Can a good but unremarkable PhD student become an accomplished professor?

Yes of course.

Some PhD’s are really good at research, or they just prefer research.

Others however, like to pass on knowledge and when a student « gets » something they are pleased for them.

So being able to explain concepts to others and remembering or understanding why you found certain concepts difficult and using that experience to help other students can be very rewarding.

The downside is it comes with things like grading... But having clear marking schemes helps with that, both when you mark and when students want feedback.


Research Associate job reposted, shiould I reach out to the PI?

A significant proportion of academic jobs are advertised publicly, but in reality they are created for a pre-selected candidate. It is extremely frustrating that many talented candidates routinely waste time end effort applying for jobs where they will not be shortlisted, even if their skills are a close match to published job specification.  I am sorry to hear you find yourself in this situation. The old boys' club is still strong in academia and it hurts normal candidates a lot.
For an individual like you, it is probably advisable to move on and apply elsewhere. Some places have a more fair assessment process for all applications, and the more you apply the higher is the chance you will be invited for an interview.
Good luck.


Your question was tagged 'publications' - if you plan on submitting work to a particular journal, it would be worth checking to see if they have a house style for jargon.


How to highlight the importance of past positions in CV?

If a title or position is unclear, or an institution is possibly not well known, just explain it in a few words:

  Director of Supersonic Operations department (15 researchers) at Small U.
  Time-management officer, Funny Inc. (in charge of scheduling company-wide meetings)
  Information officer, U. of North Virginia (CTO-like position, managing computing resources for 10,000+ students and staff)

Be as concise as possible, but give the reader some idea of the scope of your activities. And if the position is clear or well-known, just don't add any details.


Is there a clear etiquette on providing full text paper when you are a coauthor?

It's your paper, even if you are just a co-author.  I can't imagine why any of your collaborators would not want to share them.  Keeping in mind that not all journals are accessible to everyone, I see no reason not to promptly acquiesce, even if  you are not the corresponding author.


Instructor's manual -- model answers from it by instructor

Assuming that you want to teach your students good academic practice in general as well as your specific subject, then you should let them know the source of the answers you provide, at least in general. "This comes from the book's authors" is probably enough. Otherwise they might get the idea that copying and plagiarism is fine. And if you represent the answers as your own work, then, yes, it is a form of plagiarism..
However, providing the answers verbatim, raises also the issue of over-copying from published material. It may be, however, that the instructor's guide provides specific guidance for use, possibly granting (or forbidding) such release. For some books, the questions/exercises are the most valuable part, and releasing this information can definitely lessen the value of the book, especially if students are likely to put such things online or otherwise cache them for others. That would be a copyright problem, but not a plagiarism issue if you give the source.
Third, while not an ethical issue, courtesy and respect for the authors might imply that you not give out answers verbatim, to protect the investment they made in producing it. And also courtesy and respect for future instructors (and students) who want to use the book in a way that maximizes learning and lessens the likelihood of student cheating.
Finally, there is the issue of serving your students. This can raise many issues, but, in general, hints for producing solutions are more valuable to their learning than just providing answers. In fact, minimal hints, that help them develop insight, are more valuable than extensive hints. There is a vast difference between developing an answer on your own and reading a solution. Developing a solution with minimal hints is very much closer to the former than the latter. This will aid their education rather than giving them the false impression that they have developed some skill or insight when they have not. Hints are also sometimes necessary to dispel misconceptions. Unfortunately, tailored hints don't scale very well.
To answer one of your concerns directly, you can deny them access on the basis that having those answers would inhibit their learning and that they should try a bit harder to work out the answers themselves.
So, my suggestion, as an experienced educator, is that you don't give these out for a variety of reasons, the most important one is the value that actually doing the exercises has for your students. Even if they struggle. Perhaps especially if they struggle. The purpose of education isn't "answers", but learning.


How to respond to someone plagiarizing my work?

I would definitely contact the chief editor of the journal and place the evidence before him/her/them. Plagiarism should not be taken lightly. There is a tendency to be lenient when it comes to self-plagiarism of non-critical parts of the text, for example, parts of methods sections (in experimental work). Regardless where one draws the line, copying sections of text verbatim from others is a clear breach to me.

Anyway, it will be the editor's job to pursue the matter after you made the point. If the journal belongs to a publishing house they may receive legal help to deal with the author. If the editor does not react and there is a clear publisher behind the journal it may be relevant to bring it up a level. If you have someone in your university working on copyright issues, perhaps at the library, then you could also talk to them. They may be able to provide further assistance and help evaluate the case.


Different journals are set up differently. Some journals have an editor-in-chief who assigns an associate editor who assigns a member of the editorial board. Others have the journal office assign an editor who assigns the reviewers. Yet others could let the authors choose.

It sounds like you've submitted your paper to a journal using the last model. My guess would be that the chosen editor will be the one handling your paper (unless she declines). So don't worry about it and let the process run its course.

About the roles of all these editors, the word "editor" has many possible meanings and it's not really possible to tell without insider information what everyone does. Editor-in-chief is generally the highest-ranking position, and is responsible for everything published in the journal, but beyond that anything goes. "Managing editor", "Senior editor", "Consulting editor", "Assistant editor", etc - they could all be doing the same thing. It all depends on how the journal is set up.

Finally, about the salutation, I wouldn't worry about it. Chances are the SE will be reading your cover letter. If it's the EiC (or journal office) reading it instead, they're not likely to take offense.


Proper way of marking dimensions of a drawing in a paper

In my opinion it depends on why the figure is part of the paper.  Say you wont to emphasize a particular set-up , for instance in experimental section or whatever section dealing with experimental details (size and shape ) because necessary for the discussion, then I would explicitly quote the numbers.

If you are to discuss relation which are general then use letters

If a wish a particular triangle I would cite three numbers. If I discuss Pytagorean theorem is fine and more useful to draw A, B e C.


Why is manuscript review in mathematics taking so long (over 8 months)?

Mathematics tends to have a long refereeing process.  It's nice when it can be completed in a few months, but eight months is not especially worrisome.  The editor should be sending the referee(s) periodic messages to make sure they aren't just forgetting, and you can send status inquiries to the editor every once in a while if you'd like (it shouldn't be necessary, but it can't hurt and could conceivably help).  I tend to ask for a status update every six months or so.

One reason it takes so long is that refereeing a mathematics paper is difficult.  The referee has to read and understand the proofs, which is one of the slowest and most painstaking forms of reading.  Another issue is that there is no expectation that it should be done quickly: a referee who takes eight months isn't generally considered problematic by the journal or the community at large.

In practice, the lengthy refereeing times are not a problem.  Mathematics papers are typically circulated publicly (for example, on www.arXiv.org) long before they are accepted for publication, so the publication process isn't holding up progress in the field.  And the mathematics community is well aware of how long it takes to get papers officially published and takes this into account in career evaluation (hiring, tenure, etc.).  For example, if you're applying for a job, nobody will expect your papers from the last year or two to be published yet.  If they are at least on the arXiv and submitted for publication, then everything is as it should be.


What universities are recognized by USA universities?

There is an official list of accredited US institutes of post-secondary education, the database of accredited post-secondary institutions and programmes, but according to that page, the Department of Education does not maintain a list of recognised institutions worldwide.  Instead, there is an educational NGO, the Council for Higher Education Accreditation, that maintains a list of accrediting bodies that are recognised by its member organisations (which include Stanford and UC Berkeley, but not MIT), the Database of Institutions and Programs Accredited by Recognized United States Accrediting Organizations.  The institutions recognised by the member organisations are the institutions accredited by one of these bodies, which are national in scope.

As a state university, the University of Western Sydney is accredited.  For other institutions with less international visibility, rather than look up this information yourself, it is better to contact the HR department of the institutions to which you apply to get their direct judgement on whether that institution is recognised by them.


Why would a potential supervisor emphasize kind of doctoral degree?

I'm guessing that he has had a number of candidates who were unclear on that from the outset and that he's simply clarifying to make sure there's no confusion prior to your joining the lab. I don't know whether this is likely to affect your long-term career, hopefully someone who knows more about German academics can clarify in the comments.


How to react when a professor give back the corrected version of a test just before the finals?

Was it ethical/fair that B gave the grades two days before the exams?

I find it unfortunate. However, the question about fairness or ethics does not have a definite answer, as it depends on what was announced in class. If, for example, it was announced that the mid exam was to give the students feedback on their progress, such a large delay was not appropriate. If, on the other hand, the purpose of the exam was to give the instructor a feedback on how the students digested the material, than there is nothing bad about such a large delay. I, personally, would find the latter a bit weird and think that a mid exam which is corrected but not handed back to the students timely is a waste of time for everybody.

  How could A, if it has to happen again, handle the situation?

Ask in advance. Ask what the purpose of the exam is. Ask when you can expect the results back (and explain that you value the feedback and that he feedback will be helpful for your learning).

  Could A talk to B about his feelings?

I don't think that feelings should be discussed. However, A may bring it to the attention of B that it would have been easier for A to get the feedback earlier (or not at all), and explain how a timely feedback could have been helpful and so on.

  Should A report to B superior about the situation?

Not unless B had violated some rule. A prior discussion with B is better.

  Should, as a student of another class, handle the role of a “mediator” between A and B?

If A is too angry to discuss the matter properly, a mediator may be a good idea. However, I think that this would look rather unprofessional and that it would be better if A could calm down enough to discuss the matter themselves.

What could be a good idea, is to gather more information from the rest of the class, i.e. what they think about the situation, and then let one or two representatives discuss with B. These guys should be well prepared (e.g. with notes from the discussion of group) and try not to speak for themselves but for the whole group.


How to add citation for a whole paragraph?

Generally it is sufficient to cite each source only once in each place where you refer to material from this source. "Place" may be one sentence, one paragraph, one definition, etc.

If you cite a paragraph verbatim from another source, put it in quotation marks or in a quotation block and add one reference to the source at the end.

If you have a whole paragraph referring to one source but don't actually quote it, it gets a little bit more tricky. You have to make sure that a reader clearly understands that the whole paragraph is based on the source you are citing. A simple citation in parenthesis just added at the end of the last sentence may not be sufficient to make this clear. One way to cite in this case is to write something like "The following argument is based on (source)" at the beginning of the paragraph in question.


Is supporting Sci-Hub illegal/unacademic?

In my view it is foolish to describe Sci-Hub itself as illegal. Acts can be illegal, but not "things" or groups of people. Only activities. While it is true that they may engage in illegal activities, that is not the same thing.

However, if what they do is copyright infringement (very possibly) then you can't participate in that.

However, if you want to upload things for which you hold copyright to Sci-Hub or a similar site then you aren't engaging in any illegal activity, nor is any downloader, provided that you grant an appropriate license.

Countries and other jurisdictions make laws. People (and organizations) can break those laws, but the people themselves, and the organizations do not themselves become illegal.

I think your university is right to open a disciplinary hearing only if you advocate breaking laws to students.

I agree with you that publishers have put a lock on science and culture that is very unfortunate. Especially when copyright no longer seems to expire after a reasonable period, and fair use is losing ground. Publishers are transferring what should be a common good into a private profit making enterprise. They are, IMO, stealing from the public. If you can afford not to give them copyright on things then I encourage it, but the whole system has made it hard for academics to build a reputation otherwise. Long term this tends to make us dumber, not smarter. As they say: Sad.

I'll add an historical note. There was once a valid reason for publishers to want to hold copyright on articles they published. There was a lot of friction (read cost) between an author and a potential reader. As such, since the publisher bore a lot of the cost (not the creation cost, of course), they needed assurance that they could recoup what they spent in making scientific articles available - especially since the material itself had value, but the number of potential readers was small (relatively speaking).

But that world is now long past. Publishing is nearly frictionless now. Publishers can still provide a useful review (done by volunteers) and editing (done by paid professionals) function, but the distribution cost is near zero and borne partly by users in any case (internet fees). Most of the real cost of the creation of publishable material today is borne by the author, by universities and scientific organizations, and by government. Publishers in the old model are an anachronism if not an oxymoron.


A good way to start could be drumming up a short list of concise, but interesting questions you might ask him about his work. Then try to connect it to your own work or tease out how your interests going forward actually build on this idea. You can try to ask if he/she'd be interested in collaborating, but big names are notoriously hard to get a hold of, even for their own students, let alone other students outside their wing. Don't know if this is the case for your field, but I'm fairly sure it's a common problem.

A more realistic expectation at this point would be for you to (1) pique his/her interest and ask if it's alright to keep them updated about your project or keep in touch with his/her work. (2) Begin the project on your own, and keep them updated when you've demonstrated a good amount of progress (and success!) in the project. (3) Then, down the road, they'd be more interested/motivated to collaborate on a paper.

Good luck!


Realized a co-author inserted plagiarism into our paper 8 years ago - what to do now?

Move on. In the abstract, of course, we should care about these things but, in reality, a paper that has been out there for 8-10 years has passed the statute of limitations. It is exceedingly unlikely that anyone will go back and check papers that old -- indeed, even if someone finds textual overlap with other sources, it will require quite a lot of work and human intervention to determine who copied from whom.

The point for you to take away is this: You learned a lesson to be more careful in the future. That's a good thing from your perspective, and it will make sure that you won't get into a potentially embarrassing situation again in the future. In the meantime, relax.


Where do I find the funding information for each math PhD program?

In the US almost all doctoral students in math are eligible for either a TA or an RA position, but mostly TA. The universities require a large number of TAs to manage the undergraduate program so as to free up professors for research and doctoral advising. Funding is modest, and 1/3 or so of your time might be spent on TA duties. Tuition is also normally waived for TAs.
Some professors might have funding for an RA or two, but there would still be duties.
But for those wishing a career in academia, starting out as a TA gives you some experience on the teaching side, if only (initially) grading and holding small tutorial sessions. An RA would be more valuable for someone wanting to go into industry, but they are not as common, and likely much more competitive.
There are relatively few positions that have no duties attached. At one time there were widely available federal scholarships under the National Defense Education Act but those ended long ago. A few, more tailored, programs remain.


Former advisor committed financial misconduct. How to apply to PhD programs

From what I can deduce, your advisor was involved in financial misconduct, not academic misconduct such as plagarism or using falsified data. This means that the actual integrity of your research has not been compromised (from what I can tell). If this is the case, the papers you have written still stand and offer valid insight into your abilities as a researcher.

Applying to Univeristy of X

Personally, I would just avoid applying to University X altogether. If you would still like to apply to U of X and you personally know the affected professor, I would actually consider writing an email directly to her. Tell her of your intentions to apply to the graduate program at her school. Ask her what her thoughts would be on you applying.  Tell her that you are considering her as an advisor and then ask her if she has openings for students. This should allow you to gauge her feelings. And the worst that could happen I guess is that University of X rejects you and you are out an application fee.

Applying to programs in general

As for the field in general knowing of your advisor's misdeeds, it is indeed feasible that other programs will be aware of some portion of the story. This will depend on how large your field is and how well known the university you got your master's degree from is. If you feel that a significant portion of the field would be aware of you advisor's misdeeds, it may not actually be an awful idea to include a short statement in your application acknowledging that, yes, he was your advisor, but that you were in no way involved:

  Because my former advisor was recently implicated in fraudulent use of grant money, I feel that it is important that I provide full disclosure as to my association with him. [Dr. Fraud] misused grant money after he was my advisor and I have no knowledge of any misuse of funds while I was a student of his. I believe that the integrity of my work with him still stands and is a positive reflection of my work in research-level [basket-weaving]. If the admissions committee would like to speak to me further about the situation, I would be happy to do so.

This acknowledges the issue head-on and does not leave them speculating as to your involvement. It also opens up the possibility of them contacting you directly and allowing you to explain the situation at further length. Admissions committees always prefer full disclosure. They want to know as much as they can about an applicant's situation and portfolio.

Because most universities will not have any professors who were personally affected by the fraud, I do not think they would really hold against you the fact that your advisor cheated on his use of grant money. If I had an application like yours come across my desk, I would personally hope I would be reasonable enough to understand that you were in no way complicit with your advisor's scheme.  This is all you need to say about the matter. Focus on your credentials and potential, not your advisor's misdeeds. Trying to explain too much will actually make you look guilty. Just be short and up front about what happened, then focus on how you will be an excellent choice for their PhD program because of your research and capabilities.

One option I would certainly look at for sure is applying to the same university that you got your master's degree from. They will be fully aware of the situation and they will know that you were not involved in any way. It's sort of their mess to clean up.

Whatever you do, do not have your former advisor write you a letter of recommendation.


Should the glossary in my dissertation be minimalist or comprehensive?

If you think it will improve the usefulness of the thesis, and it isn't too much trouble for you, then I'd say by all means go for it.

I would not worry about page count. I don't think anyone cares how long the thesis is.


Are abstracts confidential during the review process?

I checked the peer review policy of Nature and Science, I guess that should is the best we can get. The policy can be found here, here (both Nature) and here (Science).
A bunch of relevant quotes from the Nature policies:

As a condition of agreeing to assess the manuscript, all reviewers undertake to keep submitted manuscripts and associated data confidential...
Nature journals keep confidential all details about a submitted manuscript and do not comment to any outside organization ...
Referees of manuscripts submitted to Nature journals undertake in advance to maintain confidentiality of manuscripts and any associated supplementary data.

And some from the Science review policy:

Reviewers are contacted before being sent a paper and are asked to return comments within 1 to 2 weeks for most papers.
The submitted manuscript is a privileged communication and must be treated as a confidential document.

I would read it conservatively. That is, consider an abstract to be a part of the manuscript, hence the same rules governing general manuscript should apply. Apart from that, both journals state that in advance to being sent the manuscript, the (I guess still potential) reviewers agree to keep the matter confident.
I think an answer may also lie in the exact process handling review. First, a potential reviewer is invited and sees a title and possibly paper's authors. Then he/she has to log-in into a review system, but I guess, somewhere in the process accepts general terms and conditions which established the contract. And only then the reviewer sees the manuscript. I am not sure if all journals do it this way, but those I reviewed for did so. Well, besides some special issues handled outside the journal submission/review system, where the case would be unclear.

I just checked the reviewer invitations I received from journals in my field and I found that the only disclosed thing in the invitation e-mails was the submission's title. I must accept/decline to review and only afterwards I saw the manuscript, or its abstract.


I have multiple journal articles, but I do not enjoy conference presentations. Is it bad for my job prospects?

[I am talking from a STEM perspective, not from social sciences, but from what I hear from humanities, interaction may even be more important there than in STEM. However, take it with a grain of salt:]
A faculty position involves interacting with people and giving lectures regularly. Where will you get the practice from if not in conferences?
Assuming even that you get a faculty position. Where will you get your networks that you'll need for tenure and promotion, if not by meeting colleagues at conferences and explaining your work. Yes, some extraordinary scientists may actually achieve faculty positions by their journal papers alone (I am aware of such examples), but they are extraordinary people and very rare.
Better, you face your challenge and get used to learn how to present good talks. We all had to develop this skill and I promise you it will come handy at some point.


should I fight to choose journal my work is submitted to?

If the journal is junk, you should not publish there, period. So, the real question is: Is the journal as bad as you think it is or this journal is just not one of the top journals in your area but still a legit, reputable journal? So, confirm which of the two applies. How to distinguish journals has already been discussed several times in this forum. Check the editors, look their homepages if they mention their editorial work there, see who else publishes there and check some of the published articles.

In case this is actually a legit, reputable journal but still not top of the line, you should really consider if your work is actually as good as you think it is. It already has got a rejection and perhaps your advisor suggests some medium (and not top) journal, since he may believe your work might actually have a chance there. So, be open about this and ask him. What does he actually think about your specific work? Is it not good enough for the top journals? If he believes it is not, perhaps you should reconsider your stance.


What is the meaning of pre-doctoral program?

In some parts of the world, this is the term used for a PhD program.

Before you obtain your doctorate (i.e. PhD), you are a pre-doctoral fellow or a doctoral candidate. After you have obtained it, you may become a post-doctoral fellow.

Example: http://www.ral.uni-leipzig.de/en/home/postdocs/pre-doc-award/

In other parts of the world, "predoctoral" may refer to the period before a student enrolls in a PhD programme.

On a related note, the term "PhD" is much abused these days with students who have not yet obtained a PhD being referred to as "PhDs". This is quite inaccurate as they have not yet obtained the degree and are thus not "doctors". They are a "PhD students", i.e. studying towards obtaining a doctorate.


How to Scale or Curve the Grades for an Examination?

First, let's acknowledge that this was a horrible test.  You have almost no power to discriminate between the different abilities of the students with a mean of 23% and a standard deviation of 5%.

Then you have to decide what to do.  Personally, I'd decrease the weight of this test in acknowledgement that it was a poor test (or allow students the option of letting something else count for more).  But if you just want to solve it numerically, there are the following constraints:

You can't have a top score of more than 100%
The mean is required to be 72%
You want all differences to still mean something

If you add 49% to the grades, you get a mean of 72% but your top score is now 117%.  You could cap it at 90-95% or so, but the top students would be indistinguishable.  So you'd have to scale back by squashing the grades also, e.g. by multiplying the difference from 23% by (28/45) to get it back in range.  This will make the students distinguishable but not meaningfully so.

Really the best option is to change the grading scheme so that you have a higher mean and more distinction between different scores (to the extent that this is possible).  For example, you can give a number of points for attempting a problem at all, a number of points for writing down anything which has a bearing on the right answer, etc..

You can just directly transform your old scores into new scores with the mean and deviation you like, however.  Let icdfG(p) be the value at which the probability of getting a lower percentile score p from a Normal distribution with mean 0 and standard deviation is 1.  Then you can just calculate percentiles and map

new score = 72 + icdfG(percentile)*10

or something to get a mean of 72 and a standard deviation of 10.  (Your top student in a class of 84 would have a percentile of 83.5/84 if you did it this way.)  Your top student would have a score of 97 under this scheme (and the second to top a score of 93)

Otherwise, you're probably best off using a nonlinear transform; arctan is a nice function for that since it will squash down the tails; and you probably want a SD of at least 10 not 5, so you could do something like

new score = 72 + 50/Pi * arctan((score - 23)/10)

which would give a max score if 93.5, a min score of 54.7, and one standard deviation up and down would give 79.4 and 64.6 respectively.

But again, the better options are to devalue the test as a bad test, and to change the grading scheme (an awful lot of work, but it will give fairer results).


Returning to grad school after several years in industry, who to ask for references for NSF graduate fellowship?

I have reviewed for the NSF GRFP before, including a few applications from students with extenuating circumstances.

Your potential advisor can still write you a reference letter. I have seen some first-year graduate students get relatively strong reference letters from their new advisors. The advisor writes their impression of the student based on the first 3-4 months of working together, plus the student's application materials to the graduate program if they were particularly strong. The best thing your new advisor can do, though, is attest to the level of support you'll get from them and the university for your research project and training endeavors. If they can speak to the feasibility of your project and how it potentially ties into the work that they're already doing in the lab, but still how it stands independently, that could go a long way.

And yes, your other recommendation letters should be from those former professors, who can speak about your scholarly promise. The best thing would be if one of them could address the gap in some way and confirm that they are confident you are passionate and that your time away only renewed your passion for graduate school, or whatnot. A reference writer who believes in you and who you provide with a resume and a statement that attests to this might be the best person to do this.

If your supervisors at Microsoft were not PhDs and did not do research they are not suitable references, so don't submit any from them.

However, I would also consider whether you might be eligible to apply next year, and consider waiting to apply in fall 2017 if you are. The NSF says this:

Applicants who have completed more than twelve months of graduate study or have earned a previous graduate or professional degree are eligible only if they have had an interruption in graduate study of at least two consecutive years prior to November 1 of the year the application is submitted. To be eligible, applicants must have completed no additional graduate study by August 1 of that year. Applicants must address the reasons for the interruption in graduate study in the Personal, Relevant Background and Future Goals Statement.

It sounds like you might be eligible next year as well, given that most school years don't begin until after August 1. You may be more competitive next year as your advisor would've known you for a year and you may also be able to get one other reference letter from someone at your graduate institution. Since you can now only apply for the NSF GRFP one time, consider when is the best time to apply.


Is it possible to re-open a withdrawn article on arXiv?

It might be best to upload a new version that's essentially a note explaining that there's a flaw in the original. Then when you patch the proof (if you patch the proof) you can post the latest version.
Since the flawed original will be there in any case, this keeps all the corrections in one place.


Is there an unwritten rule against quoting literally in some fields?

Yes, but it is better described as an "unwritten custom" instead of an "unwritten rule."


How is a graduate school application affected if an undergrad does research in fields outside of their major?

When looking at graduate applications, the fact that a student has done a some research is much more important than the content (or even the field) of the research.  It probably does not even matter much whether the people reviewing your application even understand your research.  The key point is to have a one or more strong letters of recommendation from your research supervisor(s).  Many research skills transfer relatively well from one field to another, and faculty letters than can attest to your skill level are extremely important to your application file.

Some professors may have a marginal preference for students who have done undergraduate research in the same area in which they pursue graduate studies.  Personally, I do not.  However, it is unquestionably better to have research experience in a relatively unrelated area than to have no research experience at all.


Permission to include a segment from Google Maps as a figure in a publication

Why, of course you should contact Google. More precisely, the Google Permissions page states that it is okay to use Google Map images for the purposes of research assuming that you provide proper attributions.


Does a reference to a work inside a footnote have to be in the bibliography?

You did reference it, it is in the document, so of course it goes into the bibliography.

Imagine the other way round: Someone reads the text, finds it interesting, sees that there is more to be found about this topic in a source and then can't find said source...


What should I put as my GPA for a pass/fail class?

Pass isn't a letter grade at all.  Don't enter anything from the A-F scale; they are all inaccurate.  Check if "P" or "S" (for Satisfactory) are possible options.

Otherwise, reread the instructions for the application.  It may be that they don't want you to include "non-academic" classes like driver education at all.

If you don't find clarification, then contact the school that requires the form and ask them what you should do.

If you are computing your GPA by hand, then pass-fail classes are not included.  Disregard the class completely for the purposes of GPA; leave it out of both the numerator and the denominator.


What is the name for the copies of a paper that you receive once it's been published?

They are called offprints.  From Wikipedia:

  An offprint is a separate printing of a work that originally appeared as part of a larger publication, usually one of composite authorship such as an academic journal, magazine, or edited book.
  [...]

  Offprints are used by authors to promote their work and ensure a wider dissemination and longer life than might have been achieved through the original publication alone. They may be valued by collectors as akin to the first separate edition of a work and, as they are often given away, may bear an inscription from the author. Historically, the exchange of offprints has been a method of correspondence between scholars.


How very high reading/listening but low speaking/writing TOEFL scores are usually judged on graduate admission?

Speaking ability is considered very important; the TOEFL is used to determine if you can speak well enough to teach as a TA at US universities.  Keep in mind teaching is also high pressure, like taking an exam.

These scores might do better with degree programs which do not require the graduate student to teach.

http://www.ets.org/toefl/ibt/scores/understand


Does having much knowledge in other branches help one's research in mathematics in one's own field?

The answer is yes. It helps. Mathematics is very broad. In the various major branches, such as Analysis, Algebra, etc. different insights are needed to really understand what is going on and what is important. In addition to the all-important insights, different proof techniques are common.

When you are doing real research in mathematics you are engaged in a very narrow study. But having a wide variety of ways to attack a problem, even if they might be suggested by ideas from another subfield, will give you an advantage.

Both breadth and depth are needed. Depth is usually what is most valued, but the breadth of knowledge helps you get there. So, don't completely neglect other mathematical subfields than the one you are most interested in. You don't need to be equally skilled in all of them, but being able to grasp the essential insights is a plus.


I wouldn't consider it dishonest, if only because I personally don't list them separately. The fact that they are notes ("squibs" we call them in my field) can generally be inferred directly from the low page count.

But then, the number of such very short publications is a very small fraction of all my publications. If it was a significant fraction, maybe I would consider a separate section.


How to find one or two good recent PhD theses (that are internationally recognized as best) in your chosen area

In general, doctoral theses do not receive much recognition outside of a university, let alone on an international scale. The reason for this is that nowadays the thesis is nowhere near as widely circulated as the papers that can be extracted from the thesis.

Moreover, if you want to find out about good thesis topics, look up what's going on in the scientific literature of the area you're interested in—in this case, internal combustion engines. Find the most highly-respected journals, and see if they've published recent review articles in different areas related to your topic. That might give you a sense of where recent work has been, and provide you with a good body of reading material to work from.


Why is it customary to call people with doctoral degrees doctors but not people with masters degrees masters?

If you're talking about the use of doctor as a title, as in "Dr. Smith", I doubt there's any compelling explanation.  Most degrees don't come with titles: nobody say Master Smith or Bachelor Smith or Associate Smith.  Historically, magister (corresponding to the master's degree) was just as appropriate a Latin title as doctor was, but it simply isn't used in modern English.  These titles are nearly gone, with just one remaining.  It's probably no coincidence that the last remaining title is also the fanciest, but that's just speculation.

Even for the doctorate, the use of the term "doctor" has degenerated to the point where in English it can only be used as a title, and not as a general noun.  If you say "my friend John Smith is a doctor", practically everyone will assume he's a medical doctor.  You could only get away with the more general usage in the narrowest academic context, and even there it would be considered pretentious and archaic.


There are two basic approaches to citing a "live resource" of this type, depending on whether you are citing an aspect expected to be durable or that is expected to be particular to that particular version.

To cite an aspect that might be particular to a particular revision, e.g., a text quotation taken from a certain entry in the manual, you should cite in just the way that you have shown (modulated for the particular referencing style).  In this case, a good way to think about it is that "Revision 2 of Second edition" is just a fancier edition number that includes some sub-structure.
To cite an aspect that is expected to be durable, e.g., California having a high diversity of plants due to the high degree of variation in geography, it is more appropriate to use the citation form for an online resource, where you note the date retrieved but might not bother reporting the particular version, since the reader should expect that future revisions will still be just as valid sources of the same information.


Are old (>35) faculty candidates discriminated against all over the world?

Absolutely not.

Age discrimination is explicitly illegal in the US.  (I believe the same is true in Canada and most European countries.)  Even as the chair of my department's recruiting committee, I am forbidden to ask the age of any applicant.

If you're worried, just don't put your date of birth on your CV.  But this really is a non-issue.


What are the archiving policies of arXiv?

From their FAQ:

  What are CUL's preservation strategies?

  Digital preservation refers to a range of managed activities to
  support the long-term maintenance of bitstreams. These activities
  ensure that digital objects are usable (intact and readable),
  retaining all quantities of authenticity, accuracy, and functionality
  deemed to be essential when articles (and other associated materials)
  were ingested. Formats accepted by arXiv have been selected based on
  their archival value (TeX/LaTeX, PDF, HTML) and the ability to process
  all source files is actively monitored. The underlying bits are
  protected by standard backup procedures at the Cornell campus.
  Off-site backup facilities in New York City provide geographic
  redundancy. The complete content is replicated at arXiv's mirror sites
  around the world, and additional managed tape backups are taken at Los
  Alamos National Laboratory. CUL has an archival repository to support
  preservation of critical content from institutional resources,
  including arXiv. We anticipate storing all arXiv documents, both in
  source and processed form, in this repository. There will be ongoing
  incremental ingest of new material. We expect that CUL will bear the
  preservation costs for arXiv, leveraging the archival infrastructure
  developed for the library system.

It looks like they're relying on a) multiple offsite mirrors; b) periodic stored backups at LANL; and c) deposit in the institutional repository at Cornell.

It's a little unclear if that deposit is actually happening yet or is still part of a long-term plan, but it's worth noting that the arXiv program director is also the librarian responsible for Cornell's digital preservation work, so it's unlikely to have been forgotten about!


PhD application: my country isn't listed

The United States does not recognize the statehood of Palestine (meaning technically that can't be your home country as far as that government is concerned), which makes it somewhat unsurprising that an American university might not have it listed as a country.

The Department and School likely doesn't have a particular stance on the issue - they probably didn't even design the application. Of course the ideal option would be to call them, but as this isn't an option at the moment, I'd put something close (Jordan - which as you mention you hold a passport for) and then call them to clarify as soon as you are able to do so.

Also, as this is clearly a recurring problem, you should seriously consider finding out if a given school's application has this problem well before it is due.


Why don't some U.S. colleges celebrate American national holidays?

The observance of holidays in the United States is a complicated issue.

Holidays declared by the federal government are generally (but not universally) observed by state governments, which oversee public universities here. Private institutions, on the other hand, have no obligation to observe those holidays, and can choose to close or remain open according to their own decisions about what best serves their students’ needs. For example, my undergraduate institution did not take any days off from the first day of classes in the fall semester, but did provide a week’s break corresponding to Thanksgiving. It’s an unusual arrangement but perfectly legal.

It should also be mentioned that while universities have core “business hours” where faculty are expected to be present, in reality, faculty largely choose their own working hours.


Should I send a "cease-and-desist" letter to ResearchGate?

I am a law professor, and I am equally pissed with research gate.

It would be unwise and inappropriate to give you specific advice about your own situation: this would likely constitute the unauthorized practice of law; for actual legal advice about the claims and defenses and legal strategies that apply to your situation, consult a competent lawyer admitted to the bar in your jurisdiction.  I will recount my own experiences below by way of generally informing the world what one person's approach is to one specific situation (i.e., mine).

That being said, here's how I've dealt with Research Gate.  They committed four serious affronts against me:

Fraudulently inducing me to sign up for the site by sending invitations claiming to be from my coauthors,
Forging my name on e-mails to other people claiming that I invited them to sign up to the site
Posting a draft of a paper of mine without permission, and
Maintaining a profile of me on the site without permission. (This one, as others have noted, may not be illegal---I am not sure---though it is certainly offensive in context, and to the extent it involved misleading attributions of endorsement may be illegal.)

In response, after learning about 1, 2, and 4, I sent their customer service people a nastygram over e-mail demanding the forged emails stop and be unsubscribed. They sent me some useless response claiming I could unsubscribe.  I thought nothing more of it, but continued to hear of forged emails.

I then discovered 3 via a google scholar alert and really blew my stack.  So I contacted their general counsel, also listed as their contact for DMCA takedown notices and send them a DMCA takedown combined with an incredibly nasty cease and desist letter.

Their general counsel promptly replied and informed me that he'd taken down the paper referenced in #3 above.  I haven't verified that this is true, or checked on any of the other ongoing acts of wrongdoing (the serial email forgery etc).  I have some hopes that this will work, however, I am prepared to file suit against them on my own behalf should it not.

What can others learn from my experience?  It's not clear yet.  I am of the opinion that this company operates by massive fraud and needs to be put down, but if my attempt to menace them into acting a little more law-abiding at least with respect to me succeeds, it may only be because I'm a law professor and they know that it would not be hard for me to drag them to account.

Of the various wrongs they inflict on the world, the posting of unauthorized copies of papers is the easiest to stop---the DMCA is a blunt instrument, and, moreover, the publishers also have an incentive to put a stop to this.  The next time I see a paper of mine on their site, I may not even going to bother with doing my own DMCA, instead just turning it over to the publisher.

The rest?  As I said, for myself personally, if the forged emails don't stop I may go looking for a class action plaintiff's lawyer, or just file seeking an injunction myself.

But otherwise, the best choice may be prevention.  Don't sign up for their site.  Tell your friends not to sign up for their site.  Let people know if emails inviting them to do things on that site show up under their name.  Publicize their practices so that others stay away from them.  Starve the beast.


Is it worthless to cite a paper as X et al. when X is not first author but performed the work?

References have one major purpose: to be able to trace the information provided in that source. This is why the first (named) author is always given in "et al." references. The problem you encounter is that references are also used to cast merit in the academic system but that is actually a secondary task. So if you decide to use another authors name, you make it more difficult for others to locate the paper n question. So I would strongly advise against the action your propose since it violates the purpose of the referencing system. So even though one can trace papers with for example, doi-numbers breaking the systematic representation of cited sources is not good.

There are other ways to state the source of the work in the text by stating that "the work by X (A et al. yyyy)..." or something similar. But, I would not recommend doing this for just reasons that are beyond anyone's means to control and the risk is that you will not be perceived positively or at least a bit odd. I am sure that the circumstances, if based on unethical behaviour or the like, will become common knowledge in the field.


Submitting Workshop Proposal by A first Year PhD student

In theory, since your advisor agrees, there's nothing which stops you from submitting a workshop proposal as a PhD student. Your proposal will be evaluated by the conference organizers and they will decide whether they want to go forward or not with your workshop. If you submit this proposal completely on your own, I think there's a good chance that they will doubt that you can pull a successful workshop, and consequently reject the proposal. So in order to make the proposal more convincing you should probably partner with some experienced researchers who already have a reputation in the field. You will probably need an editorial board anyway. You seem to have good contacts so it should be reasonably easy, since they should be happy enough to co-organize if you tell them that you're going to take care of the logistics.

The problem with your ex-supervisor and his presence at the conference is something that only you can decide. If he has enough influence in the community to convince the organizers to reject your workshop, it's a shame but that would end things there. If not, it's for you to evaluate how much damage he might cause to you, to your career and to your workshop. But hopefully you and him would just behave professionally and leave each other be.

If you have friendly contacts with experienced researchers in the fields, I'd suggest that you discuss your concerns with them. Their advice would be precious as it would save you investing time in this if they think it's not reasonable, and save you some sleepless nights if they think it's completely fine.


How important is journal prestige when researchers publish a paper?

In principle, publishing in a prestigious journal may help reach many readers and/or boost your career. The practice of judging articles by the journals they appear in is widespread although also widely denounced (cf the San Francisco Declaration on Research Assessment).
In practice, a lot depends on your field of research, your career stage, and the organizations that pay your salary and/or grants. At one extreme, some people would boycott "luxury journals" as a matter of principle (Randy Schekman) or ignore journals altogether and just post their results on arXiv (Grigori Perelman). At the other extreme, some will tell you that their careers entirely depend on how many articles they publish in their discipline's elite journals.


Using Cambridge's "short-title reference system"

I can't give you direct advice about the Cambridge short title but there are quite a lot of applications to go from bibtex to different reference styles. I would suggest using one of those to help. I found the easiest way to do this is to add items to zotero and then export as bibliography, they have hundreds of styles based on journals as well as common ones like Harvard and Chicago Manual.


Publishing a very mediocre paper as undergraduate?

So you want to publish rubbish, just to have a publication on your CV? If you really are a good student, you will find other ways to get publications. Remember that such a publication will stay with you forever, everyone googeling you will find it. On the other hand, once you have some publications, no one will care if you made your first one during your undergraduate or later.

Also: Talk to your professor. He will have reasons to decline and will be able to tell you more about the pros and cons of publishing this paper, given your academic plans. I would put quite some weight on his opinion, as he knows the paper and has lots of experience when it comes to the field, accepting or declining PhD students, etc.


Applying for research assistant (What can I speak about?)

I've been interviewing students recently and there are three questions I ask myself after talking to the student:

Motivation. Is this person independent and able to solve problems on their own?
Overlapping research interests. Is this person genuinely interested in the type of work that I'm doing?
Technical ability. Is this person going to be able to complete tasks without being hindered by a technical limitation?

It is difficult for me to accurately answer these questions from a short interview, but you can learn a lot from just talking to someone. My advice for you would be to figure out how you can honestly answer those three questions for the professor. Some things for you to brainstorm about: Have you read some of their papers? Have you worked on any class projects or side projects that may be relevant? What do you want out of the position? Do you have an interest in publishing or going on to a PhD?

Of course, there are other factors at play. Can the student communicate well? Will our personalities clash? But those are mostly out of your control.


Can we submit (an updated version) of a work previously submitted to arXiv to a conference?

Yes.

Assuming the conference doesn't forbid that (many don't). If it does, then just update the arXiv version before submitting to the conference (or before signing anything).


Consider Canadian universities. If you're looking for the best, check out the Canadian U15 Research Universities.

If you only have a bachelor's degree or equivalent, you can apply for what are usually called a "direct-entry" PhD program. For example, on the University of Toronto graduate admissions page:

  Direct entry from the bachelor's to the Ph.D. is possible for some eminently qualified applicants.

By eminently qualified they likely mean a few things:

Grades: you will likely need to be near the top of your class.
Research Potential: you will likely need to have qualifications demonstrating your "research potential" such as journal articles to your name, research terms with professors during/after your undergrad. An honours thesis might also count. They will also gauge your potential by your application, which generally requires submission of an outline of proposed research.
Awards: you will likely need to have a history of getting awards and scholarships in your undergrad.

It would also help your cause if you contact potential supervisors before applying. It is common in Canada to establish who you'll be working with before you apply for a PhD. They can then help speed your application along and coach you on some of the details (like your outline of proposed research).

As a non-citizen you will need to get a study permit but considering that Canada is a Commonwealth country it shouldn't be much of a problem for a UK citizen.

If you can't qualify for "direct-entry" you'll have to slog it out like the rest of us in a Master's degree first. That being said, there are options to transfer from Master's to PhD after your first year at most Canadian universities, if you demonstrate the aptitude. It's easier to transfer than it is to get direct-entry. It will also give you time to gauge whether or not you are ready for the full four-to-five year commitment of a PhD.

Take a look at this international degree equivalency chart for the University of Toronto. It won't be exactly the same for all Canadian universities (UofT is pretty top notch) but it can give you a pretty good idea of how you stack up.


Scholarships for mathematics international students

Your best bet would simply be to apply and hopefully get accepted to a PhD program somewhere like the U.S or in Europe. PhD programs in math, or in STEM in general, almost always guarantee funding which is free tuition + research/teaching assistantships which give some salary.

Once you are enrolled in a PhD program and impress in your 1st/2nd year, then a lot more opportunities open up ranging from grant funding from professors to prestigious scholarships from big companies like Facebook or Google . Note that these programs are extremely competitive like top 1% of top 1% PhD students are accepted. That's why I am encouraging you to get accepted at a PhD program first.

I am also an international graduate student and when I was applying to PhD programs in the U.S, virtually all programs in the top 75 range had guaranteed support in the form I mentioned above. Even Fulbright would be more competitive from what I heard from its recipients.


Is it acceptable to use the word "trivial" in lecture?

"Trivial" often means "too simple to be a real problem". For example, in an class on optimisation methods years ago, the lecturer said "for our first example, we're going to study the problem of maximising the number of ones in a binary string of length n". My thought for most of the class was "well, that's bloody obvious—you just write n ones in a row—why are we looking at this". I eventually realised that it was being used because it made it easy to describe how the algorithms worked, not because it was a challenging problem in any way.

I think that's a good example of where the word "trivial" is good shorthand—the problem isn't of any importance, but it is being used to illustrate a point. This is similar to how trivial is used in a lot of pure mathematics, where it often means "the simplest example that satisfies the definition" (like "the trivial group"). As with all such jargon, though, it is worth explaining to students what you are going to be meaning by the word "trivial" and why trivial examples are worth looking at at all.


What happens if your research doesn't get published?

In academia it's true that by "publication" people often mean "peer-reviewed publication", that is a publication which has been checked and validated by other researchers and consequently accepted in a more or less reputable journal or conference (see below for the "more or less"). Peer-reviewed publications are the only ones which matter in terms of academic career and in any kind of academic evaluation.

However there are plenty of other options to publish: pre-prints, technical reports, books or even simply putting a document on a webpage, all of these are valid publications which can be cited, even if they are not peer-reviewed. Of course they wouldn't be considered as valuable publications in the academic world (unless they get cited a lot, but that's not common), and for good reasons: non-peer reviewed publications can be full of mistakes or claim that the Earth is flat, since by definition they haven't been evaluated by the expert community. Anyway, this implies that it's virtually impossible to be unable to publish a research work because it gets rejected.

Even if we assume that the author wants to publish only in peer-reviewed journals/conferences, they would still have a lot of options to choose from and it's unlikely that they can't get accepted anywhere: in every field there are venues which are known to be very reputable and consequently very selective, but there is also a spectrum of journals/conferences which range from "very competitive" to "desperate to receive submissions". Of course publishing in a bottom tier venue is not going to boost an author's track record, but at least it's reasonably easy.

Finally, even in decently reputable journals/conferences, any serious research work can always be accepted... eventually. It might take a very long time, but if the methodology is correct, the state of art is properly covered, the motivation for the work is demonstrated, etc., in short if there is a real scientific contribution then it's very unlikely that the work would be rejected everywhere. Even in the case of negative results, e.g. the author attempted a new method and it failed, there is a legitimate contribution: provided it wasn't already done and the method makes sense (that's part of the scientific ground work), it's useful for the community to know that this method doesn't work. Additionally every rejection comes with reviews which explain why the paper is rejected, and normally addressing the shortcomings identified by the reviewers makes the paper more likely to be accepted next time.

  "Is publication the only way researchers can validate their work?"

Not necessarily but the other ways I can think of are more specific to the field. For instance in computer science developing a software system which turns out to be successful in the scientific community or even beyond would actually prove the value of the work and certainly contribute to the author's reputation.


I want to write a blog post building upon someone else's paper, how can I properly cite/credit them?

You have two issues to deal with. If you properly cite and attribute the ideas to the original author, you avoid plagiarism issues. If you don't copy too much, but properly quote, from the paper then you avoid copyright issues.

But, ideas are free to use and to adapt. Simplifying what you find in a paper is a good thing to do.

One doesn't obtain ownership of ideas by writing a paper.

I therefore see no ethical issue at all with what you suggest.


Publishing figures in conference abstracts - will this constitute formal “publication” that will preclude our publication of this figure in journal?

There are several questions hidden within this one. The first is whether you retain copyright after the abstract appears. If not, and if the figure is fairly substantial (in the information conveyed and in design elements) then you may need to seek permission from the copyright holder to reuse it. And you will also, then, need to cite the abstract. This is the same as if you want to use a long quote from an article, yours or that of another. Short quotes and standard figures don't usually require permission, but do require citation. However, TOC isn't clear to me. I assume it is more that "Table of Contents".
If you do hold copyright then reusing it, with citation, is fine. But the citation is required to avoid the issue of self plagiarism.
However, if the figure is to be reused on its own as a complete work, not part of another paper, then publishers would probably consider it as already published and therefor not now innovative. I doubt that is what you intend, but note that it is up to the publisher to make determinations about such things.
My best guess, with limited information, is that you will be permitted to reuse it even if you don't hold copyright. But you will need to ask and you will need to cite. One can, of course, make reference to ones own work and even quote from it, but there are limits on how much you can use in copyrighted work.


Evaluating potential supervisors on the basis of past graduate student results

It's perfectly acceptable to ask a supervisor what their former students are doing now, and I think the majority of supervisors would be more than happy to discuss it. They might even give you email addresses of their old students -- I myself have been contacted many times by prospective students of my supervisor and am always happy to answer their questions.

How much you factor the information you gain into your decision is really up to you, and depends a lot on your own motivations for doing a PhD and what you want to get out of it. For example, if you want to go into industry afterwards but a supervisor tells you that all of her former students are still in academia, would that influence you away from studying under her? Or if the majority of a supervisor's students are now in industry, how do you know whether they had to leave academia because they couldn't get a postdoc or because they really wanted an industry job instead?


Expectation of perfection vs. the never ending list of 'to do's'

I don't know if this is the best approach or if it works for everyone, but here is what I did in the past when I was paralyzed by just looking at the never ending list of things to do.

I simply broke down every task into more manageable pieces. Now I have an even longer list, but the good thing is non of the items on the list looks scary. After making tasks manageable, I set deadlines for every task. Deadlines forced me to stop working on a simple task just because it didn't look "perfect". At the end of the day if there is still time and I have energy, I can easily start working on the items that didn't look "perfect" to me without delaying any other task(But at the time I was burning out, and I realized that. So I stopped working on the things that didn't look "perfect" to me. Instead I took a break to clear my mind.).

If you can prioritize the tasks and break them down to more manageable pieces it is great. If you can't, may be you can ask a friend to help you.
After completing a task without over thinking about it and without missing a deadline, what I felt was success and that is what kept me going.

This way I kept my sanity and started to regain self respect, instead of punishing myself for not committing to work and spending the day paralyzed.


Comparing career prospects across fields in Applied Math

I work in inverse problems, more or less a field of applied mathematics.

Conference plenary talks are prestigious.
People are invited to also give other talks. This might carry some prestige, but I am not really sure.
People give contributed talks. This gives little prestige, but is a good idea for other reasons. Typically, for small conferences, all or most contributed talks are accepted, though it might be different in larger conferences.

The thing to learn is that conference talks are of minor importance. Publications in journals count far more. This depends on academic field.


Who is typically in charge of a typical US graduate school?

There is no single governing board for all US universities. Every university is different.
In very broad strokes, as your question is quite broad here's how it breaks down.
Board: The Board of Trustees or University Board functions in much the same way a company board does. They meet regularly and make large decisions on spending, hiring, etc.
Chancellor: In some schools, this is the President. Think of them as the CEO that advises the Board and executes the vision.
Provost: Usually the ultimate head of academics in a university.
Deans: Usually lead various colleges. For instance a Dean of the Law School or Dean of Undergraduate Admissions

There are various various administrative staff within all of these. And again, all schools vary in terms of nomenclature.


Parentheses to indicate the word can be singular or plural (APA style)

Stylistically, it is recommended to choose the most clear and unambiguous terminology, to minimize the risk of a reader misunderstanding. By this metric,

  the props

is a poor choice, because the reader might have forgotten that there might only be one prop, and your writing fails to correct their misunderstanding. I suggest

  the prop(s)

because it is common and standard terminology, unambiguous, and less clunky than "prop or props", which tends to interrupt the flow of the sentence.


Is it okay to begin a chapter without an "introduction section"?

In general, sections should be organized to create a chapter just like subsections are organized to create a section and subsubsection should be organized to create a subsection.  In other words, the important unit is the largest one, and the smaller elements (sections, subsections, etc.) are used only the assist and guide the reader in their understanding of a large chunk of narrative.

As such, I would consider it the normal and preferred case to begin a chapter with prose, setting forth an introduction to the chapter before the first section heading.  In fact, a particularly short chapter might have no section headings at all, as it is a good rule of thumb to note use any textual subdivision until you need two of them (e.g., don't divide a chapter into one section, or a section into one subsection).


2nd master's degree in "slightly-different" field? data science and machine learning specifically

I don't know of any generic rules which forbid this. Indeed taking a masters degree after another higher degree is an accepted, although uncommon, method to switch career paths fairly deep into one's education. On the other hand, as you note yourself, that's not really what you are suggesting here, and any application is going to have significant barriers to overcome, firstly as to how you'll be funding this (masters courses are expensive, after all) and secondly as to why you aren't following the more natural career path of moving on to a Ph.D. if you want to continue your studies. Which isn't to say that a sufficiently strong narrative wouldn't manage to get you an offer if numbers weren't limited and you could explain your funding.

(It's worth noting that while the University probably doesn't have a rule against this, many potential sources of funding do)


A software engineering position probably doesn't improve your competitiveness for graduate school, unless your graduate school wants you to code (which isn't a requirement for a PhD in computer science). Is coding something you'd be interested in? If so, then the software engineering route would be advantageous. Perhaps more importantly, the software engineering route will make you more competitive to a research company after graduate school.


Are these good reasons for starting a new PhD project?

There are dozens of parameters that seem to be influencing this decision. I will try to touch on a few points as best as I am able:

Coming up with a PhD topic is hard for a lot of PhD students. This is a common feeling; it does not mean you cannot succeed as a PhD student.
How does representation theory relate to your current subject? Are there papers connecting the two subjects? If so, what do they say? If not, can you discover a link between the two subjects (representation theory and applied?) Your advisor seems to think there is a link. What is that link? (These are questions I would be asking myself as a way to try and discover a dissertation direction).
Graduate students are sometimes distant with one another. They all have their own projects to be doing. That's the reality. I would look for social connections outside of your department if necessary.
It may be easier to change advisors internally, if possible, than switching universities. Being from the US, I have no idea how feasible this is in your case.
In my opinion, passion for your subject is overrated as a PhD student. Graduate students I have advised are rarely deeply passionate about our research. But they realize that it is 4-5 years of learning and thinking about a subject in order to develop the ability to perform independent research.
I work at a national lab in the US now. No one cares about the topic of my PhD (probability theory). My master's degree was in representation theory. I never use these topics in my current work. But I've proven that I can think about math and statistics, and I use these skills in my job now as a researcher. I do not know your goals (academia or industry), but industry usually only cares if you have a PhD in a generally relevant field and if you can program. It is that binary.
Being in your early 30s when you finish a PhD is somewhat normal. There is nothing magical about being 27 and having a PhD. It just means that you have to start going to a full time job earlier in life. If your finances are in okay shape, finishing a PhD at 32 is not the end of the world.
We speak of a PhD being able to do "independent research." This does not mean you never need help or collaboration. I have a PhD. I collaborate with other researchers. Sometimes I come up with an idea, sometimes they do. And some of their ideas blow my mind--I would never have thought of them in a millions years.
Being honest, it sounds like your advisor may not be the best advisor on the planet. At least not for your case. Some students really like a hands off advisor, some do not. Both types of PhD students exist and both are successful. Changing universities to get to a better advisor position may not be as huge of a deal as you think. It might actually make your work more enjoyable.


How to exchange email with potential professors

Don't be intimidated that she is a professor. It is certainly appropriate to continue your "conversation". Let her know of your interest in joining her team (possibly subject to funding) and give any constraints you might have. You don't need to say a lot, but thank her for her interest and express yours.

Ask her for any advice about what you can do at the current time if it seems like there is a possibility to work together.

In other words, write as if you are a colleague, not a subordinate.


Research team writing using different tools

I have worked in similar cross-platform teams. Mine in the past was more Latex on Linux with bibtex versus Microsoft Word on Windows with Zotero. In that case, we were working on multiple papers together, so our policy was that everyone went along with the tool that the first author preferred, so we all got a lot of cross-platform experience. That worked for us, but it sounds like what you labelled as "other than mandating the tools to be used".
That might not work in your situation, since your team members seem more inflexible about using tools that other people prefer. In that case, I would suggest something like this:

Everyone should use Open Document Text (ODT) format, not .DOCX format. Both LibreOffice and Microsoft Word can handle this format just fine, and I think that they can work together (though I have never actually tried this).

Although LibreOffice can edit the original version of DOCX, I understand that the current (as of 2021) version is not the open standard version, and so it could probably get messy if people tried to work on the same DOCX document with both LibreOffice and Microsoft Word.

For reference management, only one team member should edit references. Whether that team member uses Zotero or EndNote, that is for you all to decide (though I have the impression that Zotero might work better on ODT documents; I'm not sure how good EndNote's support is).

Whenever any other team member wants to add or modify a reference, they should leave a comment instead that contains the full reference; then the team member that handles references should format it later.
This might sound awkward, but it worked quite well on teams where I have done this, due to Zotero versus EndNote member preferences. It is simple and clean to say that only one person is allowed to modify references directly.
Of course, if more than one member uses exactly the same platform setup, there should be no problem if they are all allowed to modify references (e.g. Zotero on LibreOffice for Linux only).

I hope one of my above solutions (either everyone just follow the leader, or use ODT and only one reference-handling team member) works for you. In any case, be sure not to let technological tool flame wars burn an otherwise great research collaboration team!


Supervisor used graphic without crediting me

How to proceed from here?

You don't do anything. You did something small your supervisor asked for, and he used the figure that you made for him.

It's very unusual for figures to be labeled with the name of the actual person that made it, and it would be a lot to expect this without asking / demanding this beforehand. Take the closest textbook and you'll find that indeed,  a lot of figures will be copied from publications and references are included. However, there will also be custom-made figures that don't have any note. And you can be quite sure these figures are not drawn by the authors themselves, but by their students or employees.

There would probably also be no copyright implication, as this sounds like you just re-created some schematic figure and you just copied the idea, not the work itself.


Non-salary fellowships and US income taxes

Fellowship funds used for personal expenses including room and board, food, etc, are taxable, just like it says in the passage you quoted.

If social security taxes, medicare, etc, is not withheld, you don't need to pay those, since it is taxable income but not taxable wages. In that way, a fellowship is treated like any other academic scholarship that includes money for living expenses, rather than like an hourly/salaried position.

See also How much are taxes for a postdoc in the United States? though that question is not specific for fellowship-based income.

Fellowships awarded to individuals that include other expenses, like research expenses, are typically granted to the institution not to the individual, so those other expenses would not be part of your personal income even if it is an individual expenses. If they were paid to an individual, you would likely be able to deduct them as business expenses, but you would be best off working with an attorney or tax professional in that unusual situation.

If you are talking about receiving a foreign $50k fellowship in addition to a foreign $50k salary abroad, then yes indeed you are approaching limits for exclusion of foreign income but it is unlikely you will be taxed twice on the same income due to foreign tax credits for US taxes, but that is really now an issue of tax law for expats and not really related to academia specifically; that situation seems like it would be quite unusual in academia for a post doc, and although it may place a burden on a researcher, an income of $100k+ would place you in a fairly high percentile of individuals where the US government expects that there is a burden on your income to pay for the costs of society - this is true in many other countries as well.


Is it appropriate for a prospective PhD student to contact phd students at a target school?

It is absolutely fine to contact current PhD students of programs and departments that you are interested in. On an average, I get about 1 email of this sort everyday and I make my best effort to reply intelligently.

Keep in mind though that many PhD students will simply not reply to your email. Sometimes folks are inundated by too many emails and commitments to respond to any additional emails and sometimes people just have bad emailing tendencies in general.


different online Harvard citation styles

I completely agree with the comments. It would be useful to see what the journal wants. You could also check recent works published in the journal you are interested in to verify the appropriate Harvard citation format for publication.
Having said that, personally, I like option 2 for its brevity:

Cillizza, C. (2020). The absolutely remarkable social media power of Alexandria Ocasio-Cortez. CNN. 24 July 2020. Available at: https://edition.cnn.com/2020/07/24/politics/aoc-ted-yoho-cspan/index.html (Accessed: 23 October 2020).


What should I comment on when contacting a potential advisor?

It's good to look into a potential advisor's research. If there is a specific reason you are interested in working with them, that is also good to mention that (briefly) in an initial email.

However, I think making detailed, specific comments about the professor's papers would usually be a bad idea in this context. It is far too much detail for an introduction, and if you are doing it just to demonstrate your knowledge and/or interest, it will come across as forced and artificial. If someone was advising you to do this, I don't think it was good advice.

Keep the initial contact brief: introduce yourself and say something about why you want to work with them.


Including a segment of constructive criticism of another paper in my manuscript

If you make choices that only make sense if the article contains mistakes, then point out those mistakes to justify your choices. Then it becomes a matter of necessity to point out the mistakes, not one of nitpicking.
However as a matter of courtesy and due diligence, you could contact the original authors to ask them about the mistakes. Be sure to approach the subject gently. Along the lines of: "in the article you state that A was the cause of the performance gain, but in my tests I found the performance gain in C. As you see in these results.  Do you know what I did differently than you?"


Do price and value of degrees correlate much?

High cost and high quality are not related in the United States.

First, remember that there is a large fixed base cost of room and board, which amounts to around $10K-$15K, depending on location.  Just a quick glance at a few top schools will show that the cost of tuition beyond that is correlated primarily with state-run vs. private rather than quality:

Harvard: $43,938
MIT: $43,720
Berkeley: $12,972
University of Michigan: $13,977 (in-state)

Also, remember that many of the high-priced colleges do need-based rather than merit-based financial aid, so these numbers should be seen as a "ceiling" rather than an expected price: even a super-genius will pay based on what their parents make, rather than based on how smart they are.  That same Harvard article linked in the original post notes:

  During the 2012-2013 academic year, students from families with incomes below
   $65,000, and with assets typical for that income level, will generally pay nothing toward the cost of attending Harvard College.  Families with incomes between $65,000 and $150,000 will contribute from 0 to 10 percent of income, depending on individual circumstances.  Significant financial aid also is available for families above those income ranges.

Thus, even at a super-expensive place like Harvard, the cost of education is completely uncorrelated with its quality.


What typically incentivizes a professor to change jobs to a lower ranking university?

The most important reasons I can think of are private reasons. People do not live to work, but work to live.

What good does a job at a highly ranked university do, if your family/your friends can not live there or are unhappy to live there?
What good does a job at a highly ranked university do, if it is in a place you find boring or don’t like?

I would suggest you to change your mindset from highly ranked university to high quality of life (which is subjective and also includes a little bit the rank of the university, if you value this).


Citing a country's constitution in the OSCOLA style

While the OSCOLA style guide does not give specific guidance for a constitution, the MLA guide suggests citing constitutions using the same form as laws.

As such, I would conclude that appropriate citation for a constitution would follow the OSCOLA style guide for legislation, e.g.,

  U.S. Constitution, Article I, Section 2


How would it look like from reviewers' point of view if one submits off-topic works for application to phd programs?

Being a mathematician, I must address a logical loophole: I will assume that your field is a STEM field and thus poetry and songs are actually off-topic (and not just called off-topic).

  How many legs does a dog have if you call the tail a leg? Four. Calling a tail a leg doesn't make it a leg.
  -- Abraham Lincoln

Assuming this: no, I would not submit such creative materials as part of an application to a STEM PhD program.  I wouldn't go so far as to say that submitting such things would be deemed an "affectation": however, unless you make a clear connection to your chosen field, they are simply not relevant.  Including irrelevant things is not a disaster, but it does indicate that you don't have a clear understanding of what is relevant information in the consideration of your own prospects in that program, which is not great.

Most such applications have a personal statement.  Mentioning somewhere in the personal statement that you write poetry and songs sounds about right to me: from one human being to another, that is interesting, and personal statements are often not so interesting.  But be careful here: a "personal statement" is not a statement about you as a person!  It is really an essay explaining why you would be a strong candidate for the program, so things which are not relevant to that should not be dwelled upon.

Many programs do look at the personal statement as a writing sample -- and good writing skills are very relevant in any PhD program, probably more so than any other single quality -- so if you are an unusually good writer the personal statement would be a good opportunity to show your superior skills.  However, trying to do that in the genre of either poetry or song would be so risky and open to negative reactions based on personal taste that I wouldn't recommend it: after all, in most STEM programs you need to be able to write prose, not poetry, and you are not really permitted to burst into song.  This is probably a "color between the lines" situation.

Added: I spent four (recent) years on the committee in charge of graduate admissions in the UGA mathematics department, and I still read some PhD applications every year.


How do selection committees ensure that they won't steal an applicant's ideas as presented in his/her research statement?

Academics are presented with confidential material all the time. We review manuscripts and grants and we are expected to not steal those ideas. A research statement is very similar to a grant proposal. When we are given applications to review we are reminded that they are confidential and should not be circulated. This is the same as when reviewing a grant. While many funding agencies and publishers have clear statements that reviewers must agree to, departments generally do not produce such guidelines. That said, a department would likely come down very hard on an individual who did not respect the confidentiality of an applicant.

With that out of the way, it is often that a reviewer has similar ideas as an applicant. On the face of it, it may appear that the reviewer has stolen the idea from a proposal, when in fact it was an independent idea that the reviewer had already had. One question is should reviewers decline to review based on a conflict of interest when the proposed work is similar to their current/future work. In my opinion, they should not since they are in the best position to review the work and the similarity is likely the reason they have been asked to review. This then does leave the burden on the reviewers to be able to document that the research agenda is in fact their own and not stolen from the confidential proposal.

The final issue is to document anything that is unique to your proposal. Saying you want to study topic X does not make it yours. Saying you want to study topic X with method Y, isn't much better. If the proposal says I want to study topic X with novel method Y because of reason Z, then the linking of X, Y, and Z might be important. If you document this, then at least if someone studies X with Y, you can get the credit for coming up with the brilliant idea of using method Y on problem X. In some ways realising that problem X can be solved with method Y is more important than actually solving the problem.


As a postdoc with a one-year contract in Switzerland, am I allowed for a B visa?

When did you graduate? A new law came into effect in 2010 which requires that all new postdoc hires of individuals who held a PhD for more than 2 years at the start of the contract be only given L permits. (I only found out after I had a similar discussion with human resources a few weeks ago.)

If you have had your degree for less than 2 years, it is possible your university can sort it out for you. If you have had your degree for more than 2 years, there's pretty much nothing the universities can do (aside for lobbying for a change of the law).

In regards to bank services: for a place to put your money, try PostFinance for which you can open an account at most post offices. They care a bit less about the issue with the permits. The main problem with having an L instead of a B permit, with regards to banking in general, is that they may be unwilling to give you a credit card or extend you a loan; you shouldn't have problem getting a place to put your money.


How will an application for graduate admissions be affected if psychological issues prevent student from getting strong recommendations?

A graduate school probably will not make any exceptions for psychological issues: by the time that you are at the level of graduate school, people are generally evaluating you as a "whole package."  If a person has cognitive or psychological issues (and many successful people do), what will likely matter is whether those impair them to the degree that they will have trouble succeeding.

For example, consider a person on the autism spectrum: this covers a huge range of different issues and many different levels of functionality and types of coping strategy.  One person might have a strong focus and coping strategies that cause others to feel just that they are "socially awkward" and get strong recommendations regardless. Another with less adaptive coping strategies might instead find themselves perceived as argumentative and hard to work with and have a hard time getting good recommendations.

In the end it boils down to this: a person has to have people willing to advocate for them.  If they can't get advocates, then it doesn't matter whether it's because of bad grades, bad attitude, mental illness, or anything else (unless you are dealing with a clear case of discrimination against a specially protected category, e.g., in the U.S., religion, race, or gender).


What to do about repeated PhD rejections?

I know that you want us to say "It will all be ok", but it may just be true that either (i) you have to take the GRE test again and get a better score, or (ii) change your approach to applying. The fact is that apparently things haven't worked out with your current approach, and so to keep trying isn't likely going to yield different results.

So take the test again, with more studying, and get a better grade. And/or, broaden your scope. Of course everyone wants to get into their favorite graduate program, but not everyone can. So apply to other programs at other universities and see how that goes. You don't have to go to Harvard to get a good education, nor do you have to go to Harvard to have a productive career and a job you're happy in. There are plenty of places that will give you a shot at all of these, and that are less selective.


Yes, you can certainly publish your own work under your own name. There should never be a question about that. You should acknowledge help you got within the paper, of course.

There are sometimes strategic reasons for including a supervisor as a co-author even if they haven't helped, but they fail the academic honesty test at least in minor (and maybe major) ways. But sometimes it helps a paper to get published if it has a well known co-author.

There are also some places in which institutional pressure is placed on students to include other, non participants, as authors. This is also wrong, though done. Sometimes you have to yield to such pressure, just to protect your future prospects.

There are other situations in which it is more appropriate to include the supervisor. For example, if he/she runs a scientific lab that you depend upon to do your work, then the supervisor (and usually many others) get included as authors because of the environment and help that they provide.


How can an undergraduate Computer Engineer start making publications before his Thesis?

Take classes from professors you'd like to do research with. Do really well. Ask good questions. Participate. Go by office hours and talk to the prof. Show interest. Try to read and understand their work. But don't be so persistent that you become annoying. You're looking for a personal fit as well as demonstrating your interest.


Should you state multiple degree titles in your CV next to your name?

If this is an academic CV (as this site is about Academia), then you should not include your titles next to your name in your CV, but describe them in the "Education" section.


How can I keep my ideas of a new theorem safe?

The word "theorem" implies that there is a proof.  If you do not have a proof, you do not have a theorem.  Let's call it a conjecture instead.

  I have tried disproving my theorem for over a year.

That's a slightly strange thing to say: how long have you spent trying to prove your conjecture?

  Should I just publish it without a proof, Can I even publish without a proof?

It is possible to publish conjectures, but it is significantly harder to do so than to publish theorems.  I would not recommend that a young researcher -- especially, a high school student! -- try to do this.

  I have contacted professors and have conversed about this and they all say that it is definitely publishable, but that I should prove it myself.

It's no help if I'm not honest, so: this sounds fishy to me.  It is often not so easy for (even) a professional mathematician to know what is "definitely publishable": after more than a decade of submitting math papers I find that I still have some things to learn about this.  But anyone who is telling you that your mathematical work is "definitely publishable" if it does not contain a proven theorem is either giving you bad advice, or you are misinterpreting the advice.

  How can I ensure that my ideas are not stolen, Can I provide direct proof that the idea is mine somehow?

With probability extremely close to 1, professional mathematicians simply do not steal ideas in the manner you are worried about.  The "I did something great, but oh no I can't show it to anyone" train of thought is a sad one that amateurs often fall into.  Rather, if you do something great, show it to more than one person, and you're fine.  One way to do this is just to upload it to the internet in some public or semi-public location.  For instance, if you have an account on facebook, just post a scanned copy of the paper as photos.  Facebook posts are archived with date and time, so that's that.

I will extend to you the following offer: after you archive your paper publicly on the internet, send me a copy.  I will spend up to one hour looking at the paper and tell you one of the following:

The mathematical content of your work is such that you should try to publish it.  I will then tell you some places you might send it.
In my opinion your work is not publishable in a reputable, professional mathematical journal.
I am not qualified to judge whether your work is publishable, but I recommend that you send it to third party X.

You should understand that unless the work is very directly connected to my own I will not have the time to help you with it, nor to send more than one email.  (I simply can't: I have a lot of other people who are counting on me to spend my time on them.  In many cases I am being paid to do so.)  But I will give you a professional evaluation of your work so you can (probably) know where you stand.


I want to quit my PhD and it's only been 6 weeks

Yes, it's OK to quit if what you signed up for is really not what you want (professionally). Plenty of people who start PhD's don't finish.
That said, in your particular case perhaps consider finishing the year. Use the time to learn the kind of applied mathematics you could use when (if) you return to physics. It's too late for your department to use your slot for someone else. They might save a little money if they are supporting you - but if you are earning that support by teaching or grading then your leaving has  no financial value to them.
I don't think you should decide this rashly. You should be able to talk about it with your advisor. Perhaps try to set up an appointment (virtual if necessary) rather than discussing in email.


Can I use text from my dissertation in a manuscript?

In general this is OK or, in some fields, even recommended. It does not make any difference if the dissertation comes first and then the publication or vice versa.

However, I would reference the thesis/paper(something along the line: this paper was part of my dissertation ... or this chapter was published as ...) and you should talk to someone (your supervisor? the postgrad coordinator?) in your department about that. There might be some rules regarding that practice (I never heard of anything like that but just to be on the safe side).

Btw: Self-plagarism has nothing to do with copyright violations.


Is there any service that can i use or rent supercomputer for an hour or two?

The answer will depend on where you are, who your funding is from, and what you mean by "a supercomputer".

Various countries, research councils, etc., let you apply for computer time if you are eligible. Some universities have their own in-house systems too.

But also, the major cloud providers - Amazon, Microsoft, Google (?) - will let you rent computing resources. This may be suitable for your needs.


Sharing research results in platforms that may soon disappear

You could publish the papers and raw-data on the platforms available now, but also store both yourself. Then you could re-upload when platforms change in the future.