How much emphasis should be put on programming ability in a letter of recommendation for CS graduate studies?

Let us put aside the question of you vs. your letter writer, because the same question could apply to your statement of purpose.

The notion of "programming ability" per se is a bit of a red herring.  The problem is: how do you actually measure what a "good" programmer is?  The only meaningful answer that I know of is to illustrate what somebody has accomplished that required programming.  Any other assertion of programming ability, I regard as a red flag.  In fact, one of my litmus tests for whether somebody is a good programmer is to ask what languages they know: if they can readily and simply answer the question, they probably aren't a good programmer (the logic behind this: getting significant things done with software tends to, over time, involve being forced to deal with lots of random types of code in order to get things done).

Thus, I would recommend you instead focus on emphasizing what you have accomplished using programming.  This way, you will show not just "programming ability" but also personal organization, ability to accomplish difficult and complex tasks, ability to think in a computer science manner about problems, and other such qualities that actually matter a lot more for demonstrating your potential in a program.  If you did a cool and complex project in the class, that is what you should be talking about, with SAS and R being mentioned in passing as the tools you used.  If all you did was problem sets, well, I would have a hard time seeing how this could be a strong LOR in the first place.


A professional reference letter for pure math graduate school

That is of course always hard to answer, as we don't know you, we don't know what would be written in the letters, we don't know about the person reading your letters. Thus, the answer below is just my personal opinion, it might or might not align with the opinion of the persons in charge of admitting you:

I would go with the letter from your job. Your job is math related, the person writing the letter is working with math daily and she knows you better than the third professor. Thus, you would get a personalized letter instead of the generic "Andrew is a good student and passed my class with an A" that admission boards surely read way too often. Furthermore, it shows that you really enjoy math and not just study it to get a degree. With the right wording, this could show you as a really motivated mathematician; and every professor knows that to do a master's or maybe even a PhD in pure math you need tons of (self)motivation.

I wouldn't worry too much about the fact that she doesn't hold a PhD. On the contrary, she has been allowed to work and lecture at top universities without having one, that tells way more about her than a piece of paper saying that she wrote a thesis at some point in her life.
Oh, and if she already worked at top universities, maybe she also worked at the one you are applying to and has connections there? That would put her letter even above the two from your professors I'd guess.


How to handle research advisor meeting stress

It sounds like you're a new graduate student, and that you clearly care about performing well in your program. You stumbled, and you've accepted responsibility and looking for ways to correct the problem. That's great, and suggests that you will end up doing very well in your program. As a master's student, you're not expected to be able to work completely independently, and your professors will likely be happy to help you navigate your program (they certainly should). The key is to ask for help early and often.
I would consider scheduling an appointment with my adviser, telling them exactly what you've said here, and asking them for advice on how to prepare for meetings, and perhaps even advice on how to structure your independent learning so that you're learning the specific techniques/concepts that want you to know at each stage. Every adviser is different, so the best advice you can get will come directly from them. It may be intimidating to ask for help, but it is completely appropriate at this stage in your graduate education.


Can someone else publish a paper based on independently achieving a result that is in a preprint of mine?

Do you know that they were aware of the preprint? Scoops are bound to be common if many groups are working on the same problem or starting to flesh out a new area with lots of low-hanging fruit. If they were aware of your preprint, and you can prove it, they should have cited your preprint at the very least, and you might get them to publish an errata with the citation. But, if they didn't know about it, they got there first, and you'll just have to accept that.


Preprint on CV - should I include journal I submitted to?

No, do not list the journal you submitted it to.  Frankly, it means nothing: anyone can submit anything to any journal.

Of course, you want to your CV to accurately reflect how much work you've been doing lately, but there's always a chance that the paper gets rejected in the in-between phase.  A good enough compromise is to just post the arXiv info, when it was revised (this reflects that it's been recently reviewed), and perhaps "Accepted."  Once you get the proofs, you can change to "To appear in [Journal]."


Are multiple APA citations supposed to make the same claim or do they combine?

I'm not sure how fully these issues are part of protocol versus just style, but my approach is to try to be clear which works are cited for what purpose (Marks, 2011), which can include separate citations within a sentence (Edgar & Poppins, 1999).

For the example you have there, I would assume you are citing different studies that had different results, rather than three sources that say "there are mixed results": however, I would also expect the later references to refer back to the older results if they are in conflict. I don't think it's necessary for you you clarify any more than that, but if the results of those works are very important to what you are writing, you would probably go into more detail about those particular studies and cite them individually.

To add to my answer based on your additional question in a comment: the citations should be inside/before the punctuation in almost all cases. And I would typically avoid referring to the same work in more than one place in a sentence unless it really made sense to do so (i.e., chronology/natural order).

  Children like to play games (Ralph, 1967), as do teenagers (Harris &
  Brooks, 1985) and young adults (Ralph, 1967).

I wouldn't consider the following wrong, though, either:

  Children, teenagers, and young adults all like to play games (Ralph,
  1967; Harris & Brooks, 1985).


Thought Exercises in Deciding Whether to Stay in PhD Program or Leave?

Been to similar situation. Here couple of points:

Decision and Responsibility: You have enough personal reasons to leave. In fact, I'm impressed you figured it out in the first 6 months, which is a good thing. Here is the thing: You need to make a decision, and take the full responsibility for it. Other people in your research group, might have different agendas, and therefore might give you the answer which is good for them. Probably your supervisor spent decades in research and does not get you, or doesn't want you to leave, because he/she spent time and energy in the last couple of months to guide you through your early PhD stage. you see what I'm trying to say here?

Burning Bridges: If you decide to leave, this is your answer to your current situation, and other side effects are out of your hands. They are not your wife/husband that you need to take to your consideration. It is a professional decision you made for yourself. Good thing is, you are a PhD student and not a supervisor to leave number of students and their future behind.

Interaction To Your Supervisor: First have a meeting with your supervisor, and tell him/her, your decision. Tell him/her sorry for the situation created but you have to do what you have to do.

Interaction With Friends: You can also let others know about this, and wish them best of luck.


What do you do when you don't know how you came to know something?

For purposes of citation in a paper, all you need is some appropriate source where the reader can find the relevant information.  It doesn't have to be the same source from which you originally learned it - indeed, nobody really cares how you originally learned it.

So this comes down to general literature search techniques: check standard textbooks, find other papers that use the fact and check their references, talk to collaborators or other experts in the field, ask on CS Stack Exchange, etc.  If you can find the original paper that introduced the idea, that's ideal, but a textbook that gives a modern presentation is also useful, and you can cite both.

If the fact is "common knowledge" in your field, it may not be necessary to give a citation at all.  Again, if you're not sure whether that applies to this particular fact, you can ask other experts in your field what they think.

  It is considered very bad practice to search for literature about something after the fact that you used it in your work.

Says who?  Sure, if you're sufficiently well organized, it's nice to find references for all relevant facts as you use them.  But if you're not quite that well organized, or find that this would break up your workflow, I don't see anything wrong with going back to fill in references after the fact.  This is very common.


How to cite a specific organization in APA?

In the text:

  "This aggression will not stand," confirmed Bob Loblaw, attorney at the Texas non-profit organization Trial Lawyers for Public Justice (Loblaw 2018).

In the references section, you will write up whatever medium you found the quotation in, and TLPJ might or might not be explicitly mentioned.

If it is a blog post or technical report or such authored by Loblaw, hosted on the TLPJ site, you would have Loblaw as author and mention the organization only if it is in the overall blog name or as the distributor/publisher of the report.
If there's an unattributed press release from the organization, within which is Loblaw's statement, Trial Lawyers for Public Justice is the author to list.
But if Loblaw was quoted in a newspaper, say, then you cite the newspaper article in the references, and your text would be something like:

  "This aggression will not stand," confirmed Bob Loblaw, attorney at the Texas non-profit organization Trial Lawyers for Public Justice (as quoted in Lane 2018).


Are math grad students increasingly consulting SE and Wiki, ignoring research librarians and libraries, to their own detriment?

I think wikipedia is good for mathematics topics that are fairly settled. There are few errors and the ones that do appear (I've found some) tend to disappear quickly. You can get a good overview and if you follow up on the sources provided you can get a more complete view. So, I hope students use this for background on things they need to study.
But, by its nature, it is less useful to bring you to the state of the art: stuff that isn't yet "settled".
I think SE is the opposite, in some ways. You  might find answers to contemporary questions, but the sources may be less reliable. Wikipedia has many editors (formal and informal) keeping things right, SE, less so and not everyone commenting really has a good answer. So, again, I hope that grad students use it when necessary, but with caution.
If the alternative is to set for ten hours at a time in a library, pulling older and older books from the shelves, it is no contest.
But reading things and being given answers isn't the best way to gaining insight into a mathematics problem. Not deep insight, anyway. For that you need to do some work yourself.
And, as you say yourself, it is a professional approach to use such resources. You do it yourself. And, I would say "to the detriment", actually. It is a supplement and/or a place to start.


Sending several PhD applications to professors in the same university?

Your situation isn't that uncommon, actually. You have many options in front of you, and more than one appeal to you. There's no shame in that...

To answer your questions:

  How bad would it be seen if I sent applications to several professors?.

I can't see why this would considered bad. If anything you are excited about applying to projects. If you have a good portfolio/application, and if you don't look too desperate there shouldn't be much of a problem. Just make sure that your applications are relevant and fine-tuned for each position. Nobody likes boiler-plate applications spammed all over the place..

  Will the professors even find out that I sent applications to their colleagues?.

They may or may not, it depends on the requirement process (whether it's electronic/web-based etc) used by the institution, as well as the ethical considerations by these professors in question. If you are but a name to these people, what makes you think that they'll even recognize that you have applied to more than one position?

  How many are too many?

See the part above about boiler-plate applications, and spam. You don't want the person reading your application to get the feeling that you have applied to every possible position. If you can actually muster up a solid application to 15 positions, I say kudos and good luck! :)

But seriously, you don't want to come across as "I'll do anything, just pick me!" Take your time, think about your interests, strengths etc.. And submit one or a few strong applications to positions that are most relevant to you.

If you don't get one of your favorites, but your profile fits some other open position they'll likely call you in for an interview anyways. Especially if it's the same group.


Ethics of staying in PhD program with no intention of being an academic, and misleading my advisor about this

As a PhD student, you don't have to want an academic career. It's not unethical to pursue a PhD with no intention of staying in academia afterward.

But lying about your plans and deliberately misleading is wrong and unfair to your advisor.

You wrote:

  However, my advisor seems to be especially invested in making me a viable academic researcher because I am their first student and have used a lot of their startup funds. My field is also not typically industry-bound like, for example, engineering, so any reputation boost my advisor could hope to get from me is nil.

If your advisor is a new professor whose own career success really depends on graduating PhD students who go on to academic careers, letting them invest everything in you under false pretenses is obviously wrong and unethical.

It sounds like you don't really want to finish your PhD (I infer this from your "apathy for my subfield and academia in general"), and you think your advisor wouldn't want you to stick around for a few more years under the circumstances, either. On the other hand, finishing out the academic year - giving you time to look for a job, and giving your advisor time to find another PhD student in this application cycle, while you wrap up and publish your current work - sounds like a win-win. But you should tell your advisor right away, so that the two of you can make informed plans for the future.

I suggest you come up with a plan for preparing yourself for the job market during this academic year, then have that talk with your advisor, and make the most of your remaining time.

On the other hand, if you really do want to finish your PhD, tell your advisor that you're not interested in academia, but are interested in finishing your PhD and getting a job that takes advantage of your PhD-level research skills. (Many of the skills acquired by successful PhD students are fairly transferable.) Your advisor may be more willing to support you than you think - successfully graduating PhD students is important for new professors, even if the student isn't interested in academia in the end. But you need to let your advisor make that choice: lying to someone so that they will give you multiple years of research support just so that you can buy time to train yourself for an unrelated career, is wrong.


Application form for lecturer position provides a template for an academic resume, should I follow that?

There is nothing in the statement ``(an Academic CV template is available here)'' indicating this is a required format.  I would assume that most applicants would not use the template.
I suspect the template is there to help applicants.  Does it have a place for hobbies?  If not, probably you want to not list hobbies.  It does have a place for ``contributions to the university'' so be sure it is clear on your CV if you ever sat on a campus-wide committee or some such thing. Different cultures put in different things in a CV, but in this case you have a guide.
The fact that the template has separate sections for different types of service makes me suspect this is a generic format used for scholars at many ranks and many departments. There may be many sections any specific person would have blank.


Difference between research question and research objective

Although the specific formal definition can be field specific, Farrugia et al do a nice job of laying out "research questions", "hypotheses", and "objectives" in their open access article (linked above). Note their article targets medical researchers, but applies to other fields as well.

To summarize/highlight their definitions:

Research questions "arise out of a perceived knowledge deficit within a subject area or field of study." These may be answered either using literature reviews or primary research.
Research hypothesis are the formal ideas one seeks to test. (The linked article focuses on null hypothesis test, Chamberlin (reprinted in Science 1965, first published in Science in the late-1800s)) does a better job of explaining hypotheses. Chamberlin advocates for multiple working hypotheses where you have multiple competing ideas.,
Research objectives "should be coupled with the hypothesis of the study". These are what the study specifically seeks to do. (e.g., what is to be measured to test a hypothesis?).


How to treat a paper accepted at a conference and included in proceedings if I could not attend the conference?

If it's published in the conference proceedings, it's published.

You can list it as a conference publication in your CV.
You can't publish it again in conference proceedings.
Regarding publishing it (or an extended version) in a journal, see Under what circumstances can one republish a conference paper/presentation? especially this answer.


Can authors email you for free PDFs of their textbook sold for profit

I am the author of a textbook. The book retails for $50. I get 50cents for every copy sold.

I do not own the copyright on the book and it would be illegal for me to sent you a copy, even if I had a copy to send (I mean, I have the original word documents, but the final PDF looks nothing like that).

The book has been scanned, and when it was not so old I know that copies of it did float around Pirate Bay. I wasn't particularly upset.


For planning purposes you'll want to carefully read the program announcement from the NSF to see if they state a policy on deferment. For instance, in Instructions for Preparing and Submitting
Mathematical Sciences Postdoctoral Research Fellowships (MSPRF):

  The postdoctoral appointment must start between June 1 and October 1
  of the year of the award.

The GRFP guidelines (for graduate students - not a post doc), just to show another example and outline the NSF's typical policies, has a similar provision:

  May I defer my Fellowship?

  No. There is no general Fellowship deferral - only approved Military
  or Medical Deferrals. Deferrals are different from Reserve years.
  While on deferral, a Fellow's clock stops, i.e., the remaining time
  available for Tenure or Reserve periods is not affected. Reserve years
  are counted in the 5-year period allowed for the Fellowship.

Regardless of published policy, "you can always ask", as there may be some special exception granted because of your particular situation and proposal. But the official policies will give you a reasonable expectation of what to expect - if they say you can, you can, but if they say you can't, you might not be able to (but it's not utterly impossible - just less likely).

If someone who has been in a similar situation and requested a deferral (even against stated policy) could share their experience that would be even better, but the official printed guidelines is always your best starting place.


Can I use only one of my two last names for publishing?

You can use any name you like for publishing - even a pseudonym. You are wise to consider the future so that publishing will always be under the same name, simplifying searches and keeping the maintenance of your reputation simple.
In some ways, keeping a birth name as your official "professional name" is the simplest for most people.
And people who are active in more than one field, might want to use different names in those fields, just as novelists often do.


Consequences for foreign students of being dropped from a class?

My wife, who has some experience in these matters, says the following:

If the student is dropped from the class, making them no longer a full-time student, then they may lose visa status and be required to leave the country within days.
If the student fails, however, then it is up to the college whether to kick them out or not: so far as immigration is concerned, what matters is whether they are a full-time student, not how well they are doing.

Another possible option, which may or may not be possible in your institution, would be to try to arrange a late transfer into another "class" like an independent study, which would have no transcript value but would preserve full-time status.


Can an undergraduate attend a conference without a supervisor?

The answer is "yes", in that I'm not aware of any conferences that have any rules prohibiting unaccompanied undergraduates (or, indeed, recent graduates - congratulations!).

With that said, depending on the conference in question you might get more out of it by talking to somebody from your university who is going and spending some time in their company. They might be able to introduce you to interesting people, you might learn by being in conversations with them, and they might be willing to provide context for what you hear. (but do remember that they are there primarily for their own reasons, not for your benefit!)


Master’s in computer science or free online classes?

What OBu said: This is going to depend on what your goal is.

If you want to work as a programmer, generically, then a MOOC might be a good way to skill yourself up. As far as studying, fundamentals are going to pay off no matter where you work: Algorithms, Software Engineering, Math, etc. The problem with MOOCs is that it's not clear if they are going to get you through the door when job hunting; so be sure to focus on creating work that can demonstrate your skill, and help get you over that barrier.
If you want to create research, write papers etc, then you could always try to create your own research program. Having said that, if you don't have an established history of auto-didacticism then this is going to be difficult to maintain. A real masters program helps guide you down paths, and force you to prune those search trees.
If you want to work as a programmer, in the NLP/MT/AI fields, then you might have to do both: MOOCS and an MSc.

A side note; be warned that there are lots of MSc. programs out there, varying in style and quality. Some are essentially just more courses, while others are intended to produce new research. Be sure that the MSc. program you register for is going to get you what you want. Do your research.


How to overcome fear of answering/asking questions in big class

There are several difficulties you're dealing with:

It is genuinely not easy to formulate and ask a good question. You know how they say that a good question is more than a half of the answer. That's why it is so important to learn how to ask a question and how to split a question in several smaller questions.
You usually do not have a lot of time in class as the lecturer tends to move on quickly. It is harder to come up with a good question in limited time.
Other students are also present and you may feel that they are "smarter" and they are "judging" you. Whether this is true or not, is another question (spoiler: it's probably not true), but the perception makes it harder to act.

Now, what can we do about it? My suggestion is to decouple the problems. First, start by learning to ask a question outside of the classroom setting.

As soon as you have a question in a class, write it down on paper. After the class, re-read it, and try to find the answer yourself. Try also to re-formulate the question in a more clear, concise and answerable way.
If your professor offers office hours, attend them and ask your question in person. Talking to your professor one-to-one will help you both to learn the subject and to learn how to communicate more efficiently. It will also improve your confidence and build a good relationship with your professor.
When you are ready, ask more questions in class. Write down professors' answers and (if you have time) note your own reaction. Hopefully you will find it easier to ask questions as you do it more often. If not, meet your professor and discuss your questions again.


What are the things you feel that you should have known before your first postdoc position?

Answering the question in the body (about you) rather than the one in the title (about us, it seems?):

Work on developing your own research agenda. Try to move away from the work model where your advisor tells you what to do and you do it, which is often (although not always) the modus operandi during Ph.D.; and towards asking your own questions, developing and honing your own taste of topics/techniques/areas, mapping in your mind the important and promising directions in your field, etc.

Obviously, in doing so, clear communication with the advisor about their expectations and your goals is essential. E.g. some people like to keep their postdocs on a shorter leash than others, or may have specific obligations to the funding body regarding your research.


Does D2L have a way for the instructor to access my submission while it appears "unread"?

I don't know about D2L specifically, but some software can have issues with properly recording whether some has been read. It is possible for example with some systems that if someone has Javascript not enabled they may be able to  read a file without getting recorded as accessed.

That said, if this isn't happening, the best thing may be to talk to Department Chair, and ask them to keep your concern anonymous. This will help minimize the chance of blowback/retaliation to you since the individual will not know you were the one who complained.  It may also make sense for similar reasons to wait until the end of the semester before talking to the Chair.


Is it acceptable for professors to plagiarise material for an academic textbook?

Replicating large portions of material from other books without permission; copying major portions of published work without citation -- this is blatantly plagiarism at all angles. This is downright unacceptable unethical practice.


Should I mention while applying to another PHD program that I have resigned from another one

Reading through some of the previous posts the OP has posted in regards to leaving a PhD program, it seems that the main issue is that the assigned advisor was perhaps combative and difficult to work with. I will proceed with this being the assumed reason for leaving the previous PhD program.

First of all, it would be overall wise to briefly mention in an application that you were a former PhD student elsewhere. Omitting any mention of having been in a previous program will likely come back to haunt you. Thus, the question is not so much if you should disclose having been in a previous program, but how you disclose it.

Stick to the facts, not ad hominem arguments or accusations. Universities will usually avoid applicants who bad mouth their previous program/advisor. Even if your previous program caused major issues for you personally, you never know what buddies your former program may have at other schools.

I would simply indicate which classes you took, the grades you received, the research you performed. If you are able to attach indications of strong and positive work during your first year as a PhD student, this can certainly bolster your application. Obtaining a letter of recommendation from someone in your former PhD program could also be a strengthening point of your application.

All of this being said, you will need to be prepared to answer the question as to why you left your previous program. My advice in that regard is to pivot this question into answering why you want to join the program you are applying to. Be ready to be very specific. Mention specific professors and what you like about their work (which means you need to actually know about their work). Insofar as is possible, pivot everything to speaking of future positive work, not previous negative experiences and shortcomings.


How to sort search results from SCOPUS or Web of Knowledge by number of citation in a specific field?

There is no automatic solution to this - it is an extremely time-consuming labour, sometimes performed by bibliometricians - and often only by those with access to full editions of either database (not the web-interfaces, with strict limitations to download sizes).

It is also a tricky subject, as the defionition of e.g. a statistics paper may differ from what you are actually looking at: journal categories. Papers on any topic are also published in journals not directly related hereto, there are plenty of translational and multi-disciplinary journals as well - in other words, what may appear to be a trivial task is actually very complex.


Should I cite logos and clip-art in my thesis?

You should cite anything you use, and you should make sure that you have an appropriate copyright license for any material you do not own the rights to. Look for Creative Commons and other pre-licensed materials to use in your work.


The mathematical community often considers a very short, highly focused paper to be a note.  A few journals officially categorize the papers they publish into notes and full papers, but usually no formal distinction is made.  There is no clear dividing line between these cases in general.  Typically it comes down to the author's intent: a note is just meant to record some observation in the literature, even though it may not be important enough to justify a lengthy or detailed paper, while anything else is a full paper.  Nash's paper would probably not be considered a note, even though it's short and focused, because it's too important (and arguably wouldn't have benefited from being longer).  The Watson and Crick paper is not so relevant, since papers from other scientific fields have completely different length distributions from mathematics papers.

I'm not fond of the term "true research paper" in the referee report, since it suggests that there's a clearer distinction between notes and papers.  But what the referee means is simple: you have found something worth recording as a note, but not yet enough to justify the length of your paper (in the referee's opinion).

  Lastly, how does publishing a note vs a research paper affect a scholar, e.g. prestige and/or income?

The prestige depends on the note/paper.  The ceiling is vastly higher for papers: the world's best papers are far more impressive than the world's best notes.  If you are looking for a job at a major research university, then publishing a note might help a little, but ultimately you will need to have really good papers.  On the other hand, there are plenty of mediocre papers out there, and a good note can be better than a not so good paper.

As for income, the relationship between publishing and income is tricky.  To the extent your publications help get you a job, promotion, or raise, they can make a real difference for your income.  Aside from that, you won't make any money from them.  In any case, it's difficult to quantify their effect on income.


Necessity of tenure for lifetime academic research

The reason is simply that possessing a tenure-track faculty position (and then obtaining tenure) is the primary performance indicator for long-term careers at most institutes where research is the primary responsibility.

There are some exceptions - some universities offer a research professor position: you pay your salary from grants you secure, and as long as you do that you can continue working there.

You can also work as a lab manager/research scientist in a university, which is a term contract that is extended based on merit.

Some private research institutes (Google/Facebook/Amazon etc.) offer research positions (that are highly competitive and well-paid), but there are also many other private research laboratories that offer a similar deal to what you describe (though in that case your research needs to be focused on what these institutes care about, and is not entirely up to you).

I'd also mention that tenured professors are still expected to be productive and get grants. Though it is more difficult to fire them, becoming completely inactive for no reason is probably not going to be good for your long-term career. In other words, to some extent tenure track faculty face the same agreement, especially when they're not tenured yet.


Can mathematical ideas applied to CS problems count as "undergraduate research"?

Undergraduate research is whatever research that you do as an undergrad, period. So if you do something that ends up being publishable, or feeds into another research project in a real way, it's undergraduate research.

However, for practical purposes, you want to get some faculty involved in your research project. It will help with funding for travel (you do want to submit to conferences rather than journals in CS), it will make the work better, and you will end up with a good letter writer afterwards. And if you think your project won't be interesting to faculty in your current school, what makes you think it will later on swoon an admission committee?

  would it look good (to future graduate schools to which I will apply) if I, for example, write a paper or two based on things I do applying mathematics to Computer Science and programming, e.g.- solving optimization issues in GPU processing of large data sets, etc?

Sure - if the paper is good. Solving optimization issues does not sound bad at all to me on first glance, but of course it is impossible to tell without seeing the paper or knowing in much more detail what you would want to do.

  Even if the papers aren't so interesting, would it at the very least look good on my "resume", so to speak?

I guess that depends on what you mean with "so interesting". It does not have to be A* / Transactions level quality, but the paper certainly needs to be published in a reasonable, peer-reviewed, non-spam venue. Papers in pay-to-publish OA journals don't help at all.

This seems to me to be an unfortunate side effect of the "prior research experience required" mantra that many admission committees nowadays seem to have - many students seem think that sending crap papers to pseudo-venues will help them get accepted. They don't. A paper that is substantially below the level that a prof. would want to submit himself won't help you.

  For the record, I'm hoping to go to graduate school to study mathematics, not computer science, which is why I can't quite answer this question myself.

If you want to continue in maths, a maths paper will help more than a CS paper. Still, a good CS paper will be much better than no paper at all, I suppose.


How to justify selection of existing algorithm for a new application area?

There is a pretty standard method in my area of research for design of experiments and I have discovered that one step could be automated to save time. The automation can be done with a variety of standard machine learning algorithms and I've selected one that:

It sounds like you are working out a problem in your field that has never before been addressed using machine learning algorithms, and you are the first to try this approach.

  is used pretty often, according to literature
  provides very satisfactory results (high accuracy) on my data

The application of such machine learning algorithm has provided you good results, where I assume that good means at least good enough as the state-of-the-art in the field.

  My question is, how could I rule out the alternatives or at least justify my choice (for example, in the "related work" section) against other algorithms that could possibly work better/be more suitable?

If my assumptions above are correct, then your paper's main contribution is to solve a known problem in a novel way. This is sufficiently good an achievement that does not need to be justified. It sounds like your only problem is to convince a community of academics that are not normally exposed to machine learning, that your choice is reasonable (NOT optimal) and your results robust.

In machine learning - both in academia and in industry - you often find yourself
using a model that is good enough: it does not have to be the best, nor the most complex; what has to do is do the job correctly and provide interesting results. All you have to do in your paper is then to explain the algorithm and show why the results are robust.


Is it okay to get partial funding for a conference from two institutions?

I would say you could apply, yes, but you should mention that you also applied for the other funding. To make sure that you don't run into problems, I would first discuss it with the responsible people at both institutes, as the rules might differ from conference to conference, institute to institute, depending on country, etc.
Then, I would write down a short statement of cost. For example:

Flight:  500
Hotel stay: 350
Conference fee: 100
Meals (if not included in hotel cost): 50

Total: 1000.

For this cost, student ... received partial funding from institute A: XXX and from institute B: YYY.

Make sure that $XXX + YYY \leq 1000$ and then have both institutes sign it. This should put you on the safe side, as you can use it to prove that both institutes knew about the other partial funding and that you weren't "overfunded". Of course it would be best to have an estimate of the costs beforehand and to discuss these things also before you receive money, so once again: Go talk to the people responsible.

And I hope that it's clear that you should, under no circumstances, get overfunded here. Don't risk it for a few bucks, this might strongly backfire once someone finds out.


How should I interpret a book editor not responding to me after accepting my chapter proposal?

Your clock is running faster than their clock. They have a lot of people to coordinate with and a lot of editorial work, I suspect.
This isn't the only publication they are dealing with, most likely. And if everyone is sending them mail every few days it just bogs down the process even further.
It may even be a good thing that it is taking time. A predatory publisher would be after you quite quickly for payments.
Perhaps you should just relax.


What are these mathematical groups in U.S. universities?

Mathematical research groups are, as you seem to have surmised, just groups of faculty members and students (i.e., graduate students, postdocs, tenure track and tenured professors) whose research interests all involve some common subfield of mathematics. Thus a number theory group will be composed of number theorists and perhaps faculty members whose main interest is in some other area of math (e.g., combinatorics) but involves number theory in a substantial way. Continuing with the example of a number theory group, at some schools all of the members of the group will be involved in the same flavor of number theory (e.g., the group might be biased towards arithmetic geometry), while at other schools the group might have people representing many different area of number theory (algebraic, analytic, arithmetic geometry, etc).

So what is the purposes of these groups? Well, they're just as much for the faculty members as they are for students. As you mentioned in your post, students in a research group are likely to hang out and talk math with one another. (You'll also be taking a lot of topics classes with the other students in your research group.) The same goes for faculty members. If you're a professor working on a project it's very nice to have someone who works down the hall from you that you can ask fairly technical questions to. (Or perhaps "stupid" questions whose answer you don't know but feel you should.)

Research groups will also generally have their own weekly seminars. Sometimes these seminars have a lot of talks by the faculty and students at that school, while other times the speakers are primarily visitors from other schools. This gives graduate students the opportunity to see what sort of problems people are working on at the moment and a bit of perspective about the nature of their research area that goes beyond the particular problems that the local professors are studying.


Advice for somebody who considers to join a PHD program in order to go to research about the possibly negative sides

There are some 2008 statistics on PhD completion at Ph. D Completion and Attrition

The ten year completion rates vary drastically by field: 62% for Chemistry but only 41% for Computer Science.

Part of the variation may be to do with the availability of attractive jobs that do not require a PhD. I personally knew at least one person who came to work for my employer as an operating systems developer after starting a Computer Science PhD and deciding it was too theoretical for his taste. He didn't need a PhD to have a successful career in his chosen field.

From reading questions here, the anecdotal evidence is that the worst pain is among those who are very strongly committed to an academic career, and therefore cannot do what the OP did, walk away "without big damage to my life, career or psychological health".

The OP, and especially the OP's friend, need to balance the problems with the joy and fun of immersion among people who share your enthusiasm for a particular field. A PhD may be the right choice for the friend, even though it was not the right choice for the OP. People are different.


Is it unethical to not give feedback on final exams or assignments?

I think there's a distinction between automatically providing feed, and having access to feedback.

Like many people, I give little to no feedback on final exams for basically the reasons you describe: students don't have a chance to see it until the next semester, and very few of them bother to.

On the other hand, when a student does come see the exam, I'll spend a few minutes answering questions and explaining the grade. I think this is necessary, because students should have the option of asking for  mistakes or inconsistencies to be corrected, and they have no way of doing so unless they know why they were marked the way they were.

Many of the accusations of unethical behavior in the discussion on the question you linked to seem to be driven by concerns about the latter issue: the suspicion that students wouldn't have access to any feedback if they requested it, and that this was an intentional attempt to prevent students from appealing their grade.


Is it possible that I can get a Duke University user account to access math videos?

As a commentor wrote, "ask Duke". In practice, that means the following.

Note from the URL that the page is maintained by the math department. If you can, try to figure out who specifically is maintaining the webpage (i.e., a person's name), and contact them. Otherwise, I'd recommend writing to anyone in a position of responsilibity in their math department -- say, the graduate director. Tell them that you are interested in watching their videos, and ask if there's any way you could be permitted to do so.

The most likely outcome is either that they say no, or that you get no response at all -- but in my estimation it's okay to ask, and they might say yes.


Should I cite a paper that I haven't read if I use a theorem in it?

It depends how well-known and wide-spread the result is. If by now it is a very well-known  result and the publication already happened quite some time ago, it may not be necessary to quote the original paper.
In doubt I'd quote the article and the books, or at least one of the books. A possible formulation could be:

  The result below is due to Paul [reference to article]; we recall it in the form given in a monograph by Miller [reference to book].

I do not think it is necessary to have read the original paper to be entitled to write this. If it is not too much work to track it down, it could still make sense to at least take a peek at the article you quote.


How did someone receive an arts degree and then become a scientist?

The thing to remember is that an individual is more than their degree classification.

Every person has their own interests, hobbies, skills, and personal projects.  While a BA in one field may be an indicator of a person's interests, it does not mean that the person in question knows nothing outside of what was required for that degree.

For example, it is very possible that a person receiving a BA in philosophy may:

enjoy a STEM discipline, leading them to take classes in it for their own enjoyment
enjoy a STEM discipline or topic and choose to learn about it on their own
end up in a job that requires that they learn skills that are applicable to a different discipline
apply to graduate school for a STEM discipline and be willing and able to invest the time to catching up on the material
be naturally gifted at whatever the STEM discipline is

Most likely, in cases where people change disciplines, it's a combination of several of the above.

Anecdotally, I got a BFA, but continued taking calculus as a free elective in my undergraduate degree.  I had to learn programming for work after graduating and ended up in graduate school for Computer Science.  I entered graduate school with the knowledge that I would need to work at least twice as hard to catch up on the material and just went ahead and worked at it.

It may be completely different in other countries, but even in those countries, I can't imagine that anyone is completely limited to only knowing things that are required for their degree.  There are a lot of situations that can force you to learn new skills, and that's without taking into account that some people have hobbies that are cross-discipline.

Another way of looking at it is: would you be surprised if a famous physicist played the violin well enough to perform?  There's no logical reason why someone who plays the violin shouldn't be able to do the same the other way around.  Both require a progressive learning of skills and a large time investment, unless you're naturally gifted.


Do generous donations to U.S. universities influence STEM PhD admissions committees?

My guess is that this probably happened at least once, but that it is rare, and for it to have a non-negligible effect on admissions is very rare.  Let me give a few reasons:

1) Admission for an undergraduate program at a US university is a very different process from an admission for a graduate program at the same university.

In the former case, most of the people handling admissions are admissions officers: these are staff members of the university that are in direct contact with the administration.  They also meet students and parents of students in large quantities.  They have a variety of motivations for admitting students, and they admit such a large number of students that any one admission decision could be chalked up to breadth / desire for (e.g. geographic) diversity / individual taste.

In the latter case, all of the people who are materially involved are faculty (usually tenure track faculty) in the department.  As a tenured faculty member in a research university, my communications with students' parents outside of a quick handshake at graduation day (if I attend, which I most often do not) are exceedingly rare.  When we admit a student into a graduate program, it's because we think that they are (i) likely to successfully complete the program and (ii) likely to be more successful than other students whom we did not admit.  One wrongly admitted student can really drain a lot of departmental resources.

In some STEM fields, admissions are not even done by a committee; they are done by the PI who wants the student to work with them.  Whether this situation is more or less susceptible to generous family donations, I can't say.

2) The idea of a "legacy student" makes less sense at the graduate level.  In most cases that I know about, large donations to universities are made by alumni of that university.  Moreover, a successful alumnus of university X often wants their children to go to university X, spends a lot of time telling their children that when they are growing up, is a generous donor to university X over a period of many years, and so forth.  It is less likely that a child of someone who attended university X is going to want to attend a graduate program in university X: the best graduate programs in a given academic field are only mildly well correlated with the best undergraduate programs.

3) While it is very surprising to many, there really is infrastructure in place for "legacy admits" to undergraduate programs at many universities.  There is no such infrastructure in place in graduate programs, so far as I know (certainly not in my STEM US graduate program).  Most faculty are by nature highly independent and not very amenable to being influenced by administrators.  In fact many faculty are quick to spot the possibility of influence and push back against it.  If a dean in my university came into my office and told me (I am the graduate coordinator of my department) that a certain Mr. Y was the son of an extremely generous donor and that I should take that into account accordingly...well, suffice it to say that I would have to steel myself not to allow that to have a negative effect on Mr. Y's admissions.

However:

4) At the graduate level, the decision is not just admit / reject, it is admit with funding / admit without funding / reject.  Most departments do have lower standards to admit students without funding.  If someone came to us and said "We'd like you to admit this student to the program.  His funding will be totally covered for as long as he's here.  Moreover, we will give you [enough money to be able to fund another student, say]" then...well, this has certainly never happened.  But would we give it some consideration?  Probably we would, if the student had a broadly suitable background in absolute terms.  In the field of mathematics in the US at least, being a graduate student and paying your own way is not a position of prestige.


There are many formal roles that generally fall under the category of "post-doc":

The simplest is as a post-Ph.D researcher working with a faculty mentor and doing their own research
Some postdocs have a role as "lab manager": they help with advising students.
In addition, if given an appropriate title, a postdoc (as "visiting/research faculty") can write their own grants or collaborate on grants that might support them.
The limit of the above is a pure soft-money position that is not "supervised" by a faculty member. Such faculty are also often called 'research faculty', and may be many years away from a Ph.D
In wetlabs, a postdoc role might also be as a lab technician or lab manager, handling supplies, tech work (making knockout mice for example).


Include content in my PhD thesis from my paper whose content previously appeared in the PhD thesis of one of the coauthors of the aforementioned paper

Just be honest: Be clear who contributed what. (And follow institutional guidelines.)


This is more in the realm of opinion than fact, but I would always use the affiliation. This gives the reader a bit of context that will most likely increase your credibility. If the reader is open to believing what you say even before beginning reading the paper the mindset will be different than if it is just a bit of work by a random, completely unknown person.

Of course, once you become Stephen Hawking the affiliation is no longer needed.

But for the rest of us, knowing that we did the work as a faculty or staff member at the University of the Universe (or whatever) will give us that opening that allows a fairer reading of the work.


Fellow student asked question from take-home exam on Stack Exchange

Let's be clear here. From your description, the student clearly cheated by violating the take-home exam's stated policy that (quoting from your comment on @user2768's answer) "it is prohibited to ask anyone for an answer". Thus, your question reduces to the generic question of "should I report a fellow student who cheated?", to which the answer is "yes", as discussed endlessly on many previous questions on this site, e.g.:

Is it okay to report classmates cheating on exams?

Is it reasonable to report another student for cheating when it has no impact on me?

When is it acceptable to report classmates who cheat on an exam?

Should I report cheating to my professor? If so, how?

One can debate (as some here are doing) the viability of take-home exams as an assessment tool, since such exams create relatively easy opportunities for cheating, but that is besides the point. The student cheated, and should be reported. The "moral dilemma" you are referring to is a completely bogus one created by the outdated cultural conditioning that exists in many societies according to which "ratting people out" for bad behavior is morally wrong -- see my analysis of this issue in this answer.

Edit: I noticed that you wrote in a comment that “his account is filled with questions related to assignments in different courses”. Thus, he is not just a cheater, he is a serial cheater, which makes the case for reporting him much stronger. I suggest saving evidence of his cheating (screenshots etc) before reporting to prevent him from hiding his wrongdoing by deleting the questions.


How to build relationships with professors in such a way that results in good letters of recommendation?

Strong recommendation letters come from professional relationships, rather than personal relationships.  Of course, the two are often related, but if a professor hasn't seen much more than getting an A in a class from a professional perspective, then they can't say that they have.  A wise and helpful faculty member will warn you of this fact in advance, but faculty are human and many may not be wise enough or  helpful enough to give an appropriate warning.

The canonical answer, of course, for getting a good recommendation to grad school is to work with a professor on an actual research project.  What you actually need, however, is for a professor to be able to speak to your potential to become a good researcher.  Even working on a research project will not necessarily demonstrate that, if your role is as a cog in somebody's machine (a friend once worked on a research project as an undergraduate where her job was literally to grind rocks into powder with a mortar and pestle: the project was awesome, the job they wanted done was not).

What does research potential really consist of?  In my experience, research potential means:

Creativity in approaching difficult or ill-defined problems
Initiative enough to accomplish hard work work independently
Skill enough to solve complex problems effectively
Intelligence and background enough to acquire new skills when needed
Social skills enough to do all of these things as part of a team (semi-optional)

There is another excellent way besides actual research projects to demonstrate all of these as an undergraduate: project-centric classes.  Many graduate or upper-level undergraduate classes have an large optional or required capstone project.  When you take on such a project, it gives you a chance to do something really cool, above and beyond the base minimum.  With a good project, you can demonstrate all of these qualities to your professor and provide both the evidence and the motivation to write a really good letter.


Publishing dissertation with ProQuest and include CC BY-SA 4.0 images

Presumably the question is whether the "sharealike" requirement of CC-BY-SA would "contaminate" the copyright of the dissertation. If you are OK with having your dissertation under CC-BY-SA, and your university and advisor are OK too, it is not really an issue. (Your university and/or advisor may impose restrictions on what goes into your dissertation. Follow them even if unrelated to copyright and even if they seem nonsensical.)
If not, in the US (and most Western jurisdictions), there is some form of "fair use" doctrine under which critical discussion allows to reproduce otherwise-copyrighted material, sometimes with a particular notice, indication of source etc. Under this, whether the image is CC-BY-SA or any other license (or no license at all) is irrelevant - you reproduce it under fair use or the local equivalent. Again, check your university is OK with this.
(On a side note, many scientific journals will refuse that you reproduce graphs from other papers without written permission, even though that use would usually satisfy fair use requirements. That is because being sued is costly even if you are guaranteed to win.)


How much do European PhDs care about GPA?

There are a number of relevant differences between North American and European PhD programs. First, it is key to note that practices differ greatly from country to country. The following answer will focus on general trends across Europe, but be aware that there will be exceptions.

One big difference is that in Europe you generally would not be applying to a PhD program, but for a specific position with a specified group/professor. As such there are typically less requirements set by a graduate school (such as a minimum GPA) to deal with. Since there is typically only one position to fill, the hiring tends to be more risk averse, and things like recommendation letters become more important than pure grades. People will still however look at the grades and a 2.0 GPA will certainly raise some eyebrows.

Another difference (also mentioned in other answers) is that in continental Europe, it is typically expected that PhD applicants have already obtained a Master's degree. It is very unlikely you will be hired without a Master's. The only exception to this (I know of), is the UK where it is more common to start a PhD directly after the Bachelor (and PhD's have a short nominal length of three years to boot.)


Geographic differences in bioethics and effect on experimental research in biology

The short answer to your question is yes, there are differences in local laws related to bioethical concerns in different countries (and even different states in the same country).

For example, consider the difference in local laws related to stem cell research. According to Wikipedia (I don't know how up-to-date this is):

  These laws have been the source of much controversy and vary significantly by country. In the European Union, stem cell research using the human embryo is permitted in Sweden, Finland, Belgium, Greece, Britain, Denmark and the Netherlands; however, it is illegal in Germany, Austria, Ireland, Italy, and Portugal. The issue has similarly divided the United States, with several states enforcing a complete ban and others giving financial support. Elsewhere, Japan, India, Iran, Israel, South Korea, China, and Australia are supportive. However, New Zealand, most of Africa (except South Africa), and most of South America (except Brazil) are restrictive.

More broadly, the International Compilation of Human Research Standards (compiled by the U.S. Department of Health and Human Services) lists relevant laws and guidelines on human subjects research around the world.

Regarding

  does it mean that e.g. in Israel (Jewish culture) it is possible to carry out experiments forbidden in India (Hindu culture)?

Civic and legislative systems are highly complex, as are the degrees and the ways in which they are affected by cultural and religious influences.
So reducing Israel to "Jewish culture" and India to "Hindu culture" is not a particularly useful way to reason about what is permissible in each country.


You could add a note to the figure caption as follows:

  Figure X: [figure_caption ...] (This figure is based on work by Foo
  Bar 2016).

In addition to the citation in your text, you can also add a proper citation in this note (using your citation style of choice).


Clarifications needed: UK research positions

Re the middle point: on anything but a casual labour contract, "at-will" employment does not exist in the UK. You cannot be fired by your employer without a reason, although note that many of the protections do not kick in until you have had a certain number of years in the job, and hence may not apply to fixed term contracts (IANAL).

From the employee's side, legally, there is nothing to stop you leaving at any time, after the period of notice specified in your contract. That does not mean that it might not have career implications - but I will leave that for more experienced people to discuss.


Classroom participation – is there a gender issue?

One part of the difference is not that women are different in their willingness to ask questions, but anyone visibly different is. I was an undergrad in a class of 44. There were 4 women: two of one visible ethnicity, and two of another. My hair was a different colour and length than the other woman of my ethnicity. This meant everyone knew who we were. If we were late, asked a question that showed we hadn't been listening, or did anything else, everyone knew who did that. In contrast there were 5 or 6 white guys with short dark hair and football player builds who wore leather class jackets and sat at the back. There were 5 or 6 guys of several other ethnicities, and 5 or 6 nerdy glasses-wearing white guys with bad fashion sense. I got some of them confused sometimes. They all had somewhere to hide. They could blurt something out without much consequence.

If you would like more people to participate in your class, make sure you don't punish "bad" participation at all. It may be fun to be the person who answers a question with "I see somebody skipped the pre class reading" and then just turn away, but it ensures a large chunk of the class will not ask that sort of question again, and those who do will use up class time with defensive speeches about how they were reading the blah and blah "and on page (flip flip yes here it is, 73) it says (read sentence) and so I was wondering whether "permanent" is really appropriate here" and so on.

You can also call on students who don't ask many questions, asking them questions. My PhD supervisor did this constantly. Like 5-10 times an hour. "... and so if we reduce this completely, the result is ... Mrs Gregory?" (he was such a formal guy, called us all Mr and Mrs) and if I was following I would say the next line in the work, and if I wasn't I would say "I don't know" and he would call on someone else. This kind of approach keeps people engaged (you never know when you'll be called on) and gives everyone practice speaking up in class. (Plus it teaches you when to say "I don't know" - and he never had a problem with us not knowing.)


Back to academia for physics after M. Sc. In mathematics and 4 years working

First of all, I would say that you need to be sure on which are your academia aims in the mid-long term. If you really want to aim for a PhD and you already have a Msc, it might not be very useful for you to aim for a second one (unless, of course you really, REALLY want to). Groups nowadays are pretty interdisciplinary and having multiple background in a lab is not only allowed, but welcomed.

That said, coming back to academia, even after a long period, should not be a problem. Nowadays most grants are milestone-base (that is, x years after finishing the degree, the PhD...) so even as an older PhD student you shouldn't have any problem. At the end, all that matters is that you can convince a PI that you can bring some expertise to the lab, and, if you are eligible for grants the better. The recommendation letter part... that might be complicated. Even if it is not directly from your last employer, you might need something... maybe from your advisor during the master thesis?

If you are looking specifically for suggestions, and you are OK with moving around Europe, at this point I would suggest to search for opportunities in Switzerland. For all intents and purposes it works as a European-associated country, it has pretty high scientific standards and also offers quite good conditions for PhD students. This last part, specially I can tell having done my PhD in Spain where investment in science is not a priority.

This, of course, depends on your fields and topics of interest, but I would give some thought to the EPFL and the ETH, the two federal universities in the country. They are very welcoming to foreign students and offer quite good opportunities. As it is out of my field, I don't know about good groups focusing on the field of physics, but I'm quite sure that with a bit of search you might find some interesting labs.

hope this helps!


Where do general researchers make general discussions, online?

A lot of them are indeed on Twitter, but as usual with humans, cold asking them is probably not appreciated by many. What you can do, though, is simply follow them and see what they're saying, as they're saying a lot. You can find the people you might want to follow through hashtags indeed - the ones probably most open to your ideas will be talking about #OpenAccess (or #OA), #OpenScience, #ScholComm, #ICanHazPdf, off the top of my head.

Something that might work better is addressing them in real life. I'm told they mostly hang around universities, so you might try and approach people there to ask whether you can have five minutes of their time.

PS. I don't think there's a way of messaging on Stack Exchange, but if you make a Twitter account and share your username I'd like to contact you.


How do I find a journal's type (e.g. SCI, EI)?

I have set up a webpage (click here) which provides links to the list of journals that are SCI, SCIE, ISI and EI and also let you check the impact factor of a journal. You can follow the links on that page to find out if a given journal is EI, SCI, SCIE, etc. Hope that it helps!


How long to wait for an optimal/good PhD thesis/program, should settle for less exciting topics?

If you know precisely what you want to do, I am impressed---but not as impressed as the person who will want to hire you! Instead of applying for programmes near what you are want, why don't you write to people in the appropriate discipline and sound them out. Funding can often be found for a bright, enthusiastic student. That isn't to say you are likely to get a big grant, a corner office and be left to your own devices. But with the right supervisor you might be able to get support to design your project.

However you should not really expect things to pan out as you plan them. otherwise it wouldn't be research.

Finally it is not unusual to have a period of "meh" or "second year blues" as we used to call it. So think very carefully before jumping ship.


Cite a developed version of an algorithm (citation chain)?

Space savings aside, your choice in this must be guided by two factors: help the readers understand what your work is built upon, and acknowledge scientific contributions of your predecessors.
With those principles in mind, I would say the choice depends on the relationship between A and B, and whether either (or both) are well-known. Let's take two simple cases to illustrate:

if algorithm B is world-famous, and algorithm A is a not-so-well-known extension (e.g., because it is specially optimized for a specific type of data): you will have to cite both, as you cannot assume that all readers are familiar with algorithm A.

Herein we highlight an extension of the Abersmith algorithm,[ref A] which is itself based on the Borodin sort algorithm with specific improvements for the handling of p-adic input.

if algorithm A is very well known in your field, and algorithm B was an earlier algorithm that was almost completely superseded by A and little used nowadays (except for historical considerations): it is not useful to cite B.


PhD thesis: novelty at the time of proposal but not submission

If your advisor thinks your thesis is acceptable at your school (which seems to be the case) then it's their job to do what's necessary to make that happen. Perhaps that means telling your committee why it is OK even though some of what you discovered has been published while you were working.
Standards for a thesis are not the same as those for publication.


How acceptable are the outputs of automatic LaTeX converters for journals with LaTeX requirement?

The most probable answer to what acceptable is the conversion from word to LaTeX is probable too little. The main reason is that word is more based in local format (visual appeareance) rather than semantic tags.

For instance, you need to specify that a group of specific paragraphs are the abstract. LaTeX made this using an instruction like
\abstract{ ... text ...}. A converter needs to look in styles to learn the meaning of the text fragment against its list of heading, leyends, abstract, section, subsection, etc.

But if what you want is have a simpler medium to wrote and rewrote contributions to the text, provided that you have a a solution to create graphics in jpg, png or pdf format and a transfer the more complex tables to LaTeX way, you can use Pandoc to convert from word to LaTeX.


Is it acceptable for paid online course to use quizzes and materials from elsewhere on the internet?

Is it ok for a course to do this?

It is common for instructors to use teaching materials from outside sources. There is generally no expectation of originality when it comes to teaching materials, including lecture slides, assignments and exam questions (which may be provided by the publisher, especially at the high school and undergrad level). See this answer for details.

This is similar to the way we don't consider politicians to have plagiarised when they give a speech that was written by a speechwriter - in that scenario, too, there is no expectation that the material was written by the politician who delivers it. (In that situation, we only seem to mind if the speechwriter lifts parts of the speech from another source...) But if a student submits a homework assignment that was written for him by someone else, or an advisor puts chunks of her student's thesis in a paper without proper attribution, we would consider that plagiarism, because there is an expectation of originality.

You wrote

  I'm not getting taught off a textbook here that comes with a set of slides and test questions, I'm supposed to be paying them to write their own material.

I'm not sure why you think so. You're not paying anyone to develop course materials. It is common for instructors to use prepared material, including slides, test bank questions, etc. that might come with the textbook. It's also common for instructors to share material between themselves.

What you are paying for is for them to deliver an effective educational experience to you. If they have been educating you effectively, it shouldn't matter whether the materials are original, or whether they came from a test bank or other outside source. If they haven't been educating you effectively, you can complain on those grounds - not because you expect them to develop original materials.

  If not, is there any official organization I can complain to.

If you believe you have been treated to a sub-par educational experience, you can complain to whomever is responsible for the course.


Is it worth it going to academic conferences as undergraduate without any research to present?

If the conference is "affordable" to you in terms of time and money, go for it! It will be a great way to see more about how academia works. As others mention, there are often some workshops for students, and poster sessions are great ways to learn about new ideas and ask (even basic) questions.

You may not get very much out of going to more than one conference without presenting, though. (If you love the first one and it inspires you to work hard on your research, maybe attending another without presenting anything would be a good thing, but much of the value for you at first will be in understanding how academics communicate with each other.)

Also, check if there are interesting conferences coming up in your region. Often local students can volunteer to help with registration desk or other key work during the conference in exchange for admission to some parts of the conference. This would be a way to get many of the benefits of attending the conference, without having to spend a lot of money to do so.


Can faculty do research during a labor strike?

Consider the following FAQ from West Chester University discussing the possibility of a strike:

  Will the Pennsylvania State System of Higher Education universities, includingWest Chester University close if a strike is called?
  No. The universities will remain open if a faculty strike is called. By law, individual faculty members have the right to decline to participate in a strike called by the union so individual classes could still be held.

and at University of Northern British Columbia:

  I am doing research as part of my degree. Will I be able to continue during a strike?
  It depends. Some research may be allowed under the terms negotiated at the start of job action. Also, anyone may cross a picket line during a strike unless the Administration declares a lockout (in which case nobody is allowed in). You should discuss this with your supervisor.

  How will a strike impact the delivery of supplies, reagents, enzymes,
  etc.? During the 72 hours prior to the start of job action, the
  parties negotiate “essential services,” that is those things that are
  deemed essential. In general, anything not declared an essential
  service would be impacted, which would probably include most
  deliveries. You should discuss this with your supervisor.

And a report about the University of Puerto Rico (admittedly, this is a student-led strike):

  Since the University of Puerto Rico strike began, faculty and students have only had intermittent access to its labs. Even when they are allowed to enter, they are working with dwindling supplies of some chemicals and other research materials. Closed campuses mean new shipments cannot be delivered.

These suggest, in a formal capacity, some research might still be able to take place, either from crossing the picket line, or from negotiations for research that is time sensitive (for example, many biology experiments which must be monitored, changed at certain intervals, etc.) but that they may certainly suffer during long strikes.

Beyond that, one imagines that it's impossible to faculty not to do "research" in the more expansive sense of the word, as occasionally that involves idly musing on a subject, and there's no reason to suspect that faculty would stop thinking about their life's work during a strike. Rather, it's far more likely to impact classes.


Does pure math have an application in communications engineering?

I'm in a similar situation to you. I'm finishing my masters in digital communications and doing my thesis right now. Math is an issue for me definitely.

In my experience, a bit more complicated math is helpful if you're going to be developing systems that do statistical signal processing (which seems to be very popular now) and anything that has "smart" in its name.

What exactly do you need depends on what you want to study in detail. It might be a good idea to first dip your toes in the fields you want to be working with first and the pick math courses you want to take. You could try looking at some books or papers about say adaptive filters or modern receivers or estimation theory. This should give you an idea what's usually needed. If you're lucky enough to have approchable professors, do ask them about what will be useful to you.


I entered a PhD program out of fear of being unemployed and regret it. How can I gracefully undo my mistake and switch fields?

These are my thoughts as someone who is a data scientist, but also someone who used to teach and advise students at the university level.
Becoming a data scientist

I want to switch careers from PhD in chemical engineering to data scientist.
At the end of the day I just want a high paying job.

If you want to be a data scientist and earn a lot of money, you are either going to need to start your own company and hit it big, or get a graduate degree. (Or both).
Being a (well-paid) data scientist requires much more than programming. (That is still part of it, of course. But it is necessary, not sufficient). High end data scientists usually have a pretty extensive background in statistics and probability theory. I used to work for an engineering firm as a data scientist. They converted several mechanical engineers into "data scientists" because they could program. This ended up leading to many wasted months of work when I informed them that the test they were using required certain assumptions on distributions of the population they were sampling from.
Making an impact as a data scientist is much more involved than people think. Online classes and boot camps make some people think that they can get a certificate in Python and land as a data science lead at Google or something. It doesn't work like that.
Essentially what I am trying to tell you is this: I would probably not look at someone with a 3.5 GPA in chemical engineering and very little formal data science training for any sort of high paying data science job.

I had to take a bunch of online courses and I lacked the motivation to complete them.
I know I am capable of achieving these things as long as I have some motivation.
At the end of the day I just want a high paying job.

Avoid telling a future employer this.
Ask yourself if your motivations to become a data scientist are the money or the subject. Part of any job is being self motivated by the subject matter itself.
The money in data science is not guaranteed. Some of the very high paying data science jobs also require extensive education and immense dedication to working 60 hours a week.

Leaving the PhD program

If it didn't harm my lab, I would just drop out now without even bothering to complete my masters. Because I care about my lab, I don't want to drop out and harm things.

I would not feel obligated to waste 4 years of your life so that your lab mates don't feel bad.
If you are not enjoying yourself, do not feel bad about dropping out. You will be doing yourself a large favor in the end I think. There is no shame in dropping out to do something different. People drop out all of the time from graduate programs in order to pursue something they enjoy more.
Let me absolve you of overall guilt: Your situation is much more common than you think. I think there will be many people who will support you in pursuing a career you will enjoy and be productive in. Take confidence in yourself and don't let others discourage you.
Especially don't become your own worst enemy by tearing yourself down.

Overall advice

If you are not enjoying your PhD program, your first priority is yourself. Drop out. Now. Tell the program administrators your thoughts. You do not need to ask their permission to do what is best for your psyche and career.
Look into becoming a software developer if that is something you will enjoy. A BS in Chemical Engineering and demonstrated aptitude in C++ or Java can usually set you on a pretty good career path.
Don't look back.


Do all universities have a minimum required GPA for graduate school application?

I can't say "all" for sure, but I think you'll find that many if not most schools do have a minimum GPA requirement.

Whether you can compensate for a low GPA depends on how the school handles it.  In some cases it may be difficult, as admissions committees may literally scan apps for GPA and put all that do not meet the standard in a "reject" pile without even reading the rest of the application.  In other cases the minimum may be "soft" and they will read the app.  My advice would be to: A) get advice from a professor at your school you have a rapport with; and B) contact faculty at the schools you're applying to (or considering applying to).  I would not just bluntly ask the GPA question on its own, but email them in general saying you're interested in the program, and mention the GPA issue along with whatever else you ask them about the program.

You almost certainly cannot "throw away" your undergrad GPA in a PhD application.  Even if you have an MA, most schools will want to see all your college transcripts.

You should also take advantage of the time you still have during the year to bring your GPA up as much as possible.  Even consider doing this by taking easy classes that you might not otherwise take.  Personally, if I were in your situation, I would even consider delaying graduation by a year or part of a year, if it's financially feasible and your school will allow it, just to have more time to take classes and bring up your overall GPA.

You have already made a significant blunder in letting your GPA get that low, as a GPA below 3.0 will be a red flag to many graduate programs.  However, from what you say, you would be a strong candidate in other regards.  If you can get people to look at your app long enough to read your statement of purpose and see your grad coursework, then you probably have a decent shot.  To do that, you should leverage your strengths.  If you have taken many grad classes, done research, and published a paper, you presumably have good contacts in the physics department.  Lean on those people to write you glowing letters of rec.


Is it appropriate for professors to ask students to type notes for their classes (with or without paying students) in United States?

It would be unethical for a professor to publish something written by students under the professor’s name without express consent (which is to be given free of any coercive pressure) and coauthorship for the student. (See this recent discussion on a related type of abuse.)
It would also be self defeating and something that no competent professor I’ve met would ever wish to do. Students do not generally write notes at a level that comes close to the level most professors can write on their own. Publishing someone else’s subpar notes under your own name is a sure way to hurt your own reputation even if you do technically get some publication credit.
Setting aside the publication issue, it’s fine to have note-taking as an official course assignment if there is an educational rationale, which there often is. For example in mathematics graduate programs we try to get students to work on improving their mathematical writing skills, which are extremely important for success in research, and some writing assignments of this type are not uncommon.
If note-taking is not an official course assignment but the professor simply asks students to do it on a voluntary basis, the request should be made in a way that makes clear the students should feel free to say no. To put pressure on the students to do things they don’t want to do and that are not an explicit course assignment is unethical, regardless of whether the professor publishes the notes or not, and regardless of whether some payment is exchanged.


What is the location of the nomenclature section in a scientific paper?

The correct position for a nomenclature section is the location normally used by the journal in question. While as Paul suggests, the logical location for this should be at the start of the paper, in many journals, the nomenclature section is placed at the end, largely because it does not "look as good" to have the nomenclature section right on the first page (which is optically the "prime real estate" of the paper).


Do they know about previous submission history of my article?

There's at least two types of rejections:

Desk rejection where the editor says an article is out of scope.
Rejection upon review where the editor in consultation with the reviewers' recommendations rejects the paper for publication.

For a great description of the process, see here.

Forgive the convoluted wording on the second one -- basically, it means your paper was reviewed and then rejected. The precise relation between the reviewer's reviews and the outcome varies by journal, but it is the editor who ultimately rejects.

In contrast, a "desk rejection" means that the article never went to reviewers and was rejected upon receipt due to some issue -- scope? formatting? bad English?

If you got a desk rejection, the odds that the next journal or reviewers will know anything about this paper is nil. If you were rejected post-review, then it's quite possible (and in some fields probable) that the same people might be reviewers even for a different journal.


Does it make sense to get an LLM in preparation for "law school?"

No. It does not make sense to do a LLM before a JD.

The length of the program is not the relevant thing to consider.

The standard course is to do a JD -- which is a first degree in law -- before a doing a LLM to gain specialized knowledge. Usually a JD or equivalent is required for admission into an LLM program.

I understand the confusion since usually a doctorate (JD) comes after a masters (LLM). Note that, outside the US, the first degree in law is often called a bachelor of laws (LLB), which makes more sense.


Is it okay if a professor friends a student on social media sites?

It depends a little on the circumstances, but generally not.  If the student is your Ph.D. student, then it's probably OK to accept a friend request, but you shouldn't initiate it (and some people might not even approve of accepting it, depending on the sort of advising relationship you have).  If it's an undergraduate in one of your classes, then I don't think you should even accept a friend request, and sending one would be very improper.

There are three basic principles:

You shouldn't put your students in situations where they might feel awkward or uncomfortable.  For example, would turning down a friend request from one's professor come across as rude?
It's not healthy for class dynamics if there's a perception that you have a closer, friendlier relationship with some of the students than with others.
You need to be very careful not to do anything that could be misinterpreted (or, worse yet, correctly interpreted) as showing romantic interest.  Some people will interpret things that way if it's even vaguely plausible, and fair or not you've got to keep this in mind.


GRE Scores for Graduate programs in Chemistry

While I am not in Chemistry, I can tell you from a US perspective that there is no such thing as a GRE score that guarantees acceptance. As long as you are above any "minimum score" (which most places are moving away from, but many admission committees reportedly still privately use), it guarantees your GRE won't alone prevent your file from being considered, but that's really it. Even a 99% on all sections is no guarantee of admission to anywhere I've ever heard of.

In general, higher scores are of course better, but the general advice is that retaking the GRE should only be done if you have a good reason to think you would do very differently. I retook the GRE once after a month of brushing up on some of the algrebra and geometry I had not touched in years, and it still only changed my quantitative score by just a few points. The only reason it wasn't a total waste of money is I didn't have to wonder, "gee, if I had just taken it again, would I have done much better?" I got the answer, which was no, I would not in fact do better without a lot more work that I didn't actually want to do :)

The GRE overall is pretty good at test-retest reliability, and if you prepared reasonably well (went through a practice test or two, were familiar with the type of questions being asked, were not very rusty on the topics covered) it takes considerable effort to do substantially differently. However, you can test this out for free in an afternoon by looking up the ETS free POWERPREP software (from the makers of the GRE), which allows you to simulate a full test at normal testing conditions, in the comfort of your home. If you follow the test protocol on your own (no outside source, only blank paper and a pencil, timed breaks with no food, etc) and the estimated score is not wildly different than what you got on test day, then you just have to decide if it is worth spending many hours of intense preparation to try to get better at taking the test.

Regardless of what you end up choosing, don't let a focus on the GRE score prevent you from making the rest of your application as good as you can. A well written statement (edited and reviewed multiple times) and working with your letter writers to get good letters (delivered on time) is essential, while extra points on a test are just "nice to have".


Becoming department chair while being good friends with some but not all members

You should expect some professional distance between yourself and anyone you supervise. You can be "friendly" of course, and you can interact at departmental social functions in a friendly way, but you have to recognize that whenever a dispute arises you are the boss, not the pal.

Some departments, however, with a long history of very collegial relationships, mutually supporting in every way, these sorts of things are unlikely to arise. This is especially true if lots of things are decided by committee or by consensus, rather than by fiat. In such a place your fears would likely be misplaced, until something unexpected happens.

There are places, very collegial, in which the department head position rotates among the tenured faculty, with the job lasting a couple of years or so and then passing on to someone else. If a place has such a history, then it seems to change the dynamics a bit. The 'head' is an administrator but is seldom called on to be an 'ogre'. Note that such things as tenure are normally handled by committee, rather than by the head, but annual salary adjustments might fall under your control.

The more the position calls on you to be a personnel manager, the more likely it is that conflicts can arise and the less likely it is that you can be "just a friend" to other faculty.

If you already have graduate students under you and are responsible for their future, you can get a small sense of what the relationship might be like. You can be friendly, but you need to keep a certain professional distance so that your authority is recognized when it is necessary for it to be recognized. Hopefully not often, but it happens.


Are ERC starting grant preparation courses worth it?

Yes, but this is strongly dependent on the course. For example, will the teachers give you personalized feedback on your proposal, or is it simply a course that offers general guidelines and tips? Usually the "tips" type courses are helpful if you're a first-time grant applicant without a strong external network. However, if you have colleagues who have been awarded these grants or have served on review committees and are willing to look over your proposal, their feedback will be more valuable. Especially because they will be more similar to your actual reviewers (pressed for time, not in your field, etc.).
If it's a course that includes specific feedback on your proposal, or if it's a private grant preparation service, these can be more helpful because they are more tailored. I have some colleagues who run this kind of grant editing/grant preparation service, and they usually offer some statistics in their promotional materials. For example, of those whose grants went through this process, how many were funded? My colleagues' success rate is about 80% at the moment, so clearly these kinds of services can really improve your chances. However, they also require substantially more money that may not be reimbursable by your university.


What do I do if someone studied the same topic before, but did so inadequately?

But there is nothing online except some initial pages of thesis (as a blog post on the student's website [...]. It has not been published in a peer-reviewed forum, and it looks like it was done in around 4 months with a small sample size for coursework thesis. Moreover, it seems to be in a different field of study.
From the available pages it looks like research has tried to touch most of the things but at a very superficial level: three pages of data analysis and one page of findings also make me question how in-depth the analysis was.

None of this indicates that the previous study was 'inadequate'!
You should definitly mention this study in your proposal, but use better arguments than 'three pages of data analysis and one page of findings' to describe its limitations!


Second master's degree in another field without bachelors

Short answer is: Probably ok, so long as you demonstrate graduate-level competency and have good undergraduate grades in the adjacent field.

Long answer: Graduate work (at the Master's level) looks very different from undergraduate, so the key is demonstrating, via your application to the program (support from a faculty member in that area goes a long way too--so contacting such a person and discussing it with them before your application is important), that you are capable of self-learning and can pick up the introductory principles of the adjacent field as you go.


Paper with a spelling mistake in author affiliation in publication

I suggest doing nothing. Once a paper has been published, making further changes is a difficult thing. With electronic versions it's easy to correct the typos, but since the electronic papers have already been disseminated, lots of copies of the paper with the typo included are already worldwide. The publisher cannot recall those copies, fix the typo, and then send them out again. With paper versions there're obviously even more problems since implementing the correction is hard.

If you must make a correction, it depends on how severe it is. If it's very severe, enough so that the veracity of the results are threatened, I would contact the publisher and ask to issue a corrigendum or erratum (see this link for more details about either). But in this case it's just a typo in the affiliations. This typo makes no difference to the research conducted or the results. Nobody is likely to care, especially not the researchers who will be using the work. Many might not even notice.

tl; dr: relax! There are far better things to spend your time on.


Should I mention teaching experience in my cover letter?

I've been on the faculty recruiting committee of my American R1 top-whatever computer science department for more than 15 years, including three years as committee chair.  (But my experience is only in one department, so take this with a grain of salt.)

To first approximation, nobody will read your cover letter.

It's quite common to get faculty applications that have no cover letter at all, or that include a plain-text email "cover letter" that reads "I'm applying for an assistant professor position; I've uploaded the requested documents and the contact info for my references.  Kthxbye!"  I have never seen this affect discussions about who to interview or who to hire.  Nobody ever notices.  Nobody ever cares.

All the information we care about is already in your other application materials, your recommendation letters, and your papers.  In particular, recruiting committees already expect to see a detailed description of your teaching experience in your CV and in your teaching statement.  That's where everyone puts it, so that's where we look.  And we'll look there regardless of whether you mention it in your cover letter.  So why would we look at your cover letter?

In my experience, cover letters are only useful if they contain information that potentially changes the hiring process — like "I am applying for a tenured position at the rank of full professor." or "Please keep my application confidential." or "My spouse is also applying to your chemistry department."

Cover letters do play a more important role in some departments, because they want convincing evidence that you are seriously interested in a job there.  After all, if you're just shotgunning your application to every ivy-colored building in the country, then interviewing you is probably a waste of their time and money.  But this is much less likely to be a concern in a top-50 R1 department.  It's never been a concern at mine.


In part to forcefully disagree with @Buffy's remark that it's generally easier to move from research to teaching roles... my own and others' PhD students from my "R1" university in math in the U.S. have encountered disbelief about their sincere interest in teaching at an undergrad institution... Indeed, given the way computerized job applications often work (mathjobs.org), it's nearly effortless to apply to any place listed on mathjobs.org. In particular, making such an application is absolutely not a proof of sincere interest, beyond not wanting to be unemployed.

I suspect significantly for that reason, some (I don't know what fraction...) of non-research-fixated math depts in the U.S. simply do not list themselves in mathjobs.org, so that "the bar" to apply to them is set higher than clicking boxes.

So far as I can tell, "sincerity" (or its appearance, ack, ...) plays a significant role. I see this, and am not entirely opposed to it, in graduate admissions, postdoc applications, and tenure-track applications. So, if one intends to "game" the system (well, why not?) one needs to do so well enough to fool a certain number of people.

Depending on your personality, it might be less stressful to just follow the direction you want, rather than having your day-to-day life determined by some dubious long-term strategy.