When referring to races, should 'black' and 'white' be capitalized? (MLA)

Firstly, the MLA has the following on its website;

When Merriam-Webster indicates that a term is “capitalized” or
“usually capitalized,” the MLA capitalizes the term in its
publications. When Merriam-Webster indicates that a term is “often
capitalized,” our practice varies. We usually lowercase sun, moon, and
earth, but, following The Chicago Manual of Style, when the does not
precede the name of the planet, when earth is not part of an idiomatic
expression, or when other planets are mentioned, we capitalize earth:
The earth revolves around the sun.
The astronauts landed on the moon.
The space shuttle will return to Earth next year.
The four planets closest to the sun—Mercury, Venus, Earth, and Mars—compose the inner solar system.

From Merriam-Webster Dictionary
Part of the Definition for black

(1) often capitalized:  of or relating to any of various population groups having dark pigmentation of the skin  (black Americans) (2) :  of or relating to the African-American people or their culture (black literature) (a black college) (black pride) (black studies)

From Merriam-Webster Dictionary Part of the definition for white

a :  being a member of a group or race characterized by light pigmentation of the skin

This makes no reference to capitalization. From the MLA definition it appears that they should be lower case.
This MLA stylesheet also says;

Capitalization in MLA style is mostly conventional, with the
exceptions noted below.  Generally, specific designations are
capitalized, as in the American West. But more general
designations--or designations used as adjectives--are lowercased: The
western United States, eastern Europe.

The names of ethnic or racial groups are capitalized if they represent a geographical region or language group. For example,
Hispanic, Asian, African American, Appalachian.
Terms based only on color, direction, size, habitat, customs, or local usage are usually lowercased

Irrespective of the above, as per guifa, Ben Crowell, and ff524 comments, a number of other factors can also be considered in making a decision to capitalise or not such as

Those that read MLA will be pretty flexible so you can always explain your choice in a footnote. It's actually quite common to do that with certain terminology issues. For example, you could say "In this paper, for [insert reason], we/I capitalize all adjetives referencing ethnic or racial groups."
You could preface an article on this kind of topic with an explanation of your usage and why it suits your purposes.
Capitalization can be field specific (even irrespective of the citation style). For example, in medicine lowercase is used most often, while uppercase is often used in some social science fields.


What is required of a mathematics referee?

My experience as a both reviewer and author in pure math suggests the following:

there is no universal standard for refereeing (some referees check papers thoroughly, some are much more cavalier)
editors may have different expectations/desires of reviewers, depending on the situation and on the editor
the typical expectation is that you assess a paper from several aspects: importance of the paper (this includes factors such as usefulness of the results/methods and novelty), correctness, and presentation/clarity.
refereeing is a process, not a "yes/no" assessment
refereeing well takes a fair amount of time, and results in little personal recognition, but is important for the community

Based on your specific questions, here are my suggestions for how you might go about refereeing a paper:

First assess the results claimed in their general context.  If they do not seem interesting enough for the journal in question, or are clearly wrong, you can simply say that (preferably with more details) and recommend rejection.
Understand the general argument of the paper.  Read the introduction in detail, and then try to understand the main points of the paper.  (You might not read the rest of the paper in order, particularly for long papers.)  Assess the novelty and feasibility of this approach.
If all seems good so far, convince yourself of the correctness of the paper.  This might entail checking all details, or you might be convinced after only checking certain details.  While you should definitely assess the correctness of the result, ultimately the burden of correctness lies with the authors.  Of course it's great if you can check the paper completely, but in my experience most referees don't.  How much effort you put into this may also depend on the situation (e.g., for a completely novel approach with an amazing result, you probably want to put more effort into checking details).
Very often in this process, there will be things you don't understand.  There could be a couple of reasons for this: (i) you aren't an expert in the methods being used, (ii) the authors' explanations are lacking.  In both cases, you can simply ask the authors for more explanations or explicit citations of the results they are using.  It's not necessary to understand everything for a first report, but hopefully you will mostly understand the paper after a successful refereeing process, which may include several revisions.  However, if (i) is a very serious issue, you might consult with the editor.  E.g., if you can read though the details in Parts I and III but Part II is a complete mystery to you, the editor may find someone else to referee Part II.  (Possibly this is a conversation you could have when agreeing to referee the paper.)
In the above process, you'll likely come up with a list of questions/suggestions, both about the mathematics and the writing.  While you should of course include these, these are typically of secondary importance in the referee report (though sometimes if you have some really good suggestions, it can dramatically improve the paper).


Does Iran's sanction play a pivotal role in rejecting papers from a journal?

Speaking as an associate editor of a US-based journal that receives many international submissions, I can tell you that:

There are absolutely no guidelines or even informal suggestions that any paper should be handled differently based on the nationality of the authors or their institutions.
I have never heard of anyone making editorial decisions on such a basis or suggesting that they should.
In my own opinion, which I believe is shared by most or all of the other editors, to do #1 or #2 would be highly unethical.

I couldn't even tell you, without going and checking one by one, whether any of the papers I have handled recently had Iranian authors, because it absolutely doesn't matter.

Edit: following up on @Allure's answer below (which links to some older information), it seems there is a very slim and rare legal basis that would hypothetically prevent some editors from handling some manuscripts from Iran and other countries under US sanctions.  It definitely does not apply to the case discussed here, and would not be grounds for rejection since practically any major journal will have editors who are not bound by this restriction.  The most clear and recent explanation I could find is here.  The current rules are the result of a 2004 lawsuit that overturned much more restrictive rules in place back then.

Further edit: It seems that there is a recent instance of misinterpretation of the laws mentioned above, which led to rejection of a manuscript purely on the grounds of one author having an Iranian affiliation.  Eventually this was resolved and the rejection decision was reversed.  Note that in that case, the authors were specifically informed that the decision was based on US sanctions (albeit misinterpreted), and the decision was not made by or communicated by the journal editors.


Should I mention the name of a professor on my resume if I'm not getting a recommendation letter from him?

Whatever the reason is that you're not asking a letter from the professor, would that not also extend to being contacted about the work you did? My point being is that if you think a letter wouldn't be favorable then you would also be worried about an email or phone call also not being favorable.

If however that isn't the case, then it's entirely circumstantial. Does the program you're applying for require letters of recommendation? If so, why not just ask? If it doesn't require a letter of recommendation then you can just mention it to the professor that you've applied for a position and would it be alright if they are a reference?

Don't stick someone on your CV and not tell them about it. Professors don't like being cold called about this kind of thing.


Is it worthy to publish an extended abstract in a conference?

The aspect of what an extended abstract is differs from one field to another. Refer this page to get a better idea on what does it mean in your field:

What is an extended abstract?

For example, in CVPR,
extended abstracts are handed out to the attendees before the start of the conference. They are much more handy than a huge proceedings book as each article is much smaller than its full version and includes all relevant details at a glance. It serves as a means to attract attendees attention especially when there are multiple venues occurring in the same time.

However, whether the amount you pay for it worth it or not depends on various factors, such as the field, the tier of the conference and so on. Sometimes in top tier conferences, there may be funding agencies who might be attending the conference. In such cases extended abstract would be a pretty valuable. But in any case, this decision would be better sought out by consulting it with your advisor or faculty members of your department as @ff524 suggested.


Whether/how to list a failed student on my CV

One thing to keep in mind is that tenure-track faculty generally do not list failed PhD students on their CVs.  One might argue that they should actually, since -- unlike a non-academic resume -- a CV is supposed to be a factual, comprehensive record of one's academic career, but nevertheless academic culture doesn't cut this way.

The next thing I will say is that in my experience at least, "co-advisor" refers to a member of a group of more than one faculty member -- usually, though not absolutely always, tenure-track faculty members -- who jointly share the role of advising.  You seem to be using the term as a kind of "lieutenant advisor," but that could be misunderstood.  When the student's other advisor is your PI, it is likely that your advising duties are less official and more subsidiary.  In particular, you write "[M]y professor decided to dismiss him from the doctoral programme and from employment," not we decided...Nor did you hire the student, fund him and so forth.  However, from the sound of it, you played a large intellectual role in supervising the student.

So: I would not recommend you put a line on your cv which says "co-supervised a PhD student."  If potential employers are interested in that, they are likely to ask you about it, and when they find out that the student didn't graduate, I think that sounds bad...in particular, it sounds not completely forthcoming.  On the other hand, "co-supervised a PhD student who did not finish [or however you want to put it]" also sounds bad, as I mentioned above.

I would suggest instead that you put a line on your CV saying that you mentored a PhD student and that mentoring relationship resulted in a joint paper.  That's a successful mentoring relationship.  The student was not ultimately successful in the PhD program, but I claim that you're not on the hook for that: you didn't hire him and you didn't fire him.  If they ask for more information about the PhD student, you should of course be completely forthcoming about the fact that he was dismissed after six months, as well as all the help you gave him.  If/when this additional information comes to light, it does not undermine what you said before in any way.  Since you are not claiming the PhD student as your own, his fate is not your responsibility (which is true!), and so your involvement in the situation looks (and was, based on your description) entirely positive.


Should I tutor a student who I know has cheated on their homework?

Whether their cheating should impact your role as a tutor is not the primary issue here, so I'll set it aside.

You should not be tutoring a student for additional money when you are also grading that student as a TA, even if the grading and tutoring are for separate courses. That sets up a financial relationship between a grader and a student. That's a big problem.

I certainly don't believe you've done anything unethical here, but you should most likely report the inadvertent conflict and stop tutoring this student immediately (I'd also offer to your superiors that you return any payment for the one session, or just do it yourself anyways). It's not a big deal that you did this accidentally not realizing the connection. It could be a problem if you continued with it now that you know.


One of the authors changed idea before submitting paper

Talk to the other collaborators who probably agree with you, and then take a unified front to tell him that holding several collaborators hostage is not ok.
Additionally, if part of his new publication uses a jointly developed idea which he intends to publish alone while blocking your joint work (that should be in the references of his planned solo paper), then this strikes me as borderline plagiarism. In any case, it’s very bad form.


How to find a scientific review of a theme?

I think the easiest option is to use Scopus (if your University has access) and in the title, abstract, etc, fields type your keywords and in the document type field just select "Review".


Will publishing all my papers in a single journal endanger my career?

Your first few papers don't determine your career. The answer to the title question is, of course, "it depends". If your research focus is narrow, especially narrow, then there are fewer journals that are appropriate venues and the others won't have appropriate reviewers in their "stable". But continuing to publish in a very low impact journal would have negative consequences, that aren't the case here.
I'll guess that "a paper in the same journal" is a better outcome than "no paper" at this particular point in your journey, so your advisor is likely giving good advice. I doubt that an editor, even one who knows you will bias decisions in your favor if they want to keep up the reputation of the journal.
But, the indicators seem to be positive, not negative; getting published in a good journal.
You can also ask the editor of the journal you submitted to about the likelihood of a decision in a reasonable time frame, saying that if that isn't possible you will "be forced by circumstances" to withdraw the paper.
I'll also note that, assuming everything you say is accurate, that people believe in you and your work. That support alone should lessen your fears about getting a good position in the future.


Contacting authors at conference after refereeing their work

This is just my opinion; in some conferences and journals, it is specifically mentioned that the review process is blind and the authors should not know who the reviewers are.

If I was the author, I would be more comfortable with your opinion about my work, without mentioning that you have reviewed the paper.

You can simply say: "Look, I have read your paper and listened to your talk, some might say ..., but I believe .... You'd better work on ... etc"

You don't need to mention that you reviewed it at all (although they can pick it up quickly). If you explicitly mentioned it, you can put the authors in an awkward situation.


Why doesn't the academic year start on January first?

Basically because schooling is the inverse of farming. That is: Historically farming and feeding the family (and community) took precedence over all other considerations. This is primarily a job that takes place through the spring, summer, and fall -- with little or no activity possible in the winter. Therefore in most cultures the original calendar year starts in the winter and so spans one farming cycle, i.e., spring-summer-fall (in the original Roman calendar, the winter period didn't even have assigned months!).

When schooling historically started to be of some value, it came secondary to farming, and occurred only as farming allows. So the winter is an excellent time for it, because no useful farming can be done. On the other hand, the harvest season, around August-September, is the busiest time for farming, and critical in traditional communities to have "all hands on deck" for that work, and thus schooling would not occur at that time. And therefore the main school schedule would begin after the fall harvest, and run through to the summer of the next year.

In short, the fact that schooling and farming have an inverse schedule is not too surprising, because traditionally the former only occurred in the time not being used for the latter. Having grown up on a farm in the U.S. in the 1970's, I still experienced some tension between my family and school, because I would need to be out of school for about a week in September for a particular job that we were expected to do with our livestock at that time.


A grad school professor contacted me about research before I applied

This isn't very common in my field, but my field doesn't involve labs so I'm confident our fields are different.  I can see why you would feel skeptical of what seems like, on the surface, such an important stroke.  Always investigate things that seem too good to be true.  Here's some steps I would take:

Talk to your undergraduate advisors and letter writers.  This is the most important one; knowing you, your work and your field, they can help you with your specific questions, and possibly suggest things to find out that you haven't even considered.
Research the facility and professor.  It sounds like you've already done this, or at least started on it.
Ask the professor how your work came to his attention.  You don't have to make it challenging, just tuck it in with a reply along the lines of "Thank you for contacting me, I'm very interested.  Can you give me some more information about (research specifics)?  Also, what brought my work to your attention that made you feel I would be a good fit for your lab?"  The answer to this should help you answer your questions about whether he's seen your letters of rec or your application, or something else.
If everything looks good and you feel you're a fit for this lab, don't sell yourself short!  Most grad students go through some form of imposter syndrom, so this can actually be an obstacle you'll need to overcome.

Good luck with grad school regardless; applications can be stressful and a lot of work.


Advice on writing a research paper in a less time

I think this question is highly dependent on your personal writing and working style. I can give some suggestions, but some of them will not be a good fit for some people, and I may not list many suggestions that work well for others simply because they do not work for me (or have not occured to me).

You may not need to write one paper faster if you can work on multiple papers concurrently. If you start four projects and it takes you a year to write a paper for each project, then you are releasing a paper on average every three months even if in practice all four papers took a year. This works especially well when you have coauthors since there can be a lot of time spent waiting for feedback or work to be done by others, which you can spend working on another paper.
One of the smartest and most prolific people I know has been rumored to tell his graduate students "just write it". I take this to mean "get a rough draft on paper quickly even if it is an ugly rough draft." Even if you have a lot of editing to do, things will become easier going from a draft rather than a blank page.
Time off can be just as important as time on. The mind is a truly remarkable thing, and in my experience, it works on a multitude of problems subconsciously. After I write an outline or a rough draft of a section or a paper, I don't try to edit and polish it immediately. Instead, it can be better to set the project down for a few weeks and work on other things or get caught up in your every day life. If one returns to a paper with fresh eyes, they are going to do a lot more quality work in less time than if they try to think, write, and edit all in a short time span.
Find a place to work that works for you. Everyone is different here. Some people need absolute silence to the point where they wear earplugs in a quiet space. Personally, I thrive in relatively loud, chaotic places such as busy coffee shops. I can get into the groove much easier there than say a library or my office, so I use this when I am trying to write.

These are the only tips I can think of right now. If I think of any other tips, I may add to this list later.


How to respond to papers that put forward unreasonable criticisms of my research area?

You can't change what is already published, so there is no point in trying to.

What you (and the people in your research area) can do is ask yourself why they used A instead of X. Maybe there is an easy-to-use free implementation of A, while it takes a PhD to really understand and implement X properly? In that case, you and your peers should fix the problem by releasing a tool to do X. Possibly an automated one, with a simple interface and no magic parameters to tune. Then you can recommend it to people in the other field.

Another thing you can do is collaborating with someone in that area, and publishing a benchmark paper where you test several algorithms and you show that X really works. A paper of this kind may be easier to publish in their area than in yours, where this fact is common knowledge.

If you simply call them idiots, you will never fix the problem. This is the wrong attitude; the blame can't be all on their side. You should borrow this principle from user interface research: if your users make mistakes frequently when interacting with your program/website, it is not their fault because they are idiots, but it is your fault because your interface is bad.


Is it okay to talk about a topic you want to research in but haven't done anything beforehand in your sop?

This should be fine, since you seem to have the necessary background if not the specific experience. This would be especially true if this is in the US, where there is a lot to do in most programs prior to starting serious dissertation research. It will be different elsewhere, of course.
Again, for the US, the professor may have little actual influence over your acceptance.


I want to do an independent dissertation type research project, not being part of a uni, how can I find out if my Question has already been answered?

To directly answer your core question, "how can I make sure my research question hasn't already been addressed/answered by previous researchers", the only real answer is a thorough literature review and an associated deep understanding of your research area. This is universally true of all research disciplines; knowing what others have done and learned before is a fundamental part of conducting research that advances human knowledge. If you just want to investigate something for your own personal interest, then this is not completely necessary, of course. But rediscovering something already known within a field may mean your research is not of interest or able to be academically published.

There are other dangers of not knowing background before you start, of course. The simplest is that you go about things wrong, and previous researchers have established that your approach is fundamentally flawed, dangerous, harmful, or otherwise inappropriate. It may be that others have done almost exactly what you intend to do, and you may simply be setting about to replicate a previous study. Replication is fine, but replicating something already found out to be flawed or insufficient to answer the key research questions may just be an exercise in futility.

As mentioned in the comments, there are major ethical issues if your proposed research involves human participants, such as doing sociological/anthropological work. This includes activities such as asking questions, giving surveys, and reporting on naturalistic observations. At best, not observing certain precautions and methods can mean no legitimate academic publisher will touch your work, and others in the field will reject it entirely as unreliable or unethical. At worst, you can do real harm to others and get yourself into serious trouble. Understanding and applying principles like informed consent, protection of privacy, respect of autonomy, etc, are important no matter what your goals are. Working with "at risk populations" (which can include indigenous tribes) requires an extra level of care, and may even have legal requirements of registration and authorization to be acquired in advance to avoid criminal proceedings, fines, or more.

But back to the core question, there is no simple, fast, or easy way to see if a question has been asked and/or answered before. It simply requires intimate familiarity with your field and line of research, preferably assisted by speaking with a network of fellow experts familiar in the field, and a lot of searching and reading through work on your own to determine what is and is not an open, interesting, and potentially answerable question. If your field has "survey papers" that explicitly call out a certain area as an "open area of inquiry" or an important question for future research, that's certainly a great place to start! But how exactly to conduct a good literature review is beyond the scope of this forum, and requires intimate knowledge of your particular field. You can start with Google Scholar and some clever search terms, but even knowing what terms to use is often a highly field-dependent issue. It is not insurmountable, but you should at very least be aware that this stage of research is both very important, very time consuming, and will require a great deal of work if you are not already deeply well versed in your field of inquiry.


Research proposal for PhD application - should I talk about my background?

While it may be institution/field/country-specific, from the description I assume that you are applying to the program and do not have a prospective advisor who has already agreed to supervise you, nor a project onto which you will be allocated. In this case, that seems similar to the American "statement of purpose" (SOP).

The first guideline is: follow the guidelines. They tell you exactly what they want to see in your statement. You should absolutely touch on all of those points.

In fact, many statements add nothing to the profile exactly because the applicants fail to understand its purpose. The only way that you will have the reader's attention is if you talk research. The statement should not be the place where you state everything that they could have read (in a more appropriate format) in the CV. Your background is, of course, relevant, and you should absolutely include it, but only as evidence of your motivation and involvement with the field and the tools that you wish to learn or use during your PhD. The key to a good statement is to seamlessly merge your interests, background, experience, fit and the necessary tools to accomplish your goal. You should leave a strong impression that you have a solid (not necessarily deep) understanding of the field you are getting into.

So, for instance, don't write this (parentheses are my comments):

  I have always liked to be boring and make people uncomfortable. Since
  I was a child, my parents would roll their eyes every time they read
  one of my essays. Rarely they would be able to finish. As I grey up, I
  felt the need to contaminate my friends with my excitement, and made
  them listen to incredibly long and meaningless talks. (Sorry to be
  blunt, but nobody cares about your childhood.) I graduate in May from
  Boring University and so far I have maintained a perfect GPA. In fact,
  I took several courses in how to be boring, such as Being Boring I and
  I have published a paper where we explored the mechanics of
  self-expression in boring situations, along with Dr. Cheeky Jokes. (I
  have your CV and your transcripts, I can see that.) Now, I want to
  further specialize in making people annoyed, and Awkward University's
  program in Social Engineering is certainly the best in the world (I
  know, why do you think I work here?) and will give me a strong
  background to make people uncomfortable while simultaneously being
  boring (nice, but what do you bring to the table?).

Rather, maybe you should word your essay like this (note how I touch on all three topics while simultaneously referencing the background and fit):

  The strong background that I acquired in boredom from Boring
  University has motivated me to further specialize in awkwardness.
  Working directly with Prof. Cheeky Jokes on the mechanics of
  self-expression in boring situations, I noticed that awkwardness
  emerges directly from personal interactions under these conditions.
  Under the supervision of Boring University's Ethical Review Board
  (ERB), we designed an empty room where we put people who knew each
  other but hadn't talked in several years. Upon examining the data, we
  found that they not only were extremely bored, but also engaged in
  very awkward conversations about their past and how their kids had
  grown up. This very exciting finding was later published in the
  Journal of Awkward Situations. Now, during my PhD and motivated by my
  previous research experience, I want to continue exploring the effect
  of boring situations in the emergence of awkwardness. During my
  research, I became interested in Prof. Clumsy's research on how to
  maximize awkwardness in daily situations. In fact, I believe that
  providing experimental validation for her recent work on finding the
  optimal number of people who will maximize awkwardness in a highschool
  reunion, which she modeled computationally, can be a major
  breakthrough in the field. While Prof. Clumsy has already disclosed
  that she is already working on that, I believe my experience with
  experimental social engineering can be a solid addition to her group,
  especially given that I have had thorough contact with ERBs.

Note, however, that in many cases the SOP is not heavily weighted in admissions, but that's probably field-dependent. And I am not in CS nor in the UK, so take my advice with a grain of salt.


How to make a paper anonymous for reviewers when it heavily extends on your own previous work?

Disclaimer: I work in a field in which double-blind reviewing is either completely absent or so rare that I have never encountered it.

  Would it be acceptable that I mention that this paper extends my previous research that cannot be cited in order to accomplish the anonymity of a double-blind peer-review, and that the citation will be added later?

No, I don't see how that's possible.  The principle that you must cite work that you use or build on -- no less so if it's yours -- seems much more basic than your desire to get genuinely double-blind refereeing.  Moreover, if a paper continues previous work, can anyone sensibly evaluate its added value without having access to that previous work?  I can't see how.

  I am a new guy in the field, and I can imagine that this is where a reviewer could have prejudices. Stupid reason, but I already have an unpleasant experience with this.

When you self-identify your reasoning as "stupid", there's a clear opportunity to think it through again.  The process of journal submission and publication has a non-negligible random component: it would be unwarranted to assume that an experience that you had once or twice will necessarily recur.  Your desire to circumvent an unfair refereeing process seems premature.  If you feel like you're being treated unfairly as a new researcher, there are more productive ways to react to this: make it more clear why your work is competitive with or superior to the work done by more established researchers.  I don't know of any academic field in which journals systematically don't want to publish work by new researchers that they believe is better than prior work just because those researchers are new.  It is also true, unfortunately, that new researchers can overestimate (and also underestimate!) the value of their work.  It is hard to hear that the thing you slaved over for months and years is not good enough for a second-rate journal in your field.  But it may be true nevertheless.

Let me say finally that I see a little irony in your approach: you lament your treatment as an unestablished researcher, but you are in fact more established than most people: you have published a paper that your present work builds on.  My experience is that it is much easier to publish a second paper on the same topic in a reasonable journal than a first paper, just as it is easier for an artist to sell their second painting for a reasonable price than their first.  In publishing the first paper, the journal has conferred on your work the important imprimatur of publishable value.  Insisting on throwing that away will probably increase your chance of receiving "anti-newbie bias" in the evaluation of your followup work!


As an academic with a history of consulting, the proper way to approach the person in question is to contact him directly. Email might work but for initial contacts phone might be better. If he/she is geographically close, a face-to-face would be even better. The initial conversation is really about whether he/she is interested in consulting in his/her area of expertise. If yes, then you can start to dig a little deeper into the project.

Be clear and up front with what you have and what you hope to achieve. Make it clear what the limitations of the project are and that the project might or might not move past the initial phase.

It is unlikely that the size of your business would be an issue but that really depends on his/her personality. You'll know when you ask.

About evaluating if he/she can be a good consultant, explain very clearly what your concerns are. There is no reason for the Prof to be concerned since you do not know each other there is not an issue of personalities and you are not doubting him/her, you are simply saying what you are concerned about. If you have read this person's work you should have an idea of his/her ability to communicate clearly.

As far as managing this person toward the goal, handle him/her as you would any other employee. Normally consultants expect a little bit more freedom but, to repeat myself, be clear with what you want and that might include an update every 2-3 days (more or less depending on the nature of the project - you might want daily updates).

As for protecting your intellectual property, have the Prof sign an NDA/non-compete. This might be an issue if it will in any way limit the Prof from exploring his/her own work. For this, you will need to negotiate what kind of legal protections you feel you need. If you write the non-compete in a narrow enough way, the Prof might feel comfortable enough (he/she is getting something out of the deal).


Do you agree that cheating on exams provides an unfair advantage? Do you think it is “okay” to tell on your peers?

I know of a case in the 80's where a workstudy was assigned to run off physics exams.  She was keeping copies for herself and selling them to students in the class.  On the day of the final exam, a student went up to the professor and handed him a copy of his final.  "Where did you get this?"  The student explained that copies of all his exams had been readily available for $50 all semester.

So the prof made up a new exam on the spot, wrote it on the blackboard and announced to the class that because of this cheating, the final exam would now be 80% (rather than 30%) of the grade for the course.

A certain student named Mike, who had not cheated all semester and was doing well in the class ended up kind of bombing the final.  If the final had counted only 30% of the grade, he'd have been fine.  But he ended up with a C because of the new weighting.  Mike had a "Regent's Scholarship" at this school, which was worth thousands of dollars (tuition, fees, dorm, meals all paid) and which was re-newable every year.  Because of this C, Mike lost his Regent's Scholarship.  The young lady selling exams for $50 a piece cost Mike $1000's of dollars plus a nasty hit of a C in physics for an engineering major.

This is a stark example of cheating affecting others.  But in general, when there is a "culture" of cheating, then this undermines academic standards.  In most cases, some student cheats, passes Calc I and then goes on to Calc II.  It seems like a victimless crime, but now the Calc II prof has a class that's just a bit less prepared for Calc II than it should have been.  It drags down the class a bit and everyone in the room ends up being just a bit less prepared for Calc III.

As to your question about whether you should rat out the cheaters:  Yes and no.  Yes, tell the prof that there is an unreasonable amount of blatant cheating going on and that you don't think you're being treated fairly when you study so hard and they bypass learning.  But naming names is another issue.  If you say, "Jimmy copies off Jenny on every test", there's nothing the prof can do, because he didn't see it.  You've alerted him to the problem and hopefully he'll keep a sharper eye out or make multiple versions of the exams or something else to squelch the cheating.

(The workstudy was, of course, found out and expelled.  IMO, she should have been prosecuted for fraud.)


What are some tips to keep in mind when solving back of the book exercises?

There are probably lots of similar questions on this site and on mathematics SE. Two suggestions.

Find a friend or group of friends to work on problems with.
Take a look at Polya's How to Solve It for problem solving tips.

I think your goal should be learning from problems, not necessarily solving them faster. Good problems ask for more than  calculating correctly and quickly. If that were all there was to problem solving then computers would be better at it than people.


I cannot speak for the UK/EU but in the US, your funding is not generally "updateable". It always increases by a non significant inflationary rate amount every year.

The only way in which funding is generally updated is if you acquire for yourself some other funding sources which replace your base funding because they have a higher stipend level eg. NSF graduate fellowship, MSR fellowship, Facebook fellowship etc.

The other way in which my funding has been supplemented at least in my case is my ex-adviser used to give me some more funds as research expenses out of his discretionary funding (or other grant funding, I am not sure) because I was involved in extra projects (not directly related to my own but I was brought in as an analyst) on his request.

I do not think that publishing in great journals/conferences will bring in more funding for you (in general)


Overlap between individual parts of BMBF funding proposals (Germany)?

Ask the Projektträger (preferrably via phone). They will help and tell you the rationale behind the approach (which I don't understand either).


Is it possible to get a researcher position in a prestigious institute with a degree from a not very well-ranked university?

Yes, it is.

When you apply for a postdoc position several things will be important:

what you have done (i.e. does it fit with the future PI's research
agenda),
how successful it was (i.e. did you publish your results
    in a top journal) and
you know what you want and you are burning for it

The name of the university might matter as well but once you graduated from your PhD your personal profile should be distinctive enough and the name does by far not matter as much as after your undergrads where everyone looks the same expect from the university name, marks average and some internship.


Should student or supervisor be corresponding author for publications based on student research?

"The corresponding author is the one who take the responsibility of a paper". I've never heard this before. For example: http://sciencecareers.sciencemag.org/career_magazine/previous_issues/articles/2010_04_16/caredit.a1000039 says "The corresponding author is the point of contact for editors, readers, and outside researchers who have questions about the contents of the paper. Often, the corresponding author is also the last author, but she or he may be listed first or even in the middle of the author list."

All authors take responsibility for the paper (or should). The point of the corresponding author is who to contact if you want to correspond about the paper. If this were someone who was likely to move institution (because they are finishing, or have finished their study), they are going to be hard to contact, so make it someone who's likely to hang around for a while. I've never seen anyone take any notice of who the corresponding author is.


Should I contact potential referees for a job application?

As I don't know about the academic practice in Switzerland, I may contribute some theoretical thoughts.

What is the benefit of having people evaluate one's achievements or products in general when they do not know you in person? I guess the key is to have them unbiased. Then it will be better to name them without contacting them in advance.

A drawback may be, that if you name a person who has no time or interest in judging your scientific output it may look unprofessional if you provided their name without checking for their willingness to do that task.


Be a member of TPC of a low quality conference

I strongly suspect that these are fake conferences, ultimately designed to scam you, other researchers and/or grant agencies for money. Any voluntary association with such events is a sign that you are rather clueless as an academic, and should be avoided.

There, however, plenty of small, very specialized conferences with high acceptance rates. These serve more as meetings and get-togethers for their research community than as highly respected publication venues. Being asked to serve on the TPC here is essentially a statement by your community that you are a respected member of this community, and would be a nice addition to the CV of a recent graduate.


Include a mistake that cost extra when asking for reimbursement after faculty interview?

Assuming they liked your presentation, and consider putting you on the shortlist, but are not sure at which position compared to some other candidate; now, reflect, which impression this makes.

You made a nontrivial mistake which is also quite costly.
You ask them to cover that mistake of yours.

Even if they would be willing to do so (and assume it would be eligible at all, which is also not clear - why should they reimburse you for your mistake?), consider how this comes across.

Unless you really are in dire need of the money (and it's not clear you are going to get it anyway), it's probably the wise thing to let things be.


Writing "thank you" note to professor who will write more LOR's?

If you are worried that sending such a letter would be something of a bribe for the future letters, you can rest easy. No one is likely to think that. But there may be a lot of reasons to thank professors, including what they contribute to your education.

But in the case that someone writes you a letter and you get an award or offer partly as a result, then you should definitely thank them.


Why did I receive a negative response from a professor when emailing about course content and prerequisites of a course I am considering taking?

There is nothing inappropriate (that anyone can see here) in the way that you've written your email. The response from the professor suggests that they're some combination of (a) incredibly time-constrained, (b) sloppy and unclear in how they communicate, and (c) a jerk.

It's possible (as user2768 suggests) that the essential "offense" in their eyes was to ask about things available in the online site. If so, then their first sentence was a sloppy and mostly mindless piece of aggression that doesn't really mean what it says.

The curtness, snarkiness, and level of aggression communicates that they don't like interacting with students by email, do not want to spend time on it, and want such querents to go away and not bother them.

Given the above, writing them again and asking for more time to be spent on even smaller minutiae -- like revisiting what they meant in a hastily-written throwaway email, and to spend even more time parsing the grammar of the original student email that they've already expressed contempt for handling -- is only likely to make things worse.

I suggest that you accept this line of inquiry as not useful and likely to produce only further confusion and frustration on both sides. Do not email them again on this matter. If you must email them again in the future, on some different matter, make it as brief as you possibly can (shorter than your original email), and try to pose a question that can be given a very short, clear-cut answer.
I'll say that the only thing the professor really got right there was in accurately predicting your next instinct would be that, "very soon you will be writing many more official emails", and to be aggravated-in-advance by that prognostication. Resist the temptation to fully prove them right!
Also, consider asking around if this professor is good to interact with (maybe people you know or a ratings website). If their course is not required, then you may be getting a signal that they're just not a good professor.


Is the journal "The Winnower" scientifically trustworthy?

"Scientifically Trustworthy" is not something with a fixed meaning. But lets break down some things that it could mean:

Is this as good as a peer-reviewed journal?: If you believe in pre-publication peer review, the answer to this is clearly "No". The Winnower is an experiment, a philosophical stance, an an extreme exercise in transparency in the publishing of scholarly material.
Does it have the reputation of a good journal in X field: Again, probably not. I do know some people who have considered fairly extreme principled stands in favor of the same things The Winnower supports - open science and post-pub peer review, who look on it favorably, but I very much doubt it carries much weight in most fields - at least the ones I'm familiar with.
Does it count as a publication?: Maybe. This will very much depend on whose reading your CV, etc.
Is it predatory?: With it being free to post things, and a DOI being relatively cheap, I think it's hard to argue that The Winnower falls in the category of a predatory journal.

But mostly, I think the question betrays a misunderstanding of what The Winnower wants. The whole stance behind the site is that you shouldn't "trust" a journal because it's The Journal of Whatever. You should interrogate what's published there yourself, and the back and forth between reader and author should be made public.


Is it possible to do a PhD in Environmental Policy and Economics if I do not have an academic background in Economics?

Sure you can. However make sure your supervisor(s) know the economics better (e.g., by looking at his/her current publications) than you. This is because if the supervisor doesn't know the area very well, he/she doesn't know if your work is in fact a contribution because he is not an experienced yet; and therefore it will create a very unpleasant situation in which you work hard; without knowing you are on the right track.


"Transparent"

If I had to condense the meaning of open in open science to a single word, it would be transparent.

The primary purpose of having open source software, accessible data, open access publishing, permissive licensing, and all of the other things we associate with open science, is to "open up" the scientific process as much as possible: allowing and enabling free and anonymous scrutiny of research outputs and the process that produced them, and for the repurposing of those outputs and processes for new research.


For STEM fields, is there self-segregation in United States academia?

There probably is some self-segregation, but nothing above what people normally do in everyday society.

I think it's worth keeping in mind that much of the dialogue regarding segregation deals with the actions of government, an extremely powerful 3rd party. Self-segregation is at best an ethical issue, not legal. Moreover, everyone has a right to free association and can decide who they want to deal with.

Arguably, I would say that academia self-segregates less than society at large, due to more liberal attitudes of academics and students.


You should indicate that the figure was taken from an existing article and that you have modified the figure. My usual means of doing so includes

  Figure adapted from Fig X. in Ref. YY.

inserted at the end of the caption.

You should also make sure to include whatever copyright notice the journal or repository in question expects to be added.


What to do when a co-author submitted corrected proofs without the first author's knowledge?

Of course, I tried to submit a revised version of the corrected proofs and convince the journal to use these, but I assume this is pointless.

It isn't! This happens very frequently. But do talk to some human contact person (at least via email) to make sure this is accepted.

  Team work

It seems like there hasn't been much team work. Talk to your former advisor, directly, on the phone; tell him you want to coordinate the proof work with him, and mention that in the currently submitted versions there are problems X, Y and Z. This should piss him off.

Don't leave this to email - either face-to-face or voice call, for a stronger impression and sense of urgency.


Is it appropriate to use emoji or similar icons in a paper?

I'll answer from the perspective of a different field. In the biomedical sciences, it isn't uncommon to use some cartoonish representations to depict animal tasks/procedures, particularly because actual pictures of animal subjects are often avoided for a number of reasons. The same can be true for human subjects.

I wouldn't think twice about seeing a smiling versus frowning monkey indicating task performance in a figure, as long as it was instructive/guiding and not interrupting/distracting. Same for other types of icons like thumbs up/down. Certainly emojis in text would be totally different.


Etiquette for effective workshop comments

I am not sure that your questions at a conference are necessarily a major concern. If you look at how science is propagated, conferences are typically a step before publication. Therefore, it is noble of you to think of it as a point where you can provide constructive comments to authors about their work. However, the most critical point comes when work is published and peer-reviewed.

Based on your experience at conferences (which I to some extent share) you can ask yourself the following: Is the author/presenter interested in your comments. If he/she is, then it would be counter productive to ignore your questions. The question-and-answer format, on the other hand, is too brief and fragmented considering the time constraints of a presentation schedule to be the forum for constructive criticism. That is probably also why the more aggressive questions dominate. In the end, there is nothing wrong with approaching a person during a break to initiate a deeper discussion. you will then also get a better feeling if your comments are welcome.

A final thought. I tend to think as the saying: it is sometimes better to be silent and seem a fool than to speak and prove it. You can exchange "fool" by whatever trait you wish.


Should the PhD supervisor's name be first in a scientific journal?

I am just wondering if the ordering of author names matter?

In a small number of academic fields -- like mathematics -- the overwhelmingly majority of jointly authored papers list the authors' names in alphabetical order.  In these fields, a non-alphabetical ordering of the authors stands out like a sore thumb: the average mathematician knows it is meant to look bad for the latter-listed author but is not sure exactly what it means.  In a field like this, if you hear a potential advisor say this, you should say "Thank you, I'll look for someone else" and walk out the door.

In most other academic fields, the ordering of the authors conveys important meaning in a manner which can be subtle and vary from field to field.  There are some academic fields where being the last named author carries a lot of prestige, but in my understanding this is the kind of prestige awarded a very senior person.  I don't know of any academic field in which putting the junior author at the end looks good for them.

But anyway, here is another kind of answer to your question: the ordering of names must matter to your potential advisor or she wouldn't have brought it up!  Therefore if you yourself are not sure what rights you are signing away in such an agreement, you should be especially skeptical.  I think the first thing that you should do is look around to see how common this practice is among other faculty and students in your department.  (If you are in an academic context far from the American one, it would be more prudent to do this even if you are in a field like mathematics than to immediately walk out of the office like I suggested above.  I don't know what the standard arrangement is at every math department in the world...obviously.)  This will be easy to check just by looking at the publications of the faculty members.  Also asking the other students can help.

  She is going to help me only by proof writing my article. All research will be done by myself.

Proofreading is not the same as advising.  An agreement where your advisor guarantees in advance not to advise you in most meaningful ways and that she will insist on first coauthorship sounds like an especially bad one.  It also sounds unethical to me by the general standards of academic ethics, although subfield ethics may have a role to play.

  Is she legally allowed to say it?

Not every form of bad behavior is illegal (thank goodness).  I can't speak to the law over the entire surface of the earth, but in the US there are certainly no laws pertaining to this kind of thing.

  Should I accept it?

I think that what potential advisor is really trying to say is that she does not want to be your potential advisor.  Sometimes people have trouble saying "no" outright; this happens in academia (where the tenure process takes a good shot at making "yes-men" and "yes-women" out of academics) but also in life generally.  A lot of times I have seen academics offer to do things for students only under quite unreasonable conditions that they clearly (to me) expect the students to turn down...only to have the student not know so clearly that the conditions are unreasonable and accept them.  Of course both parties end up unhappy.

In your case I feel reasonably confident that your advisor is trying to tell you to go away.  What I am unsure of is whether she's telling it to you specifically or to all students generally: the rather oafish "this is the only thing she gets from her PhD students" seems to indicate that this professor is simply not onboard with the practice of having PhD students at all.  But either way, I advise you to look around: probably you can do better.


While it is not specifically for general literature reviews, but more aimed at systematic reviews and meta-analysis, the PRISMA Statement is widely used in the biomedical literature, and even comes with checklists to make sure a manuscript has a few key elements, such as:

"Present full electronic search strategy for at least one database, including any limits used, such that it could be repeated."

Which is something that's pretty necessary for repeatability - you will often find for systematic reviews that an appendix is included with the actual queries used, what dates, etc. In a more general sense, that's what I'd look toward: "Does my review follow most of the guidelines for presenting a meta-analysis, even if it doesn't bother with summary estimates?" If you do that, you're likely on pretty solid ground.


Undergrad studies in Physics: Europe vs America?

An undergraduate degree in physics in Germany will usually leave you better prepared for PhD work than an undergraduate degree in the U.S.  Of course there are plenty of people who are individual exceptions, but what I'm saying is that the two degrees are not perfectly aligned.  You need to keep in mind that the German equivalent of the U.S. high school is not perfectly aligned with the U.S. high school "diploma" either.  You would have to do U.S. high school plus one or two years of U.S. college to be at a comparable level to the entering first-year college physics student in Germany.

I am basing this answer on what I have heard from my spouse who studied physics in Germany, and my spouse's comments over the years about what our son did in high school and college (physics major) in the U.S. where we live.

But the best way to check if my answer still holds would be to compare programs of study, course descriptions, and syllabi.

Bottom line, for physics, at least, you can probably go comfortably from a German undergraduate degree to a U.S. PhD program.


How can I list on my CV that I graduated from college in 3 years?

There are no magic words - you just say that thing you want to say.  The simplest way would be simply to specify the years you attended university, and then explicitly note the achievement you want to highlight.  One thing to note is that there is little point in mentioning this unless you have some statistical evidence that graduating within three years is actually a genuine achievement.  Try something like this:

  Education

  Bachelor of Doing Things (Oxbridge University) (2016-2018) Graduated with a GPA of 3.61 and won an award for being the top student in my third-course on doing good things.  I was in the cohort of 3% of student who successfully complete this degree program within three years.


How many papers does a mathematician publish (on average) in a year?

This varies on a lot of things (e.g., by field and what kind of institution someone is at), however, there have been various studies.  For instance Figure VII (p70) of this study (which seems a bit strange to me) graphs the annual number of papers per mathematician and their most recent data (2005-2008) appears to put the average just under 0.7 for "high-exposure mathematicians" and 0.2 for "low-exposure mathematicians."

That said, things vary a lot by area and what one considers as "research active."  I would guess that it rather pure, theoretical areas (which I am most familiar with), among people I consider professors research active 1-2 papers/year is pretty typical.  For postdocs I imagine the average is < 1/year (including those who are not "research successful") and for US PhD students < 0.2/year (most PhD students probably don't have anything published by the time they graduate, though they may have 1-2 preprints).


What should I do while in an undergraduate engineering course to keep a proof of the math knowledge I gain by self-study?

I feel sufficiently compelled to answer this as a recent math and physics major who completed his degree requirement.

In my undergraduate class, I was taking various combination of 4 math and physics units each semester -- 4 unit is the heaviest load one can take in a semester.
At the top end they were partial differential equations, real analysis, Abstract Algebra, Topology and geometry, mathematical physics, Advanced topics in Quantum mechanics and atomic physics such as quantum mechanics operators, measurement theory, spin and orbital momentum, LS coupling, jj coupling, helium atom, fine structure, hyperfine interaction, atoms in magnetic fields, electron spin resonance, transition probabilities, astrophysics and condensed matter physics, dynamical systems, applied and computational modelling of physical systems.
On top of these, I took various quantitative units in economics and did very well even in absence of the prerequisites.

, denotes a limiters of the different subjects/ units/ course/ modules

This is a 3 years standard bachelor but I completed it in 4 years. If you are prepared for the sheer amount of hard work, extreme burn out and a lower than average GPA, do it. Mine dipped slightly below a 3.0/4.0 but I had strong references and computational skills.

  The natural thing to do in such a case would be pursue a minor in mathematics. But, unfortunately, our university does not offer any minor degrees or dual major degrees. So, it's not possible for me to formally take extra classes in mathematics.

Everything on your transcript is just ceremonial. What is more important is you knowing the subjects and actually being able to demonstrate it on a technical test/ chalkboard when called.

I'm speaking this as someone who has recently started collaborate on a research project with a professor while looking around for industrial opportunities.

If you're looking to work alongside research members, academics or professors, you may be asked to provide some insight as to what you have already covered in your time; in this case, you are free to draw upon what you have taken in your undergraduate curriculum and free time.
People effectively wants to know what you know, not what you have taken.

In my limited experiences, professors are actually impressed with students who challenge themselves by taking advanced units, even if they consider you foolhardy.

  Upon pondering a bit I realize that I might want to pursue my higher studies in some interdisciplinary area which involves knowing things from electronics engineering as well as from the rigorous mathematical physics and statistical learning (machine learning/data science/AI). I'm not sure if such an interdisciplinary area of study even exists at the graduate level (?).

While I am equally unfamiliar with such combination in academia, you may circumvent the lack of such opportunities in universities through independent study.
Most research these days are cross functional across seemingly unrelated fields so much is dependent on the candidates to independently learn.
In my short experiences with looking for opportunities in areas of data analysis and machine learning, the common litmus test is a request for candidates to undergo a technical test much like how developers are subject to technical tests despite their year of experiences.

In STEM, hardly anyone will give you the luxury of knowing something just because something came up on your transcript.

  But I'm really enjoying learning the new things in mathematics and I don't want my spending time on learning these things go in vain.

If this is not a contradiction then there is insufficient data.


Master of Engineering vs Master of Science?

The main practical difference between the two degrees, as you point out, is the requirement of a research thesis for the MS degree.  Generally, if you have aspirations of eventually getting a PhD, you should strongly consider the MS, as research experience or potential is a large factor in being admitted to a PhD program.

To answer your specific question, you should be a better researcher after completing an MS, and you will be better prepared for further graduate work.  With an ME degree (considered a "terminal" degree), you'll simply have a Master's degree and (potentially) may have spent more time on your coursework.  Whether or not this prepares you better for a position in industry is debatable -- as you say, many ME programs are one year, which may actually include fewer classes than an equivalent MS (although I've generally seen ME programs that have one or two more classes as a requirement than the equivalent MS degree).

As to which degree leads to more jobs in industry, I'd say it's probably about the same.  Getting an MS will certainly not limit your competitiveness for industry jobs, while (as I already mentioned), an ME may limit your competitiveness for PhD programs.


What are some examples of research that does not solve a existing problem (maybe the problem is not obvious yet) but present a unique discovery?

Feynman noticing the periodicity of wobble and rotation of a dinner plate.  The fractional quantum Hall effect.  HTSC cuprates.  Initial discovery of superconductivity.  Michaelson Morely.  Many discoveries of new plants and animals.  Penicillin. Teflon.  The discovery of the Americas.


Doing a PhD in sociology as a computer scientist – is it possible?

No, there's no legitimate way for you to get an online PhD in sociology (which is a social science, not humanities, but eh, lables are silly anyway), at least not with the profile you describe. You are also extremely unlikely to be considered for a normal sociology PhD programme. Speaking as a member of a sociology department, you quite simply do not have the background in the method and theory of the discipline needed to produce PhD level work. Just like I don't have the tools to suddenly do a CS PhD, you don't have the tools to do a sociology one. Successfully applying sociological theory and producing competent, critical analysis, not to mention data collection itself, is actually extremely difficult. You can't just casually pick it up. It recently took me 8 months and 40 pages of evidence just to get ethical approval to start a sociology project...

What you can consider is a taught one year masters programme in sociology, either in the UK or elsewhere. Some of them are available online and some are willing to admit students without a sociology undergraduate degree if they can articulate why they are making a disciplinary shift. Mine wouldn't accept you with an undergrad in CS without a strong focus of that CS research being sociological in nature, but others might.


If I'm understanding correctly, the problem you're concerned about is what to do when you've just submitted a paper, and now you have a long wait before you can submit the follow-up paper.  Your question then presumes that a good solution to this problem is to try to accelerate the publication process.

I think that is a bad assumption.  There is no reason that you need to be stalled on your forward progress just because a paper is under review.  Here are two good alternatives that work within the system.

You can continue directly building on the same direction.  If you get to a major milestone and are ready to submit a new paper before the previous one is finished reviewing, you can submit a paper citing the one under review as "submitted," and include the draft paper as supplementary review-only information.
Research typically has a lot of "branching path" options getting catalogued in your "future work" sections.  Why not take a secondary path that you've wanted to investigate but isn't in the same exactly line of progression as the paper currently under review?  That will likely lead to its own interesting results that can be published without dependency on the paper currently under review.

It also seems possible to me that this concern may have arisen due to trying to publish too incrementally.  If you cluster your work into larger "publication units" the time lag will likely be less problematic and a smaller number of significant papers is generally better for your career than a bunch of little incremental papers that nobody cares about.


Does repeated retakes of a test with average score of all attempts allow manipulation?

I have never encountered a computerized exam in which you have an unlimited number of consecutive attempts on the same questions and for which your final score is the average of all attempts.  This does seem to be gameable as you describe as well as perhaps in other ways: depending on the format of the answers, I could imagine many tests in which one could eventually deduce all the correct answers with little or no knowledge of the material being tested.

This does not seem to be a very meaningful or rigorous way to run an examination.  I have never given an online examination but am rather familiar with online homework: there we often allow unlimited multiple attempts (except if the question is true / false or multiple choice, but most are not) and simply record the best score.  But the goal there is not to assess the students as much as to get them to do their homework.  Anyway, all such systems I know of certainly feature an easily "togglable" maximum number of attempts.  My feeling is that an instructor who sets up an exam as you describe is either unusually naive or -- more likely -- knows what they are doing and has reasons to want or live with an exam which can be gamed in this way.

Nowadays I and many other academics have to periodically take little computerized exams in which we show ourselves to be familiar with current university policies (ethics, security...) Many of my colleagues are indeed trying to get through them as quickly as possible and trying to minimize the amount of time they have to spend reading background material (or worse, watching in-house informational videos).  Even these exams are not gameable to the extent that you describe.


Ph.D. in UK/Ireland as "Dipl.-Ing." from Germany

In short, yes. If you're talking about the "traditional" 5 year Diplom, it's essentially equivalent to an MSc, which is what most universities require to start a PhD (although some only require a Bachelor's degree). I don't think you need to keep anything in particular in mind when finishing, apart from making sure that you get good grades for your transcript :)

The application procedure wouldn't be any different from other students, although you may have to explain in some detail what your degree is.


Can American students do research in Europe with only a bachelor's degree?

I think there are two parts in your question: can someone with a Bachelor from the US get a job from a university or research lab, and what kind of visa such a person would need. For the first question, it's really depending on the university. As for the visa, it depends if it would be for a PhD student, or for a "regular" researcher (i.e. not a student). However, in both cases, the visa application depends on the country, as far as I know, there is no Schengen Research Visa. For instance, for France, there are two types of Visa the person could apply to (Visa section of the french consulate in Washington)

The “Skills and Talent” Card visa (Carte Compétences & Talents). However, for this one, they say:

  University graduates should be PhD. Lower graduates will be required to add proof of profesionnal experience in the same field for a minimum of 1 to 3 years (the lower the degree, the longer profesionnal experience expected)

Visas for professors and researchers holders of a "convention d’accueil". According to this site (in French, I couldn't find an English version), a "convention d'accueil" would basically be the work contract with the university/lab, and the eligibility requirement seems to be a Master degree or equivalent (but it could be the case that a 5-years US Bachelor degree counts as an equivalent to a 5-year French Master degree). As far as I understand, that would be the best option for someone who wants to do her PhD in France.

It would also be possible to apply for a student visa, but I think it's not possible to get a work contract with such a visa. Another solution could be to apply to a:

 Employer Sponsored visa / OFII. There does not seem to be anything specific to research in this case.

So, to sum it up, I don't think there is a unified process to apply for a visa in Europe as a researcher, and each country has its own rules. Note that these visas are not automatically Schengen visa, and I've known the case of some extra-EU students, who obtained a visa in one Schengen country, and were not allowed to travel in other Schengen countries before becoming officially resident of the country.


Are Japanese professors responsible for their students' behavior outside the university? Legally perhaps not (I'm no expert), but culturally, yes.

What happens/could happen to a Japanese professor if their student has e.g. a messy apartment?

The professor gets disgraced. It's like being the father of someone who later goes on to become a serial killer. Nothing directly happens to you, but it's still going to be very unpleasant. Did you fail as a father? Even if you think you didn't, perhaps your neighbours will think you did.

Is there something similar for undergraduate students (who, I suppose, do not have a professor in the sense above)? Is the university somehow responsible for them?

Yes, if they are being directly supervised by the professor.

Where is this responsibility stated? Is it e.g. in the law, or is it rather some non-official convention that everybody follows, or something in between?

It's a social expectation, similar to how in many societies children are expected to take care of their parents in their old age.
Check out what happened to stem cell scientist Yoshiki Sasai in 2014: his student faked data, leading to a scientific misconduct probe. Prof. Sasai was cleared of misconduct, but he felt deeply ashamed and later committed suicide. Granted, this was an academic issue, but it illustrates what Japan's expectations of their teachers are.
Edit: for a non-academic situations:

Probably the strangest tasks (in the eyes of Western teachers) are things like guarding the campus and ordering the fuel oil. They are also partly responsible for their students outside school. Japanese students have to follow several rules in their leisure time: they are not allowed to smoke and to drink alcohol, to go to discos or to have a job by the side. In case of disregarding these rules, the teacher is obliged to inform the parents or even to make home visits (cf. SCHÜMER 1999, p. 34). As one can see from all this, the tasks of a Japanese teacher go far beyond giving lessons.


Socially acceptable to email a connection of a connection requesting information?

Ideally the person who knows both of you would write a short introductory email and send it to both of you.  You could request that he do that.

If he doesn't do that, you can still mention that he suggested that you write to this person at the beginning of your email.  Just use a succinct, mildly friendly, and professional tone, and you'll be fine.


How does your area of research affect your chances of getting job in academia?

Trendiness can be factor, but a much more important factor is what needs the hiring department has. If they're chock full of topologists, it doesn't matter how "trendy" your work in topology is: there's a good chance they might be looking to expand in other areas.

OTOH, if they're looking in your area, then being at the cutting edge can't hurt. The danger of course is timing: trends rise and fall quickly, and what might be trendy right now might not be so in a year or two (maybe in mathematics, trends move more slowly).

So I'd argue that trendiness, while one potential factor, is not a universal key factor at all. Every department has their own needs.

As regards your second question, usual measures of "trendiness" include the relative frequency of publication in that subarea. In CS, it's relatively easy to determine this via conference acceptances, but in math I'm not sure how you'd go about measuring this frequency. It also helps to attend big meetings and listen to where the buzz is. An advisor can also be helpful in this regard (especially if they're pre-tenure and need to keep track of trends themselves :))


Can a student write their undergraduate thesis on the main result of a paper under review for a journal?

If the student did the work, then I see no problem at all. While its never happened for me with an undergrad dissertation (mostly because UGs get about 3 weeks to write their dissertation after the research period has finished, and a paper takes at least 6 months to go through review), this is a pretty normal thing to happen for a PhD.

Write up the paper first and submit it for publication. Use this as a good starting point for the thesis. If the stars align, the paper will be back from review with corrections at about the time the thesis is submitted, and the corrections to the paper can be done while the student is waiting for their viva.

This is all on the proviso of course that the student actually writes the dissertation themselves and doesn't just paraphrase an article written by their supervisor.


Term to describe paradox where those with less subject matter expertise can sometimes make better teachers?

This is called the curse of knowledge. From Wikipedia:

The curse of knowledge is a cognitive bias that occurs when an individual, communicating with other individuals, unknowingly assumes that the others have the background to understand. [...]
For example, in a classroom setting, teachers have difficulty teaching novices because they cannot put themselves in the position of the student. A brilliant professor might no longer remember the difficulties that a young student encounters when learning a new subject.

Writer and organizational psychologist Adam Grant nicely illustrates the concept in this article:

Two decades ago, I arrived at Harvard as an undergraduate excited to soak up the brilliance of professors who had won Nobels and Pulitzers. But by the end of the first month of my freshman year, it was clear that these world-class experts were my worst teachers. My distinguished art history professor raved about Michelangelo’s pietra serena molding but didn’t articulate why it was significant. My renowned astrophysics professor taught us how the universe seemed to be expanding, but never bothered to explain what it was expanding into (still waiting for someone to demystify that one).
It wasn’t that they didn’t care about teaching. It was that they knew too much about their subject, and had mastered it too long ago, to relate to my ignorance about it. Social scientists call it the curse of knowledge. As the psychologist Sian Beilock, now the president of Barnard College, writes, “As you get better and better at what you do, your ability to communicate your understanding or to help others learn that skill often gets worse and worse.”


Is teaching calculus important for getting a job as a university professor in mathematics?

I would be truly shocked if any hiring committee cared at all about whether you taught calculus versus pre-calculus.  Doing well at either would show that you can adequately handle teaching service classes.


Is it legal to use images from social networks for research?

In order to copy or redistribute images that you don't own, you have to comply with the terms of the license under which the owners have released the images.

Some images are released under licenses (such as Creative Commons licenses) that allow copying and redistribution under various conditions (e.g. attribution, non-commercial use only, etc.  - depending on the specific license.)

For example, the People In Photo Albums dataset was "collected from Flickr photos
with creative commons licenses", according to the paper. Similarly, Yahoo! Labs compiled a dataset of One Hundred Million Creative Commons Flickr Images. And Google released an Open Images Dataset dataset of images that are listed as having Creative Commons licenses.

If there is no license accompanying the image or no blanket license applying to all images on the site, you have to assume that it is All Rights Reserved - in this case, you would not be able to redistribute these images.


Project guide asks for authorship without any contributions – how to proceed?

Let’s start with what is going wrong here:

Requiring you to publish something peer-reviewed on the level of coursework is at least dubious. For more details, see Is it ethical for departments to have publication requirements for students
Putting somebody as an author of a paper who made no contribution at all goes against all standards of academic authorship. However, violating this is so common in some countries and fields that many professors may not even be aware of it.
The project guide is abusing her power when she pushes you into giving somebody authorship (who doesn’t deserve it).
If your institution via rules or coercion makes you give somebody authorship (who doesn’t deserve it), this is also an abuse of power.

Now, you have to evaluate the situation to pick your enemies and allies, if any:

If the curriculum has any written rules that you should make somebody a co-author, you can fight those rules – if any professors or a higher power cares about this. In my country, I don’t see much of a problem of turning this into a public scandal, but yours is probably different.
If there are no written rules about authorship, and one of the other professors evaluating your project or a dean of students or similar are trustworthy, you can present the situation to them and try getting them onto your side. At the very least, you may score some points if you can provide evidence that your project guide did not tell you about any authorship aspirations or rules earlier and also did not do her job properly.
The journal (if reputable) will not be very happy if not completely refusing to change authorship retroactively. You could find an ally here (just tell them what happened), but whether the journal has sufficient power over your department is hard to say.
It could sadly be that your institution is full of power-abusing professors and in a position that allows them do this. In this case, the only thing you can do about it is to leave.


Can I write "equal author contribution" in acknowledgment?

To add to the previous answer, I would consider that listing equal contribution in the acknowledgement section generally does not carry the weight as listing it as part of the front page. However, if it is clear that journal policy does not allow any mentioning of equal contributions on the title page, the acknowledgements may be your best options.
However, I think that you should have a clear discussion about this right away between the senior authors, the co-authors, and the editor. Co-authorship can have significant impact on the career of individuals, so you want to be certain that everybody is clear in what is going to happen and is in agreement with the path chosen.


How can I improve undergraduate students' writing skills?

Several thoughts.

Give writing assignments (goes without saying). Probably more short
ones rather than fewer long ones.
Make sure students know that form matters as well as content. To
encourage students who start from a disadvantage, count improvement
as well as mastery.
Collect and critique first drafts before grading the final work.
Allow students to resubmit essays.
More problematical: have students critique each others' work before
submission. Those critiques could even be private, so that students
wouldn't be calling each other out before the teacher, only noting
when some argument was unclear to them.

Of course this will be time consuming for you and for them. To do it properly you may have to revise the course objectives to include work done to improve writing - at the expense of "more content".


Am I aiming too high if I am applying to physics graduate schools in Canada?

Let me start with the cheat code of Canadian admissions: in Canada, the professors in the department you apply to look at your application package and decide if they, personally, want to take you on as a student.  This means that the decision is up to the professor: if they want you, you're in; if they don't, no GPA or GRE score can save you.  So the secret is to decide who you want to work with at each school you're applying to, contact them, and convince them you would be an awesome student.

More specifically, for each university, look at its website to find out who works in the area you're interested in.  Look for a list of research groups, such as this one for Toronto.  There will usually be a small number of professors per group; for each professor, get a list of their papers from their website.  (If they don't have such a list, which sometimes happens, try Google Scholar, but make sure you're finding the right John Smith.)  Pick the professor (or two) whose work seems most interesting to you and look at their papers in a little more depth.  Don't worry if you don't fully understand them -- if you did, you wouldn't need to go to grad school -- but try to get the general idea of what the authors did and why.  Then email the professor, briefly and politely covering the following points:

Ask if they are accepting new students this year. (They may be low on grant money, going on sabbatical, etc.)
Describe your research interests.  If you wrote a paper or gave any talks about your research, mention it.  Good communication skills are essential in research.
Describe how your research interests fit with the professor's own interests (which you're familiar with from their papers).
Reaffirm your interest in their work and show off your preparation by asking a question about one of their recent papers.

This is obviously time consuming, but it will greatly increase your chances of getting in.  Most professors will be impressed by your interest and level of preparation.  (I say "most" because there is one professor in my department who complains bitterly about getting emails from prospective students.  You may encounter one of these, if you're unlucky, but the good news is that you wouldn't want to work with them anyway.)  Use your institutional email address to minimize the chance of getting caught in spam filters.

One other point: in Canada, at least, many STEM fields have two kinds of master's degrees:

A terminal or coursework master's, which you get by taking a certain number of courses (8 in my department).  You cannot enter a PhD program with this degree (hence terminal) and you usually don't get any funding.  They can be often be completed in a year or sixteen months.
A non-terminal or thesis master's.  These are intended to prepare you for a PhD, so you get the degree by taking a smaller number of courses (4 in my department) and writing a thesis.  These are usually fully funded and take two years to complete.

Now, let me (finally) get to your actual questions.

How helpful is Canadian citizenship?  Somewhat helpful if you're applying for a non-terminal degree.  I mentioned that these are usually funded, which means you get a stipend to cover your tuition and living expenses.  However, the tuition you pay depends on your citizenship.  Canadian universities are subsidized by the government, so citizens (taxpayers) are charged less than non-citizens.  This in turn means that international students need a bigger stipend to cover their higher tuition.  All else being equal, a professor will choose a cheaper citizen over an expensive international student.  Being a citizen will also make it slightly easier to win scholarships, since many require citizenship or permanent residence.
How important are grades? Most programs require a minimum undergraduate average of 78%/B+, so you're definitely borderline.  Stay above the minimum if at all possible, and if there is an explanation for your grades (e.g. illness), include it in your application.  If you did better in later years or courses that are core to your degree, mention that.  Nobody cares if you failed underwater basket weaving, but if you failed calculus, you're in trouble.  Finally, make contact with the professors you want to work with; if they want to accept you, grades will be much less of an issue.
How important are GRE scores? Practically irrelevant.  Students with a non-Canadian bachelor's are sometimes (not always) asked to submit scores for the general test, but as far as I know no program asks for scores on the subject tests.
How helpful is research experience? All honours undergraduate programs in Canada require a thesis or a capstone project in the final year, so this isn't special.  Fewer students do summer research, so that will help your application.  The main issue is that "research experience" is a fairly meaningless term, so when you write your application letter, be as specific as possible about what you did and learned.  "I have research experience" is not nearly as powerful as "I learned the standard technique for measuring XXX and applied it to a project exploring effect YYY.  I then presented the results at conference ZZZ."

Final disclaimer: I'm in computer science at Waterloo.  As far as I know, everything I said is true for physics departments and other universities, but I can't guarantee it.


One perspective is from the Journal of Open Source Software, which explicitly establishes reviewer guidelines that cover these questions (http://joss.theoj.org/about#reviewer_guidelines).

A (slightly edited) quote of the demands:

  Software license
  There should be an OSI approved license included in the repository.[...]

  Documentation
  There should be sufficient documentation for you, the reviewer to understand the core functionality of the software under review.

  A statement of need
  The authors should clearly state what problems the software is designed to solve and who the target audience is.

  Installation instructions
  There should be a clearly-stated list of dependencies. Ideally these should be  handled with an automated package management solution.

  Good: A package management file such as a Gemfile or package.json or > equivalent
     OK: A list of dependencies to install
     Bad (not acceptable): Reliance on other software not listed by the authors

  Example usage
  The authors should include examples of how to use the software (ideally to solve real-world analysis problems).

  API documentation
  Reviewers should check that the software API is documented to a suitable level. This decision is left largely to the discretion of the reviewer and their experience of evaluating the software. [...]

  Tests
  Authors are strongly encouraged to include an automated test suite covering the core functionality of their software.

     Good: An automated test suite hooked up to an external service such as Travis-CI or similar
     OK: Documented manual steps that can be followed to check the expected functionality of the software (e.g. a sample input file to assert behaviour)
     Bad (not acceptable): No way for you the reviewer to check whether the software works

  Community guidelines
  There should be clear guidelines for third-parties wishing to: Contribute to the software, report issues or problems with the software, or seek support

This is a valuable way of thinking about reviewing software, and I think we should move closer to this. But it is not yet accepted! In my field, most "methods" papers don't even include software - and those that do would almost certainly fail these tests. (I'd never heard of continuous integration until recently, for instance.)


My PhD went over time - advice for explaining this on a CV

Whatever you do do not fabricate or conceal the truth. I am not sure someone would worry about finishing "on time" as much as looking at the quality of the work you have achieved. In my system there is also a 4-year research time limit (in terms of calendar time it can be extended by including teaching, maternity/paternity leave or whatever is applicable). Regardless of whether you apply for a job in academia or industry the criteria for the employment will be much more than finishing on time. So issues like quality, number of papers published, social skills, other relevant skills will be measured. If you have a reasonable explanation for the extended period of your PhD, just spell it out. Do not make a big story about it, just cleanly provide an explanation that makes the period understandable and reasonable.


Do you have any paper academic calendars or planners to recommend?

This may not seem relevant, but it is something I've found very useful/indispensible over the years, both for studying and for teaching. I actually required some of my students to use them.

It is called a Hipster PDA, which is nothing more than a few index cards and a spring clip to hold them together. I discussed it in answer to another question at CSEducators here. See that link for a fuller description and a further link to pictures, etc.

The reason it is so valuable is that it is both simple and flexible. It is easy to carry everywhere and can be rearranged as needed. Cards can be added and discarded. Valuable cards can be saved in a card box. You can use it for class notes as well as planning. You can use it to take quick notes in meetings or to jot down email or phone numbers, etc.

One advantage of it as a note taking device is that it forces you to condense what you hear in lecture rather than to try to capture everything. This makes your brain work harder, which aids learning.

At the end of a class, for example, you can make a card listing the two or three most important ideas from that class. Review that card at the beginning of the next.

Another advantage is that you are writing the notes, not typing them. This sounds backwards until you realize that writing by hand engages the brain in a different way (and more deeply) than typing.

You can develop your own "header" system for labeling the cards (dates, classes, ...). You can use different colors of cards for different things. You can carry the most currently relevant cards with you. You can spend a few minutes of otherwise "dead" time reviewing notes.


What is the grammatical number of an inline citation?

I personally am comfortable with both ways, for exactly the reasons that you give: it's entirely reasonable to refer to either the authors or the paper.  The important thing is to be consistent with your usage throughout a manuscript, else your readers may wonder why you feel it appropriate to refer to some authors directly but not others.


How to avoid exceeding normal page limits after revision?

How do I avoid this over-length after incorporating all the revisions?

There are a few tricks that authors typically use to reduce a manuscript's length (especially for conference papers with hard page limitations), but none would be sufficient to shorten a paper by 1-2 pages, and some of them might be nulled by the copy-editor. Moreover, the changes would be so substantial that the reviewers might require a second round of major revision.

Therefore, if you really can't afford those fees because, e.g., you don't have departmental funds, my suggestion is to ask the publisher if they can waive your overlength fees.


Is a Harvard PhD in applied mathematics (from engr. dept.) as reputable as a PhD in pure mathematics (from math dept)?

I got my PhD at Harvard in mathematics.  Not in "pure math" but just in "math."  Harvard does not have an "applied mathematics" department or a "PhD program in applied mathematics."  Rather, applied mathematics is one of seven "areas of study" in the school of engineering and applied sciences: see here.  What does this mean?  Well, see here.  It says:

  In keeping with the interdisciplinary nature of modern research, we do not have traditional academic departments and do not award degrees by specific research area. Instead, graduate students work toward a degree in one of seven subjects—Applied Mathematics, Applied Physics, Computer Science, Computational Science & Engineering, Data Science, Design Engineering, and Engineering Sciences.

Some of these subjects have "PhD model programs," but when you click on applied math, you find

  Due to its highly interdisciplinary nature, Applied Mathematics does not have a specific model program.  Students pursuing a Ph.D. in Applied Mathematics should consult with their Director of Graduate Studies: Professor Ariel Amir (fall), or Professor Yue Lue (spring), concerning their degree programs.

Interestingly, Professor Amir is an Assistant Professor of Applied Mathematics.  [Interesting in part because the mathematics department has had only "full" professors for at least 20 years.]  Here is a listing of faculty in applied mathematics at Harvard: the only other professor who is listed as being solely in applied mathematics is also an assistant professor.  This suggests to me that applied math at Harvard may be in the process of becoming more of an academic department than it has been or is now.  The time would be ripe, in view of the record $400 million gift of Mr. Paulson in 2015.

All that was mostly background.  Now I can tell you: when I was at Harvard (1998-2003) there was almost no direct contact between the mathematics department and the mathematics part of SEAS: I knew one SEAS PhD student who was (for some reason) teaching freshman calculus along with the math students.  (I just looked him up: he has what looks like a lucrative industry job in Boston.)  So the answer to your question is: No one I know is comparing these two programs. They are different in every way, with almost no overlap.  It's not as though you could choose to do control theory in the math department at Harvard: there is no one there that does that.  (There is one professor in the Harvard math department who does what I at least would call applied mathematics: Martin Nowak, the Professor of Biology and Mathematics and Director of the Program for Evolutionary Dynamics.)

It would make more sense to compare the engineering program at Harvard to other engineering programs.  US News ranks Harvard's engineering program at #23 currently.  If you look at this page it gives you the ranking of a variety of programs at Harvard, and actually it has the lowest rank of the more than 100 programs and subprograms listed there.  The math department is currently ranked third [it has been ranked in the top three for many years].  So maybe that is a sense in which "pure math is more reputable," although again I stress that this does not seem like the right way to look at it.


Meaning of the term "studies leading to a degree"

In every case I've seen, this term referred to coursework that was part of a degree curriculum, whether or not that was earned. I suspect this is because organizations can simply specify the degree itself if they need the latter distinction. However, without the actual context it's difficult to be certain.