What is purpose and meaning of "Propositions" in PhD thesis?

This is indeed related to customs in Dutch academia. Precise practice and regulations vary between universities, but usually there is the opportunity (or even duty) to provide this list of propositions, usually distributed as an inserted leaflet with the thesis. The propositions themselves vary from serious scientific statements (typically related to the content of the thesis), to more "humorous" statements like the example you posted. These statements can be part of the defense, i.e. the committee can ask questions about them and the candidate has to defend this thesis. In practice (insofar they do not relate to the thesis itself), this only happens when the committee runs out of "real" questions. This can happen because for the defense in the Netherlands a fixed amount of time is prescribed, which cannot be shortened.


Are there any online community investigations of PhD thesis plagiarism outside Germany?

I am not aware of initiatives in other countries. However, while VroniPlag started out with examinations of German doctoral theses, it is no longer limited to those. Today, it investigates suspected plagiarism in PhD theses written in Spain, Ireland, Denmark, the Czech Republic, Austria, and Italy. To the extent that this is a continuing trend, VroniPlag already is an international project.

So the answer to the question in your title (which differs from that in the body), whether online community investigations of PhD thesis plagiarism outside Germany exist, is yes.


How should a graduate admissions committee view (possibly false) accusations against an applicant?

If I were the head of the grad admissions committee (which I have been in the past) and either an anonymous or signed but unofficial email came to me or a faculty member, I would:

1) if the email is from an email address that is reply-able (or from a person who is googleable), I would write to them and request they make an official statement. I would also double check whether the email is actually the one from the person it denotes.

2) if the email is anonymous or the email address doesn’t match, I would instruct faculty to ignore it.

3) however, in either case it’s my responsibility to inform the graduate school that we’ve received derogatory information of unknown provenance. The grad school will likely tell us to ignore it but I need to cover my ass.

In reality, I’ve reviewed well over a thousand files in my decade plus of teaching at the graduate level and haven’t yet received one of these notes. Most faculty if they have something to say, are not shy about writing it in the main letter themselves (whether in coded form or outright).


Where to place tables/figures in APA style dissertation

Thanks for the responses. Just to clarify, I did end up checking back with the department office again to probe in case I missed something, and there were no other guidelines other than the generic ones I initially used.

Perhaps some elements of the formatting for theses are fairly common and thus what my committee member was expecting, but there was nothing from the department or the college that spoke to such things. The guidelines are actually really loose and only define how to structure the page margins, numbering, and to not include running heads. Everything else just defers to respective writing styles.

Honestly while I understand the expectation there, I was kind of annoyed to be accused of being careless when I just followed the institutional guidelines. I suppose at the end of the day it was a kind of departmental deficiency. I will keep it in mind though for the future, thanks.


Channeling bias in social science / epidemiological research?

Channeling bias is a major concern in epidemiology/medical research.  An entire technique has been developed to combat this bias:  propensity scores.  An example of a paper on propensity scores that explicitly discusses channeling bias is "Addressing the issue of channeling bias in observational studies with propensity scores analysis".


Why do most people think it's a bad idea to read from slides?

Research in the field of multimedia learning suggests that in most cases, "people learn more deeply from graphics and narration than from graphics, narration, and onscreen text". This is known as the redundancy principle.

  Previous research has shown students learn better from multimedia
  lessons containing graphics and narration than from graphics,
  narration, and redundant on-screen text (Kalyuga, Chandler, &
  Sweller, 1999, 2000, 2004; Leahy, Chandler, & Sweller, 2003;
  Mayer, Heiser, & Lonn, 2001; Moreno & Mayer, 2002a, 2002b;
  Mousavi, Low, & Sweller, 1995). This finding is known as the
  redundancy effect (Mayer, 2001, 2005c). For example, in a study
  by Moreno and Mayer (2002b), participants viewed an animation
  about lightning formation. The first condition had narration accompany
  the animation, whereas a second condition received
  redundant on-screen text in addition to the animation and narration.
  The group that received the redundant on-screen text performed
  worse on subsequent retention and transfer questions than
  did the group that received animation and narration; thus, a redundancy
  effect was found.

(source: [1])

Why?

  Adding redundant on-screen text detracts from the learning
  processes highlighted in Figure 1 because it creates extraneous
  processing—such as inducing the learner to visually scan between
  the caption at the bottom of the screen and the graphic and to try
  to mentally reconcile the incoming spoken and verbal stream. If
  the learner has to waste limited cognitive capacity on extraneous
  processing, the learner will be less able to engage in the cognitive
  processing needed for learning—essential and generative processing.

(also from [1])

Are there times when it is good to include some of the narration in a slide? Yes. For example:

  The most straightforward contribution of this work is to add an important caveat to the redundancy principle “People learn more deeply from graphics and narration than from graphics, narration, and onscreen
  text” (Mayer, 2005c, p. 193). In revising this statement of
  the redundancy principle, we can add the following limitation:
  “except when the on-screen text is short, highlights the key action
  described in the narration, and is placed next to the portion of the
  graphic that it describes.”

(also: [1])

In a meta-analysis of the literature on the redundancy principle:

  [A]dvantages of spoken–written presentations over spoken-only presentations were found for low prior knowledge learners, system-paced learning materials, and picture-free materials. In comparison with verbatim, spoken–written presentations, presentations displaying
  key terms extracted from spoken narrations were associated with better learning outcomes and accounted for much of the advantage of spoken–written over spoken-only presentations.

(Source: [2])

You perceived the talk with redundant written and spoken text to be beneficial to you; this is consistent with the research as well:

  Research on metacognition has consistently demonstrated that learners fail to endorse instructional designs that produce benefits to memory, and often prefer designs that actually impair comprehension. Unlike previous studies in which learners were only exposed to a single multimedia design, the current study used a within–subjects approach to examine whether exposure to both redundant text and non-redundant text multimedia presentations improved learners' metacognitive judgments about presentation styles that promote better understanding. A redundant text multimedia presentation containing narration paired with verbatim on–screen text (Redundant) was contrasted with two non-redundant text multimedia presentations: (1) narration paired with images and minimal text (Complementary) or (2) narration paired with minimal text (Sparse). Learners watched presentation pairs of either Redundant + Complementary, or Redundant + Sparse. Results demonstrate that Complementary and Sparse presentations produced highest overall performance on the final comprehension assessment, but the Redundant presentation produced highest perceived understanding and engagement ratings. These findings suggest that learners misperceive the benefits of redundant text, even after direct exposure to a non-redundant, effective presentation.

(Source: [3])

Note that the results above refer to multimedia presentations, i.e. those that include graphics. Presentations that do not include graphics may benefit from redundant spoken-written text (see [4]). But presentations that do not use graphics violate the multimedia principle, which states that in general, "people learn better from words and pictures than from words alone".

For more information on principles of multimedia learning, see The Cambridge Handbook of Multimedia Learning. If you're looking for something shorter, here is a brief summary of the major principles of multimedia learning, and here is a presentation by Richard Mayer.

References:

[1] Revising the redundancy principle in multimedia learning. Mayer, Richard E.; Johnson, Cheryl I.
Journal of Educational Psychology, Vol 100(2), May 2008, 380-386. http://dx.doi.org/10.1037/0022-0663.100.2.380

[2] Verbal redundancy in multimedia learning environments: A meta-analysis.
Adesope, Olusola O.; Nesbit, John C.
Journal of Educational Psychology, Vol 104(1), Feb 2012, 250-263. http://dx.doi.org/10.1037/a0026147

[3] Learners misperceive the benefits of redundant text in multimedia learning . Fenesi, Barbara; Kim, Joseph A. Frontiers in psychology 5, 2014. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4088922/

[4] Verbal redundancy in multimedia learning: When reading helps listening. Moreno, Roxana; Mayer, Richard E.
Journal of Educational Psychology, Vol 94(1), Mar 2002, 156-163. http://dx.doi.org/10.1037/0022-0663.94.1.156


What does the term "camera-ready" mean and why is it used?

From the Wikipedia article entitled "Camera-ready":

  The term camera-ready was first used in the photo offset printing
  process, where the final layout of a document was attached to a
  "mechanical" or "paste up". Then, a stat camera was used to photograph
  the mechanical, and the final offset printing plates were created from
  the camera's negative.

  In this system, a final paste-up that needed no further changes or
  additions was ready to be photographed by the process camera and
  subsequently printed. This final document was camera-ready.

  In recent years, the use of paste-ups has been steadily replaced by
  desktop publishing software, which allows users to create entire
  document layouts on the computer. In the meantime, many printers now
  use technology to take these digital files and create printing plates
  from them without use of a camera and negative. Despite this, the term
  camera-ready continues to be used to signify that a document is ready
  to be made into a printing plate.


Citing personal communication from a paper

The particular paper (Warton et al. 2012) the OP is talking about is 6 years old. After such time, the research it referred to may not necessarily be still ongoing - it is likely to be either completed, or abandoned altogether. It would be best to personally communicate with the person in charge of the mentioned research (i.e., M. J. Anderson in this case) in this matter. Either there will be a publication to refer to and cite (citing also the 2012 paper if it's still relevant), or one can just mention the personal communication like it was done by Warton et al.


What has the effect of publishing salaries been?

Have they had to pay more on average in salaries because private sector competitors (including private universities) now know exactly how much to offer someone to entice them?

I've occasionally heard of these lists being used to identify woefully underpaid faculty members who might therefore be disgruntled and easier to recruit.  However, I don't think this has had a substantial effect overall on salaries at public universities.  Most faculty members don't inspire bidding wars between universities, and recruitment is based on many other factors beyond just salary.

For context, note that average salaries vary substantially between universities, and these differences are sometimes pretty widely discussed in the community.  Even in the absence of data on individuals, that's potentially useful information for recruitment.  However, there seems to be no trend towards salaries evening out.  Instead, they tend to end up balanced with factors like desirability of location.

  Have they found it more difficult to recruit people from the private sector (including private universities) who might not want their financial details to be public?

Not to a noticeable extent, at least for ordinary faculty positions.  This could be more of a factor for mid-level administrators, whose salaries might come under greater scrutiny.  (By contrast, the salaries of top administrators are public information for every non-profit university in the U.S., public or private, because they must be reported on IRS Form 990.)

  Have there been any other negative or positive side effects?

Transparency about salaries has a weird mixture of effects.  On the one hand, it makes the overall patterns clearer, and anyone can judge for themselves whether the results are fair.  For example, it's easy to gather data on whether women are being paid less, whether there's salary compression or inversion, whether different people receive comparable salary increases upon achieving tenure, etc.  I don't know of any formal studies (which could be interesting), but there's at least a fairly widespread belief that this transparency helps cut down on abuses.

On the other hand, it can also increase disgruntlement.  The actual salaries are almost guaranteed not to align perfectly with what would seem just to any given person (because of course different people have different visions of what would be appropriate).  I've certainly looked on occasion at salary lists and wondered why on earth X was being paid 15% more than Y, and I once talked with a friend who had discovered that he was Y in such a case.


Social norms about hiring freelance assistants

I see no problem with any of that provided that the funding is appropriate. There may be provision in grants for such aid, for example. Research and publication should be about ideas extending knowledge, not about the manual preparation of documents.

And RAs often do some of that.


Does GPA/Transcript matter for academic jobs after the PhD?

In my experience on many search committees I've never looked in detail at the coursework or grades of an applicant.  We have however required transcripts as proof of the academic degrees that the applicants claim.


Math Adjunct Professor positions and salary in a big city

30% of households in Manhattan have an income lower than 36k, according to census data; 36k is actually above the average income for an African-American or Hispanic household in Manhattan.  You're right that it's hard to get by on that amount of money, but plenty of people manage it.

EDIT: A good point in the comment below:  typically graduate stipends are well below this number (31k is the highest I have ever heard for a graduate stipend in math; I'm sure the CUNY stipends are much lower). Of course, most people don't want to live like a grad student forever, but it's not as though it's impossible to survive.


Yes, research universities hire full-time faculty whose primary job is teaching.  At least in the US, these faculty typically have different titles from tenure-track faculty, such as instructor, lecturer, senior lecturer, and teaching (assistant/associate/full) professor.  For example, my department employs 12 lecturers and teaching [rank] professors; my wife is one of 13 lecturers in another department.  We work at a large R1 state university; both our departments also have lots of "standard" tenure-track faculty.

Teaching faculty in my department are primarily responsible for the large lower-division undergraduate courses.  To first approximation, each such class is taught and maintained by the same teaching faculty member every semester.  In contrast, tenure-track faculty like me normally bounce between a few different courses, including upper-division requirements, electives, and graduate classes.  Teaching faculty in my department typically teach 3-5 times as many students per semester as tenure-track faculty, mostly because our intro classes are huge.  Most teaching faculty also have teaching-related service responsibilities, like serving on curriculum revision, grievance, and appeal committees.

At most R1 universities, including mine, teaching faculty are ineligible for tenure. But there are exceptions, like Berkeley's "Lecturers with Security of Employment" or Duke's "Professors of the Practice".


Can reviewing papers help increase your credibility as a researcher?

Yes, it helps in more than one way.  Community service is a relevant part on an academic CV.  Although reviewers for individual papers are normally secret, it does not need to be secret that you have reviewed articles for journal X.  You can write that you have done so on your CV, and if needed (but I don't think it should be), a journal editor can confirm.

It works the other way around too: being asked to review a paper is an independent confirmation of your credibility as a researcher.  The first times it happened to me, it was really an ego boost.  Wow, someone else than my supervisor thinks I know something about something!  Great!


How do you hide your past online identity when you enter Academia?

Firstly look into the possibility of changing your YouTube name. If this is not possible, see if you can create a new YT account and move the videos into this.
Whatever about YouTube, your academic name is better being different to your commonly used name: we are all entitled to a life away from our work and from any "reputation" that follows from this. How best to select your academic name depends on:

The country you are in

The commonness of your first name, middle name(s) and surname

Naming conventions in your country

So, for example, if your YouTube name is Pablo Garcia, your middle name is Enrique and your mother's name is Sota you might publish under the name P.E. Garcia Sota. Likewise if you live in Netherlands and your YouTube name is Johan Van Dijk, you might, if your middle name is Willem, publish under J.W.V. Dyck as the latter form is often used in English publications. English native-speakers might use a number of first name initials and maybe omit the usual one if it is unusual enough to be searchable. Irish people have the legal option of using the Gaelic version of their name. Doubtless there are other possibilities in other countries, there may even be regional naming conventions in parts of France and Germany.
Look into the options in your own country and then do some trial searches on the main engines. Be careful to avoid a name that already has an existing big persona attached to it, especially in academia, as Google searches will associate you with them. Use Google Scholar to help with this.
Discuss your final selections with those close to you.


Masters programs would be easier to get into, since they often don’t burden the department with a graduate stipend, that means you’ll be responsible for tuition most likely.

I would apply to PhD programs if I were in your position. If you performed well on your upper division courses and have a gpa over 3.5, then you’d have a good shot of getting in. In this case, you are more likely to get a stipend and a tuition waver. That means you’d get paid to go to school and if you feel that the PhD is too much, you can also leave with a masters degree.

Edit: didn’t have time for a fuller answer earlier.

Don’t worry about the “free grade” in the graduate courses you took. Truly, all that is important there is that you have demonstrated experience and success in a graduate course, and indeed, at an apparently good Institution. No one is going to look at your grade and say “whatever, it’s just a grad course.”

Most grad schools look to your upper division courses as a measure of how you’ll perform in graduate school. I did terrible in my first couple of years in undergrad; I also failed a class or two, but I did well enough in the latter half to end with a 3.5. I was admitted into a good graduate school (in 2008).

As to your peofessor’s h index, that’s actually rather good. It means that he has at least 50 publications with 50 citations. While there is no objective measure of the quality of research, this means that he is well known in his community, his work is frequently cited, and his recommendation will carry with it some weight.

Grad schools look at several things. You need a good GRE score to get past general admissions, but no one cares past that. Your GPA matters, and yours seems good enough (better than mine was). After that they want to know how you did in upper division courses like Analysis, Algebra, etc, since you’ll be taking more intense versions of these classes, and they want you prepared.

Also having experience with graduate courses is a plus, I took a grad number theory course that helped me, and almost as importantly as the rest, they look at your recommendations. You will be part of the school’s community for the next five or more years as a PhD student, and they want to make sure that you can work with someone on research topics.


How do I apologize to my teacher for cheating?

To your credit, I think you've already arrived at a good way to respond:

"I know what I did is wrong and I know I deserve punishment. I really respect you as a teacher and I don't want you to think less of me for this. Obviously that's already happened. I just want to apologize and not make any excuses."

Many schools have a centralized system for reporting academic misconduct, so that a student who accrues infractions in multiple courses will be held accountable. Just be prepared to accept that fact, along with whatever penalty is specified in the class.

Apart from that, if you remain enrolled in the course, be a good student. Answer questions, turn in your work on time, and be punctual.


How is East European PhD viewed in the USA?

I haven't observed direct stigma against Eastern European schools, but the big indirect problem may be that US academics are not familiar with your school
When viewing large numbers of applicants or correspondents, this makes it hard to categorize things.  Rightly or wrongly, there is often a need to filter more individuals than you have the ability to research in depth, so that can count against you.  Note that this isn't restricted to one direction; I lived in Eastern Europe for years, and I had a friend who went to the US to study at Brown.  Now, she was in the private sector, but was routinely frustrated that no one in her country had heard of her school, and therefore didn't place much weight on her educational achievements relative to how an Ivy League education would be assessed in the US.
This is similar to the impact of studying at a respected, but small, regional school.  There are many of them around the US, and within that school's geographic region you're likely to be interacting with people who are familiar with the school, or possibly even went there themselves.  But in a different part of the US, the name of your school would impart no real information to the observer.
Similarly, publications may be in a language US academics can't read, or may be poorly translated, or may be published in journals they've never heard of.  In my experience it's very likely that academics will be inclined to judge you, your work, and your program, on their merits once you get past that initial filter.  So if your goal is to work in the US,  try to build personal contacts with academics in the US (e.g. at conferences, via email), try to publish in English, attend a school with some international recognition (in Prague, for example, you have CERGE-EI which is deliberately US-styled), and anything else that helps overcome that initial "I don't recognize any of this" when someone in the US reads your CV.


How to list an old manuscript on my CV/website?

Just put it in an "unpublished" or "other" section of your publications.


I know you aren't considering this possibility, but a lot can happen in a year. What happens if, for any reason, you don't wind up getting married?
There is some advantage to keeping a permanent name throughout your career, but it isn't overwhelmingly important. Eventually your future work will dominate your current work and a few exceptions probably won't be a (serious) issue. Just a bit of inconvenience at times.
I suggest, as a first option, that you just keep your birth name as your publishing identity into the future. It may be "lazy" but it causes the least problems overall.
If you don't like that idea, then a hyphenated name is probably best, though you might use the hyphen only for publishing identity, with some other form in every day usage (and even legal usage).
But neither of these is a firm suggestion, just a way to avoid the inconvenience attached to the alternatives.
A third option is to adopt a pseudonym, unrelated to your legal or common-usage name and stick with it. It isn't especially common to do this, but it has some history behind it.


Why do universities share test questions?

I am not aware of any university having agreements with other universities about exchanging exam questions and i doubt that such agreements would exist in many places. I would wager a bet that the same is pretty much true on departmental level.

On the level of individual teachers there might be many reasons why exam questions pop up in different places. One has been mentioned by Brian Borchers in a comment (questions taken from textbooks). Secondly, many first- and second-year courses teach pretty standard material which often has not changed for quite a while (e.g. basic linear algebra in many disciplines). For such courses (and even some higher-level courses) the set of questions that are useful as exam questions tends to be limited and so i would not find it surprising to find that most if not all questions have been asked somewhere and have been discussed on the web. Thirdly, it is not unheard of that teachers re-use exam questions from previous years. Fourth: sometimes teachers talk to each other and exchange experiences and material.


Advisor accused of personal misconduct -- what should I do?

There are a few considerations, at least.

First, is that if you feel personally at risk from the alleged behavior, keep your distance just for your own safety. That is distinct from academic considerations.

Next, the behavior is alleged, not proved. While it is appropriate to be wary, don't try to judge it yourself unless you have additional information.

Next, in many cases, I would say most, it is appropriate to distinguish between personal behavior (possibly very bad) and scientific/academic quality of the work. Let me focus on this aspect.

In the history of academic discourse and advancement, many fine results have been obtained by terrible people. This is true in many fields and over a long period of time. The work done by these people doesn't disappear just because they wound up chastised by their peers, or even arrested and jailed. They get referenced. Historically, you won't find all of the cases as they are often covered up, but some you will and they can be pretty bad.

My advice, even if the person is guilty, is to separate the person from the work. If the work has merit, then cite it as usual. Focus on the work.

The question of continuing to work closely with the person is a different one, however, as is the question of the value of letters of recommendation. Some separation of the person from the work is possible here also, but perhaps not as completely. For example, it is probably a mistake to become a defender of the person if it can be interpreted as a defense of the alleged actions.

Letters of recommendation may be necessary and may be fine as long as the letter focuses on your work and doesn't imply anything more. But you may have to explain, in interviews and such, that you distance yourself from any bad behavior, even if not proved. Here the distinction is between the bad behavior (distance) and the person (neutrality - more or less). However, don't depend solely on letters from someone who has been severely sanctioned either legally or academically.


Should I take the TOEFL exam if I have graduated from a high school in the U.S.?

Every school words the requirements, if any, for the TOEFL a little differently. For example, Harvard GSAS:

  Applicants whose native language is other than English and who do not hold the equivalent of a US Bachelor's degree from an institution at which English is the language of instruction must submit scores from the Internet based test (IBT) of the Test of English as a Foreign Language (TOEFL)

A quick look suggests that in general native language and the language of your Bachelor's degree is what matters and not the language of your high school.


Most doctorate programs have some amount of teaching/ta/facilitator/etc as a requirement of the program. Some people try to do more, some try to do less, but unless you're working in a research lab (with its own endowment :-) expect to do some teaching.

Re 'good skill': if your goal is to find a tenure track position then yes this would be good experience.  Assuming that you enjoy teaching, and who here doesn't grin, this would be a good opportunity to enhance and refine your teaching skills.
Re 'lectures on research': be careful here.  Odds are that any teaching roles you would be offered at this point in your academic career would be pretty low level undergraduate type stuff.  Depending on your area of research you might also run into some problems 'presenting' un-vetted data.  There are always exceptions to the rule but I wouldn't expect for you to be teaching anything so specific that your research would come into play.  YMMV but that has been my experience (since you asked).
Suggestion: Be careful with overloading your schedule. Teaching is one of those jobs that finds a way to embed itself in many aspects of your life that you didn't expect. For example: I expected to spend my middle years sitting on the porch reading books with my wife, not reading term papers.  Oh well.  While it is good to gain experience you don't want to spread yourself too thin and suffer an impact to your research (remember, the reason you're here in the first place :) or your personal life.


Other conference ranking include:

CORE Conference Portal

Also useful reading here, a Research Gate post


Finding undergraduate research mentor? Etiquette for responding to email from potential mentor

I believe a simple follow-up email would do.

Make sure you:

Thank them for their time responding to you.
Acknowledge their interest in the project.
Ask if they have a convenient time you could come and chat to them in person.

Others may have more ideas, but that would be the way I would respond in this circumstance.


Market research & consulting: perception and acdemic career perspectives

I can't speak for the IS field, but I think that there's a strong chance that your time in industry would be considered as a break from doing research relevant to academia. Unless you are regularly publishing papers in the relevant journals or conferences, your time working outside of the academy will be perceived as time idle.

Now, that being said, market research is a field frequently included in Business Schools. I don't know where your IS degree is from (Communications? Business? somewhere else), but I think that Business Schools are much more likely than other departments to value time spent in industry when hiring professors. So, there are probably different standards for evaluating your output during your time in industry. Published reports about the state of a market might be more acceptable as a valued contribution to the literature, and therefore less likely to paint you as having been out of touch with the academic literature.


phd admission- both professor from same university agreed to be mentor

I would counsel against two different SoP statements. If they are compared then it makes you look like you don't really know what you want. The university might be fine with two separate applications (or not).
But more important than the source of funding and the activities to earn the funds is the question of what would the research be with each of these people and can one of them better support your career. Make your decision on that basis.
Bot the TA and the RA experience can be valuable for an future academic, but in different ways. But that is less important than the research opportunities.
I'll guess that the TA position is probably easier to manage your time than the RA position, but that isn't necessarily true, depending on the nature of the university and of the field and department.
You might consider trying to set up a three way conversation to see if the two profs have some advice for you about which would be more suitable and advantageous. But that assumes that you know something about them first and are sure that it won't generate bad feelings.


What are the Pros and Cons of working before doing a PhD (in Machine Learning)?

I worked in industry for 3.5 years before starting my PhD. I believe I've been more successful because of this experience. However, there are advantages and disadvantages.

Pros:

You will be more mature and have a better idea of what you want in life (which may not include a PhD).
Better understanding of the needs of industry which can influence your research choices
Connections and business soft skills (being able to sell your research effectively is very important for example)
Often a better work ethic (ie. used to working regular hours, etc)

Cons:

It can be difficult to go back to being a student after making a real salary
Rusty study/exam writing skills
You will be older than your colleagues
If your goal is to remain in academia you may end up getting on the tenure track later with potential consequences for stability, starting a family, etc.
If your goal is to return to industry, the 5+ years of work experience you will miss out on is often worth more financially/promotion wise than a PhD (but this can be field dependent)
You will need to maintain connections with suitable academic references. As time goes forward they may not remember you very well. Strong references are important for getting accepted to top schools.

Many of these things will depend on what you do while in industry and what you want to get out of doing a PhD.

My biggest piece of advice for time spent in industry: take care of the people part - make connections, work on networking, learn to be effective in meetings, learn to sell ideas/products, how to deliver for clients. Watch and learn from senior people (directors, CEOs, etc). These things will help you be successful in academia and business. Don't just sit at a desk coding.


Do high-profile journals edit authors’ figures?

Yes, high-profile journals do typically edit figures for style and consistency. You will find this information on their web sites, e.g. nature physics.


How much weight does the tripos III carry for further PhD admissions?

If you are aiming for attending a top five mathematics department in the U.S. immediately afterwards, Part III of the Tripos plays almost no role.  It's not uncommon for students to do Part III, but often after already being admitted to the U.S. department and deferring for a year.  Occasionally someone who was turned down the previous year applies again while doing Part III and is admitted, either because their application looks stronger or because they have better luck.  However, attending Part III plays little role in this.  The bar for Part III admission is lower than for top five U.S. Ph.D. programs in mathematics, so merely being admitted is not in itself a factor.  The Cambridge academic year doesn't even start until October, so there's generally no useful way to get letters of recommendation from Cambridge faculty based on Part III: they simply don't have enough to say at the point at which letters are needed.  The net effect is that you are applying with letter writers based on the previous year, and the only function of Part III is demonstrating that you are doing something productive with your time (it certainly looks better than taking a year off, for example).


Are there downsides to speculative applications for academic jobs?

Here is my standard advice to PhD students applying for academic jobs:

First, look for departments that are advertising for faculty in your subfield.  Apply there.
Second, look for departments that are advertising for faculty, but not in your subfield.  Apply there anyway.  There is no way to tell from the advertisement whether the listed fields are requirements, preferences, or mere examples, or if they just recycled last year's ad without reading it first.  (Yes, I have seen all these alternatives.)
Third, look for interesting departments that are not advertising for faculty.  Apply there anyway.  There is no way to tell from the lack of advertisement whether they are really not hiring, or they just aren't advertising widely, or they just haven't posted their ad yet, or they thought they posted the ad but didn't.  (Yes, I have seen all these alternatives.)

Before anyone objects: Obviously, I'm not talking about your department.  Everyone  knows that your department's advertisements are precise, timely, and highly visible.  I mean other departments.

Of course, if you're thinking of applying to any department, whether they're advertising in you subfield or not, it's a good idea to contact someone you know in that department to find out what they're really looking for.  If your contact says "No, really, we aren't hiring X," you can save yourself the trouble.  But if you (or your advisor) don't know anyone well enough to ask?  Fire away.


Would a high stack exchange rep make a difference in a job interview?

I have seen Math.SE and MathOverflow activities mentioned by both grad students and faculty in connection with various applications and promotion-related materials. I don't see this as anything to scoff at; personally I find it intriguing and consider looking up someone's SE profile(s) a great way to get some insight into their mathematical personality (note that there can be a potential downside if said personality turns out to be uninteresting or unimpressive). With that said, I think this is only worth mentioning on your CV if it represents a major activity, say if you have been active for at least 1-2 years and have dozens of answers including a good number of highly voted ones. I wouldn't specify the reputation points as that seems like a silly thing to (admit to :-) ) be concerned about. And there can be a better place to mention it, e.g., in a research/teaching/personal statement.

As for mentioning this in an interview, like many other things this can be a good idea if done tactfully (in a no-big-deal, casual sort of way that shows a sense of proportion), or a horrible idea if done untactfully (saying it and expecting fireworks or a round of applause).

Finally, I wanted to mention that I noticed from questions such as this one that there is a common belief in the Grand Principle that for academic (and specifically math) jobs one should hide any information about oneself that attests to one being interested in anything other than doing math research all day, every day, and that any decision about what to put on one's CV or what to mention in an interview/personal statement should be considered in the light of this Grand Principle. I can't say if this is true or false as a general rule, but it's categorically false for me: personally I'm delighted if a job candidate tells me they are interested in archery, or chess, or surfing, or playing piano, or whiling away their time answering elementary questions on Mathematics StackExchange. Think about it this way: given that I already know the level of research they do (which presumably must be pretty good if I'm interviewing them), any evidence that they have other unusual skills or abilities outside of math research can only raise them in my estimation. Besides, when you hire someone you get a complete package, mathematician/academic+human being, and personally I rather like being surrounded by interesting human beings and not just paper-writing robots. But maybe I'm weird and it's just me who thinks this way, so handle this advice with proper caution.


How to get ready for a visit to a lab where I would like to do undergrad research?

You should treat it as an interview unless you get information telling you otherwise.  Yes you should bring a resume, but you may not need it.  You should read about the PI's research, lab, and team.  Usually there is some information on the national lab's website.  Typically undergraduate researchers are not expected to know how to do research, so you might be questioned about your motivations for learning to do research.  If your grades are not good you should be prepared to say what you are doing to improve them.


Should I include name of potential advisor on my statement of purpose (SOP)

Faculty at a top-10 school in aerospace engineering gave a former student of mine the advice of indicating several professors whose research he was interested in, for exactly the reasons you suggest: by showing too narrow a scope, it makes it harder for other researchers to gain interest, and by just submitting a "generic" SOP, you run the risk of looking like you're not doing your homework. Showing an interest in several faculty makes it easier for someone to advocate for you in the admissions committee.


Which institution's logo to add to research poster when research was done at institution different to main affiliation as student?

If both institutions have supported your project, you should acknowledge both in your poster.

To save space, you have a variety of options:

Make the logos smaller by scaling them.
If available, use a small, square version of the logo rather than a larger rectangular version.
Put the logos in a part of the poster that is underutilized. (For example, left-align the title and authors, and put the logos over to the right side next to the author list.)


What is the notation for inserting algorithms in scientific papers

To the best of my knowledge, there is no standard notation for algorithms across computer science fields. However, looking through previous editions of the venue you plan to send your paper to should give you a good impression for how algorithms are typically denoted.

That being said, most papers I know just use a very simple procedural notation, basically pseudo-code in a simplified structural programming language. The reason is likely that such a notation has the least "hidden assumptions" in contrast to what your average computer scientist will know and expect. Contrary, your example seems ripe with symbols and expressions that are certainly not globally understood outside of AI. Using a "compact, expressive" notation loses much of its appeal if you then need to spend half a page to formally define your notation.


Your last paragraph already says what you have to do first: Talk to your supervisor about potential second supervisors/mentors. You could bring a list of people who you would like to approach and ask about his opinion. Maybe he also has suggestions. Also make sure that he in principle agrees with the idea of a second supervisor.

Then you should be clear about what you want from a second supervisor: Regular discussions in person/email/phone? Feedback on drafts? Discussion or even joint development of ideas? Extended discussion via email? I somebody from a different place the supervisor of which I do not know would approach me about being a second supervisor, I would want to know answers to these questions and probably would have opinions about the answers, too.

The last paragraph also shows that you know at least one way to approach a potential second supervisor. Apart from personal meeting I would not recommend a non-solicited email from your side. If you can't meet the potential supervisor in person, I would suggest that your supervisor would make the first contact and let him/her introduce you.


Supervisor not allowing to submit Thesis

Perhaps you can employ a double track strategy. If the new supervisor is willing, agree to join them and do what is necessary to do so. They should be made aware that it is possible that the masters won't be awarded.

Simultaneously pursue some sort of action at your current place to "force" your current advisor to relent and let you finish. This might require a petition to higher authority with a claim of unfairness. This sort of thing can get messy if you don't have any alternatives, but in this case you have a good one.

So, rather than withdrawing, put the responsibility on your current university to do the right thing. Perhaps they will, but only if you make it a bit uncomfortable for them to not treat you fairly.

But, I would first, you could just inform the current advisor that you are joining the other. You don't need to go beyond that. Perhaps he will relent, but if not, press your case with someone higher in the hierarchy.


Is it rude to ask via email to a professor if there are any internship opportunities?

I don't think this practice is rude, but if these are not people with whom you have any connection, and who have not advertised a position, then I don't think you should be especially surprised that you aren't getting many responses.  In all likelihood, the answer is "no" and they don't feel like anything will be achieved by telling you that.

A few things which might be hurting you:

The email above really reads like a mass form email.  You aren't making any argument about how your expertise is relevant to their specific work, and you're putting the burden on them to think about how your skills might fit with what they're doing rather than thinking about it yourself.
Maybe this is different in other fields, but it's not clear to me what "internship" is supposed to mean here.  A paid position?  Unpaid?  You may be being deliberately vague, but if you're not responding to an ad for a specific position, you have have some clarity about what you're looking for.
I think that the slightly awkward English doesn't really help.  "Chemist for the conservation of Cultural Heritage" sounds very strange to me.  I think "Chemist specializing in/interested in/working on the conservation of Cultural Heritage" is much better.


Is there a repository for academic slides?

For computer science, the video lectures site is very helpful, VideoLectures

This site includes a bunch of videos from well-known researchers in the computer science world from the top conferences in this field like KDD, NIPS and many others. Along with the videos of the presentation, you can easily download the slides material of the presentation (although you can't download the video files from this site).
I recommend you to see this site.


Should I get a Second Bachelors and Masters to Make My PhD as Broad/Interdisciplinary as Possible?

I would agree with the answer from r/datascience. Go straight to MS.

The main reason you cited for waiting on the MS was that you could not afford to pay cash for grad school and you didn't want a loan. Keep in mind that cash and loans are not the only two options.  There is a significant amount of financial assistance available for grad school. E.g. you might be able to get a teaching assistantship (teach an undergrad class in exchange for tuition), research assistantship (work on a professor's research project in exchange for tuition), or a fellowship/scholarship.  I got all three of these at various points in my program. I have a MS and a Ph D and I literally paid zero tuition for both of them. My wife and my sister both have MS and neither one paid any tuition.

Research assistantship is very common in technical fields where corporations sponsor research projects. E.g. Apple or Microsoft might give a CS professor $200k to study some challenging problem. The professor will spend that $200k to hire grad students to do the work.  You work on the project part time, say 20 hours a week, and that pays your tuition. Now if you were talking about studying history or poetry or violin performance, then money is a lot harder to find. But Comp Sci, you have a good chance at finding some money.

The only reason I can think of to do a second BS before the MS would be if your BS was in such a completely unrelated area that you would be unlikely to get admitted to the graduate program. For example, if you had a BS in English Literature or Violin Performance, you would be unlikely to get into an graduate program in Statistic or Comp Science.  But I don't think that applies here.  With a Math degree (assuming you have good GPA / GRE scores) you should be able to get into a good Statistics or Computer Science program.

EDIT:
Let me try to put this a different way.  To a large degree, the value of a BS is less about the specific facts/skills that you learned, and more about proving to a potential employer or grad school that you are a hard worker (see Signaling theory).  Opinions vary, but let's says it's 50% about what you learn, and 50% proving you're a hard worker. If you get a second BS, it's only worth half as much as the first, as you've already proven you can do work at the BS level. If you get an MS, you now prove to potential employers that you can do work at the MS level, which is worth a lot more than proving you can work at the BS level. Let's just say that an MS is worth twice as much as the first BS for this. Then an MS is worth four times as much as a second BS. And since it will take a similar amount of time, why waste your time getting the less valuable thing?


Does it make sense to apply for research positions requiring a bachelor's degree with graduation still 4 months away?

My lab conducts a search for post-baccalaureate fellows every year. In most cases, the applicants are completing their final year of their undergraduate study and have an anticipated graduation date, and are able to share reference letters and a transcript with us. At least in my field (neuroscience) it's completely normal to apply for a post-baccalaureate position before you have officially obtained your degree.


Understanding an abnormal grade distribution

I agree with the other answers that this may be an artifact of the histogram. May I humbly offer a few alternative ways to plot these grades?

All of these essentially show that your effects are likely due to small n and possibly an essentially discrete underlying data generating process.

R code:

require(hdrcde)
require(Hmisc)
require(denstrip)
require(beanplot)
require(beeswarm)

grades <- c(1.2, 1.4, 1.4, 1.9, 2.0, 2.3, 2.6, 2.6, 3.4, 4.2, 4.2, 4.3, 4.6, 4.6, 4.8, 4.8, 4.9, 5.3, 6.0, 6.2, 6.4, 7.1, 7.8, 7.8)

opar <- par(mfrow=c(1,6), mar=c(3,2,4,1))
    boxplot(grades, col="gray90", main="Standard\nboxplot",yaxt="n")
    hdr.boxplot(grades, main="HDR\nboxplot",yaxt="n")
    bpplot(grades,xlab="",name=FALSE,main="Box-Percentile\nPlot")
    beanplot(grades,col="grey",yaxt="n",main="Bean plot/\nViolin plot",border="black")
    plot(c(0,2),range(grades),type="n",xaxt="n",yaxt="n",xlab="",ylab="",
        main="Density\nplot")
    denstrip(grades, horiz=FALSE, at=1, width=1)
    beeswarm(grades,pch=19,main="Beeswarm\nplot")
par(opar)

EDIT: (sorry, I'm a statistician, I can't help it...) I went and took Jack's kernel density estimate and resampled 24 "students" from it a couple of times. In each case, I plotted a histogram. The result is below. We see that even an innocuous unimodal curve can lead to pretty bumpy histograms, because of the discretization and the small sample size.

R code:

dens <- density(grades)

opar <- par(mfrow=c(2,4))
for ( ii in 1:8 ) {
    samp <- rnorm(length(grades), sample(grades, size = length(grades), replace = TRUE), dens$bw)
    hist(pmin(10,pmax(0,samp)),breaks=0:10,xlab="",ylab="",main="",col="gray")
}
par(opar)


This sort of thing varies by field. In some, there is no expectation at all of publications prior to finishing the degree. I think the push toward requiring publications is somewhat recent. When I finished (long ago) in mathematics it would be very rare to have any publications at all upon graduation.

But in some fields there is such an expectation. However, I think that in those fields, students are funded more for research (RA) than for teaching (TA). If you are part of an active research lab in the sciences it is more natural to have several publications as a consequence of your work prior to graduation.

But any effect at all on your career would likely be very brief. You establish your own reputation. Starting a bit late with publications eventually evens out if you are productive, either in academia or elsewhere.

Of course, it won't harm you to be thinking about what you could get out there in your time remaining. Your advisor should be able to tell you about norms in your field, of course.


Is there any research done on ideal proctoring algorithms?

I believe that you can formulate the problem mathematically in a way which can lead to some well-known optimisation problem.

However, I think the mathematical model you described is very restricted and the solution is not likely to work very well in practice, even if you find it. Your model only includes moving and observing a certain part of a room - plain and simple. However, in practice, cheating is prevented not only by someone who "polices" the situation. It is a more complex process, which includes some aspects of ethics, culture, community values, etc. Creating a proper culture within your School / University is much better way of preventing cheating, than walking around students following a super-optimal path prescribed by a supercomputer.

Also, the efficiency of a proctor depends not only on their path through the room, but on a lot of psychological  factors, e.g. how this person is perceived by students. A lazily walking person will not be very efficient in preventing cheating whatever the path is. A really "scary" proctor (with heavy looks, etc) can prevent all cheating sitting on their chair in a corner of the room. There is much more factors to this problem than trajectory only, and that's why I don't think the model you suggest is very useful for this problem.


Special (non-english) character in name. What to do as author? Internationalize or not?

First of all, always be consistent. Whatever you decide, that is what you will always have to use.

Considering the first point, might be better to strive and use your real name as it is with the non-english characters. You will have less problems in the future to prove your authorship in case questions rise. Complain to systems who do not accept your non-english characters...


Citations needed when using textbooks to write lecture notes/slides?

You should certainly cite your sources. Not for each and every use, a general statement like "Based on textbook and others" on your first slide (or slide of each class) should be enough. Add references to slides/classes as needed for people who want to dig deeper.


Asking a past professor to teach a workshop/short course

In general, the expenses you've listed above (travel costs, local accommodations and meals) are typically sufficient. Registration fees for the workshop would also usually be waived.

One other thing you might consider offering, if funds are available, is a small stipend to be used by the faculty member to sponsor a "young researcher"—a graduate student or postdoc—who can also attend the workshop and take part, perhaps by offering a poster or contributed talk. (Or, if it is not possible to offer a stipend, perhaps the registration fees could be waived for the young researcher instead.)


Justifying past dropping out in statement of purpose letter

The overriding goal in this situation is to communicate in a way that causes the admissions committee to believe that you have the qualities to get through a PhD program, and that you will be someone who is easy and pleasurable to work with.  It is therefore important to communicate in a way that gives cues as to your fortitude and drive to get through the program, and shows that you are calm and able to deal with conflict in a mature manner.  Anything you say that detracts from this could be detrimental to your application.

  Do I need to mention/elaborate on the reasons that made me drop out? If so, what is the best way to express them without hurting my chance of getting an admission?

This is certainly a thorny situation.  You will certainly need to give some explanation of why you did not succeed in your previous attempt at a PhD program.  However, unless there is some simple, clear, and objective evidence of misconduct by your previous supervisor (e.g., a disciplinary outcome against him by the university for his treatment of you), it is not a good idea to go into specifics, or make statements claiming psychological abuse.  The problem with doing this is that the committee will have no simple way of confirming that your claim of abuse is accurate, and it will therefore naturally give rise to the alternative possibility that you are just extremely sensitive, and perceive psychological abuse in ordinary supervisory activity.  I am not suggesting this is the case, but just bear in mind that the committee will not have any way of confirming your assertions, so they might consider this to raise a risk for them.

In this kind of situation, assuming there is no simple, clear, and objective evidence of misconduct by your previous supervisor that you can cite, I recommend that you include a short statement to the effect that your relationship with your previous supervisor was "not a good fit", and this hindered your progress.  The committee is likely to "read between the lines" and understand that there was some problem between you and your previous supervisor, so by understating the problem (e.g., saying it was "not a good fit" without blaming anyone), you signal that you are a person who can roll with the punches.

If you get an interview for a prospective PhD candidature, be prepared to field follow-up questions about this issue.  I would recommend preparing some verbal answers that take the same understated tone, but also be prepared to give full disclosure in a calm and measured way if pressed on the issue.  If this comes up, you again want to communicate that there was a good reason for your previous failure to complete, but you have the fortitude to talk about it in a calm and non-accusatory manner.


What are the default copyrights/IP restrictions for a work I post online?

In most (possibly all) jurisdictions, the default for a creative artifact with no license information attached is that it assumed to be all rights reserved.  In other words, another person cannot do much of anything with it besides look at it.

See, for example, GitHub's information about "no license" licensing. They are talking about code, but the default they mention is general.

Note that there are certainly categories of work for which this does not apply (for example, recipes are specifically not protected under US copyright law), but it most certainly applies for any substantial paper draft.


Can professors generally keep books paid for with university funds?

There's the "legal ownership" element, but given the situation you've described, I'd attach even more importance to the moral/ethical element:

Who is most likely to use these books?

I suspect if your department is being shut down, no one will care about the legal ownership specifics unless you provoke them to. So you could consider triaging:

College library, for books which in your professional judgment students or faculty in other remaining departments could use.

Keep yourself, for specialized material or your favorite books that you expect to use in the next years or decades.

Gifted to colleagues elsewhere for other useful material in your field.

"Free" box outside your door, for the stuff you'd otherwise throw out.

I have fortunately not been in quite this situation in academia proper, but I did leave a private sector research institute that got effectively disbanded with my (and others') departure. This is the approach I followed.


Should I add references to a conference poster

This may be a somewhat discipline-dependent question (and you don't specify yours), but I can say that I have often seen references on posters -- and just about as often not. When I have seen them, they have generally been in the lower right-hand corner (for most left-to-right languages, the last place anyone generally looks). Not uncommonly they are in smaller type than the rest of the poster, to save space.


How do you insert links to a printed report?

I prefer footnote or in text. Others would also consider using a citation. Check your local style guide. Here is one possibility (http://lib.westfield.ma.edu/webapa.htm)


Will graduate programs go back to GRE after COVID?

My U.S. grad program in math had already been reducing attention to GRE subject test for years, due to its manifest uselessness for predicting success in our grad program. (I've been involved in grad admissions here almost continuously since about 1985, and have been Dir of Grad Studies in math for two stints, so I've really paid a lot of attention to this.)
Until the pandemic, we did tell our own undergrads to take the subject test GRE, since many places still did expect it. In fact, faux-ironically, until recently, we did tend to wonder why someone would not have taken the subject test GRE if they had any idea what they were doing... in terms of preparation for or application to grad school in math in the U.S.
A number of other good programs had already, in recent years, downplayed the significance of the GRE subject test score for their applications, so we ourselves had come to "wonder less" why someone might not have taken it.
With the pandemic, and the at-least-temporary vanishing of the GRE subject test, we have more-unabashedly stated that we don't care about a subject test GRE (nor any other part of the GRE).
I would speculate that other math grad admissions in the U.S. have also figured out how to not pretend that the subject test score is a good predictor of success... all the more that it (documentably, both anecdotally and other) never was, and the last year or so has necessitated making decisions without it.


Students self-assess which exercises they attempted – how can I make this more homogeneous?

If the problem (being too pessimistic) is not too common, let the student check the exercises not only in the usual way, but also with "?".

Announce at the beginning that if students are totally unsure whether or not the may check an exercise, they may check it with "?". Then, whenever a student checked an exercise with "?", let them present this exercise (with no negative consequence whatsoever) and then say, if the attempt was resonable enough to warrant a checkmark. Announce when explaining "?", that students with "?" will have to present. (This has also the advantage that students see a not-so-perfect solution which is often more helpful and more intuitive then a perfect solution.) However, this only works if exercises do not get too often marked with "?" (as otherwise, this system could be gamed).

Some additional thoughts:

In my experience with similar systems, the "pessimistic" students are often the excellent ones, that is, the ones that pass the course anyway.
A lot of students have exactly the number of checkmarks they need to pass the course (and not more). I do think (but without proof) that if students are just at the border between passing and failing, they will do enough work to pass and get more "optimistic".
Announce in the first lesson as clearly as possible when an exercise can be checked and also, when it cannot be checked. It is often useful to give examples when it can not be checked as students may compare their situation to the example.


Involving additional staff members in PhD supervision (beyond co-supervisors)

That's fairly common (at least in my field). In a CV, the involved staff member could specify their role in this PhD project as "assisting supervision", to distinguish it from a  formal/official co-supervision role. Of course, such an involvement should be discussed with the formal supervisors first, since it might otherwise lead to tensions.


My previous supervisor keeps asking me to review her papers. How to deal with this?

No it should not be normal. It is the decision of the editor to pick a specific reviewer. As a reviewer, you are supposed to keep the manuscript confidential. While i would see that this can be argued if you ask somebody working in your organization and reporting/being supervised by you, i think giving material to somebody whom you do not have direct control over in another institution is a pretty bad violation of the usual journal policies.

There are a number of bad situation which could arise from this

You actually having a professional relation to the peroson which you review (without your former professor knowing)
You telling your new boss about this, and he/she deciding to do politics using that knowledge (delaying etc)
You plagiarizing the paper, without the editor being able to track how that ended up there (since nobody knows about it)
You asking for changes to include references to your papers (innocent, since the editor team wont catch it...)

So no, beyond you not getting credit, i think it is a pretty shady thing.

(Added after comment): There are essentially two options, which depend on the mindset of your supervisor.

You explain what I wrote and tell that this makes you uncomfortable - you don't have to tell about her taking credit for your work, so it is less personal.
You inform the editor about the incident, pass your review, and ask the editor to be confidential about it. (I would imagine that they may just remove you former supervisor from their list)


How to encourage students to work more carefully and independently?

I recently heard a nice angle on this problem. Computer Scientist Olivier Danvy, adapting Buddhist philosophy, stated in a recent presentation that you need to inhale before you can exhale. What he meant was that in order for grad students to produce quality work, they need to see, read, ingest and understand quality work. Perhaps you can show them the difference between the high quality work and low quality papers you've also come across. Try to get the student to gauge where his/her work fits in relation to these other papers.

You'll also need to explain that even though poor quality work can actually be published, that this is not a good thing. Not good for science. And not good for building a career.

Many iterations of corrections is important. It takes time. But for every comment that is ignored, you need to find out why it is ignored, and make the student aware that it takes your time and is annoying if you need to make the same comment over and over again. Maybe the student does not understand the comment. Maybe the student is overwhelmed by the vast amount of comments. Maybe that just missed it accidentally. Maybe they just disagree.


Should I mention a "math depression" I went through in my letter of motivation?

Actually, I kind of disagree with @TheHiary... I don't think you should put negative statements about yourself in your cover letter.
While they do not want to only here how awesome you would be, they do want to hear how, and why, you would be totally awesome working for/with them. You can look up some tips and guidelines about writing a cover letter here.
I also think that any half-page story has no place in your cover letter. It should be fairly short, clear and memorable/striking. I was suggested, two pages maximum. One page is better.
But, if it was an important experience for you as a potential researcher, there's definitely place for it in your cover letter, just not directly. What you should include, however, is:

what helped you get back your motivation
(you can say that e.g. a project made you "rediscover your love of science" without explicitly saying that you lost it for a while)

how your approach to research has changed in a positive manner
(e.g. working on the team project made me realize how important and helpful peer input, informal discussions and exchanging ideas was for my productivity)

how your vision of science/yourself changed after that
(e.g. working with Professor X. what made me secure in my opinion that I want a career as a researcher)

basically, any positive result of your experience is worth mentioning, but I would rather mention just what triggered the positive change of attitude instead of motivation-less period before


Is there an established way to lobby arXiv to expand the paper subjects it covers?

Only arXiv offers the guarantees against new takeovers.
All the cloud services around might suddenly change their open policies at best.

arXiv   platform is well engineered and there is already a Quantitative Finance category, adding more in the economics side should not be a problem, if they are willing to.

One possibility is to start a campaign on specialised webservices such as change.org.

With a lot of people asking, they might easily take into consideration the proposals to widen their scope.

The major problem would be how to advertise this  campaign. Your question got an average 80 views in 10 days.


Why do undergraduate admissions in the U.S take into account nonacademic criteria?

As with any complicated social phenomenon, there is no simple and conclusive answer.  However, here are two important factors:

The U.S. didn't have world-class universities until the 20th century.  Even ones that are world-famous today (such as Harvard or Yale) did not particularly impress 19th century Europeans.  These universities had started out as vocational schools for pastors and gradually turned into finishing schools for the elite, but they weren't scholarly powerhouses.  In the early 20th century, there started to be more academic competition for admission.  This was very upsetting to the traditional students (largely wealthy young men from prep schools), who didn't want to be around too many Jews or other minorities or to have to compete with nerds for grades.  One tactic universities used in response was quotas for Jews, but the Nazis made that look bad.  Leading U.S. universities then moved on in the 1930's to develop other methods to ensure that they could pick whichever students they wanted.  For example, geographic diversity (you should take students from Kansas to avoid having too many New Yorkers), preferences for children of alumni, athletic recruitment (you really need a strong lacrosse team and fencing team), well roundedness (students should study hard but not be too nerdy), extracurricular activities, etc.  Jerome Karabel has documented this history in his book The Chosen.
What is Harvard's purpose in educating students?  People often imagine the goal is to educate smart people, and that corruption is the only explanation for why Harvard would deliberately admit a wealthy applicant over someone more talented but poor.  However, this is thinking about it completely wrong.  Harvard's primary goal isn't to educate smart people, but rather to have an impact on the world by educating influential people.  They want to educate the people who are going to grow up to become leaders of all sorts (social, political, commercial, academic, etc.), and while they are happy to help shape who becomes a leader, they know perfectly well that wealth and privilege play a major role.  When Harvard admits someone whose wealth exceeds his intellectual talents, it's because they want to help set the national agenda by providing this person's education.  From this perspective, all the strange admissions criteria are an excuse for Harvard to select whoever they feel has the most potential to change the world, taking into account all aspects of their talents and background.

So what about other universities?  The first axiom of higher education in the U.S. is that everybody imitates the most prestigious universities.  If Harvard, Yale, and Princeton are doing something, then everyone else will follow.  Not necessarily in exactly the same way: different universities may employ very different criteria for admission, thanks to different goals regarding who they want to educate.  But they almost all use the same basic framework for what information is relevant to their decision.


Conferences without proceedings worthwhile for a PhD student?

I'm not familiar with your area, but I am strongly skeptical that it makes any sense to divide all conferences into two categories, those with proceedings and those without, and to declare based on that one binary bit of information that those in one category are more prestigious and more worth attending than those in the other category.

In other words, as with most things in life, the answer is it depends. Given two conferences you are considering choosing between, I would say look carefully at what topic each conference is about, how close is it to your interests, how good are the networking and learning opportunities you will get there, how attractive is the location, and yes, whether there is an opportunity to publish a proceedings paper; then make a decision.


Approaching supervisor for master's thesis when I have ideas but nothing concrete?

Is this supervisor someone you know/in your department? This makes a  difference in your approach.
If this supervisor is from another school, and you REALLY want to work with them, go see who he has supervised in the past and reach out to them to get a feel for how that professor might respond.

2a. An alternative to this is to call the departments graduate studies unit, convey your interest, and ask them how you might go about talking with a particular professor. Every university tends to have a prospective students section where you'll find an email for your questions to go to.

If you are sending an email, prior to you getting into a bunch of details, it would probably save you some time to ask them if they are considering accepting graduate students for the 20xx-20yy year, and if they say yes, express your interest.
Really make sure that you contact previous students to see how that professor is as a supervisor. This isn't done enough but it is so important to know what you're getting into.


I would standardize them and simply put the most relevant information on them. My (dated) business card looks like this:

Now I think it has a little bit more information than needed; fax is almost certainly not needed, but there might be circumstances where it's handy to have the mailing address. But important are:

University + department
Academic homepage
E-mail address
Perhaps phone number
The fact that you're a PhD student.

I wouldn't add too much information on them. Business cards are for core info, nothing more; they might get crowded otherwise.

My own business card is outdated: a university reform means I'm no longer at the Department of Space Science, but at the Department of Computer Science, Electrical and Space Engineering, Division of Space Technology. But I don't care, because the e-mail address is still correct, and the new department/division wouldn't even fit on a business card ;)


Using data in second study w/o consulting all authors

As with most authorship discussions, the issue is somewhat nuanced:

On a purely technical level, everything appears to be in order. The two of you conducted a study, and you published it together. You did a second study alone based on material from the first study, and credited it correctly. No academic misconduct has happened in any part of this process.
However, on an emotional, personal level, it is easy to see that your co-author probably assumed that you would continue working on this project together, and he feels betrayed by you taking a significant chunk from your earlier joint work and exploiting it without is knowledge, and without giving him a chance to partake and continue to get credit. Note that the issue here is not so much that he is not a co-author of a study that he did not contribute to, but that you presumably never gave him a chance to contribute and continue to be part of the project.

Edit:
Based on the OP's comments, it's not actually clear to me anymore whether the co-author did not in fact also deserve authorship in the second study. Personally, I would at the very least be highly uncomfortable using unreleased, so-far unused data that somebody else helped collect.

As is often the case, I feel it would help if you put yourself into your co-author's shoes. Would you feel that everything is ok if the roles were reversed, and your co-author just conducted this follow-up without telling you, and based partly on your earlier work and data that you collected?

Unfortunately, it is difficult to move forward from where you currently are without any hard feelings. Adding your previous co-author to the new study, if even possible, is not ethical as (s)he did not contribute, and obviously you can't go back in time and give him a chance to continue working on the project with you. I feel an important part to clean up this situation is you apologising for not handling this situation in the best way, and acknowledging why the other side is upset (rather than focusing on whether or not you have "technically" done something wrong). If your personal situation seems salvageable, (honest) promises of joint future work usually do wonders in smoothing over rocky current authorship discussions. However, if your personal relations are sufficiently tainted, it may be best to just store this away as a learning experience and move on rather than continue working in a collaboration where the trust has been lost.


What should be included in a support letter?

A great letter of support for a student will include the standard elements of a recommendation.

Your relation to the student (lecturer, lab supervisor, academic mentor, etc.)
The student's significant contributions to the school, the community, and the specific program.
The student's academic excellence
Other important factors. (Why are you being asked for this letter of support? What do you know about this student that supports their suitability for this award?)

In all of these, be specific. Don't just say "X is an excellent student". Say "X is an excellent student, as evidenced by their insightful participation in class, their strong paper (won an award at [student conference in field]), and their continued dedication to learning. I was impressed most by x, y and z."


What needs to be done if an editor requires "very thorough editing"?

You're probably correct, the editor is asking you to check the whole manuscript for English. If you have a friend who's fluent at English you can ask him / her, otherwise you can also contact a copyediting service such as Enago or Editage (this is not a recommendation for either service, since I have never used them before).

Good luck!


CV for PhD application: should I list a job I am yet to start?

If you have formally accepted the position, you can use the word "starting" with your start date to indicate it. Either way, you will probably be asked about what you're actually doing while you're applying for a program, but adding it on there ensures that, at the very least, if you forget to update your CV or accidentally provide an older CV for some reason, your bases are covered and the viewer is able to see that what was a prospective job is now likely your current job.
Example:

Underwater Basket Weaver, Foo Inc., Oahu, HI
Starting July 2124

Don't add in stuff you do not 100% own.


Will my supervisor also mark my MA dissertation? How will this be fair?

On the topic of anonymous marking.  Dissertations/theses are rarely, if ever anonymised, because students and their topics are easily visible.

What you are asking is really a matter of Quality Assurance, which will depend on the assessment policy relating to Master's theses at your department/institution.

It is worth saying that the bias you mention (of a supervisor's familiarity with your work and writing influencing their assessment of it) is recognized.

In my experience, to mitigate bias one of two actions are taken:

The assessment is double-marked, once by the supervisor and once by a second marker.  Any difference in marks are then discussed and agreed.
The assessment would be marked by someone not related to your project at all, and it may also be double-marked by someone else.

For Master's theses, at least from what I have seen, the subject specialism and expertise of the assessor is less essential than it would be in doctoral study, so I would expect an assessor with good familiarity with the subject to be able to satisfactorily mark it.

Also, in the UK, all assessments are ratified by a Board of Examiners who have the power to alter marks at their judgement.  The External Examiner in this Board would also have the power to read your dissertation and agree/disagree with the mark awarded - they, and the rest of the Board, won't necessarily be experts in the subject to the degree that your supervisor is.


As temporary faculty, how to deal with a colleague who, via email, questions agreements made in a meeting?

Actually, I would ignore it. It is fairly typical behavior among some faculty. It might not even be abuse, but just the other person having time to reflect after the meeting. If the comments made were on-topic and not a personal attack, then you have nothing to gain in your current position by doing anything beyond arguing for your position. It could even be that the other person is uncomfortable in meeting generally.

I once found that offering suggestions for improvement of policy, as a new faculty member, is sometimes definitely not appreciated. I suffered setbacks because I suggested that "the way we do things here" was counterproductive. People don't like to hear that from a new person or an underling.

But yielding graciously, even if you don't feel it, could put you in a better position for future employment there.

On the other hand, you are justified in responding to a personal attack, but do so through "channels".


Beginners' guide to publications in mathematics

You mention that you are not a mathematician and that you feel that your solution to a math problem is worth publishing.  If you are an undergraduate, you might want to consider journals targeted at authors who are undergraduates (search the internet for "undergraduate math journal").

If you are not an undergraduate (or even if you are), I recommend you look at the three journals published by the Mathematics Association of America:

Mathematics Magazine "offers lively, readable, and appealing exposition on a wide range of mathematical topics."  (Read more about it here.)
The College Mathematics Journal "is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. It publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years."  (Read more about it here.)
The American Mathematical Monthly "publishes articles, notes, and other features about mathematics and the profession. Its readers span a broad spectrum of mathematical interests and abilities. Authors are invited to submit articles and notes that bring interesting mathematical ideas to a wide audience of Monthly readers."


My supervisors want to make me finish my Ph.D. in 2 years. What can I do?

Your advisors telling you that you've done enough to finish your PhD in two years is a good thing.  The fact that you have extensions to do on it in future work is also a good thing.

I've also never heard of a department that would think finishing a PhD in two years is a problem.  I suspect it's most likely a neutral thing, but if not it's almost certainly a positive, since it shows you can get things done and perform research in a timely fashion.

The optimal approach I would suggest is to graduate and go on the job market, then continue working on your research.  Congratulations on your impending graduation!


Request an unpublished paper owned by another (foreign) university

If the thesis is recent enough that it would have been written electronically, you can try to locate the author and ask if they would be able to send you an electronic copy.  This is a reasonable request.

Otherwise, talk to a librarian at your university library.  They almost certainly have some sort of inter-library loan that can get you a copy, or access to the original.  Requests like this are part of their job and this is a perfectly reasonable thing to ask them to help with.

Related:

Requesting a copy of the PhD thesis from an author?

Is it okay to ask someone for an (electronic) copy of their PhD thesis if it is not available online?


How to guide more number of graduate students?

I will advise as many students as possible.

Don't do this.  It's unethical.  Graduate education, especially for PhD students, should be about quality, not quantity.  If everyone worked to maximize the number of PhDs, then there would be far more PhDs than are needed.  This has already happened in most fields, but maybe not yours.

How do I recruit more graduate students?

If you insist, then

Raise funds, probably through applying for grants.
Advertise that you have money to pay graduate students a competitive stipend.  In my experience most faculty underestimate the current free market stipend.
Publish frequently.
Ensure your students graduate promptly.
Treat them decently.
Help them find jobs.

If you have a reputation for these things, you will have plenty of students - unless your university has a reputation for not doing these things, in which case you will have to move.


How can I withdraw a publication from a predatory (fake) journal and resubmit to a legitimate journal?

I see two main barriers for this to happen, and I would not attempt to cross either unless the circumstances were truly exceptional.

If your paper is already published, you will most likely have transferred either the paper's copyright or a very wide license to the original journal. You can probably force the journal to retract the paper, but if you want the copyright you will have to ask for it back, and it is legally up to them whether they want to give it back or not.
Most journals have a policy of only accepting works which have not already been published. This would make it very hard for your paper to get into the second journal, and the editors would most likely have to make an exception to their rules. This is up to them, and I would advise you to contact them beforehand to see whether they would be willing to do something along these lines.

The worst case scenario is one where the paper is very visibly retracted, you do not get the copyright back, and you cannot republish it anywhere. I can't really imagine any degree of shadiness of the original journal that would make this outcome preferable, because a retraction will leave a very visible, very black mark on your publication record for a long time. As mentioned in the comments, retractions are vivid indications of academic misconduct, plagiarism, or just plainly incorrect findings, and rarely of anything else. Therefore, you should be really careful that this doesn't happen.

I would advise you to take this in stages. First, read all the documentation you have available. Read very carefully, in particular, anything you have signed, either in paper or electronically, to the original journal. Check all their publicly available policies, and particularly those on licenses and copyright. Check also what your new target journal states as their requirements that submissions be 'new, unpublished work'.

Armed with this information, contact your new target journal first, to see if they will re-house your paper after it's been withdrawn, and what conditions they would require for this. Do not move forward until you have good assurances of a good home for your paper, or you risk ending up with a homeless paper.

After that, you should contact the original journal. If you gave them the copyright, you will have to ask for it back but you should be prepared for them to say a plain no. I suppose that if you gave them a more restrictive license then you can ask that they take it down and find out how you can revoke it, but you should be aware that author contracts do not normally include anything like that. Be polite and explain why you are doing things but be prepared for things to turn adversarial; you are after all out to affect their revenue stream.

Mostly, though, why don't you consider your options in terms of fixing the damage this publication has done to your record? Publishing in a predatory journal without knowing it is something that can end up happening to anyone (which is why one should always exercise maximum care when opting for a new publication venue).

Keep in mind that the venue of publication does not affect the quality of your paper, but only (potentially) how it is perceived by others. This can be palliated by other means: for example, take the paper to conferences and explain and defend your findings to your peers. Work especially hard at making sure the material finds its way to the hands of people who will use it and cite it, and that will help validate it as good research in a possibly shady journal.

If the journal is not very visible or accessible, post it to an eprint repository if it is possible (though of course only if other republication options are exhausted and allowed by your original journal, or if you are prepared for your relation with them to turn adversarial). Consider building a bigger paper, formally a derivative work, which you can then publish in a journal you're happier with.

In short, there are many options available to mitigate the damage done by a paper in a journal you (and whatever review boards you might come across) don't like. Think them through before you attempt something which is as potentially damaging as this.


interdisciplinary Phd programs in philosophy and computer science (AI, ML)?

I suggest that you don't need a "program" but rather a school and a professor who is willing to be flexible and let you take the lead in large part. Maybe a couple of advisors in different fields. I think there are a lot of top institutions that can afford such flexibility and Stanford is likely one of them. But you should probably pursue this individually and in person.

I'll note that doctoral programs are normally pretty individualized in any case, and often a student needs to take a lead if the topic is not completely within the expertise of the advisor.


How to write a research proposal for a PhD position?

First of all, the research suggestion does not reach to be able to contribute to the professional environment. In fact, this condition is not required for your degree in now. And, this isn't searched. However,  while will give any suggestion to the environment; you have to especially interpret the same topics by a high-level English and the using technical tools which no one minded upon them in more before.


Do other countries have a oral exam system similar to French “colles”?

The correct answer to this question is either yes or no. To answer yes one would simply need to provide a single example of another country with an oral exam system similar to the French system. To answer no we would need confirmation that no other country uses a similar system. To start the alphabetical list:

United Kingdom: Undergraduate students at the top universities tend to begin their studies immediately following their A-Level examinations which do not have a substantial oral component.
United States of America: Undergraduate students at the top universities tend to begin their studies immediately following their high school/secondary education. Admission is based upon performance throughout high school and standardize test neither of which have a substantial oral component.


What are the ethics of getting help from online forums?

Asking on math.stackexchange often does the trick, but I wonder what the ethics involved are. For instance, if someone provides a complete answer, and the result turns out to be integral to the paper, should I offer them authorship?

If someone else made an integral contribution to your work, it seems appropriate to offer them coauthorship, yes.  You go on to say:

  I'm not talking about a result that is novel in itself - i.e. it would not be considered as a contribution to mathematics. The result will be an application of standard mathematics to a particular engineering problem.

I see what you're getting at, but still: if you did not have the knowledge to write the paper, then asked someone for help, then based on their help you can write the paper, then it seems that they deserve to be offered coauthorship even if what they provided was from the perspective of their discipline completely routine and well-known.

One example that springs to mind is the Hardy-Weinberg Principle: this is a famous (and, in my understanding, rather important) law of genetics whose mathematical content really does seem to amount to: if p+q = 1, then p^2+2pq + q^2 = 1.  The history of this is not what I had assumed it to be: it is not a collaboration between Hardy and Weinberg (Weinberg was a German physician who had independently discovered the law at about the same time).  Rather Reginald Punnett was having trouble defending Mendelian genetics against an argument of Udny Yule that dominant alleles would weed out recessive ones and thus genotypic frequencies would not remain stable in the population.  Punnett brought this up to (the great analytic number theorist) G.H. Hardy who happened to be his cricket partner, who duly submitted a letter to the journal Science.  As the wikipedia article points out, Hardy makes his take on his "contribution" pretty clear, e.g. in the phrasing "a little mathematics of the multiplication-table type is enough to show...."  It is interesting that this is not called the "Hardy-Punnett Law" (though there are Punnett squares, which seem to my inexpert eye to be pretty much the same thing).  One striking thing about this example is that the mathematics here is really trivial: it is hard to imagine any mathematician (or engineer, etc.) who would not have been able to answer the question.

Of course, just because you offer someone coauthorship does not mean that they will take it.  Most mathematicians I know are not interested in being coauthors of papers in other disciplines for which their contribution was purely mathematical and is regarded by them as "trivial", "well-known" or both.  If someone declines coauthorship then it seems largely agreed upon that you can go on to write the paper by yourself and include a clear acknowledgement of their contribution.