Should live sessions be recorded for students when teaching a math course online?

I do provide recordings. At my former university it was a policy to do that, but I had started it already before when I didn't have to. Where I am now I can decide whether I want to do it, and I do.
A major reason why I'm doing it is because students love it - at both universities, as long as it wasn't obligatory, students in the feedback always asked for recordings where they were not provided, and seemed always to be happy when they were provided, and I mean fairly big numbers of students and a striking majority of those who wrote anything about it (I think I have only ever seen a single student writing anything critical about it, and I have seen lots of student feedback).
Now I accept that we shouldn't do things just to make the students happy, but on the other hand I think it is somewhat partronising to not do something they ask for that I could easily do and wouldn't affect my overall didactical concept much.  I have the attitude to give the students responsibility for their own learning (I do tell them what I think is reasonable but if they want to do things in a different way it's up to them), and I want them to show up in my class not because they have to (due to withholding of resources that I could easily give) but because they decide to do so and they want to be there. My experience  is that providing recordings makes students' presence go down a little bit, but really not a lot (let's say 90% attendance with recordings relative to without, but I haven't systematically counted so this is a guess), and I am under no illusion about whether students who'd be there otherwise would properly concentrate on the lecture all the time - in fact in the old pre-Covid days there were student groups that annoyed me quite a bit by obvious lack of concentration and listening in presence. My impression is that the handful of students who don't come because there is a recording largely belong to the bunch that didn't get much out of being there either.
I have occasionally revisited recordings of presentations I attended, so I see where the benefit is. As others have already written in the comments, a student can go through an argument slower and more than once, or may remind themselves of something they missed in real time (we should not think that students listen all the time during live sessions - I once learnt that it is extremely hard if not impossible to keep attention up for more than 15-20 minutes). There is definitely some use in having recordings, so not only do I listen to what the students want, I also see a good reason why they want it.
A potential disadvantage is that some students may not ask questions or contribute to the class if they know there are recordings out of fear to come over as stupid. I never heard any student admitting to this for themselves, but I have heard and can imagine that this is an issue for some. My impression is that student participation hasn't gone down significantly because of recordings, but these "data" are very noisy and I'm actually not totally sure.


Teach in a university with a master degree

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


Does an economics degree qualify for the 17 month OPT extension?

CIP codes in economics include:

45.0601) Economics, General.

45.0602) Applied Economics.

45.0603) Econometrics and Quantitative Economics.

45.0604) Development Economics and International Development.

45.0605) International Economics.

45.0699) Economics, Other.

Your registrar's office should be able to tell you what the CIP code is for the degree program that you're in.  I would expect the list that you have referenced to include other codes if they were approved for OPT.


Talking about other projects in a job talk

The answer you need depends very much on how closely related your collection of interests are. What I did for my job talks was the following. I chose one of my topics that I knew would provide lots of pointers to my other ones. This way I did not just give a laundry list of "things I do" but rather at a nice point in the talk I could say something like "this raises two questions, the one I am going to talk about today is the first but I am happy to go into the second one privately later." The idea here was the other project came up when it made sense, indicated breadth (at least for my collection of topics), and did not feel overbearing.

You mileage may vary but remember that you can choose which topic to give your job talk on and choosing the one that will give you the most connections to the others is as good a tactic as any.


In computer science, how hard it is to get a job at an industry research lab?

It is much easier to get a job in an top-notch industry research lab than an R1 professorship for one simple reason: there are vastly more such research lab jobs available.

To illustrate this, let's consider an illustrative example.  The Stanford Computer Science faculty has 55 professors.  To sustain a department of that size, they'll probably be hiring 2-4 people per year, depending on what fraction fail to make tenure.  Meanwhile, right next door is its cousin, SRI International, with about 2100 employees: most of those don't have PhDs, but a lot of them do, and a quick search on their open job postings finds more than a dozen that are looking for a PhD-level candidate right now.  That's just one company, and one you've probably never even heard of.  There's a lot more big ones out there, and far more than that if you start considering the smaller ones as well.

Now, getting back into a professorship, that's a different story.  It most certainly can be done, if you maintain a good research presence.  For most people, however, the trip to industry is a one-way trip, simply because you generally don't have to publish.  Many research companies like it when you publish, and many strongly encourage it---but the fact that they have to encourage it should tell you that the incentives are just not there the same way.  At a company, you are not measured primarily by your ability to publish, and so it tends to get triaged in favor of other things, like writing proposals, delivering demos to customers, or product development.  There's nothing against publishing, but there's no "publish or perish" and so there's a lot less publishing.

Bottom line: you can move in either direction, but it's a lot easier to move from university to industry than the reverse.


Should I go back for 2nd PhD in applied field this time?

Instead of looking to start a second PhD, is there any way you could find a post-doc in a more applied field? This would be a much shorter route to obtaining more clinical/applied experience. I do not know how licensure works in your specific locale (i.e. do you need to have a certain specialization in a psychology PhD to be licensed?), but if all you need is experience then a post-doc may be the better option. Post-docs usually are much shorter than a full PhD and also pay much better (relatively speaking).

  Jobs in this area pertaining to my work seem nearly impossible, but the location is ideal.

One of the worst things you can do early career is place artificial restraints on your job search. Yes, your girlfriend has connections to the current location. Does she want to live there the rest of her life, even if it means you are unemployed? I have had several early career people that I've mentored tell me that they cannot find any jobs, only to discover that they are exclusively looking in their hometown in Alabama with 1500 residents (or whatever). They tell me "Oh, but that's where my family lives!" That's great, if your family is willing to support you financially.

Any location where you are unemployed long term without any prospects is not "ideal."  Not to be harsh, but you may need to decide whether you would rather have your current girlfriend or a job. This is entirely not my business, but perhaps a girlfriend who refuses to move so that you can find a better opportunity is not a girlfriend you want long term. This is especially true if she is planning on looking to you for any form of financial support. I understand that there is a balance there; your career certainly does not take inherent precedence over hers. But depending on what your long terms plans are together, she and you may need to have a discussion about moving or breaking up.

As has been mentioned in the comments, it is also possible that you could find work in fields that are not directly related to clinical psychology. I work with some researchers in the engineering industry who do "human factor analysis." They help companies (mostly the defense industry) determine how to make their products safer from a human-error standpoint. Many of these researchers have PhDs in psychology. Developing the quantitative skills to do work like this would be much easier than getting a second PhD. Similar work can be found in fields like political science and legal science (i.e. as a trial scientist). These are often directly related to social psychology.


How should I write or abbreviate my Indian name in academic papers?

Ultimately, consistency between papers is more important than whether it matches any of your other documents. Just pick a way you like to write it and make sure you always keep it the same in future papers.

Points to keep in mind for picking your "researcher name":

For better or for worse, anglo-saxon norms are dominant in English research publications. The closer your name looks to "Firstname [I.] Lastname", the less confusion (and hence people citing differently/wrongly) will happen. ".A", in particular, is very unusual and will likely be mistaken for a typo and "corrected" into "A." frequently.
A unique name makes your papers more easy to find. If there are already 5 people publishing under the name "Sulthan Kan", maybe pick "Sulthan Ayyup Kan" instead.


How far into the program should a doctoral candidate transfer to a different school?

There really aren't "transfers" at the PhD level as there are with undergraduates. What might happen at best is that you:

Get some credit for coursework done, or for core-course requirements (like stats, etc.)
Rarely, a student can come in with their MA/MPhil and waive coursework and advance to candidacy.

But everything at this level is ad hoc. Sometime, students can switch programs -- especially if it's in the context of their advisor moving from University A to University B and taking their students with them, other times it's impossible.

It's all up to the university, the program, your advisor, and the alignment of the stars in heaven.

Otherwise you apply as a new student and start off at zero. Most students who do this do it in their first or second year, it becomes much harder the more advanced you are.


Is it ethical to explicitly or implicitly bias against student papers unless co-authored with senior researcher(s)?

In my opinion, such a policy is absolutely unethical.

One of the key principles of science is that scientific work can be done by anybody.  Good science can be done by people who aren't even in academia, let alone by students.  A scientific paper should be evaluated on its merits, not an argument from authority based on its authors.

Now, humans being humans, reviewers will tend to bias towards known authorities and prejudice against unknowns, students, etc.  But this journal's policy, rather than fighting against such a tendency, explicitly enshrines and adopts it.  Likewise with the informal policies that you describe: anything that amplifies unfairness in judgement rather than de-amplifying it is highly suspect and likely scientifically unethical.

This doesn't mean that one should drop standards.  Rather, it means that one should treat a paper coming from a well-known PI at an august institution with just as much suspicion as one from a student author from a developing-world university you've never heard of before.  Being status-conscious primates, we're not very good at doing this, but such a condition is the goal towards which we should strive.

PS: Note that a policy the other way, i.e., student journals that don't accept papers without student authors, is not problematic because it is inverting the privilege gradient.


What are good principles for naming an algorithm?

The bumper sticker idea is quite smart, provided it is indeed the same general approach being applied. Otherwise it becomes gimmicky. Also, IMO, it would be better if XYZ has some functional meaning besides just being catchy, but I understand this is not always easy.

For instance, suppose A and B are heap sort and bubble sort respectively. Suppose your general approach has something to do with hashing, and makes the sort faster. A name like Hashed heap sort and Hashed bubble sort would make more sense and have better recall value/correct association than say, Snappy heap sort and snappy bubble sort. This may be an oversimplified example, but the point about functionality is worth remembering.

Ultimately, the line between gimmicky and legacy is not predefined, and it's not in your hands. Since you've already published XYZ-method A, you could see how the response to that nomenclature has been (are other authors using that name? Do your collegaues and co-workers call it by that name? Do other people see it catching on?). If the response is positive, and the above points are met, you could go for XYZ-method B. Else consider learning from this experience and make a fresh start with a new name.


Minor Revision with suggestion of an alternative proof by reviewer

I would not worry about the paper getting rejected one way or the other: The reviewers gave you a shorter proof, but did not suggest that the theorem is obvious or trivial. This isn't going to change once you put their proof into the paper.

So the question is how to acknowledge the reviewer. It is not uncommon in mathematics papers to show the shortened proof and then, in the acknowledgements say "We appreciate the contributions of reviewer 2 who provided the shortened proof of theorem 4." On the other hand, if you think that coming up with this proof really required some hard work even though the reviewer has seen your proof, then maybe it is appropriate to ask the reviewer (through the editor) whether they want to become a co-author.

The final option may be to show both proofs. If you think that your proof is interesting despite being complicated because it shows connections to other areas that are of independent interest, then it's worth keeping it in. In such a case, it may be useful to show the alternative and shorter proof given by the referee in an appendix, and explain why you think it's worthwhile to show both. Remember that a paper isn't just about showing a result, but also teaching others how that result came about and what it means and implies. As such, there is a place for papers with two independent proofs of the same statement.


I copied 1 or 2 figures verbatim (with proper citation) from statistics books.

You cannot release these figures under a CC license.  Even if we assume that you have the right to use them in this case, for example under fair use, you don't have the right to authorize others to use them in potentially very different ways.

However, you can easily get around this by excluding the figures from the CC license that applies to the rest of the slides.  See, for example, this blog post for further discussion of this issue.

  In some parts, I followed (and cited) the content/organisation of the class textbook quite heavily (not copied though).

This is a trickier issue.  The fundamental question is whether your slides could be considered a derivative work of the class textbook.  If so, then they are themselves a copyright violation if done without permission.  If not, then I think you're OK.

I'm not a lawyer and do not know how to draw a clear line for what constitutes a derivative work.  My understanding is that summarizing or explaining another work is not necessarily a derivative work, but for comparison an "abridgment" or "condensation" is a derivative work (under U.S. law, at least).  Where your slides fall on this continuum presumably depends on exactly what you did.  As a non-expert, I'd guess that you're fine unless you followed the book rather closely, but you should consult with an expert about the details of your situation if it really matters.


I think first it may be worthwhile to accept that in any group work situation there is the possibility that people will worked siloed (or isolated from one another) or one or two people will push the work forward while others are relegated or chose to remain in a passive state.

There are some good reasons for this. I recall being a student with a pretty solid GPA, group projects were a horror for me. If the project grade is based on the overall project and does not take into account individual contributions this meant that students who were less focused on their GPA would be willing to turn in something that was not up to my standards. This led both to situations where other students refused to do work on the project (knowing that the stronger students would carry them in order to avoid dings to their GPA) and to situations where stronger students would freeze out other students (ie the stronger students would choose to take all the work and not let other be involved) in order to maintain control over the project.

Group projects are often used as an analogy for working in the 'real world' where working in groups is the norm. The fundamental difference is that in most cases if a peer is completely slacking or sending in subpar work there is a concrete structure to monitor and handle that issue (which doesn't always work of course but there's almost always more accountability than in academic group projects). You can mimic this behavior in an academic setting by splitting up the grades for the project. Don't give one 'group grade' to everyone, instead have students report on who did what (this is particularly effective if you can have them set this early in the project instead of during turn-in) and correlate the students grade to both their work and their work in the context of the project. Having this set up early can be a great way of preventing aggressive or strong students from freezing out what are perceived as the 'weak links'.

Additionally consider regular checkpoints on the project. This will let you get a feel for the interactions in the group and the content being produced while also minimizing the opportunity for a student to jeopardize the group by waiting until the last minute to work on their part (this will still happen to some extent).

In short - add more structure to the group project. This increases the workload on your end but it mitigates the most common issues you'll see in groups during group projects.


Issues with publishing dissertation on an interest/advocacy group's website

I would be cautious. That said, I think there are easy alternatives that don't involve giving up exposure of your work through their advocacy.

If you value credibility as an independent researcher, you will be well served by not being perceived as shilling for any particular organization or political cause. I think the interests of the organization that is requesting permission to republish your dissertation is in line with this. If your research is findings that are politically expedient for them, they benefit from the enhanced credibility that you garner from perceived intellectual independence.

My advice would be something like this:

Publish your dissertation on your own website or in your institutional archive. (If you don't have a website, now would be a great time to set one up!) It should only take a day or so to get set up.
Once you've done that, suggest that the organization write a summary of your work on their website — clearly in their voice — and to link to or repost (if they feel that is absolutely necessary) your work.

You will benefit from the traffic to your website and they will benefit by having your work seem like the work of an independent researcher and not something done by someone inside. And indeed, it sounds like this is exactly the case!


Career options in scientific/academic publishing for PhDs and Postdocs

I'm in a similar situation, meaning that I'm also a recent (less than two months) Ph.D. graduate and currently focus my effort on a job search (both in industry and academia). The differences between you and me include the discipline (not essential) and my lack of postdoctoral (or any other, for that matter) job offers at the moment. Since I briefly have been considering a temporary career move toward a scientific publishing world, while I do not have a direct work experience in the scientific publishing industry, I think that I have browsed through enough job advertisements to form and share my opinion on the subject, as follows (certainly, take it with a grain of salt).

I consider the temporary career move toward scientific publishing that I've mentioned mostly as an industry career option and not an academic one. While in the context of scientific publishing, there is an intersection between classifying such career option as one of industry or academia, I believe that a career in scientific publishing cannot be considered as an academic career. Therefore, my first point is that, if you, as myself, consider academia as your main ultimate career avenue, going the scientific publishing route is not a good option (unless it is very short-term and due to circumstances). Continuing my road terminology analogy, the above-mentioned avenue and route are not parallel, thus, after some time traveling the scientific publishing career route, one can find themselves too far from the academia career avenue. That will most likely make returning back to academia very difficult, if not impossible.

Based on various job descriptions that I've looked at, a career in scientific publishing seems to involve much less scholarly activities at the expense of much more project management, marketing and operational ones (especially, for non-senior editorial roles). Moreover, internal organizational politics, tight deadlines and other time-related issues, as well as stress of juggling multiple publication projects add insult to injury.

Finally, I personally dislike the scientific publishing industry's negative role due to lack of openness in dissemination of scientific information and corresponding strategies and tactics they use (that includes their "implementation" of the open access paradigm). Therefore, it would make even more difficult for me to work in such environment and organizational culture.

Considering all the above, I would not go the scientific publishing route, even temporarily, but, instead, would try my best to join academia as a postdoc or junior faculty member and progress there or, alternatively, go the real science-related industry route (less perfect, considering the ultimate goal, but, can be either temporary, or long-term, combined - in a form of consulting - with academic positions).


I refused adding a gift author to my paper and my advisor threatened me that he won't let me graduate

It would be serious ethical misconduct for your advisor to try to publish your work under his own name. If you find that it has been done, a note to the journal editor or conference chair would have serious repercussions for his career. You could also, then, file a claim with the university, perhaps resulting in his getting reprimanded or fired. It is serious enough that few would be willing to risk the harm it would cause themselves.
However, that doesn't help you a lot at this moment. I've written in answer to many other questions here that it is very seldom profitable to fight with your advisor, even when they are clearly wrong, as here. In the end, you might have to yield on this in order to graduate and get on with your career. He holds an inordinate amount of power over you at the moment.
Let me suggest, however, that you might be able to defuse the situation if you can find allies among the students or other faculty to intervene in this on your behalf. It is hard to fight against powerful people alone. Even if someone else knows of your situation, a faculty member, it would, perhaps, make retaliation against you more dangerous for the advisor. In reality, they should let you publish with proper authorship and graduate based on qualifications. If they do anything else, then it would be appropriate to bring an action against them.
But, I suggest that you don't make a formal complaint based only on threats of bad action. Choose as you think best about the advisor's demand, and if he then takes action against you in any way, complain to whatever authorities are open to you.
You might be able, also, to find some middle ground, such as offering to help this other student in some other way than giving them authorship that isn't proper.
No one can promise that anything but submission will result in a successful outcome for you. Having a paper with a phony author is still having a paper, which is a good thing. It won't be your last paper. It likely, over your career, won't be your best paper. Don't let the short term considerations negatively affect your long term career goals, even if you have to submit to an unethical advisor. Get done. Get gone.


The general rule I recommend is extremely liberal: If you write or publish a paper while being funded by a grant in any capacity whatsoever, acknowledge the grant.  ("Work by this author was partially supported by...")

When in doubt, say thank you.


Applying to faculty jobs: how close to research area should I be?

You want a job? So apply. That’s all there is to it.
The academic job market is not some kind of neighborhood bonding event or support group where people try to be as nice as possible to each other and avoid hurting each other’s feelings. No one will be mad at you — in fact, the very notion that someone getting mad at you is a consideration you should take into account when deciding whether to apply for a job is, from my point of view as someone who in a typical year looks at anywhere between a couple of dozen and a couple of hundred job applications, completely absurd.
You might not get the job, but there’s nothing inappropriate about applying, unless there are formal requirements listed in the job application that you don’t satisfy.
Good luck with the job search!


I have a degree but it isn't actually what it looks like it is. How do I list it on my CV?

I would list it directly with the degree. I have a similar issue in that my degree is Geodetic Science, but my focus was in (at the time) computer-assisted mapping, now known as GIS. People try to call me a geodesist, but I'm not really. I would use something like:

M.S. Mathematics (specialty: Computer Science)

Edit: I finally remembered what the various tracks were called in our department--a concentration, not a specialty. Other synonyms include focus, even research or research topic.


Using a case study without company's permission

Honestly, I would not do this.
I am not familiar with US law so I cannot give you any legal advice. However, there are several other non-legal risks you have to bear.

According to your description, you intend to stick closely to the real case in your presentation. The students might be intelligent enough to draw the necessary conclusions or could even be involved with the company. I would not risk this.

As a result, the company could get the impression, that you have leaked confidential data to the students. Indepdent from the question whether this is illegal or legal, facing a lawsuit can easily have a disastrous effect on your career. Furthermore, this can also result in loss of trust, again impacting your career.

I only see two possible options here:

You ask your former client for a written(!) permission
You largely modify your example / problem

Both methods, when done correctly, will save you from a lot of risk.

I had a similar problem, when I wanted to write a paper about work I did for an industry partner. Usually, this is quite strict, since nobody wants to have their confidential solutions published. However, I was able to chance the problem and solution sufficiently. Despite the same ideas were used, the original problem and client remained hidden and I was able to publish my ideas. This was quite a lot of work to do, since I had to redo most of the code and experiments. Altogether, this was worth the effort since I do not have any fear of legal consequences and we still have a good relationship to our clients.


Reading your paper is not the only obligation your referee has. They are active researchers who, besides their own research, have teaching, administration, thesis defenses, other papers to review etc. They are also normal people, who have to make their personal life function.

5-6 months is a long time, but depending on the field and the length of your paper, it is not unusual.

Don't be so worried about other people stealing your ideas. Most likely the referees has more ideas of their own than they have available time.


My main tip would be to use a reference manager that automates the task of formatting references. There are many to choose from. But any good tool should make it fairly trivial to move between author-date format to numbered format. Good tools should also come with a wide range of tools for customising the look and feel of your references. Personally, I use Endnote and it works well for my workflow with MS Word. If you use LaTeX, then you'd want something that works better with BibTeX. That said, I think the big thing is that you get to know the features of your reference manager so you can use it effectively.
In terms of what reference format to adopt, I'd go with the format required by where you plan to submit the work. If it's a thesis, then follow any rules provided by your department. But commonly with PhDs, the format is up to you. In that case, you'd usually adopt the convention (or one of the conventions) of your discipline.


How will the 2013 US government shutdown affect NSF postdoc applications?

Documents are posted here.  Extra text so I can actually post this.

I should note that some of the documents are specific to the Mathematical Sciences Postdoctoral Research Fellowship, but some of them are general-purpose (I came to this question from MathOverflow).


I have been a small business owner for the last 7-8 years

Have you run into issues/problems in those 7-8 years? Are those problems specific to your own business? Could other business owners have the same or similar problems?

Can you generalize those problems so that you can conduct research on possible solutions to those problems in academic approach?

Can you find the causes of those problems from academic perspective? How would you propose to do so? Should the government play a role or not? How could the society as a whole participate? Etc. Etc. There are hundreds of topics out there. Take your pick. Good luck!


Reference manager with note-taking/quote-storing capabilities

I use BibTeX / BibLaTeX with Jabref.
I make use of the Annotation Field.
See this TeX.SE answer for some details on how to enable the annotation tab on all entry types.

In JabRef, the search bar allows you to search all fields, so that gives you searching. I particularly like getting search results from my annotations and from the abstracts.
And you can store by each of the fields -- including the timestamp of when you added it.
It also lets you easily link to the PDF and/or URL/DOI. I suggest if you can link to the URL/DOI in preference, since that will work on any computer if you transfer the entry.

To add things to Jabref is just a matter of pasting the BibTeX entry code -- or it has a number of other options.

Jabref just fronts the BibTex file, which is really nice if you need Bibtex to use latex referencing -- but I guess for most fields of humanities this is not so significant.

BibTeX is also really nice because it is just plaintext field, so you can version control it cleanly.
See this Tex.SE question
Even if in humanities, version controlling your referencing is a great idea, since it makes it centrally available (if you use hosting), and gives you backup, and merging.


Applying for Post Doc position with already one in hand

Typically different institutes, even within the same organization (e.g. the Max-Planck or Fraunhofer group), don't formally exchange information on applicants to their positions, so you don't need to be afraid that they won't consider your application just because you're in the process of getting hired somewhere else. However, you shouldn't underestimate informal information exchange - if you're in a small field, the PIs who want to employ you may well talk with others about that post-doc they are going to hire soon.

Moreover, if you've already explicitly agreed to an offer at one place, and they are preparing the contract, it perceived as very impolite to back out of that. Legally, it's still possible to do, and if it makes a really big difference for you, then you should probably do it, but be prepared that it will annoy the person you agreed to working for.


When does the "run, don't walk to the nearest exit" advice not apply to graduate students?

Whether a situation is abusive or not is in no way dependent on the intentions of the advisor. Terribly abusive people think they are being "tough but fair" all the time.

Different people also have different reactions to the same situation. A situation that motivates one student to do better can be destructive to another. I would question that it's even your place to evaluate if other people are being "whiny" or not - you never have enough information to know what it's doing to them.

To evaluate your situation, ultimately what you want to know is if you are getting enough out of your situation to make it worthwhile. Long hours and feeling worn out are a function of workload, mainly. If you want to pursue an academic career, the kind of output required can probably not be achieved without a heavy workload. On the other hand, I have never come out of a meeting with my advisor embarrassed - at minimum, that might indicate that you and your supervisor's styles do not mesh. Another question is, how long do these feelings persist? The next day, do you feel like you are on a better path towards your thesis than before? Do you dread the next meeting?

A common and often extremely destructive feature of abuse is distortion of reality. You start to feel like things are normal even when they are really not. It is therefore most helpful to talk about these things to as many people not from your group as you can - make friendships with people who have different advisors! If your university offers therapy appointments, it can also be very helpful to go in a few times a year to talk these things over with a neutral party.


Are Canadian applicants favored in graduate admissions or funding for Canadian graduate programs?

Without knowing the details of your classmates funding, it's difficult to say whether there's bias. Having said that, Canadian students will be at a definite advantage when trying to get funding at a Canadian University.

For some students, funding at the Masters level will be formed from multiple sources:

Government Scholarships. Some of these are open to international students, others are not. For example, the NSERC Vanier scholarships accept international applicants, but the NSERC CGS M does not.
University scholarships: These are typically funded from a variety of sources which will have varying requirements. Some must go to students from Canada, some must go to international students, some are purely merit based.
TA/RA-ships. My experience is that these typically aren't restricted based on international status, but I can't say for sure.

So, it's easy enough to imagine that your friends funding could simply include scholarship money that is unavailable to you as an international student. Most universities realize that international students aren't on perfectly even footing, and will have sections of their websites dedicated to funding for international students. This could be of great help for you, though the money  might not come soon enough for you to be able to make it work.

Another thing to mention, is that some countries have scholarships for outgoing international scholars. These vary hugely, but should also be considered.


How would someone transition from the business sector to academic research?

Is there a general way to transition to research after undergraduate study

Usually the general way to transition to research is to do research under the supervision of an experienced researcher. (Either within the context of graduate school, or outside it.)

  are there any particular mental tools that I should acquire that would be in my best interest for research

Yes, there are many, and they vary by discipline. You would learn what tools you need for your particular research and develop those tools by conducting research under supervision of someone more experienced in doing research in your field.


Obviously your idea is not 'protected' as someone else might have the same idea and/or a subset of that, and make a publication/patent out of it before you do; and you can't claim that the person stole it through your brain waves!

Write down the introduction and background to that idea you have, and prove that it is your contribution through case studies and evaluations, and submit it to be published in a conference as a poster or a paper.


I am about to fail a required course due to difficulties caused by mental health issues. How can I save my degree?

First, the most important thing is to improve your mental health. Without taking the time to recover from this illness, these sorts of professional problems are likely to recur, even if you overcome this current situation. So, two suggestions:

Begin (or continue) working with a mental health professional. In addition to the obvious medical benefits, this will give you some firm documentation of the problem, which could be helpful academically.
Talk to your someone within your program -- either the graduate director or another trusted professor or someone in the school's counseling center. They can help you assess your academic options -- for example, the option of taking a leave of absence while you recover.

Therefore, I was thinking of reaching out to my professor by email and explaining to him all what I was going through and asking him if it is possible that he gives me some work to do or something to pass the course.

I do not recommend this. I received these sort of requests at the end of every class I taught, and my response was always along the lines of "Too late, the course is over. It wouldn't be fair to the other students if I changed the grading scheme at this late time." While some instructors might be less hard-hearted than me, I think very few would be willing to give extra points for no reason, or to allow "extra credit" for one student only.
That said, there is still some hope -- if a student missed a passing mark by just a few percent, I would occasionally "round up" and award the passing grade. I would do this for every class, regardless of whether the students had e-mailed me with supplications.

Is there another way to save the situation?

I would approach this from the other side -- see my second bullet above. The graduate director, or your school's mental health office, might be able to arrange for an exception, or a leave of absence, or some other work around.


Should I be looking at the market while under first year of two year contract?

Yes, absolutely be on the lookout for opportunities

Your employer has made it abundantly clear that they intend to kick you out after two years: It says so right on the contract. If you do not plan for that time, you will be unemployed and with no appointment/affiliation, both of which are more problematic than they should be.

So it is only natural you devote some time to your future options - regardless of it being in Academia even. As an academic in particular we know, that hiring processes tend to be very long; and you very often have to move far away / abroad so the logistics and legal aspects are more complex and again, take longer. So it's doubly important to plan well in advance for an academic.

Concrete suggestions:

Don't look for a letter from the chair of your department early into your contract - unless the subject somehow comes up. I'd feel comfortable asking for something like that after I've done something impressive and/or once I have one year or less remaining.
Tell prospective workplaces that you are mostly interested in starting out in 2 - X years (with X being the time into your current 2-year contract), but also say that this is flexible. Because it is: You could wait a while, on one hand; and you could also give notice and quite earlier than the full two years, on the other hand.
Give independent consideration to whom you want to share your active job-search with. Telling people about this can have both positive and negative effects.


How to respond to a citation request which is not relevant?

Opinions vary, but I think it is very important to acknowledge prior art, that is, priority. To leave important prior (strongly related) work out of a bibliography is to communicate the idea that there was no prior work. Indeed, one can "cultivate" lack of references to one's competitors by carefully not looking at their work, thus, seemingly having no obligation to cite them (or otherwise acknowledge their existence!?!) But this is inappropriate, as it would convey a false impression to your readers, as well as being unfair to your competitors or predecessors. That is, it's not only what you use or rely on, but works that came before yours.


Why do computer science conferences (usually) not reveal the number of submissions?

Usually (most of the time) this information is shared on the opening day as part of the welcoming session.

Why do conferences use sequential numbers that could give this sort of information away? I don't know, probably because it is easy, and the information has little value in general. Since most of the review process is a pretty manual labour intensive task, this probably makes it easier to find missing papers by hand, to search for and track papers, reduce potential administrative errors, etc.

What would change if there are 300 spots and your paper was number 600 vs 350 (assuming you submitted last)? You are usually not allowed to submit the same paper to more than one conference at the same time, so you cannot act in either case until you received your acceptance/rejection letter. Good conferences cull poor quality papers, even if that means not all the spots are filled. You only know the paper is accepted when it is accepted. Estimating a probability of acceptance is merely for your own enjoyment and has no benefit to the conference organisers.

In academia, if you ask the question why is x, y or z not done, the answer is usually time and effort required without any benefit to that person.


Why are academics expected to pay out of their pockets for society memberships?

First of all, I believe the premise of your question is largely incorrect (and I know from your disclaimer that you are "not asking about that" but will take the liberty of addressing that anyway). At my university, researchers can use their research funds to pay for membership in academic societies, and my perception is that this is the norm in the United States. So, to the extent that it's not the case at your institution, my feeling is that that is out of line with the norm, so perhaps there is indeed no good reason for it and you should lobby to get this rule changed.

Second, even if it is the case that you cannot charge this expense to your research funds, the assertion that "academics are expected to pay out of their pockets for memberships in academic societies" still sounds highly questionable to me. What does "expected" here mean? I was not a member of any academic society until last year, and nonetheless managed to become a full professor and department chair at a respected university. So I maintain that no harm will come to your career if you ignore this so-called "expectation". Sure, it might be nice to be a member of a society and can come with various small benefits, but if you don't feel like paying for it, you'll be fine.

Third, even if it is the case that becoming a member of an academic society in your discipline is somehow a professional necessity, and that the only way to do that is to pay for it out of your personal money, I don't think that's necessarily unreasonable (nor is it entirely true that things aren't like that in industry - lawyers have to pay annual bar fees, for example, not all of which are covered by their employers). Your interpretation that this means "we are supposed to pay to do the job we were hired for" seems to me like a very narrow-minded view of what life in academia is about. Sure, it is a job and we are paid a salary for it; at the same time, being a researcher is much more than a job - it is a vocation, and that is why researchers are notoriously bad at separating their personal lives and their professional lives: most normal "workers" don't work late nights and weekends (not to mention holidays and family vacations) and don't spend a large proportion of their lives traveling for work, including moving repeatedly across large geographical distances before landing their first permanent job.

In fact, to be honest, as an academic, I feel like I can't draw a precise line separating my "job" from my "personal life". When I read a math book or article at the beach or swimming pool, am I "working"? When I think about a research problem while driving or talk about math with a friend over dinner, am I "working"? I honestly don't know. And that's a good thing. It means that I am doing something that makes me happy. How many other "workers" can say that? Too few, sadly. So let the industry people have their employers pay for them to do the "duties" that are "written in their contract", is what I say. If you are passionate about your work and being a member of a society is something that interests you enough, you would not find it burdensome having to pay a small amount for it. And if not, well, either switch careers, or just forego the society membership, and all will be well.


Do universities know that you have re-applied

Do universities know that you are a re-applicant who applied to the
  same program last year?

Yes, they do. Moreover, many universities directly ask are you a re-applicant in application forms.


It seems like a long time by any standard. Contact them. You can give them a date by which you will formally withdraw your article from consideration. Maybe a couple of weeks. If they don't jump you can submit elsewhere without worry.

The final nudge is just a courtesy. You could actually just inform them that you are withdrawing for submission elsewhere. But if the journal is reputable it might be worth the courtesy.


How to decline a postdoc interview if there is some possible future collaboration?

Don't go -- it's a waste of everyone's time if you go to an interview without any intention of taking the job. People get (rightfully) more upset about you wasting their time than you not wanting a job because you've already found one elsewhere.

Besides, if you will be required to collaborate with the person with whom you were to have your second interview, they (i) may have personal contacts with the research group where you accepted the job, (ii) may already know that you took the first job, and (iii) will need to be among your friends. Simply inform them that you took the first job (and not beat around the bush by saying "somewhere" or "think I am accepting" when you have already accepted). Offering to come anyway for a collaboration or a seminar is fine.


Deferred admission but funding not guaranteed

In brief, in academic mathematics, if you are "accepted" but without promise of funding, it's a very weak offer. The fact that you got funding this time around is certainly positive, but there's so much volatility involved that I think it would be a dangerous mistake to view the situation as so much promised to you (it's not) so that you have a complete obligation to go there and nowhere else. A promise of funding should be construed as obliging you to either keep your promise or decline in advance, but mere admission, without funding, while not nothing, is barely something, either.


This is a poor supervisory practice. Unfortunately, it becomes increasingly common in Universities, particularly in countries with strong marketalization of Higher Education (e.g. US, UK). Students are treated as customers, and academics are assessed and promoted based on their "efficiency" in terms of the number of students they supervise, not the quality of education they provide. The pressure on academics to supervise more students is constantly increasing, and they rarely have enough time to meaningfully prepare to supervisory meetings. It is not surprising that many academics find it convenient to reuse the same projects over and over again.
UPD: Answering comments, I want to clarify why this practice is detrimental to students' learning. Project-based learning attempts to recreate an authentic experience of doing something, then encourages students to reflect on this experience and learn from it. The authenticity of experience is the key for success. However, after some repetitions the supervisor knows all good and bad ways around the project, and unconsciously projects them to the student. Students don't have the same feeling of terra incognita in their research. Of course, realistically, we can't expect each master project to be completely new, but it's still important that the supervisor has not rehearsed it by heart yet.
A closely related, but not exactly the same reason is potential plagiarism. All theses are published and could be dug out by students. I have seen some supervisors who passed good theses from past years to new students to "get the style", effectively encouraging plagiarism. But they had way to many students to supervise and no time to do it properly. Surely, copying from someone else's paper is a poorer learning experience for students compared to doing research themselves.


How much background material should a mathematical research paper include?

I'd recommend putting in as much explanation, context, and background as you reasonably can.  In principle you could certainly put in too much, but in practice I don't think I've ever seen a mathematics paper I thought actually did have too much.  If you structure your writing so experts can easily skim things they already know, then I don't see why extra explanation should trouble anyone.  Tradition requires being concise, but that tradition was based on the economics of publishing.  Space in printed journals used to be a scarce resource, and if you spent it on unnecessary exposition you were keeping someone else from publishing at all.  Publishing still isn't free (and readers have only so much patience, as well), so you shouldn't include enormous amounts of unnecessary background, but traditional writing styles should be adjusted to account for the greater availability of space.

It's possible that a referee or editor will object that they don't like your style.  You may be able to resist making any changes (it depends on how exciting your paper is and how high your own status is within the community), and if you do make changes you can still keep a lot of explanation.

If necessary, it's worth having two versions as Paul Garrett suggests.  If you do, then you should make it very clear which is which and what the differences are, to avoid serious confusion if someone refers to the paper without realizing they need to specify which version.

  The background material is "standard" in the sense that anyone who works on this class of problems would know the definitions or results in some form. However, this is at most a few hundred people, while if I include the background material my paper should be comprehensible to an advanced undergraduate.

One reason to be generous with explanation is that it's easy to overestimate how much people know.  Aiming at advanced undergrads is a good way to make sure grad students really can read the paper.  If you aim at experts, you may write a paper only your own collaborators can comfortably read.

  Some of the background results are part of the folklore of the field, and I've never been able to find a proof of them in literature. While they are believable and not hard to prove, I feel someone should bother doing it.

This is a great reason to include a proof, although it's important to consult with experts to confirm that there really isn't an accessible proof in the literature.

  It makes the paper longer, although even with the background the paper is not long (13 pages).

You should make sure it doesn't look like padding, say with just a few pages of original content among the 13 pages.

  From what I've heard, it is generally considered bad practice to restate definitions and constructions states elsewhere and to reprove theorems available in literature. In part this is because it gives the impression that I haven't read the literature.  This is exacerbated by the fact that I only cite ~5 previous works, mostly for further reading or alternative presentations of some of the background.

This does seem like a worry, and five references is not very many, even for a 13-page paper.  You might not strictly need any more, but I'd recommend tracking down additional references for background.  As a general rule it's best to cite generously, giving plenty of credit to other authors and offering many resources to readers.

Regarding giving the impression that you haven't read the literature, it's important to be clear about what's background from the literature (with a citation), what's folklore, and what's your own contribution.  If you reprove something you say is known but don't give a citation for, it can look like you were too lazy to track it down.


Should you get your masters degree from a different school then the one your received your bachelors from

It is commonly accepted that it is generally better for a student who is going on to an academic career to get their PhD at a different institution from where they got their MS.  For an academic, the place where you got your PhD is generally more important than where you got your bachelor's degree and that it is important to have a PhD from the very best program that you can get into.  Studies have shown that PhDs from the top programs are much more successful than PhDs from lower ranked programs.

There are lots of middle tier universities with good undergraduate programs that adequately prepare students for graduate study but that don't have very strong graduate programs.  If you're at one of those institutions, then you'd be well advised to "move up" to a better institution for your PhD.

You've asked this question specifically about your MS degree, where this is much less of an issue.  If you're getting a terminal masters and planning to work in industry, then it probably won't hurt to get your BS and MS at the same institution.  If you're planning to get your BS and MS at the same institution and then go somewhere else for a PhD then having gotten your BS and MS at the same institution won't be a problem either.


Resources/methods to teach how to perform research logically

Of course there's a way to teach them: have them enroll in a research oriented PhD program and practice for five years! An effective approach to research is a skill that takes a long time to develop and will have prerequisites that also take a long time to develop (e.g. how to read scientifically, how to formulate scientific questions, how to verbally express a scientific thought clearly).

That being said, engineering degrees are largely aimed at formalizing the skills that would take a decade or more to acquire through practice. If you can describe a procedure formally in enough detail, maybe, students can just follow the procedure exactly and get acceptable results. I don't know whether this would work or be a good idea for research (BS in Research Engineering anyone?) but it's moot because science programs tend to emphasize content rather than process.


Should I send reminder to a professor in a school I applied to, for an introduction email I sent two weeks ago?

As a busy professor myself, I personally appreciate getting a reminder email. I fully intend to reply to every email I get from a prospective student, even if only to say "Sorry, your research interests do not seem to be a good match for the work we are doing in my group." But in practice, life gets busy. I'm traveling. Or I'm booked solid with meetings and so I don't have time to immediate answer the 50 or so daily emails requiring responses. And so some emails fall through the cracks. Thus I appreciate receiving a single reminder email. Such emails help me do something I want to do: namely, be the kind of person who gives every serious inquiry the courtesy of a response. (A second reminder email is not necessary. If I haven't replied the first two times, there is likely a reason.)

As for what to write, anything short and sweet and non-accusatory should be fine. Personally, I prefer the polite fiction that perhaps I did not receive the original email. You know it's not true, I know you know it's not true, but in phrasing your note this way we agree to mutually overlook these facts. I'd suggest something very simple, such as the following.

  Dear Prof. X,

  I wrote you a letter a few weeks ago, but given the uncertainties of
  email I do not know whether you received it. Thus I am resending my
  note just in case.

  With my best regards, Joe

  [and then append the earlier letter here]


How often should one evaluate a plan for an academic career?

What I tell my students starting out is to make sure that they have realizable goals. Saying "I want to be a postdoc in field X in five years" is realizable. Saying "I want to work for Professor X at University Y on project Z in five years" is probably not realizable. Making sure you have a plausible goal in mind, and the ability to work toward it is incredibly important.

However, it's important to realize that goals and opportunities change over time. What you think you want to do now may not be what you want to do a year from now. So that's why it's important not to have goals that are too narrowly defined—otherwise, it makes it harder to change your mind later and still be satisfied with the way things turn out.

How often do you reassess goals? As often as you feel you need to. But you should also distinguish between the different ranges of priorities—short-range, mid-range, and long-range.  Short- and mid-range should be reviewed on a very regular basis (weekly to monthly); the longer-range stuff at least a few times a year. But these are guidelines that work for me; you need to find a system that works for you.


How can I relate my undergrad works to professors research areas?

Answering this question is hard for me because I don't know how to define a specific direction that doesn't make me limited and lose the opportunity of working with him.

This is a thoughtful response on his part. He is not asking for you to send him a dissertation proposal, but maybe something four or five times as broad. Maybe something like "I'm interested in interventions to support learning in recent immigrants to [your country]," rather than "The effect of X intervention on mathematical learning on late teenage refugees to [your country] who did not receive formal education in their home country."

It's not a quiz to see if you come up with a good enough one and "lose" the opportunity to work with him (unless he's a nasty person). More of a determination whether you two are a good scientific fit.


Applying for Ph.D. Program when desired adviser is on leave?

Yes, certainly. Academic leaves are normally for a semester or a year. Faculty may or may not be on the admissions committee the semester they are on leave (they normally aren't if they have an ounce of sense and want to take full advantage of their leave) but they usually still participate in a shadow sense.

For example, when I've been on research leave, my colleagues on admissions forward me the dossiers of people that they know might interest me. If I know a candidate is applying, I might also proactively flag them to the admissions chair.

This way, I can ensure that when I get back from leave, I have a fresh student to work with.

Now, the trickier question is the year before scheduled leaves. Many faculty won't take a student the year before a leave as the student would arrive without an advisor. Others will ask a colleague to serve as temporary advisor for a year if they really want a particular student.

The only way you can know is to ask the faculty member in question if they are taking students.

You asked, she said that she's taking students, so you are all set. As to how to prepare for the oral interview, that's a separate question.

As to the comment that "leaves" are a sign that a faculty is leaving, this is bogus. At most of the institutions I've worked at, when you take a leave, you have to "pay back" the leave by working at least the same amount of time as your leave (one year leave is at least one additional year of work at the old institution). Often, the new university will pay the old university for the leave time, but this is a sore point in negotiations.

It's much more common for a faculty member to negotiate leave at the new university.


Recent joint papers are one of the first examples of conflict of interest most journals mention, see for example here and here. Being your advisor is also explicitly mentioned as a conflict. I would avoid suggesting this person as a potential reviewer, this will at the very least raise eyebrows unless you have a very convincing reason.


Contacting potential advisors before applying to graduate program - PURE MATH

The expected behavior here is that you talk to faculty after you’ve been accepted to the program, not before.  That way you have more information to make your decision about where to go, but faculty aren’t spending a lot of time with students who aren’t going to be accepted.
Contacting a faculty member is unlikely to give you an advantage in admissions if you don’t already know them, what can give an advantage is if you have a mentor who knows faculty at the school you’re applying to and puts in a good word.  It’s not likely to hurt you either, as long as you’re polite about it, but you’re likely to get no reply or a short reply saying that they’re not on the admissions committee.  They’re more likely to be annoyed than to help, but in 9 cases out of 10 it just won’t amount to anything.


How to handle multiple years lost to test preparation on CV?

I agree with @socialsciencedoc's comment, although I think that what s/he describes is a more common phenomenon in the social sciences than in STEM fields.  In the former, it's rare to be a 20-something PhD, and in the latter it most certainly isn't: not getting your PhD in math until you're 30 makes you (slightly, and certainly inessentially) older than average.

Anyway, I am not really scrutinizing gaps in candidates CVs until after their PhD (at which point I am!).  Having a gap between undergrad and grad is still very common in STEM fields: e.g. many people do a couple years of high school teaching before the siren song of academia lures them back.  One of my current PhD students did some high school teaching (among other things...) and will be over 30 when he gets his PhD.  In his case, he acquired some skills in his "gap years" that are proving useful to him as a student and future mathematician.

Spending multiple years only studying for an exam is not something that most Western academics would be so familiar with, I'm afraid.  I'm not sure how to spin that positively.  So I would just not explain the gap at all.  Put your energy into what you can now control: getting a PhD in a timely manner (in math, four or five years is ideal; six is still totally fine; after that it begins to look like you lack sufficient locomotion) and, of course, proving some great theorems in your thesis work.  My eye would probably slide right over this gap in your CV...and I think that is exactly the way you want it.

Added: I missed this sentence reading your question the first time: " I do understand myself that my mathematical knowledge grew in that two years, still I can't find a single demonstrable item to support my case."  That's great; truly.  So your time was actually well spent, and I'm very glad to hear that.  You don't have to further justify that that time was well spent: it got you into the great university that you now attend.  So I think you have little to worry about, actually.


I think this varies a lot from field to field. In High-performance Computing and Scientific Computing, tutorials are very likely to be a set of lectures and hands-on laboratory sessions giving attendees instruction in how to use a computer, API, or other software. This could include "Programming for Intel Xeon Phi", "Introduction to Computing System X", "Python for HPC", etc. (many of which I have personally been involved in teaching). These kinds of tutorials are typical of conferences like Supercomputing and IEEE Cluster.


Will experience in related fields help me get into my "dream" graduate program as a non-traditional student with some failures in my past?

When I started my PhD (R1 school in engineering), I shared my office with an older gentleman who was 12 years older than me, had an average GPA, been a structural engineer for 10-15 years or so, married with kids and extensive industry experience. He applied for 3 years in a row to the same university and only that university because he lived in that town and did not want to relocate (his kids were at school, his wife had a job too) and every time he would get rejected. At his fourth trail, he was accepted. He said that he was going to keep applying as much as needed! As far as I know, nothing has changed in his application from the third to the fourth year. The professor who agreed to support him has just got a project and needed somebody with technical experience (it was construction/material related).

I would say that getting to know the right people does not hurt! Maybe visit the department, introduce yourself and have short meeting with some professors. I noticed that many professors hold much respect for established industry people who want to go back to school. Although some feel it maybe a little risky as well. But, you never know if you do not ask or try. I do not think it is impossible, but maybe you would need to do some extra work to convince/explain your story/timing for such a decision.

I can also think of a scenario were if you work at a company that has an R&D department, maybe a collaboration between the company and school can open up a spot for you in a program. In this scenario, the company can provide the school with a proposal, pay fees and (raw) materials and the school can allocate the lab, equipment and an advisor to supervise you. You can work on such a project and get a degree at the end of the day. However, I'm not sure if this applicable to your case or if this something that happens often.


Which bibliometrics index to trust more?

The short answer is NONE. A longer answer is "to get the scientific excellence of an author, read their papers and understand their contributions".

The problem here is in expecting a number to characterize the contributions and quality of an individual researcher. Probably the only way in which these measures can be useful (and that's stretching it a LOT) is if they are viewed in aggregate (for a department/university) to get a very crude picture of research productivity (not excellence).

But the signal is so noisy as to be useless.

Really, there's no shortcut for the hard work of reading, researching and asking in order to assess the "scientific excellence" of a researcher.


Replying to professor who said that I can join his research group as a PhD student next year

He hasn't made any commitment to take you on next year. I would simply write to thank him for his consideration and say that you will re-apply if circumstances at the time permit. You don't need to say more now.

Saying too much might be a mistake. But thanks should be expressed, certainly. Use the year to find another position or use it profitably otherwise. Reexamine your options if you are still available in the future.


How to estimate cost of a course when price is quoted per semester but program has three semesters?

The program is designed to include two summers.  Spring, summer, fall, spring, summer, fall, spring.  That's two full years (spring, summer, fall constitutes one year) plus an extra spring semester. Here's the tuition cost for the 2019 cohort.

Here's the actual schedule in PDF format for the 2019 cohort.

What @SeanRoberson said is true in general but is irrelevant in this case.

$107,240 is correct.

(May I suggest you talk to their advising people to find out how feasible it is to work full time while enrolled in their program?)


What does top-tier mean when referring to journals/conferences?

Top tier can mean a lot of different things to different people - and indeed, can mean a lot of things to different fields. Ask a diverse group of academics drawing from math, health science, and the humanities what a "good" impact factor is sometime if you have the chance - the variability is massive.

Personally, for me, when I say "Top Tier" I'm usually thinking of soft factors - journals where solid publications go, venues that you'd highlight on the cover letter of a CV, etc. That often has an association with Impact Factor, but it's not necessarily fixed. For example, PLoS One has an impact factor that's about on par with several journals I'd consider "Top Tier" in my field, but PLoS One isn't on that list.


Should I add the "presenter certificate" to the paper presented at a conference?

As per the answer to your previous question, you are not required to spontaneously supply proof for everything in your CV, and it would look extremely unusual to attempt to do so in this case.

The fact that you could be asked to substantiate anything written in your CV, and the consequences of subsequently being caught in a lie, are considered enough of a deterrent to prevent people from lying about their credentials. The standard practice in academia is not to include "proof" of everything on a CV unless explicitly asked for proof of some kind.

So in answer to your question of whether you should merge the "certificate of being a presenter" into the paper presented at the conference as part of your PhD application: No, you should not. You should not submit such a "certificate" at all unless you are explicitly asked for it, and I have never heard of anyone being asked for such a thing.


Differences between lit review in dissertation and articles

The review section in an article is much shorter and much more stringent for two reasons.

First, the lit review in an article situates your own work within the existing body of literature. It explains the research puzzle from a theoretical angle, shows why your paper is needed and what exactly your contribution to the existing knowledge consist in. It may also introduce the theoretical concepts that you draw on (to the extent that this is not a separate section).

The review section in a dissertation does all this as well, but it also serves the purpose of demonstrating to your supervisors and committee that you are aware of and understand the relevant science. This includes literature that is more tangential to your actual contribution. By contrast, an article is about your contribution, not about your proficiency.

Second, you have much less space in an article to go off on any tangent. Thus you have to restrict yourself to the narrow literature to which you are directly contributing and on which your work builds.


Would I be spreading myself too thin / hindering my PhD project severely if i started working on a master's degree (2 years) in computer science as a free-time hobby during my PhD studies?

Everything else being equal and all things considered: YES! Unless you are specifically doing a part time PhD, a PhD is a full time job and there normally shouldn't be enough free time to take on master's level study in another subject. If you were my PhD student and you came to me with the idea of doing extra study unrelated to your PhD project, I would tell you it was a distraction from what you should be doing and could very likely lead to your PhD taking much longer than either you or I want it to. If you told me that you had a large amount of free time that you want to fill with academic study, I would help you find ways to apply that time toward your PhD so that you might advance faster on it.

Perhaps the best thing to do is to bring this idea to your supervisor and see what they think. They know you and your project, they will know if you are not being realistic about your available time.


How should I deal with being harassed by my supervisor in a non-work situation?

First, I would recommend that you put away any feelings of guilt and responsibility, and instead begin planning to protect yourself.  Unfortunately, it appears likely that your supervisor is a predator and abuser given several red flags in your story.  In particular:

Your supervisor waiting until you were impaired by alcohol before making unwanted sexual advances.  This is a massive red flag of abuse: safe and respectful people talk with prospective partners when they are sober.
Your supervisor appears to have sought an isolated environment in the midst of a group event where he could assault you and where you could run away without others noticing.
Your supervisor appears to be manipulating your interpretation of his sexual assault on you: you say things like "we are OK with this" (taking a collective view) and "I know that he thought" (taking his view) and "he is sorry" (how did you feel?) that indicate that your view of the situation is being strongly influenced by his view.  To be blunt: it doesn't matter what he thought or felt; what matters is what you thought and felt when you were sexually assaulted.  Making you feel responsible for his feelings is an abuse tactic.
It sounds as though your supervisor engages in grooming for abuse, by picking certain "favorite" students and violating professional boundaries with them (talking about personal issues).  Some people just have minimal filter with everybody, but the picking favorites is a red flag: abusers often do this in order to identify people who will be good victims for their abuse, and then may wait quite patiently for an opportunity to switch into their preferred mode of abuse.
Your supervisor chose to make a sexual advance on their student, over whose life they have a huge amount of power and control, rather than waiting until you were no longer their student and could be more of a peer as a partner.

Now, it's possible that your supervisor is not a predator and abuser, but that's a lot of red flags, including an actual sexual assault.  Furthermore, most abusers do not believe that they are abusers, and can often be very persuasive to others, including the victims that they ensnare.

So, what would I recommend that you do?  Unfortunately, the student/advisor power dynamics make this a tricky situation to navigate without doing harm to yourself and your career.  I would thus recommend that you start by protecting yourself and then find resources or otherwise get professional support to help decide how to proceed.

Never drink or otherwise impair yourself when you may encounter your supervisor, even if there are other people present.  He has isolated you for assault once, and may do it again.
Find some good resources on abuse and familiarize yourself with their information and recommendations.  One site that I would recommend as helpful is: http://www.abuseandrelationships.org/.  Even though you are not in a sexual relationship with your advisor, a) your supervisor just attempted to start one, and b) you are in an important relationship due to the student/advisor connection.
If you can, begin consulting with a professional therapist or counselor with a good reputation for helping victims of assault and abuse.  Having a trustworthy and professional third party will be very valuable for helping you get a clear perspective on your situation and figuring out what is the right path for you, as well as helping deal with any emotional repercussions of your assault.

Once you've taken all of those other steps, you will need to decide which of several paths you want to take, ranging anywhere from filing formal charges against your supervisor to quietly changing supervisors to simply protecting yourself and carrying through to graduation.  Unfortunately, all of the choices you make are likely to risk serious negative consequences to you, and only you (hopefully with aid from an experienced and supportive therapist or counselor) can decide which path and which risks are the best choice for your situation.


Given a journal policy that authors must share original data, am I free to use this data without granting original authors authorship?

I'm not a fan of "mandatory authorship" on published information: I feel that once something is published, one should collect one's rewards by means of citation rather than by strong-arming people into giving you an authorship.  Mandatory authorship on already-published data feels to me too much like a form of salami-slicing on a dataset.

That said, the journal's policy does not appear to say anything at all regarding authorship.  Therefore, the default position would seem to be that the authors must share the data with you (as mandated by the journal), but are also free to require authorship as "payment" for sharing.

The journal, however, may feel that this goes against the spirit of their data sharing agreement, and if so, then you may be able to obtain the data without being coerced into authorship.  I would thus recommend, like @BrianBorchers notes in the comment, that you write to the chief editor(s) and ask for a ruling.


Should I remind potential mentors to look at my graduate application?

It is not "necessary", but, if you are polite and considerate in your emails, at worst it won't hurt anything. Given the ease of application, most departments are deluged with applications, and it is easy to overlook (or forget to return to) any particular application.


Should I abandon an open math problem, if it hasn't been actively studied since the mid-1980s?

Based on your brief description, I'd say a more likely explanation for the lack of work on this problem is that people are stuck. Not that there's no interest in it.

Still, I wouldn't recommend this problem for a masters' thesis (or a PhD thesis). At least at the start, you should work on something manageable. If you hit a manageable problem or two out of the park, then you can start trying things professional researchers have attempted and failed.


Why do some tests have a (nonzero) minimum score?

According to the Encyclopedia of Research Design (page 629), it signals that these are interval variables, not ratio variables:

  Standardized tests, including Intelligence Quotient (IQ), Scholastic Achievement Test (SAT), Graduate Record Examination (GRE), Graduate Management Admission Test (GMAT), and Miller Analogies Test (MAT) are also examples of an interval scale. For example, in the IQ scale, the difference between 150 and 160 is the same as that between 80 and 90. Similarly, the distance in the GRE scores between 350 and 400 is the same as the distance between 500 and 550.

  Standardized tests are not based on a "true zero" point that represents the lack of intelligence. These standardized tests do not even have a zero point. The lowest possible score for these standardized tests is not zero. Because of the lack of a "true zero" point, standardized tests cannot make statements about the ratio of their scores. Those who have an IQ score of 150 are not twice as intelligent as those who have an IQ score of 75. Similarly, such a ratio cannot apply to other standardized tests including SAT, GRE, GMAT, or MAT.

Salkind, Neil J., ed. Encyclopedia of research design. Vol. 1. Sage, 2010.


Preparation for meeting the HoD will depend on the individual student's situation.

Students who attempted to warn the teacher of their non-attendance should document their efforts to do so.

Students who really could not attend should document the road closures and transit cancellations that prevented them from attending.

Minors who were told to stay home by their parents should get a note from the parents taking responsibility and explaining their reasons for keeping the student home.

Anyone who did not attend without a good reason needs to think about the wording of an appropriate apology.

Students who could not attend and made at least some effort to notify the teacher are in the strongest position. Even those should be apologetic about the group non-attendance if they encouraged it.

At the other extreme, I don't see anything other than an apology for a student who could have attended, chose not to, and made no attempt to notify the teacher.


Comments can only be updated by submitting a new version, even if the content of the paper itself has not changed. A new version can be submitted by selecting the "Replace" option against your paper. Further details can be found here.
Comments are a part of the metadata of the paper, and the idea is that the comments should reflect the situation on the date the article was submitted on arXiv. It is possible to update journal reference and DOI without creating a new version. However, as the help page mentions, these fields are appropriate only when you have the complete bibliographic information of the conference proceedings (if any) available.
Reference from arXiv (emphasis mine):

...
Why? To allow authors to make changes to the comments and other metadata fields of publicly announced articles without generating a new version, and hence date stamp, would effectively mean that all changes would be backdated to the time the last version was submitted. This is open to abuse and thus not allowed.
The exceptions to this rule are the addition of journal reference and DOI information. The journal reference field may contain only full publication information for the article; the DOI field may contain only a DOI.


Can a highly experimental paper with potentially controversial concepts published on a preprint server (not in a journal) damage one's career?

Imagine a paper which has unconventional ideas which could be controversial. Does publishing it on a preprint server have the same negative career implications as publishing in a journal?

Yes, potentially. You are making your thoughts and beliefs about a certain subject known publicly. Depending on what those thoughts and beliefs are, this can damage one’s career even if done in a tweet, email, stack exchange post (hmm...) or any other medium of expression. A preprint server is no different.

Or is a preprint server actually an appropriate place to get feedback on this type of paper?

A preprint server is an appropriate place to get feedback on scientific work that’s maybe incomplete but is very close to being complete. Nonetheless, the potential for career damage if the work is of very low quality or reveals you to be a delusional or incompetent person still exists. If that is a concern, consider looking for feedback in more discreet ways.


Is it necessary/useful to include the publishers in the list of editorial board memberships?

Unless you work in exactly the same area as someone else, you likely have no idea how good a journal is. For example, I know that the SIAM Journal on Numerical Analysis is good -- but is the Journal of Number Theory good? the Journal of Mathematical Sciences? But if I know that one of these is published by a professional society located in the US or Western Europe, then I can infer that it is likely a good journal; whereas if the journal is published by a company I've never heard of and that is located in Egypt or India, then I may have my doubts.

So, yes, I think it is useful to add the publisher.


What if the school asks the students to submit the letters themselves?

I had this experience as a letter writer (in France). I just sent my letter to the applicant and she uploaded it. My letter was very positive so I did not think much about the situation although it did seem weird to me.
I think in some US Universities (in California?), when you submit your letter, you should indicate whether you allow the applicant to look at it or not. I do not write bad letters so I always indicate that I do not mind.


How to negotiate with collaborators on adjusting procedures to interdisciplinary projects?

It seems to me that the problem lies on a psychological aspect of their lives and your way of questioning is triggering this response on them. Maybe they're insecure about their academic formation or have been challenged in the past in a way that made them develop a very defensive stance when questioned. My suggestion is that you change your way of obtaining this info to a more friendly one. usually lowering your guard creates the same behavior on others. You could go for something like "I have no knowledge about this. Could you please teach me X? I feel it's important for my formation."


Academic integrity question on self-referencing and changing a paper after acceptance

By my understanding:* You've presented some work-in-progress at a workshop, without proceedings. You have a conference paper accepted and you've been invited to make some minor revisions. The workshop presentation is built upon data used by the conference paper, but the methodologies are different. The workshop presentation drew a conclusion that you're contemplating including in the conference paper, albeit, that would change the narrative a bit. You feel that you made a mistake by not [citing the workshop presentation] in the conference paper. You're also concerned that not citing the workshop presentation would mean that you pretend that the improvement is bigger than it is, albeit, you're concerned that adding a new citation, which reviewers haven't seen, is very unethical. You're considering building upon your workshop presentation in the future and publishing that work later (and you consider this as the proper solution).

My thoughts:

You are under no obligation to cite your works-in-progress, especially those that are unpublished. That said, you may choose to.
You should not extend your conference paper to include new ideas - e.g., the conclusion you drew in your workshop presentation - since they haven't been peer-reviewed.
You could later publish your work-in-progress with citations to your prior conference paper. Alternatively, you could combine that work-in-progress with your conference paper to derive a journal article, the former aspect would be considered a new contribution (since it hasn't been published previously). In both cases, you could - if you wanted - cite your workshop presentation, since it presented some early results.

*I've summarised my understanding, since I'm not sure I've correctly understood the details presented by the OP.


For non-English-speaking countries: Can I use my PhD to prove my knowledge of English for a UK visa?

I went through exactly the same thing (PhD in France, all publication and thesis in English, diploma in French, I come from a non-English speaking country and don't actually speak French, then applied for a postdoc position in the UK and needed prove my level of English for my immigration documentation).
So, the answer is yes you can, but it will (likely) be very very slow. The procedure is as follows: You send in your diploma (with a certified translation, you can get those for about 30 euros). Unless you finished your PhD at a super-famous French University (think Sorbonne), you go at the bottom of a very long pile. This is for "previously unknown Universities" (to NARIC), the ones they have to check in detail. When inquiring, I was told that this would take at least 3 months. Knowing how much some of the gvt admin ground to a stop during the pandemic, I wouldn't be surprised if it took a couple of months longer at this time.
Normally I would recommend going for IELTS test. Despite them being quite infrequent (I am told there used to be more dates some 8-10 years ago), I only had to wait about 2 and a half months to take the IELTS (compared to "maybe 3+" for NARIC approval). It is also quite neat that there is a "scientific track" for IELTS, so the writing assessment is focused on describing and reading out simple graphs, which helps if your vocabulary is science-centred.
However, these are not very normal times. Right now, you might feel more comfortable waiting 3+ months for the NARIC route instead of travelling to take a 2-day test with a group in a small classroom, even if the latter is quicker. As far as I remember, price-wise it was about the same expense (not sure if that included my travel to take the test or not).


Can we submit comment paper to some other journal other than the paper's journal on which we are commenting?

It might be allowed from journals of the same editorial group (cf. example) if there's a scientific reason to frame the discussion in another journal (e.g. interdisciplinary publications and the comment pertains only one part). Aside from these cases, no.

In other journal is of course allowed to submit full fledge articles that critique or initiate a scholarly exchange with respect to a paper appeared elsewhere. The "comment" format, is specific to articles appeared in a journal and should not be placed elsewhere. It should also be timely, and be submitted within a certain time frame from publication.

You can find the rules specific of your case in the journal webpage and contacting the editor.


Should the presented points by different referees within the LoRs be convergent or divergent?

With due attention to the applied consulting with some experienced faculty members my final conclusion is that a mixture of the convergence and the divergence better be taken into account within the LoRs.

In other words, the investigator of the LoR is not eager to read all repetitive points about the applicant within the different LoRs, neither be distracted by the bombardment of the many non-overlapping points from different referees, will which not lead a coherent imagination from the applicant.


I Plagiarised, what punishment can I expect?

I am considering turning myself in, unless the punishment would be too severe.

You are describing an extremely serious violation of most university's academic integrity policies.  The most likely punishment is that your credit for those classes would be revoked, your grades would be changed to Fs on your transcript, and you would be suspended or expelled.  (That would certainly be the most likely result at my university.)

Nevertheless, I believe you should turn yourself in.

Ari gives a good summary of the ethical argument, but there is also a selfish practical argument.  Since you mention being caught once, there is good reason to believe that your work will face additional scrutiny.  If you get caught before turning yourself in, the result is much more likely to be permanent expulsion.  If you admit your plagiarism, the punishment will be slightly less severe; in particular, even if they decide on expulsion, the university will be much more likely to readmit you after 2-3 years.

Even if you decide not to turn yourself in, I recommend taking a short break from university, if you can afford it.  The amount of cheating you describe indicates that something is very wrong — maybe you were overwhelmed, maybe you were scared, maybe you were lazy, maybe the homework were insultingly stupid, maybe you just didn't want to be there — but something was preventing you from engaging in those classes as a responsible student.  You need to figure out what that something is and address it, or you'll just fall into the same pattern again.


What should I do about my non-English publications when applying to a University in an English-speaking country?

It depends on the language

The accessibility of academic publishing is not a binary of English vs everything else. Rather, one can think in terms of a continuum, with major world languages towards one end, and languages with limited global reach at the other. Moreover, this continuum is highly dependent on geography (e.g.: French is spoken widely in Africa; Spanish is spoken widely in the Americas) and context (literature, area studies, and linguistics are obvious examples, but by no means the only fields where languages other than English are very important). In assessing whether the language in which you publish is a "major" language for your purposes, consider:

is it one of the handful of languages used very widely in large parts of the world?
is it used widely in the publication's sub-field/specialism?
is it used widely in the field/specialism of the job/position for which you are applying?

I am based in the UK, and most of the literature I cite is in English, but my field has a lot of important literature published in German, to which I make reference (like many scholars in my field, I can read German reasonably well, although I would not describe myself as fluent). Some of my colleagues have published articles in German despite being native English speakers.

The point I want to make here is that publishing in English is not automatically more prestigious.

For the purposes of applying for a job in an English-speaking university...

it is important to demonstrate is that you are capable of publishing in English in a medium subject to peer review, and...

...translating your existing publications would be one way of demonstrating that, if you then publish the translation in a peer-reviewed medium (in my field, it is quite common for collected volumes to include chapters that are translations of work published originally in another language -- usually, these translations are done by a third party, such as the editor of the volume)
...writing a new article/chapter/book and getting it published in a peer-reviewed medium in English would be another way of demonstrating that, with the added bonus that you are enlarging your publications-list

publications in English are more accessible, but publications in other languages are still valuable, and...

...providing an English-language abstract is an excellent idea (in some fields, there are scholarly databases that do this for you)
...there is still a good possibility, if the language is used widely, that the publication will be read. When applying for a particular position, you could scrutinise the profiles of your prospective colleagues. It may be the case that one or more of them has published in your language, reviewed literature in your language, or translated literature from your language to another language. If so, there is a good chance that somebody would be able to read your publications.

so-called "internationalisation" is very fashionable in UK academia at the moment, many British academics take their obligations as global citizens seriously, and engage with non-English publications and...

...may value a colleague who has a track record of working and publishing in multiple languages (as long as English is one of them)

Conclusion

Since you have already written English-language abstracts for your existing non-English publications, my advice would be to concentrate on writing new publications rather than spend a lot of time translating existing ones. Having said that, if you have a particularly significant/groundbreaking paper, it may be worth translating that one into English (and into other major languages), ideally with view to publishing the translated version in a peer-reviewed medium (when you do this, make sure that you get credit as the translator of your own work). You may need to get permission from the publisher of the original version, but any decent academic publisher should be accommodating (provided that all parties sign a licensing agreement).