it. But as you said, you should first talk to your main supervisor to let him know. He will normally be ok with that. Then, you can talk with the other professor. If the professor is too busy or not interested, s/he will let you know. From my experience, it is generally quite positive for the students to get a co-supervisor for several reasons.


Basically, it's a "free masters degree" to members who otherwise don't qualify for the masters degree, for various reasons.

Here it is, direct from Oxford:

  Conferment of Degrees
  7.1. The procedures for the conferment, both at the Encaenia and on other occasions, of Degrees by Diploma, Honorary Degrees, Ordinary
  Degrees, and Degrees by Incorporation shall be determined by
  regulation, and the regulations concerned shall be published from time
  to time in a Handbook for the Conduct of University Ceremonies.

  7.2. (1) In the case of a person in any of the categories set out in paragraph (2) below who does not hold, and is not qualified for, any
  of the Degrees (other than Honorary Degrees) of Doctor of Divinity,
  Doctor of Civil Law, Doctor of Medicine, Master of Arts, Master of
  Biochemistry, Master of Chemistry, Master of Earth Sciences, Master of
  Engineering, Master of Mathematics, or Master of Physics of the
  University, Council shall as soon as possible propose to Congregation
  that a Degree of Master of Arts by Resolution be conferred upon that
  person without fee, if (and only if) he or she holds both a bachelor’s
  and a doctor’s degree (other than an honorary degree) of any
  university or universities or of any such other institution or
  institutions as Council may determine by regulation from time to time,
  or that at least twenty terms have lapsed since he or she first became
  a member of a university or such other institution, or, in the case of
  a person who is not a member of any university, that he or she is at
  least 25 years of age.

  (2) The categories referred to in paragraph (1) above are:

  (a) the Chancellor;

  (b) the High Steward;

  (c) the Vice-Chancellor;

  (d) the Proctors;

  (e) the heads of all the colleges, societies, and Permanent Private
  Halls included in Statute V;

  (f) the members of the governing bodies of all the colleges and
  societies included in Statute V (but not of the Permanent Private
  Halls);

  (g) the principal bursar or treasurer of each of the colleges and
  societies included in Statute V (but not of the Permanent Private
  Halls), if he or she is not a member of its governing body.

  (3) In the case of a person excluded because none of the conditions in
  paragraphs (1) and (2) above is met, Council shall proceed as soon as
  possible after one of them has been met.

  (4) Nothing in this regulation shall restrict the power of Council to
  propose to Congregation that a Degree by Resolution be conferred
  without fee upon any person it considers appropriate.

  7.3. A Degree by Resolution shall be deemed to have been conferred with effect from the approval of the resolution by Congregation.


Bragging about previous funded PhD position to acquire another?

This is just an opinion:

You will need to be very clear why you left, and you cannot leave room for the suggestion that it was just because things got a bit uninteresting. The way you have described it in your question leaves me with that presumption, and on that basis I would feel uncomfortable with working with you on a fixed term (or fixed goal) project such as a PhD.

i.e., the obvious question in the mind of the reader of your CV will be, "How do I know you won't disappear on me as soon as things get a bit boring or difficult?"

Frankly, I think you have more to lose than you have to gain by discussing it.


Pros and cons of booking a hotel through the conference website versus finding your own hotel

When I attend conferences, I rarely use the "official" hotels.  Frequently there are better, closer, and less expensive alternatives nearby that are perfectly fine.

The only reason to book at the conference-approved hotels is if your travel funding requires it as a condition for reimbursement.  Otherwise, save some money and book elsewhere so long as it's within walking distance.


"Be a small fish in a sea, or a big one in a pond"

Apply for, and fully investigate, all such possibilities. But I would go even farther: 3 places is not nearly enough to apply to, especially if you are interested primarily in tenured track positions.

Deciding which job you want to take before you've actually been offered one is perfectly natural, and is a perfectly terrible practice! It so often leads to disappointment, missed opportunities, and general dissatisfaction.

Now would be the time to expand your horizons! Find new institutions you might like and apply to them; put the word out about your availability through advisors, fellow researchers, friends of friends in academia, etc.

The chance of getting any one position is terribly unflattering, regardless of your background or standing. If you can find a dozen places that you'd be happy to go to work - relative preferences for one over the other not withstanding - then your chance of getting something you want improves remarkably. Don't put yourself in the position of being disappointed because you had to "settle for your last choice", instead of "winning one of your top 3 picks" just because you didn't look into more possibilities. (This is advice I have to give myself over, and over, and over again.)


Anecdotal, but: I was 31 when I started my PhD, and it wasn't an obstacle at all. There were more than 80 applicants for two places. I have the impression that what matters a lot (at least in neuroscience, at least at my institute) is how much training the supervisor would have to invest in you. I've seen many times that the applicant who already did some similar research gets the position, even though there might have been someone else who is in principle just as good. Previous research experience carries a lot of weight.

From what you write, it seems to me that you would have a very good chance in getting into a program - publications and good GRE scores are both a big plus. Recommendation letters are also important. I would be surprised if your age would be an obstacle. But beware that it might be an obstacle for some sources of funding! I don't know if it is the case in the US, but I'd guess that's the only potential problem with your age.

...And now we wait for someone on the other side of the application process to give their answer :)


Mosy probably, your thesis is not supposed to read like a collection of unrelated articles. Therefore, you will need one general introduction. It could contain information on

which components exist
how each component is connected to the whole
why components were separated as they are.

This does not preclude additional per-section introductions to explain more in detail what the upcoming section is about.

Proceed analogously for the conclusion and, of course, talk to your supervisor for any specifics.


How can I quit an internship before the agreed upon end date without burning bridges?

You haven't said where you are, but from your reference to living in an unfamiliar state, I'm going to assume you're in the US.

I honestly think your best course of action is to say you need to quit for medical reasons requiring treatment. You can stop there, any US employer should know better than to pry at that point.

This has the upsides of a) being entirely true; and b) doesn't leave your employer wondering if they did something wrong.


At my institution in the United States, reference checks are done by members of the search committee for the position, who call those people the candidate has listed as references.  We use a structured list of questions, ending with, "is there anything we should know that I haven't asked you?"

We verify academic credentials by requiring official transcripts, including those from undergraduate institutions.

The institution separately does a criminal record background check, handled by the university police department.  The candidate must explicitly authorize this, in writing.  But, of course, we cannot consider candidates who will not agree to the background check.  As far as I know, there is no credit check for faculty jobs.  There probably is a credit check for anyone who handles money.

Finally, the institution does a driving record check every year.  This is because we are covered by the university's insurance when driving university vehicles or driving our personal vehicles on university business.

What I've written (except the bit about the driving record) applies to people being hired into a tenure-track position.  Applications for promotion or tenure for those already on the faculty are much different.


Is it ok to show up to a conference without registering if I don't eat any meals?

No, it is not acceptable.

You can of course email the organisers and ask if you can participate without paying, but do not be surprised if they say no.

(Please note that conference registration fees cover lots of things besides the lunch. Among others, conference registration fees may cover the rent of the hall in which you are sitting, and expenses related to the speaker who is giving the talk. Conference organisers are definitely not expecting random people to come there without registering, unless they explicitly advertise this possibility.)


How much data should be shared in the collaboration?

All of it.  If I don't trust you with my data, why would I collaborate with you?

Note: I'm in favor of sharing all the code and data with the whole world, not just my collaborators.  Once you make intellectual property public, it cannot be stolen.


Does PhD GPA matter after grad school regarding academic funding?

It is extremely unlikely that anyone would care, especially a source of funds. They are interested in you research potential and your productivity. There might be various aspects to that for specialized awards, but no one will ask you for your doctoral level transcripts. They are largely meaningless in any case.
If you passed comprehensive exams then you learned enough to go forward and that is assumed if you completed a doctorate.


What to do about top students making other students lose confidence?

When I was a TA, I always found these types of students the most difficult to handle.  You don't want to crush their enthusiasm, but you also don't want to let them dominate and make it harder for other students to learn. It's also important to remember that just being way out ahead of other students doesn't cause this phenomenon: you're dealing with somebody who is both ahead and feels a need either to show off or to receive affirmation from you the instructor.

Some tactics that I found effective were:

Establishing clear ground rules that people had to raise their hands to be acknowledged, rather than just shouting out.  Then you need to become comfortable waiting long enough for other students to raise their hands too.
Saying things like "Everybody needs a chance to learn, so I'm going to make sure that we get some folks up to the board who haven't been there very often."
Rather than asking for volunteers, actively calling on students who have been silent.  It's embarrassing for them, but if you do it kindly and make it into a guided learning experience at the board rather than a test of their abilities, it can be a very good thing.
Privately discussing with the enthusiastic student, something like: "I'm very pleased at how well you're mastering the material, and I need to make sure other students have a chance to have the same learning opportunities, so I'm going to call on you less often."
Giving "extra credit" work that the enthusiastic student can be working on to occupy themselves.

In all cases, what you want to emphasize is the importance of active learning by participation, and how it's important for all students to have those opportunities.

Addendum: I was talking about this with my wife and she told me about a tactic that she uses that I think is another excellent addition to the toolkit:

Divide the class up into rough geographic zones and call on zones round robin, e.g. "Left side answered the last question.  Let's get an answer from the middle now."


Is it okay to ask a professor from another university for class lecture notes of a course that he offered on that university?

You can always ask as long as you are polite.  There are many reasons that an instructor wouldn't want to release their notes, though.  Among them (there are others):

Their notes are copyrighted and don't belong to them, either because THEY are using another person's notes or because their notes are part of a textbook that they wrote and signed copyright over to.
Their notes include important assignment information for assignments that are given every year, so they don't want them in the wild
They want to protect their copyright and just straight up don't want to give you the notes

I, personally, would have no issue giving my notes out to anyone who asks, but I'd give the big caveat that you can probably find better resources.  Other instructors may just ignore you.  However, a polite query is fine.


Responsibilities of PI to PhD student post PhD submission, but pre-viva

This answer is a bit blind as some information needed to give a more complete answer is missing. I'll try to give some guidance, but it is probably incomplete.

You say that you haven't gotten along well with your advisor. You don't say why. There could be a lot of reasons, but if you have, through your own actions, given the advisor reason to question your commitment or ability to finish, then you may not get very far here. It is impossible to say what is "owed" in such a situation.

You say you want to "fight for this project...", but I'd suggest that you change that approach a bit and stress why and how you are the best person to complete the work and how you guarantee that you can and will do it. Funding is a separate issue and, again, it is impossible to say what is "owed" here.

Depending on the nature of the work, it may be completely reasonable for the professor to pass it on to someone else since you are no longer involved. In a lab situation, students very seldom "own" the research thread and that thread may be so important to complete that personalities matter less than the work itself - childhood cancer, say.

Technically, your advisor owes you what was in the contract. Morally it may be more, but there isn't really enough information to judge it externally.

On the other hand, an attempt to deny you your degree or prevent you from publishing your results or impeding your career would be unjust.

If you want to stay with the project, however, convince your advisor that you can and will be the best person to do it. Any other approach is likely to fail.


How casual is too casual for a PhD application personal statement?

That sentence already sounds very flippant. Contrary to its name there is very little that is "personal" about a personal statement (and it's definitely not the kind of soul-searching essay you write for college). It's mostly a document to describe your research experience and how the program fits within your vision of a scientific career. You should certainly demonstrate your interest and passion (in a concrete manner devoid of cliches, of course), but I'd rather err on the side of being too formal than the other way around.


Invited to give a talk but could not attend, can it be on CV?

No: Don't list anything that you didn't do.

From a comment on my answer:

  He's not saying he'll pretend he gave the talk. The invitation itself is a good indicator of his status as an expert in the relevant field, at least in the eyes of the people running the conference. If this is relevant to the job, I don't see a reason not to include it, as long as he makes it clear he didn't give the talk.

which was extended to add:

  If Google or Apple offered me a job, but I couldn't relocate or whatever, I'd absolutely put it on my CV.

A comment on another answer provides an excellent response:

  if I saw such a claim on your CV I wouldn't even invite you to an interview. If you didn't take the job, if you didn't go to the presentation, if you didn't do the thing, it doesn't count. It never happened; it doesn't count.

Another commenter writes:

  It may be a accomplishment, but it is also a opportunity wasted. You do not really want to underline your failures to execute. Its a bit like saying businessman saying they got a big contract but never fulfilled it. People are looking for people who can get things done.


Pre-tenure strategies to spend less time on bureaucracy, and more on research

Learn to say "NO" (especially to people that do not decide about your tenure)

It is discussed in length here and here but these are my favourite points:

Short and simple answers like "Thanks for coming to me but I’m afraid
it’s not convenient/possible right now" or "I’m sorry but I can’t help with this (at the moment)". Don't start to write endless time-eating apologies.
Avoid feeling guilty about saying "no".
Interrupt the "yes"-cycle using phrases like "I'll get back to you" -
you might not hear from them again if it was not that important after all (which is the case for very many things). My ex-boss did this on a master level: we would only answer requests from people lower in the food chain if the requests were already reminders - the original request was ignored straight away. (I personally think that this is a bit over the top but it worked for him (post-tenure)).


Can I apply for a post-doc in theoretical physics without publications?

You could apply to a post-doc without a high-school degree -- an application only involves sending in the application package. No one is going to stop you from mailing it in.

That says nothing about whether or not you will get the post-doc, let alone if the secretary will just toss it in the recycling bin before it even gets seen by the faculty.

The real questions are:

What are the eligibility requirements of a post-doc?
How competitive is the post-doc?

For the first question, most post-docs require a PhD in hand or late-ABD status. Most do not require publications and if they do, they will state that clearly on the application page.

The second question is the real question. Post-docs are usually extremely competitive. In order to be a finalist, you have to be n+1 of whatever quality and quantity the faculty is looking for.

If your peer group has no publications (0) and you have 1 publication, you will stand out as the +1. Since it's not possible to have -1 publications, it's hard to stand out from a group  with 0 publications to your name. If your peers have 10 publications, you need to have either more in number or more in quality, or something else that your competitors don't have.

For example, some post-docs in some fields value other things than research publications. I occasionally read for post-docs in the humanities and there the quality of your dissertation and proposal is more important as most post-docs in those fields apparently have zero or near zero publications at the ABD stage.

And finally, there are some post-docs that just aren't very competitive -- either because of geography or topic or paucity of funding or other reasons.

I would also be remiss if I didn't mention the social/human factor. Many people get post-docs on the strength of their recommendation letters, as Pete Clark mentions. Strong recommendations attesting to your brilliance and to the problems you faced with your current project would go far in convincing a postdoc committee to take a chance with you. You could also try to ask your supervisor to use some of her/his social capital to try to persuade a colleague at another university to take you on.

Your mileage may vary.


Graduate Certificates or Additional Masters as addons for Terminal Degree?

From my experience teaching and applying to teach at various colleges and universities, in academia, only academia counts.
Having a degree, such as a Masters, or PhD, or DA counts.  Generally, a grad certificate, and/or any industry certificates count for zero.  A grad certificate might count if they have a requirement for a certain number of grad hours in the field.
Most universities with PhD programs want people with PhD's to teach, at any level.  They might accept a Master's, they might not.
A technical college might let some people in certain areas teach with a Bachelor's, or Bachelor's+15 (for example).

Essentially, look at job postings for what and where you want to teach, and see what they are looking for.  You might find that you are already qualified, or that you need a doctorate.


Some non-native speakers of English are eager to improve their English and grateful for corrections. Others have, unfortunately, a very different attitude.  Ahmad correctly suggests caution if your adviser is easily offended, but it may be difficult to determine whether he's easily offended. So I'd suggest beginning with just one of your adviser's errors, perhaps a spelling error where it's easy to check in a dictionary that it really is an error.  See how he reacts to that before correcting more errors.


Detect cheating in Microsoft Excel submissions

Figure out a way to generate data sets and results programatically so you can uniquely verify each student's assignment separately.  This would imply lots of effort initially but may payoff for later courses.
Use a single dataset and a single result set.  Ask them for their reasoning behind for achieving the most complex tasks of the assignment.  Use this to check for cheating.  No one person thinks exactly the same or describes something complex in the same manner.

My recommendation is for the latter.  Most jobs that can be done with tools like Excel will be automated in the near future.  The best that your students can learn is to reason (and articulate this effectively) and choose the appropriate tool/technique for the job.


Mention getting an offer to the adcom when in waitlist

I don't think that notifying them will change anything. And it might even work against you if they know  you have another possible situation already. There might be rules that prevent dropping you from the waitlist. But if not, you are more likely to be dropped than advanced.

They won't, in particular, put you ahead of another candidate rated higher on their list for learning of your other offer.


When is it okay to ask your advisor solution to a technical problem?

Your approach to asking -- "this is what I have tried, I am stuck here...can you point out how I can continue?" -- is the right one. Without knowing how difficult of a problem you have gotten stuck on, and how often you ask for help, it is very hard for us to judge how your advisor will interpret your request.

That said, in general I very much appreciate it when my graduate students and postdocs let me know when they get stuck on some step of a research project. My students and I are collaborators after all, and if I can help them get going again, or alternatively if I can recognize that we've been heading down a dead-end, this is very much to everyone's benefit.

Of course, they should not be coming to me with trivial problems: "I can't get this expression to format properly in LaTeX" or "I don't know how to compute the Jacobian matrix for this function", nor would I want to get these requests on a daily basis. But if a competent student has made a serious effort to solve a problem and is still stuck, I'd like to know about it and to help if at all possible.


"Challenging" Teaching Experiences for Math Grad Students?

One possibility is to get involved with a program like Learning Unlimited (full disclosure: a few of my friends are heavily involved in running it).

I've also heard (through the grapevine) that a short while back AoPS may be looking for instructors. I don't know whether the position is still/was ever available.


How long can you give job talks on your thesis-book project?

I’m in a vastly different field, but if your work is progressing at approximately the same rate as your community’s then I wouldn’t worry about it.

Perhaps you can talk about your ongoing work as well just to signal that you’re not stagnant. The point of the job talk is to assure the department that you’re going to do good work while there!


Does the time taken to do a PhD affect post doctoral applications?

The fact that you took 8 years for your PhD, the fact that you barely managed to finish it and also the fact that you are in your late 40s influence your chances of getting a post doc.
However, from the given information alone, it is not possible to tell how strongly.
If we assume about 5 years of study for bachelor/master/other and 8 years for PhD, there are still 15-20 years missing here to get you in your late 40s. What you did in this time might play an important role on your job search.
Furthermore, it is important if you just wrote down something that was barely accepted as a PhD thesis, or if you took 8 years to work everything out properly and write the perfect thesis. I think the quality of your thesis will play a bigger role than the time you needed to finish it.


Contact the author first.  Assume the best, that their memory is faulty, and suggest alternative text in a friendly manner.  If you do not get a response, contact the editor of the journal they have submitted to.

Ultimately though a lot of people get misquoted, and a lot of publications get misunderstood & cited inappropriately.  If it's really a big deal you might get a publication out of contradicting it, but otherwise just be glad that people think you are important enough to mention.  It's better than not being given credit for your own ideas!


Doubts about PhD advisor and unsure how to continue

It's your project, not your advisor's.  Your lack of progress/motivation and supposed lack of time have nothing to do with him.
Nevertheless, you must sit down with your advisor and have a serious talk about both of your expectations. Be honest about your lack of motivation, be honest about your disappointment, be honest about your intellectual loneliness.  Ask for suggestions. Listen.
You have other senior collaborators that you can work with, so if you need senior collaborators, work with them. Ask your advisor to fly them out to visit you, or to fly you out to visit them.  Schedule regular Skype/Gchat meetings. Similarly, get to know other faculty in your department, who might serve as more experienced mentors/advisors, if not collaborators.
You're surrounded by colleagues who are excited enough about their research to want to draw you in, and you turn them away because you feel stupid?  What a wasted opportunity!  Of course you feel stupid.  Everybody feels stupid listening to other people talk about their ongoing research, because by definition, they're talking about stuff that nobody understands (yet).  You're simultaneously complaining about intellectual loneliness and turning away potential collaborators.  So what if they're not working on your project?
Of course you're constantly forgetting important things you once knew well.  It is totally unrealistic to think that you can keep everything you've ever learned/read fresh in your mind. Don't even try. Write things down. Maintain a library of papers, or at least a close personal friendship with Google Scholar. Let yourself forget details, confident in the knowledge that they'll come back amazingly quickly when you read them again.
Since your feeling is shared by other students in your group, it sounds like your advisor is a bit overexcited and has bitten off more than he can chew. All the more reason to sit down and talk with him directly, and to develop mentoring relationships with other faculty in your department and elsewhere. Also, start looking into other potential advisors, even if it means moving to another university.


Should I prepare a research statement or cover letter for postdoc ads. with general descriptions?

Nobody here can know about the documents that are required, but typically a job announcement has a contact person. Ask them about such details.

The position sounds similar to many postdoc positions in mathematics - they want someone who can do research, be useful to the university, and co-operate with locals. I would suggest taking a look at what the faculty and PhD students are doing at the moment and trying to find shared interests there. Check out the faculty website, personal webpages and Google scholar profiles - wherever you can find list of publications.

You do not need to be doing precisely the same thing as they do, as long as you can make a case that there might be cross-pollination and that you will be doing good work.

If there is a current line of research they are pursuing, mention that. If you could help them move or expand their research, also mention that. You are not setting anything in stone, but rather trying to figure out possible shared interests with the locals. The details of what you actually do will get decided once you are there, most likely.


Carry your PhD project with you to post-doc and beyond

From a career perspective, it's a bad idea to carry your PhD project as your primary work further into your career. It's perfectly normal for people to finish up the publication of papers related to one phase in a later phase of their career, but it's not so good to keep working on basically the same project.

The reason for this is that you don't want to be "pigeonholed" as a researcher who only studies a narrow topic. In most fields, it's not conducive to a successful career, because it makes a researcher look as if uninterested in other research fields (even if that's not the case).

So even if the funding and willingness of the advisors is available to support such a path, it's not one you should follow (absent a very specific reason to do so).


Can I collaborate outside my supervision on a work and add to my PhD thesis, me being the first author?

I wish to work with my Master's supervisor on an idea. The idea is mine and I do the implementation and write the manuscript. My Ph.D. supervisor is not open minded and will surely deny a collaboration.

Since you specifically want to know whether this is ethical and legal, I will answer these aspects first.

Legal

Sure, why not? It's your thesis, and an advisor is just an advisor. There is definitely no law or regulation that says that you need to run every contribution you wish to include in your thesis by your advisor.

Ethical

Here things become a little more nuanced, as your advisor usually has, or at least should have, a vested interest in your academic well-being and success in grad school, and you purposefully doing something decidedly unsmart (more on this below) could be considered unethical towards your advisor. That being said, it's easy to infer from your question that you are not on best terms with your advisor anyway, so I guess doing something that may put your advisor into a bad spot may not be that much of a deterrent to you.

The elephant in the room

So sneaking a surprise research contribution behind your advisor's back is legal and not overly unethical (imho, at least), but it's also decidedly not smart. Keep in mind that your advisor will typically also be the most important person in your thesis committee, so it's hard to imagine that a research contribution that he does not like in the first place (otherwise why would he "not be open to a collaboration", as you say?) and that you have also hidden from him will in his mind improve your dissertation. You should also consider the mindset that finding out that her/his student mistrusted her/him enough to hide work will put your advisor in for the final, crucial phase of your thesis.

I understand that as a student who has troubles with their advisor it is frustrating that they are in such a position of power, but trying to ignore this fact and hack around her/him is most certainly not the way to improve one's situation (changing advisor, while awkward, typically is).


When to use a table vs. a plot to present numeric information?

I would say: Use tables if the actual values are of importance and use plots if trends (or similar things) are important.

The rationale is simply that one cannot extract actual values of a function at specific places from plot. Vice verse its much simpler to see linear growth or periodicity from a plot than from a table.


What's my PhD status after I passed my oral defense (UK)?

This is always a tricky time period. Trying to make such a complicated situation clear in a single line on your CV is impossible. Write something on your CV that suggests that you have not completed your PhD yet (you do not want to mislead people), but that you are very far along (submitted, defended, passed with minor corrections, etc). Then in your cover letter use a sentence or two to explain the the situation. For example:

  My thesis on Under Water Basket Weaving was approved by my examining committee and my PhD will be awarded in May 2016. I have already published 6 articles from the thesis and based on discussions during my viva voce, I am currently revising portions of the dissertation for 2 further publications.


Why do PIs say no to students working during grad studies?

I have the impression that you are pretty aware of the main reason why PIs tend to frown upon outside jobs - they take time and mental energy, and most PIs will expect you to commit as much as you can of both to your grad school project. Hence, working on the side will typically  affect the student's performance negatively.

There is also the added problem that outside jobs often provide unwanted rigid commitments, which tend to interfere with the somewhat unstable nature of grad school workload. It is exceedingly annoying for a PI if a major paper deadline needs to pass, because the student also had important duties at their day job that they could not get away from.


Where can I find examples of research misconduct reports?

Retraction Watch has a separate section for these:

misconduct investigations


My paper was cited but their citation text had very little to do with my paper

If they are referencing ideas in your future work section then they are doing the right thing in not claiming credit for something that wasn't there idea. They should be congratulated for their honesty. Of course they could have been forced to put the reference in by a hostile reviewer. See many other articles on here about people being forced to add references they think are minimally relevant.


Should I tell my professor to print a retraction if I feel it will harm my career chances?

Let me start with a standard question: are you sure that what you noticed is an significant technical error? Have you considered the possibility that your professor's reaction meant something other than a tacit admission that you are right?

OK, let's assume you're right and the paper really does have a significant error. Then according to me:

  You have fully discharged your ethical duty by pointing out this error to your professor. In particular, it is not your job to "tell" your professor to fix it nor to "insist" that they do so.

Pragmatically speaking, if you do press the issue with your professor, it is possible they will write a less favourable letter for you. Needless to mention, I don't say the professor would be right to act in this way, but it would be naive to think it couldn't happen.

One commenter recommends that you discuss this with your professor's "supervisor", presumably meaning a head of department or dean. I would not recommend this: if the supervisor brings the issue to your professor, it would not take a great leap of insight to figure out your involvement, and the professor's reaction in this case is likely to be rather more negative in the previous scenario.

In short: you have made your professor aware of the problem. It is now their responsibility to see that it is resolved.


Can I accept two federal fellowships simultaneously and defer one?

Answer: No, it is not possible.  I called the NSF office concerning this issue, and they told me that I have to decline one of the fellowships.  The same is true of any two federal fellowships: you can only accept one, period.  This page also says the same thing, addressing the specific proposal mentioned in the question.


How can I hire a professor to answer my advanced technical questions in a niche area?

Unless you are in a place where professors are greatly underpaid and generally abused, this seems like a quest that is bound to fail. People are busy and they aren't normally driven by money (other than large pots of grant money).

What I think you want, instead, is a collaboration. That can be started with just an email, provided that you have something to contribute yourself. This requires you to do a bit of research to find someone with common interests to form a two-way partnership.

Perhaps the story of Srinivasa Ramanujan and his relationship with Hardy will be instructive.


What is the best secondary language for an academic to know?

It depends on what kind of job we are talking about. For a PhD student, or for a postdoc, knowing the local language is not necessary in general. I know plenty of examples of people who got such a job without knowing any shred of the local language (in France, Switzerland, Korea...). The general expectation is that you make an effort to learn the language after some time, though. If only to have an easier time ordering food in restaurants and talking to your colleagues during coffee breaks.

For a professor job it depends more on the location. In some countries (e.g. Switzerland, the Netherlands, and many others) some classes are taught in English, so you don't need to know the local language immediately, although that is probably expected after some time. (In fact, I've been told it's a "disadvantage" to know the local language, because only lower-division courses are taught in it, and they are less interesting than upper-division courses.)

In some other places, courses are taught in the local language, but new professors get some teaching-free time (say, six months to a year) before being required to learn enough of the language to teach. (I know an example in Norway.)

In some other countries (e.g. France), you need to know the local language before getting the job, because teaching is mandatory in the local language. But I expect that if you are a good candidate, they will make an exception and arrange for you to only teach during the second semester, so you have time to take a crash course in the local language. But you would have to make it worth their while...

There exists some permanent or long-term research-only positions, all around the world (in France CNRS, in Germany Max-Planck...) It's often possible to get hired for one of these even without speaking the language, since you do not have the constraint of teaching.

In any case, it is impossible to give a general answer to your question. It is not helpful to look at global statistics, because a particular person is interested in getting a job in their own particular subfield. Which countries have the most jobs is not uniform. Even in "the sciences"...

But as you can see from above, learning a language in the hopes that it will land you an academic job is rather pointless. Your academic record is infinitely more valuable. You would have to be in an extremely specific situation for it to give you any kind of edge. Unless you have another reason to learn the language, I expect that your time is better spent on research. You will have time to learn the language later.

Also, most people don't approach the job search as "I'll take any job anywhere in the world". Most people have family, friends... that they like to see every now and then. If your whole world is based somewhere in Western Europe, will you take a job in East Asia or the Americas? Some people will, some people won't, especially if it's a permanent job. (Other make an effort for their postdocs.) So I'm not sure that you can approach this as "I'll learn the language where the most jobs are".

PS: it is not "obvious" that the person you are talking about will need English. In some fields, English is not the main language. For example in "history of [location]" the main language will probably be the language of [location].

PPS: Your Wikipedia link is about R&D, not academia...


Decision letter: disagreed with few comments

A general principle that may increase your chance of acceptance is as follows: the reviewer is always right.

Of course, this does not mean that you cannot actually disagree with the reviewer. But at least for your answer letter, you should package your disagreement so that it can be understood as agreement. For example:

If the reviewer criticizes the lack of a performance experiment that you actually described in your draft, say "We agree that a formal validation alone would be insufficient to show the benefits of our technique. In fact, our previous draft already contained a section describing its implementation in a protocol verification tool and a simulation based on that implementation (Sect. X). However, we see that the structure of the paper was such that this section could easily be overlooked. In the updated submission, we have improved the structure of the paper as follows: (describe small changes)"
If the reviewer critizes the lack of a usability experiment (because you have concentrated on performance experiments), say: "We further agree that usability is another important concern of XYZ schemes. While the current submission focuses on the performance aspect, we have updated the Future Work section to give an outlook on planned user studies."


Taking math or stat course to prepare for my PhD?

Recommendation letters for PhD programs are weighted by the reputation of the writer only up to a point.  When an admissions committee reads a letter saying that the student will thrive in a top XX PhD program, we want to believe that the writer is qualified to make that statement.  In mathematics (my field), this means that we generally want the letters to come from faculty members with PhDs in mathematics (or a closely related field).  It helps if the faculty member has some experience and perspective with evaluating undergraduate students, and it helps if they have met or interacted with graduate students from top XX programs.

That's about it.  Notice that I did not say that the faculty member has to be especially eminent in the field.  Just because one faculty member has a more distinguished research program than another does not imply that she has more insight into which undergraduates should go to which graduate institutions.  I might go so far to say that many superstar faculty members I know did not get to be superstars by paying extraordinarily close attention to the undergraduates in their institution: a more teaching oriented faculty member could actually be more insightful.

Another thing to realize is that taking a single course from a faculty member is not a recipe for a really incisive recommendation letter.  A lot of times these letters basically convey the information that the student got one of the highest grades in the course, just like other students from years past who went on to graduate success. In this situation it is probably the quality of the program that matters more than the reputation of the faculty member.

So I do not recommend that you choose individual courses based on faculty reputation for future letters.  Remember that admissions committees are also looking at your coursework, and that you took the strongest courses available to you and did well in them is both one of the most important aspects of your application and the aspect that is under your most direct control.  So taking an undergraduate course as a master's student just because you think that a superstar will be writing for you is a bad idea, I think.  What is the superstar going to say about you: that you really nailed a "very basic course for undergraduate students"?  (Note though that you might still want a letter from this person, but if so you should have a more meaningful interaction with them.)  I don't know enough about statistics programs to help you decide between options 1) and 2).  The only thing I can think of is that you have already taken Real Analysis II, and the fact that this version is more in-depth might be lost on the committee.

Finally, all in all most master's students do not switch to PhD programs at significantly higher ranked institutions.  It's certainly possible, but it would be safer for you to plan in a way which is good for you whether you go elsewhere or not.  So I suggest you talk to your advisor and explore which of 1) and 2) is actually a better course for you to take...I mean, better for a student in your current situation.  Then take that one.


How does Semantic Scholar count influential citations?

Semantic Scholar's algorithm for counting "Highly Influential Citations" is described in this paper:
Identifying Meaningful Citations (Marco Valenzuela, Vu Ha, Oren Etzion)
https://www.semanticscholar.org/paper/Identifying-Meaningful-Citations-Valenzuela-Ha/1c7be3fc28296a97607d426f9168ad4836407e4b


How to properly address an unsolved problem that is very hard to solve in mathematical thesis?

I am assuming you're talking about a presentation to be given at the defence of a PhD thesis.

Let me address a few points you raise.

It is perfectly appropriate to include subjective judgements about the difficulty or significance of certain results in a mathematical thesis (or paper). Mathematicians make these judgements all the time in deciding what to work on and in evaluating other people's work. What matters is that you have a solid rationale for the judgements you make. In your situation, the rationale for considering the general case "very hard" is that it involves non-isolated singularities. That seems perfectly reasonable to me.
If you're worried about presenting subjective judgements as if they were statements of fact, there are various standard forms of wording you could try. Instead of writing "solving this problem... is very hard" you could write "solving this problem... appears to be very hard" or "solving this problem...is generally considered to be very hard" (assuming the latter is true). If there are published works affirming that the general case is hard, you can cite them in support of your point.
Finally, asserting that the general case of a problem is very hard does not imply (in any sense of that word) that a special case is easy, only that it is easier. But that is completely fine: experienced mathematicians are well used to people restricting themselves to more tractable special cases. I don't have any examples to hand, but I have read many papers in which the author does exactly this. This is not interpreted as an "admission" that the special case is "too easy". (In fact, often when someone does prove something that really is too easy, their rhetoric is the opposite: they try to puff it up to make it sound more difficult than it really is.)


The professor takes me only if I continue up to finishing PhD. What should I do?

I would highly appreciate for any advice for the most suitable ways of
  approaching and opening up the issue with the would-be supervisor?

When you apply for a PhD, you will need letters of reference. Among them, the one from the supervisor is the most important. If you lie to your supervisor, it may be extremely difficult to get a PhD wherever you apply.

If you don't plan to pursuing a PhD after your Master, tell the potential supervisor exactly that. If he doesn't agree, move on until you find the one that agrees.


Will going part-time in undergraduate affect my graduate admission?

I did something similar.  My final semester in undergrad, I had two options: stay full time and finish two minors, or go part time (really just one class) and complete an intensive EMT-Paramedic training program.  Since I was seriously considering med schools, the second option seemed like a better idea to me.  (How good of an idea it was remains to me seen, since I did not go to med school, but anyway...)

I have since gone to grad school in two different fields.  Absolutely no one gave a dang about my last semester being part time (although I did get some questions about being a paramedic).

So, to quote guest:

  Just get the sheepskin. Nobody cares about the details.


Is there a correlation between how enthusiastic reviewers are and how much impact a paper has?

I doubt there could possibly be a measurable correlation. I don't know of anyone collecting data on "reviewer enthusiasm". But even informally, can you expect that in general enthusiastic reviewers is likely to result in more citations?

Here I doubt it also, but only because the number of researchers in arcane subfields of a field isn't uniformly distributed. Your profile suggest that you work in Physics, which has a lot of quite different subfields. Some of those have a lot of current activity and others are more arcane. If you work in a popular field you are much more likely to get citations than if you don't.

My own early work, for example, was rarely cited, but there were only about five people worldwide who worked in that tiny subfield. That was true even though the main result was very interesting. A lesser result in a more popular subfield would have likely generated more citations because more people could make use of it.

However, there is enthusiasm and there is enthusiasm. If you prove a long studied conjecture that has been a bottleneck in your field, reviewers will be enthusiastic and the nature of the work will generate the citations. On the other hand, a great result the completes a field, meaning that there can be little follow up (rare, I know) would generate citations in the popular press, but, since there isn't any follow up, few in the scientific literature.


What do people usually ask letter writers to emphasize in a letter of reference?

People are sometimes asked for such things, if for no other reason than to remind the writer about what the applicant has done. But, there is a more important consideration.

The fundamental requirement of a supportive letter is for the writer to make a prediction, even if not explicitly stated, that the subject of the letter is both highly qualified (the past) and has great prospects for success (the future).

When possible, provide some evidence, especially about things that might not show up in a CV.

Everything in the letter needs to support that primary goal, no matter how stated. Anecdotes might help, past research, great questions in class or the office (curiosity). But make sure that the main goal is addressed. Otherwise the letter is just noise.

Qualified (check). High likelihood of success (check).


What does it mean that after withdrawal of arxiv paper 'previous versions can still be retrieved'?

Here is an example of an arXiv paper that has been withdrawn.

You can see that if someone visits the non-version-specific URL, http://arxiv.org/abs/0812.0848, they will see a notice that the article is withdrawn. There is still a link to the previous version(s), which they can click on to see the original paper:

If someone clicks on the link to the first version, or visits the version-specific URL, http://arxiv.org/abs/0812.0848v1, they will see the original paper without any withdrawal notice.

(You can see other examples of withdrawn arXiv papers with this Google query).


The reason we do lots of strange and probably useless research is that predicting which bits will turn out to be important is only possible in retrospect.

Consider, for example, the internet on which we are discussing the apparent uselessness of research. It is now driving a significant fraction on the world economy. Twenty years ago, it was just starting to be publicly noticed. Twenty years before that, my company was playing with the prototype versions in experiments you likely would see as largely useless and known only to a small niche audience. Thirty years before that, in 1945, Vannevar Bush laid the basic principles of hyperlinked text, in what was clearly an ivory tower fantasy... and yet here we are.

Almost everything ever done in science is useless... But the parts that aren't make a real difference. Sometimes only a little, sometimes a lot, and sometimes they shift the fate of civilizations. You just have to hold a vision of how it might matter, and chase that dream with all your heart.


Can you defend your thesis without any slide presentation?

Of course, slide presentations are a very recent development. Even the humble overhead projector didn't exist when I defended. We wrote with chalk on a slate like material.
Yes, you can do a presentation without slides. In some ways you can make a better presentation unless you are very skilled with slide creation. Most slide presentations are incredibly boring. They have been described, somewhat accurately, as the private notes that a speaker would normally keep to themself rather than making them visible. I know a couple of people who can do a good job, but it is, in my view a poor technology in general.
However, the expectations of your audience should be taken into account. If they expect slides, then you should probably do it that way. If you distribute the slides, printed perhaps, before the presentation then the audience has a place to take "notes in context". So, the "penalized" question is an entirely local one. Make sure you understand the local expectations. And, don't be boring.

At one university where I studied, the chalk boards were actually slate and there was a chalk tray at the bottom. The classrooms were very seldom cleaned and after several weeks a small cone of chalk dust would be growing on the floor just below the end of the tray.
Since the boards were seldom washed, just dry wiped, it sometimes occurred that the writing on the board would start to slide down the board on the "lubrication" of the still remaining dust from earlier uses. It would get distorted as it slid, of course.


Does making Youtube videos improve your CV?

Universities are usually interested in the degree to which their teachers can gain wide recognition for their teaching, and thereby spread the reputation of their institution.  If you are able to publicise your teaching work to a wide audience, this enhances the reputation of the institution you are in, and so the university has an interest in that outcome.  Universities like their academics to be in the public-eye, since this adds to brand-recognition of the university, and shows that their academics are influential in the public sphere.  Hence, any activity which gains you wider recognition for your teaching or intellectual work is going to be something worth putting on a CV.

A useful case-in-point for the potential career value of academic YouTube videos is the case of Prof Jordan Peterson at the University of Toronto.  Peterson was a successful academic in a Canadian university, but was not widely known outside his field until he began producing YouTube videos of his lectures and his general thoughts on social issues.  Coupled with him taking on some controversial topics, his use of direct communication to the public created a great deal of interest in his work, which has led to him being widely featured in conferences, interviews, etc.  Two years ago I hadn't heard of Peterson;   six months ago he was described in the New York Times (albeit second-hand, with agreement) as "the most influential public intellectual in the Western world right now".  This is an extreme case, and it is also influenced by the social topics that Peterson discusses, but I think it is fair to say that if he had not produced YouTube videos, his work would not have spread as widely.   So yes, YouTube videos of your teaching can make a difference.


Using a graphics tablet to support recorded lectures?

My personal experience with different media used during lectures (basic calculations during an engineering course)

Tablet:

I experimented with my tablet (Galaxy tab S) but to be honest, my handwritten notes look like a child had written them. The Galaxy S is not particularly designed for taking handwritten notes, so maybe other tablets are suited better.
Graphic tablets from Wacom may be suited well. The possibility to project the notes live while explaining something to a particular group anywhere in the classroom may be a big advantage but in my opinion it does not outweigh the unprofessional look. Unfortunately, no shop in my town has Wacom tablets in stock. Otherwise I would try them. One of my students uses the new tablet-laptop from microsoft and is very satisfied with his handwritten notes. Still, the writing looks not very professional.

Document camera:

There are different models and I used a document camera in the price range of 700 $. The camera itself can be used to capture the notes while writing on a notebook. The video can be streamed live using standard video software. Additionally, it is possible to record the session and save the data on a SD card (including your voice). I like the feeling of a pen on paper and my notes look much better than on a tables. In my opinion it is the easiest solution right now.

But nothing beats the white or chalkboard. The possibility to teach while using my whole body for supporting the things I said is most comfortable for me. Furthermore, there is no device or desk between me and the students. As a consequence, it is easier to focus their attention.

Since most questions do occur every year again and again, I produce short videos at home using my hq-webcam. It is much easier for me because I can focus on one particular goal (producing a video, or explaining something to one student in one particular class). I am not the multitasking type.

To sum it up:
If you like the feeling of a pen on a paper you might want to search for "document camera"

You may want to look at those two videos:
Tablet for Tutoring Wacom Pad in Teaching


There might be two parts to this question here, so I will answer them separately.

Is it plagiarism if I do not cite my own published results?

Answer: Yes, that's called self-plagiarism. It does not matter if the results you want to cite where published by yourself or another person. It must be cited. Even if you have the same data and plot it differently, it is essentially not a new source. Since you usually have more data accessible from your own publications, you might come into temptation to use an altered figure from a previous publication. These must also be cited as part of the published paper. Better safe than sorry, just cite it if it can be attributed to a previous piece of research.

Do I have the right to reprint figures from a publication in my thesis?

Answer: Well, that depends on which licensing agreement your published paper falls under. For example, the very popular open access CC-BY license allows you to retain the rights to your images and to reprint them. However, attribution (i.e. via citation) must still be specified.

If you do not own the rights to reprint the pictures as they are, you can always redraw a figure (as suggested by Oleg Lobachev in the comments) and correctly cite the source as "Redrawn from Author et al. [54]" or similar.

TL;DR Yes, if you rearrange data from an old publication in a new form you still have to cite the old publication.


How can I determine whether a conference is reputable?

I'm assuming you are really asking how to check whether a conference is reputable (meaning not a scam), not how to check whether a conference is actually good.

Short answer: If you don't recognize the conference or its organizers, stay away.

You should already know a relatively short list of established, reputable conferences in your research area.  If you don't, ask your advisor to give you such a list.  (If your advisor doesn't know, you need a new advisor.)

If this conference isn't on that list, it might still be reputable, but either very new or slightly outside your research area.  In that case, take a serious look at the organizing committee.  If the members of the organizing committee are well-known active researchers, the conference is probably fine.  Otherwise, it's probably a scam.

You mention that you were invited to submit to the conference.  At least in computer science, such invitations are almost unheard of; conferences are normally advertised by impersonal calls for papers.  Did the invitation come from someone you already know, at least professionally?  Does the invitation mention specific technical details of your work (more than just a paper title)?  If you answered "No" to both these questions, the conference is almost certainly a scam.


Do I need to report that the professor I have been assigned to TA hasn't assigned any work for me to do?

First try some other methods of getting in touch with him.  Call him on the phone, go to his office (during scheduled office hours if possible).  It's possible that for some reason your emails are not reaching him, or he's just overwhelmed with other stuff and forgot to reply.  Don't throw around words like "stonewall" unless you have proof that he received your emails and is willfully refusing to reply.

If you can't, then yes, you ought to report it.  Your advisor may not be the right person; I would look to whichever faculty member supervises the TA program in your department.  It could be the chair, or graduate vice chair, or some similar person.

It could be that this is a sign of bigger problems, and if so, it will reflect poorly on you when it is found out that you knew something was wrong and took no action.


Procedure for having multiple advisors for a PhD thesis

Unfortunately, I think the answer is going to be - "it depends"! I have advised several graduate students, including 2 who are currently "co-advised" with other faculty. In one case, the student approached me first, but I already had a working relationship (co-teaching, serving on supervisory committees together etc.) with the other faculty member. In the other case, I was approached 2nd, and again, I had previously worked with the other faculty and knew them well. When talking with potential students, if it is clear that a different faculty member would have better or equally relevant expertise, I always suggest talking to them. However, that's my opinion. I also have colleagues who would flat out refuse to consider co-advising a student.

I think the key "test" is to imagine your dissertation work as a 3 way collaboration - what does each faculty member bring to the table? What are they going to get out of it? How you approach them is completely dependent on the individual personalities involved. You should also find out if there are any policies on co-advising at your institution or department - there are none at mine, but that might not be universal.


Is it possible to earn a PhD in mathematics with emphasis in teaching?

The "doctor of arts" degree was created in the 1960's to solve this problem.  It's like a PhD, but it doesn't require original research for the dissertation.  The goal is to prepare students for teaching careers that do not involve research.

Several universities in the U.S. offer DA degrees in mathematics, but they have never become popular.  Many people aren't even aware that such a degree exists, and those who know about it generally consider it inferior to a PhD.  Even institutions that do not expect their faculty to conduct any research at all often prefer to hire candidates who have some research experience in the past, in which case they would prefer a PhD to a DA.  (And many institutions require at least a little research to get tenure.)

For most people, getting a DA would be a bad idea: the time and effort required are comparable to a PhD, with worse career prospects.  However, there are some narrow circumstances in which it could make sense.  For example, some institutions (particularly high schools and some community colleges) don't require a doctorate at all but pay a higher salary to faculty with a terminal degree.  In that case, a DA might work just as well as a PhD.


An instructor has a responsibility to develop their own forms of assessment. What others have done before can serve as an inspiration but what they did is never adequate for several reasons.

Your students are not the same
You are not the same

Since you and the students are different. Prior assessment would probably not be appropriate as you will teach and they will learn slightly differently. You may stress aspects of the course that the other teacher did not and the students might ask about information that was not covered in the last class.

There is a common three step process to developing a curriculum called backward design.

What do the students need to know (as defined by the goals and objectives of the course)
What evidence will the students produce to demonstrate mastery of the content (i.e. the assessment, activities and assignments they will do)
How will you teach (lecture, discussion, etc)

This simple format can be used in any field to provide learning experiences that are consistent with the assessment and goals of the course.


Quoting a typo: Do I really have to do "sic", or can I just fix the sentence?

Academics are old-fashioned people who care about things like truth, facts, and accuracy. By making sure that everything you write between quotation marks is what the person you quote actually wrote (with "[sic]" inserted as appropriate), you will contribute your small share to perpetuating these values, which, although temporarily out of fashion these days in some parts, have served humanity well and will continue to do so in the future.

It may seem silly to resist the urge to make a correction when it's just a typo, but it's a good way to get yourself and others into the habit of speaking truthfully and accurately. So please write "sic" rather than correct the quote. Silly as it may be, in a small way it makes the world a better place.


What should I put in the "about me" section of an academic job talk?

The job talks I'm familiar with don't generally have an "about me" section, so you may be thinking of a different sort of talk from what I have in mind.  (I'm envisioning a research talk at a U.S. university.)  But in my experience, you shouldn't include anything in a job talk unless it illuminates your work in some way.

Hobbies are completely out, except in rare cases when they seriously influence your research.  Your career path could be relevant for conveying your background and interests.  For example, if you worked in an industrial research lab or have substantial background in another field, that could be worth highlighting.  However, there's no point in giving an oral recital of your CV.  Same thing with how you got into your field: you should mention this only if it somehow shapes how people should think about your expertise (and this will rarely be the case).  On the other hand, pointing out that your work is half collaborative and half independent sounds reasonable to me.

More generally, you want to put the specific topic you'll be discussing in the context of your broader research program.  How does it relate to other work you have done or to ongoing interests?  What's noteworthy about your overall activities?

  How much is about me as myself versus about me the professional?

It should all be about you as a professional.  You don't want to give the impression that the best argument you can make for hiring you involves your hobbies.


Is it okay to publish my personal notes from a lecture?

The ethical thing to do, in my opinion, would be to ask the professor's permission.


How to write a paper with a parallel but non-trivial approach?

Getting into the details would be too technical for this site, but my suggestion is spell it out explicitly.

If this issue is a concern for your readers and for the referees, there should be a section in your paper titled Why is this nontrivial? (maybe just after the introduction) where you argue on why your approach is relevant. If you can, include an example where it is apparent that your approach is more simple or more insightful.

Don't be afraid to toot your own horn.


For applications like the NSF Graduate Research Fellowship, candidates are explicitly told not to include such links, because it creates an unequal playing field, and that these websites might be used as an "end-around" against page and length restrictions. Similar rules might also hold for other applications as a result.

On the other hand, some schools may ask you for such a link, in which case there's a good chance it will be seen if someone is interested in you. But if you're not specifically asked to include such a link in your application, there's no guarantee that anyone will look at whatever's posted.


How do you verify facts claimed by a deceased author?

Assuming you cared about it enough, would you contact the family of the author, to see if they had notes the author had used in writing the book, or is that impolite?

It's implausible that the author's files are well-organized and clear enough that a non-expert family member could easily answer your question.  And unless the answer is dreadfully important, it seems inappropriate to ask whether you could fly into town and spend hours/days searching through any files the family possesses.  (One can accumulate a large number of boxes of papers over the course of a career.)  That could make sense if you were working on a major project about the author and the family was eager to help, but for an isolated question it feels like far too much of an imposition on the family.

If the family felt the files were likely to be of continuing academic or historical interest, then they may have donated them to a university library or archive (most likely at the university the author worked at, if any).  I'd start by doing web searches to try to find out.  If you can't find out online, you could enquire at the most likely university library.

Before trying to track down the author's files, it's worth convincing yourself that there's no other way to get an answer.  For example, maybe the author is alluding to something well known among a certain community, or maybe the author supplied more details in a different publication.  You could try ask online (e.g., on a suitable stack exchange site) and see what happens.

If the author worked with a collaborator or had a student who specialized in this topic, then they would be natural people to ask.  You could also try asking another expert (e-mailing someone out of the blue will come across best if you give an explanation of how you have tried and failed to find the answer).

If nobody else knows and the author's files weren't formally archived anywhere, then I'm not sure how much more you can do.  The author's information may simply be lost and will have to be reconstructed from scratch.


What to do when you are invited to another university?

Offering to give a presentation about your work sounds like a very good idea. I would suggest contacting the professor as soon as possible saying that you would be keen to present your work. By giving them early notice, you give them the chance to either arrange something for you, or to pass your details onto anybody in the wider department who may run the sorts of seminars/colloquiums where such talks often take place.

In terms of other things you could do, if they've already told you that you'll be introduced to other members of the research team then that sounds like a lot of that will be organised for you. Another thing you may want to consider is to see what other regularly seminars, journal clubs, research groups, etc. already exist that might be of interest to you. If this is somewhere that you may have the opportunity to go and work at then you want to have the fullest sense of what your working environment would be like.

As for putting it on your CV, I'm not entirely sure that a visit is entirely relevant. If it was a visiting job then include it, but something casual like this probably not. It is the sort of thing that may be well worth discussing (if it's relevant) in a cover letter or supporting statement that goes alongside applications.


How important is advisor's supervision for a Ph.D. student to be an independent researcher?

There are two major types of advisor approaches which I've encountered during my studies:

Hands-off, abstract guidance only. Hint at which areas are interesting or currently active, but do not throw yourself into your student's work. Usually such advisors will gladly proofread the student's work for errors, but they rarely know what to do if a student gets seriously stuck. Advisor sessions may be spent discussing current trends, future work of either the advisor or the student or, in some cases, simply "life advice".
Co-worker approach. The advisor treats his student as an equal and tries to immerse himself into the student's work (or vice versa). By having a lot of exposure to the advisor's routine (how he goes around solving problems, how much time he spends doing research, how he prepares for lectures, etc.), the teacher aims to guide the student by example.

These two approaches are often seen in combination (while the student may be treated as a coworker, he still is usually the one to do the typesetting, the programming, and other time-consuming tasks).

Personally, I prefer the second approach, which is likely because I am not that settled in the "theoretical research" routine. Some of my friends, who have known since their Master's studies what they want to do, are very enthusiastic about having a well known professor with the hands-off approach.

To answer the question about either approach fostering independence, I believe the hands-off approach leads to much larger independence as a researcher, but the coworker approach may lead to a much better work ethic (mirroring the professor), which is tremendously important in science.

It seems to me that students have a harder time successfully completing research (asking the right question, having the right insights, etc.) than being independent. Therefore I believe that student/advisor relationship does not need to promote "independence" in any substantial way.


The short answer is no. There is no comprehensive list of academic journals, and I doubt there ever will be. The major reason for it is there is no real need as publishing culture varies a lot by field and geography. Plus, in the recent explosion of scholarly publishing, there is probably a new journal every week or so.

However there are curated databases of journals. For example, Thomson Reuters has a service called Web of Science that provides libraries with a large list of journals (about 12'000 according to Wikipedia) and publication metrics, such as citation count, rank by discipline and impact factor. I used this service a few times to check the ranking of journals before submitting papers.

Libraries often let affiliates download the full report as a spreadsheet that you can manipulate the way you want. Contact your local library, most institutions subscribe to this database.

Also, this list might be useful to you.