Is original research required for an undergraduate thesis?

The professor is suggesting you do the final project and keep it easy for both parties. I got data, my name on the paper, and research presentation at academic conference in undergrad by playing ball and working on the professor's pet project.  And just because the school calls it an FYP doesn't mean you have to call it that. I'm not saying you can call it a thesis but if you applied elsewhere, FYP would sound really obscure and student-ish.  If you own a quality piece of written work, you can rework the intro and publish it wherever it fits in your field. If nobody wants to publish it, hold onto it and maybe it can get worked into something else later. Maybe that FYP is "currently submitted" for publication on your CV at just the right time later. Thesis may be property of the school. Final thought: professor may commit time to messing around with data and getting complicated with you if he can co-publish something. It's a lot of extra office hours with you to do a thesis when they could be with their family at home. Can you make it worth their time? Let them hint to you how it can be worth going the extra mile.


How to fruitfully utilize faculty-student orientation sessions at institutes you don't want to attend?

I don't think you can expect to get the opinion of a professor about another institute/lab. You can probably get some facts (like this other institute has more/less money, they are more/less active in this area), but nothing subjective. Academia is pretty small world, and people try as much as possible not to say anything negative publicly (and since everything said is positive, it can be hard to distinguish the real positive from the fake one).
You need to have a real interest in their work. As mentioned here, it's already pretty hard to maintain collaboration between people interested, so if there is no clear interest, it will very hard to be on email terms. But, the question is: why do you want to be on email terms?
See the previous point. You need to really interested, meaning you've read and understood their papers, and are able to ask questions that go beyond "what are the possible usage of your approach?".

As a general remark, professors are usually already very busy dealing with their own research/teaching/students. Of course, they usually are open to new collaborations, but they might lack the time to work with a student who is not theirs. A good solution could to try to visit them, academically speaking, for a month or so, to work on a very specific topic.


Can a hypothetical question be chosen as a research question?

At least in the hard sciences your question would not constitute a good research question. A scientific theory is considered a 'good' theory, if it makes falsifiable predictions (i.e. predictions which can be compared to observations of the real world) and has not been falsified despite comparing it to lots of observations.

Suppose in researching your question you come up with the theory "Hotdogs would never have been invented if the USA did not exist". This is not a good scientific theory, since it can not be falsified by comparing it to observations.

Things would be different, if it would currently not be known whether the USA exists or not. If in this case you can logically argue that "Hotdogs would never have been invented if the USA did not exist", this would constitute a valuable scientific contribution, since it would provide a link between the observation of Hotdogs and the existence of the USA.


Fraternity/Sorority and Graduate Application

Non-academic activities do not count in any way towards graduate school applications unless they were successful or notable to a heroic degree.  E.g. if you sold cupcakes as an undergraduate and made some money doing it -- or were popular at your church / club / frat's socials by doing it -- no one cares.  If you sold your cupcake company for a million dollars, we'll care a bit: that's an exceptional level of competence and gumption, enough to reasonably expect that some of it will transfer over to whatever you put your mind to.  Essentially, unless you're getting national media attention for your extracurricular activity, don't bother.

(Note: @jakebeal says "non-research-related".  I think "non-academic" is more accurate: teaching / tutoring / TAing in your field is highly relevant.  Being an active member in an economics club which, say, brings econ faculty to speak on campus is relevant, though not a game-changer.  Also: please remember not to use "science" as a synecdoche for academia!)

Participation in "Greek organizations" is totally orthogonal -- I mean, has zero correlation; I MEAN: is completely irrelevant, either positively or negatively -- to graduate admissions.  To be honest, I find the suggestion that it could be viewed negatively quite far-fetched: there is no "conflict of interest" here, any more than a Jewish or African-American or Republican student has a conflict of interest in their dealings with other Jewish or African-American or Republican students.  An otherwise capable graduate student should be assumed to be capable of reasonable, professional behavior until evidence to the contrary comes up.

There is no reason to list this on any academic CV.  As I said in a comment, the only real negative I see is that by putting something on a CV which is completely irrelevant, you show an ignorance of what academics think is important which makes you look less clueful about what graduate school is really about.  It does so in such a mild way that I think almost any faculty member doing admissions would take it as a point of honor not to be influenced by this, but still: anyone who has read this question is now more clueful and knows to leave such things off an academic CV.

P.S.: Hold on:

  I fear that that may also hurt my chances--either because the admission committee associates me with a rowdy chapter

So you think that the graduate faculty in the economics department will see your affiliation with, say, Alpha Omicron Pi and say "Well, some fraternities are fine, but not that one -- they're trouble!"  Are you writing this question from the inside of an eighties movie?  In the real world in 2016, the majority of faculty live far away from campus and have precisely zero dealings with Greek life including whatever incidents may occur on campus, and in many departments, at least a substantial minority of faculty were educated outside of the US and are thus completely unable to tell one Greek organization from another.  As one data point: I live walking distance from campus and was educated in an American university with some amount of Greek life.  Thus I happen to know that "AOPi" is a sorority rather than a fraternity.  I would expect less than half of my colleagues to know that with any confidence.  The local chapter of AoPi is two blocks from where I've lived for many years.  What can I tell you about them as a group? Nothing.  Don't care.  Not my business.


Is it ethical to withdraw a conference long version paper after being accepted as a short paper?

Yes.

Publication requires both the consent of the publisher (via the editor or program committee) and the consent of the authors.  If you do not consent to publish under the conditions imposed by the publisher, you can just say no.


Will retracting a paper from biorxiv hurt our future publication chances

No, many submit and have to rewrite or withdraw for many reasons. Do you really need to withdraw - this may be an interesting result for people to see even if it was on limited data...


How to provide in-text citation for Appendix

The easiest solution is to provide a reference to the Appendix (e.g., "for further details, see Appendix) wherever the additional information is relevant. If your Appendix contains several different types of content then subheadings would be helpful. Then, you can reference the specific Appendix sections in your text. Seeing as you're at the copyediting phase now, you likely don't have many other options.


After quitting a PhD program, would time off before applying to a new program be harmful?

A respectable wish, but perhaps not the best approach. I would suggest a few points to consider:

If you want to form an opinion about what it's like outside of academe based on one single work experience (at one company or organization), then indeed it will be a biased opinion as it will be based on a sample of 1...and you don't know if it's representative of that 'life' or is an outlier. Best case, it will be representative of only one category of jobs outside of the academe (e.g. for profit, non-profit, NGO, small, mid-size, or large orgn, in one industry or another).
I would compare leaving the academe for the 'real world' to not dating another girl to appreciate one's girlfriend, but to hooking up with a guy to see if you like guys better than girls. I think that would be a more accurate reflection of the difference in culture, incentive structure, relationships with superiors/bosses and colleagues, compensation/quality of life, work schedule/flexibility, free time after work, etc. Or like living in a foreign country for a while.

Is it a great learning experience even if it turns out to be a very challenging, boring, and generally unpleasant job? Absolutely. It will teach you how to work with different kinds of people, how to handle responsibilities - in other words you will become more mature and 'seasoned' for what life may bring to you at some later time. You will be better prepared to handle reality.

Leaving a PhD program before graduating is a strike against you, which may result in a vote of no-confidence from past advisors. A more mature approach would be to take a 12-month academic leave, which is perfectly 'legal' and within the boundaries of acceptable professional conduct.

Academic leaves were designed for students whose life circumstances make continuation in a program very challenging, thus providing a way to continue in 'good standing' while taking time off in a structured way. That leave of absence may not need to be explicitly stated on your CV, it will merely postpone your graduation by a year. If employers care enough, they might ask; otherwise it will be hidden in that space on your CV between the graduation date from your Bachelor or Master's program, and the graduation date for your PhD program.

I would recommend against taking a leave of absence for more than a year (there may be a maximum cap of 12 months set by your university's graduate school policies anyway - check with them to find out for sure).
If you do end up taking a leave (which I think is really the way to go in your case), there may be some really cool ways to spend the year other than working the 8-5 drudgery for some firm.

There are countless graduate fellowships, community service organizations, foreign exchange programs, etc. that would be happy to have another warm body in their ranks for a year! Something like an international fellowship or community service experience could give you much broader exposure to different organizations, different kind of people, different workplace settings and cultures, than being stuck in a cubicle somewhere on the 40th floor in a concrete jugle.

So I would cast the net broadly and see what's out there. Your university's career services office could be a great place to go for advice.

Lastly, leaving a graduate program mid-way will mostly likely result in wasted time in terms of what it will take to re-start graduate studies and get to the same place where you are now. Not all credits might be transferred, thus some quarters or semesters that you have already spent in the program may go to waste (at least on paper). It will take renewed effort to build new relationships to secure RA/TA funding. And of course there is always a risk (which someone mentioned already) that you might not come back. A half-finished degree is really no degree, and doesn't count for much on a CV other than explaining what you've been up to for N years (though not necessarily to your credit).

Bottom line: I would suggest to stay in the program but take academic leave for 6-12 months. Before you do, first find a solid opportunity and get accepted/admitted to it, so you know for sure you won't be fumbling for months and wasting that precious time getting something lined up.

Hope this helps. Good luck!


If I saw a research result similar to mine from my PC/editing duties, should and how should I contact the authors?

If you have already read the paper, do not contact the authors. Here's why:

You would have to admit to them you read the paper. Since that is a conflict of interest (and you should have recused yourself), you would essentially be outing yourself and the journal for less than ethical reviewing.
You would be providing an incomplete opinion on their results. Your paper hasn't been published yet, so you don't know for a fact that your results/contribution are considered more valuable than theirs. Telling them of your research may sway them to continue or abandon their work unfairly.

Going forward, make sure to recuse yourself from editing before you read the paper. When the editor/assigner emails you about the assignment, make sure to read the abstract thoroughly. If one is not provided, email back and ask for one. If the abstract suggests a line of research that appears close to yours, recuse yourself at that point -- before reading the full submission. If you have any doubts about how close it is, I would recuse myself anyway. Most editors appreciate this.


Should I tell students that it's my first time teaching the course?

Recommend not on the first day.

I'm actually in exactly this situation for the fall term, so I was prepping myself mentally for just this issue. In my experience, expressing any uncertainty about the course on the first day prompts almost instantaneous pleading/negotiation/argumentation over any and all stated procedures (parameters for assignments, grading, due dates, etc., etc.)

Now, this is partly influenced by the fact that I work at an urban community college where the student maturity level can be quite low for certain courses. If you work at a more high-powered institution then the environment might be different. But I still think it best to be authoritative at the start, gauge the environment on subsequent days, and then if you feel comfortable admitting the situation and/or asking for feedback later on, you'll be more confident about doing so.


If I wrote a textbook, or other form of academic material, is it okay to use problems found online?

In general, no. You may not republish materials found on the web unless you attend to copyright laws in your jurisdiction. These laws vary quite a lot, but for your intended purpose - inclusion in a book - you will need permission in most places.

Sometimes the original publisher will explicitly give permission on a web page, such as a Creative Commons permissive license or a statement the the material is public domain. But even a license comes with restrictions, such as, perhaps, attribution.

Sometimes the original publisher will include something like terms of service like these from Lamar University. Your use is bound by those unless you make other arrangements with the copyright holder.

In the absence of any statement to the contrary, you should probably assume that the creator or other copyright holder "reserves all rights".

When in doubt you can and should contact the creator of any materials. Both of the links you provide actually have contact information.

In addition to copyright law, for which you can be sued, there is the question of plagiarism. It is considered unethical to claim any work created by others as if it were your own.

I'll note for the record that there are a few exceptions to copyright law, but they don't include republishing the work of others. If those problems have "value", then that value is owed to the creators.

Also, copyrights generally expire, but the terms are normally very long - something close to 100 years at this point.

There is one subtlety, however, that partly explains why you see the "same" questions in multiple places. Note that it is words and "expression" that is the subject of copyright, not ideas. The only "ideas" that can be protected from reuse are those covered by explicit patent. That is a completely different thing. There are some things, however, for which there may be only one way to properly express it in a given language.

"Integrate f(x) = sin(x)"

is one of those things. The sin function and integration are ideas with common terms. There are very few other ways to write that problem. So it will appear in that form or one closely similar to it in most calculus books. In general, the ideas are free to use.

Finally, you seem to be asking for legal advice and no one here can give it. In particular, no one here can give you permission to do something that is illegal to do under civil or criminal law. I am not a lawyer. My advice is conservative to help you avoid stepping into a problem that is best avoided.


Course load expectations for teaching track and how to negotiate for courses

As usual, there is no clear answer. People are different. "Requests" are different - maybe, the request in your case was an honest, open-ended question and your department head is not surprised that you said No. Maybe the request was supposed to be a rhetorical question, and the department head was really surprised that you said No.

  How does one manage such a "request" from the department chair?

Well, as you would handle any request. Check if it is ok for you to comply with it (do you have the time? is complying with the request aligned with your interests?), and if it is, agree. If it isn't, carefully explain why you can't do that, and offer alternatives. From your descriptions alone it does not sound like you did anything particularly wrong. However, most people are a bit more accommodating when starting a new job, so I would say that your department head was probably at least a little bit surprised that you turned him down.

  Did I shoot my career really early in the foot by declining such a request

"Shot in the foot" is maybe a bit strongly formulated, but it is certainly possible that the head has the impression that you are not overly flexible. I mean, asking somebody to teach a second course is not really an unheard-of request.


Chance of applying as a prospective PhD student in semesters

In the UK, most PhD studentships for home (UK/EU) will be advertised in the autumn, and also those few places that have PhD programms will have closing dates just after Christmas. In most cases this will be to recruit to programs that will start in the autumn of the following year.

This is not a hard and fast rule, and plenty of people will get positions later in the year, although many of them will still start at the start of the academic year in October.

This is not to say that no one starts inbetween, its just much less usual, and often suggests an unorthodox funding route, such as self-funding, foreign government fellowship or industrial sponsorship.


How to effectively locate older studies and papers?

Although many journals have done a good job of putting their archives online, it does indeed get pretty difficult to find an electronic copy of any but the most prominent publications if you go back earlier than around the 1970s.

Fortunately, there are still people who know how to deal with this, and whose job it is to help with issues like this: university librarians.  When I've faced problems of this sort, working with librarians has been the way to solve it. They often are able to locate a physical copy within their own collection or, if they cannot, often also have relationships with other institutions' libraries who can loan or scan materials from their own collections.

I would also suggest, however, that you may also wish to consider whether you really need to go back this far.  Go back the better part of a century, and you will often find that notations and vocabulary have changed to the point where it becomes difficult to understand the paper. Moreover, if the phenomenon has not been entirely neglected, there will often be later reviews or textbooks that present it much better and more comprehensively. Unless you are specifically interested in the historical circumstances of the original work or the perspective of the particular investigator, such later references may turn out to serve your needs much better.


It can't hurt to try to withdraw the article and get your money back.  You can send an e-mail and request this, but they may not agree.  Once you have signed the publication agreement and paid, they are legally allowed to publish the article even if you have changed your mind.  I can't predict the likelihood of success, but you can't make the situation worse by asking.

You might want to withdraw the submission even if you don't get your money back, to avoid having it appear in a place that could damage your reputation.  If you ask them before publication, then they ought to agree to this.  (They aren't legally required to, but I don't see why they wouldn't if they can keep the money.)  Of course I wouldn't request this until you've found out whether they will refund some or all of the money.  Leaving them with the money would  be frustrating, but you may not be able to get it back, and a publication in a predatory journal won't help you.  It's better to be able to submit it somewhere else.

After publication, they shouldn't just remove the paper from the academic record.  You could ask them to retract it (which would leave a retraction record), but they might not agree to this if there's no problem with the paper, and it would be embarrassing in any case.  Once the paper has been published, you best bet may be to accept it and move on.


Ethics of writing another paper to be graded for use as a work sample

I guess you sound like you are trying to game the system and that your "graded assignment" isn't really the sort of thing that is expected. If you are trying to deceive, then, of course it is unethical.

However, you might ask to submit a second writing sample along with the require one, stating that you think it represents your abilities better than your coursework.

It would probably also be a mistake to ask your professor to participate in a deceit. But, his comments on a second sample would be fine as long as you are clear about the situation.

Guard your honor.


Maximizing opportunities to be admitted in top schools

Your approach is wrong and will be a hindrance in maximizing your chances for acceptance. No school wants to accept someone who only wants to go to their school because of its ranking. You need to tailor your application to demonstrate why you want to go to the particular school. Once you have identified some schools/supervisors, ideally one of your recommendation writers can introduce you. You then need to build on that relationship. Talk to them about how your work fits in with their past and current work. As your relationship with the potential supervisors builds, figure out how they fit into the department. They will likely have the inside knowledge needed for writing a really good application.


Imminent unemployment, I have a screwed up CV; incompetent in my own field of PhD. Hoping for some perspective and advise?

Actually, I think that the way you did your doctorate implies that you can, in fact, learn the things you don't know now. In fact, you may have more skills than you realize, but I'll leave that aside.

But first, the courses you took in the past are nearly irrelevant to the process of getting a job once you have a doctorate. The skills, yes, but not the courses. But few employers will feel the need to do any real examination of your coursework.

I agree, however, that having some structure to learning is a big help. But you can address that in a variety of ways. Your alma mater might permit you to take some courses for a reasonable fee, especially if there is some service that you can supply to them in return. This might be an option if you do wind up unemployed for a bit.

But there is now a world of online study possibilities. For many people they have little actual value, since the credential they come with might be suspect, but you don't need credentials at this point. But, if you do sign up for online instruction somewhere, be aware that just reading and watching videos isn't enough. You need to put the new information into practice so that it becomes actual knowledge. Use exercises for reinforcement and try to find a place that will also give you appropriate feedback on your work. Some online courses are better at this than others.

So, I think that a two track plan would be worth pursuing. Work both in the job-seeking realm but also in filling in knowledge.

If online courses don't appeal to you, but you have research skills, then there is no reason that you can't start on some project that requires the skills you don't have but can, as you did in your previous work, fill in via self study. If it results both in publications and in skill building all the better. Perhaps your old advisor can help point to some things, even if you are now remote.


What happens if a math PhD student fails to find a proof that is the main objective of his/her thesis topic?

I wrote a failed dissertation myself.  No papers resulted from it.  Fortunately, I had a significant side project which was published, and 11 years later, the main thread of my research still comes from this side project.  (I suppose I could have written up the side project as my dissertation instead, but I didn't.)

First, no project is ever a complete failure.  At the very least, you manage to prove some (possibly almost trivial) special cases, you prove some helpful lemmas, you find that certain lemmas you might have hoped would be helpful have counterexamples, and you find certain methods that you might use don't apply because some hypotheses needed to use those methods aren't satisfied in your case.  It's possible to write all of these things up, ending up with a dissertation that's basically about "How not to solve Problem X (except in this very tiny special case)".  (This is basically my dissertation.)

Second, it's rare for mathematics graduate students, especially at top programs, to work on only one problem.  Your advisor might suggest a main problem for you to work on, but you go to seminars and hear about other problems, talk to other graduate students or postdocs and learn about other problems, and so on, and graduate students are generally encouraged to spend at least a little time thinking about these other problems.  If you get stuck on your main problem, you still have other problems to solve, and it's quite common that what you learned to work on your main problem ends up helping you in solving these other problems instead.  (This is basically what happened to me, except this other problem didn't end up in my dissertation.)

Third, especially in the early stages of working on a problem, advisors are usually fairly quick at pulling the hook if it looks like no progress is being made.  Most advisors know of lots of problems, and they know what complete lack of progress due to a problem being too hard looks like.  Even later on, advisors can sometimes suggest simpler problems that can be solved in a shorter time frame (given what a student has already learned).  In some cases, after a few rounds of failed problems, the student ends up with a dissertation that's about as weighty as a half-decent undergraduate research project (and results in zero papers or one paper in a "write-only" journal).

It's true that a dissertation written out of a failed or almost trivial project tends not to bode well in applications for jobs where research matters (unless there is a more substantial side project).  Sometimes an influential or convincing advisor can make a strong enough case in recommendation letters for the student to get a postdoc, but this is harder now then it was 10 years ago given how much more competitive the job market is.


Final round of reviewing for a Program Committee

In my experience, usually the PC chair sets expectations by providing explicit instructions and guidance on the process.

In my field, the deadline for submitting all reviews is usually a week or two before the PC meeting.  That last week or two is reserved for a "online discussion phase".  During the discussion phase, reviewers are expected to read the other reviews on the papers they were assigned and discuss what to do on each paper, to try to reach consensus on the final discussion.  This might involve some discussion on points where reviewer opinion differed or on technical points of disagreement, for instance.  Each reviewer is expected to take the lead on beginning the discussion, without waiting for the PC chair to prompt you or ask you a specific question.  The goal is to try to reach a clear decision before the PC meeting in as many cases as possible, or at least reach agreement on what the strengths and weaknesses of the paper are so that a final decision can be made on an informed basis.

If there is no in-person PC meeting, the online discussion phase becomes especially important.

But that's just my personal experience and my field.  Practices may vary in other fields, for all I know.  If your PC chair did not instruct you on what he/she expected, it is completely reasonable to contact him/her and ask what he/she should like you to do.


Can I write the same text in method section in two different project?

Reusing the text from a previous paper in a new paper is a form of "self-plagiarism" that publishers are increasingly unwilling to accept.  It's true that this was a relatively common practice in the past, but the advent of plagiarism detection software has made this practice visible and publishers are starting to crack down on it.

One reason for this is that publishers want to publish "original" content and not repeat previously published material.  Another reason for this is that publishers want to avoid violating copyrights owned by other publishers- the publisher of the first paper could easily sue the publisher of the second paper for copyright violation.

The way things now, chances are that when you submit the later paper you'll have it sent back to you with instructions to remove the self-plagiarism before the journal will review the paper.


Yes, citing books is fine (including anything from research monographs to elementary textbooks).  The question you should ask yourself is what the citation is for.  What are you trying to convey to the reader?  For example, if you are trying to assign intellectual credit, then you should cite whoever originally made the discovery.  However, that's far from the only reason to give a citation.  If you are providing references to background or more detailed explanations, then all you need is a source that explains what you need, and sometimes a textbook will be clearer or more useful than a research paper.  If you are supplying a citation to back up a potentially controversial claim, then you need an authoritative source.

The specific topic you mention is mathematical, in which case the distinction between primary, secondary, and tertiary sources is not particularly important except for assigning credit.  As far as explanations go, any derivation will do.  Of course, the form of your citation should indicate your intention.  For example, if you cite a textbook, you can say something like "See [insert reference] for an exposition of the theory of irreducible tensor operators" to make sure it doesn't look like you are claiming this book is where the theory originated.

Of course other fields may attach far more weight to these distinctions.


What is the best way to propose one remote collaboration of this kind?

Decide on what this field means to you and act accordingly.  From your post, you are a PhD student and therefore presumably already have a field of study.  If this is your first semester it will be a simpler conversation than if this is your sixth.  I'm going to assume that you don't want to change your current field of research, but would instead like to work in both fields to some capacity.
Whether your current field and this new one are related, and the extent to which they are related, is also important to consider.  If they are basically unrelated, or only tangentially so, then you'd be asking this post-doc to train you to be a collaborator.  If they are related well enough, then you'd be a useful collaborator to start with.
I personally would not begin a conversation around collaboration.  You appear to be too new to the field to do that.  Instead, I would begin by contacting the post-doc about his research, or potentially his talk, and discussing those open problems.  Are there any open problems that interest you and the post-doc, and in which you feel you could meaningfully make a contribution?  Start talking about your ideas, discuss it as though you are curious in a deeper way than someone who just watched a talk, but still not ready to jump ship and switch fields.
Through those conversations, you'll gain the insights you need to start proposing relevant questions for further research, and from there be able to ask this post-doc about collaboration opportunities.  Remember, this person also has their own projects.  They probably won't just bring you on to their own because you sent an email.  If you can both work on a truly new contribution though that would further your mutual careers, and if this doesn't negatively impact either of your abilities to get done what you need to do already, then it's a better conversation.
So, TL;DR: don't ask to collaborate, just start talking about a mutual interest, and see where it goes.


How common is spousal hire (academic or non-academic) in the Australia/New Zealand system?

My experience on this is more anecdotal, but perhaps it will be helpful.

In Australia, I've certainly known plenty of couples that work at the same university. I can also think of a few where I imagine a package arrangement was organised (although I don't know details). Equally, I can think of cases where academics have left a department because the department decided to no longer employ their spouse (i.e., they moved to a new university that would employ their spouse). The ease of making such arrangements depends on how desirable you and your spouse are as academics. It certainly helps if at least one member of the couple is a super star, and  the other member is at least competitive.

Another general point is that Australia has a lot of universities. In particular, if you are in Melbourne or Sydney (and to a lesser extent other major cities) then you would have six or so reasonable universities to work with. So I also know a lot of couples in the university sector who are able to solve the two-body problem by working at different universities in the one city.


Seven years of postdoc with no first-author publication – what are my career prospects?

First, if you feel depressed you should seek professional help. Naturally because you should take care of your mental health in general, but also because you're less likely to achieve anything useful (let alone get a new job) with a negative state of mind.
Ok so publications as first author is not going to be your selling point. Now there are certainly a lot of other things that you have done: maybe grant proposals, supervising students, experiments which require particular skills, organizing scientific events... The publication record is an important indicator in academia, but it's not the only one. And outside academia, it's frequently useless.
Try to objectively identify your skills and motivations: what are you interested in? Which skills do you have that most other people don't? Clarify the direction you would like to take and study your options, usually there are quite a lot for somebody with a PhD anyway. Your PI's suggestion could be a good idea, depending what you are looking for. You could also use some of the year you have left to perfect your skills or expand your professional network, for instance.
A simple way to get an idea of your career prospects outside academia is to contact a recruiter, they are usually eager to find skilled people. Even if you don't apply for the jobs they propose to you, this might give you a nice little ego boost ;)


Should I prefer a grad-school recommendation from a PhD holder who doesn't know me well, or an MS holder who does?

Person A. Person B, as a recent graduate, is not really in a position to assess your caliber as a researcher -- he is still settling into his own career. He cannot compare you to dozens of others he has known at this stage of your career. Further, he is hardly in a position to judge your suitability for a PhD program, not having one himself. There is a fairly firm unwritten rule that grad school LoRs have to come from faculty, not grad students or post-docs -- I imagine person B is the industry equivalent of a post-doc.

You may want to ask Person A if they would appreciate notes or a draft letter from Person B. This is one way to get more specifics into your letter. Another way is to write your own notes and provide them, just to "remind him" about the things you've been involved in. Alternatively, if your school accepts extra letters, you can ask both.


No, you don't need to translate the entire dissertation just for an application.  That would be an unreasonable amount of work.

However, you should at least translate the abstract.

Better yet, write an extended abstract in English.  This would be a 1-2 page summary of the contents of your thesis (brief background, methods, results, future work, etc).

Submit this together with the original Portuguese text of your thesis.

Commenters have suggested writing and submitting a paper (in English) based on your thesis.  That might be a good idea in the long run, but it might not be practical to do before your applications are due.  And you shouldn't rush the process if it would hurt the paper's quality.  So I wouldn't focus on that as a solution to this particular situation.


Based strictly on the information you have provided to me about this mystery person, I'd say the instructor engaging in these activities is highly unethical and may have some other psychological issues. That's just what I sense "prima facie". "Absolute power corrupts absolutely", but I could easily be wrong.

Then again, maybe the mystery person has explained the grading criteria, but hasn't explained it clearly enough.

Be very careful about making a formal accusation against this person. If you make an accusation, make sure it's iron-clad and infallible so that you're certain to win.

Many years ago, in an Engineering Mechanics class, I openly accused my professor of erring in his solution to an exam question. My exam question was marked as "incorrect" with very little partial credit. I stared at that problem for some time and concluded my solution was correct and the professor's was wrong. I treaded very gingerly as I described my disagreement with his solution, but I went step by step and ultimately, before the entire class, he admitted he was wrong and I was right.

I was about 18 or 19 years old at the time. Trust me. Be very careful. Professors are smart and they don't like to be proven wrong. My professor was, thankfully, a person who loved truth more than being correct.


How to decode a difficult citation in Wikipedia with "Historical Library"?

It may help to look at the text that was added along with that footnote, in Sept. 2019:
https://en.wikipedia.org/w/index.php?title=Ligures&diff=prev&oldid=914851412

You might wish to ask the user who added it, Shack76, by leaving a note on the bottom of their talk page:
https://en.wikipedia.org/w/index.php?title=User_talk:Shack76&action=edit&section=new

This user was active on this article within the last month, so I'd guess your chance of getting an answer is fairly good.

Yes, by the way, it is indeed a less than helpful citation; it would be good to improve it with more thorough information. I'd urge you to do so, once you've figured out what it is supposed to refer to. You will find the code for the footnote near the bottom of this edit window:
https://en.wikipedia.org/w/index.php?title=Ligures&action=edit&section=22
If you add any bibliographic information between the <ref> tag and the </ref> tag, and then click the "publish changes" button, it will be a big help to the next person who has a similar question. Don't worry too much about logging in, or about proper formatting; it's relatively easy for an experienced Wikipedian to tidy up the formatting, the hard part is tracking down the information you're seeking.

(Also note a helpful comment from @mkennedy in the comments section.)


What licensing concerns are there for using content from Stack Exchange in an academic paper?

Making a reference to CC Attribution-ShareAlike content is always okay. In fact, referring to any work is okay, regardless of the copyright status. Only content is copyrighted, not bibliographic elements (including author names and title). For example, the U.S. Copyright Office says:

  Copyright does not protect names, titles, slogans, or short phrases.

Quoting is a more complex matter. It depends on copyright laws, and thus your country. In most cases, if the material is quoted raw and the quote is kept short, most academic use should fall under the doctrine of fair use. By contrast, read also the article on derivative work to get an idea of these two extreme cases.

This is mostly a theoretical question, however: the scope of fair use is grey are in US Copyright Law, and provided you do it for academic purposes and in a good faith, you won't get into trouble.

Finally: if you really want to quote in a bulletproof way, either (a) consult with a lawyer or (b) ask the copyright holder for a waiver to relicense his content to you.


Do i really need a masters degree for data science / machine learning ? Applied Maths background

I work as a data scientist. We hire many people with a bachelor's degree in computer science, statistics, applied math, etc. Having a master's degree is better. If you have a master's degree in applied math, most data science jobs will be happy to look at you.

Be warned of course that there are various levels of 'data science' positions out there. Some of our junior employees literally just sit and query data bases for us all day. Or they are responsible to create nice looking images in Tableau. (Which has very little to do with "real" data science). I personally would find it to be mind numbing work. But it pays the bills for them, so it is what it is. To get onto the teams that do real research, we often require a graduate degree and some formalized abilities in machine learning.

Compile a portfolio of your strongest projects.

Being able to demonstrate some projects in ML you have worked on can go a long way. The more examples of independent projects in ML and data science that you have done, the better. Projects that demonstrate an understanding of what is going on beneath the surface are the best. (Anyone with basic R skills can run a RandomForest analysis. Being able to explain how you changed your parameters to optimize your model is another story).

I will comment on your grades here. For junior positions, grades honestly do not matter for the most part. All we would care about is if you can do the work. For higher positions, someone with a mediocre GPA is not going to be looked at as strongly. Most of us excelled in school. Much of our work requires study and applied learning. Applicants with mediocre GPAs usually do not have the specific study aptitudes we want. If your GPA is lower than about a 3.7, and you want to work into senior positions, be prepared to really demonstrate your value with a strong project portfolio.

One piece of advice on applying for junior level positions. Data science positions tend to fall into two categories: data analyst and data researcher. There is not a lot of fluidity between the two tracks. People who start out as analysts tend to get stuck there long term. If you want to get into machine learning and big data, avoid applying to data analyst jobs.

One other thing I will say: Avoid paying for a data science "boot camp" or the like. At least at my place of employment, we tend to place very little weight onto such things. I see applicants who have a BA in Classical Greek (very interesting subject, but very little job market) who have gone to a coding boot camp and expect that we will bring them in as a ML researcher or something. It does not work like that.


Is it possible to publish an erratum in another journal?

What can be published in a journal is up to the editors. If the original was sufficiently important and the errors less than obvious to readers, then an editor might consider it. But they would rather, I surmise, publish a full paper with correct results, citing the old, than just an errata. If you can't make the new work seem significant, I doubt that editors would be interested.
But the editor decides, perhaps with advice from reviewers. You can possibly make a proposal to an editor before spending wasted effort.


For most journals, do peer reviewers expect common notions such as arithmetic mean to be formally defined?

You do not need to define common "notions" such as the mean.
You do need to define common symbols, such as "μ", because they are common symbols for more than one thing.
These are just broad guidelines.  Each research community has its own practices.  If unsure, avoid ambiguity.


How important is it to work in industry before attempting a PhD?

From my experience in CS in Canada, most student do not have industry experience before doing their Ph.D. And I have not seen this as a requirement for entering the Ph.D either.  The reason is that a Ph.D. is not an industrial project although it could be related to the industry in some cases. But it does not need to.  During a Ph.D. the goal is not to commercialize a project. But it is to advance knowledge in a given field. Some people do a Ph.D. project in collaboration with a company. But from my experience, most people don't. So to answer your question: it is not important to have industry experience. But it can help. Perhaps that you will know how to better manage your time, etc. and this may be help in carrying your Ph.D project.


Not motivated for the second part of thesis

Sorry, but there are parts of math that are just messy. Worse, there are subtle parts that can throw you off. If you don't follow her advice you may be stepping into a mine-field.
But, it also sounds a bit like burn-out, and that you need a break. How much time can you take off without thinking much about the problem and come back to it fresh. It may still be a slog, but depending on intuition only gets you to the point where you seek the proof that validates it. Insight and intuition are good (essential), but the proof is in the proof.
Relax for a while (week, month?) and then get cracking.
But also guard against being sloppy in your thinking. If the second case really is a bit more subtle and difficult then (a) you might skip over the real issue and (b) that part might be the essence of a better paper/thesis/whatever.


Cover letter v/s statement of research interests

Statement of research interest seems to deal specifically with you potential future research. Though, you can obviously base your future project describing your proved past record. The cover letter seems to be a general info, something that you are XYZ  who completer PhD in ABC university, has the following background and you are interested in this position. In the cover letter I would briefly mention your research interests and refer for more details to the  statement of research interest.

I think that there is nothing special about this two-letters format, but it is just some bureaucratic requirement of the university.  May be worth asking them  how long should be research statement - because you can potentially write one page or 15 pages like a full grant.


Is it ethical to request additional money for non-research related work in a research lab as a grad student?

From one perspective, adding these niceties to the software increases the likelihood that the software will be used and thereby increases the impact of your research. So although these niceties are not research per se, they help achieve the goals of doing research (at least from a funding agency's perspective), namely making an impact. Such tasks are often a necessary part of the research process (and someone has to do them).

Whether or not it is ethical to ask for additional money to hire people to do this very much depends on the rules of the funding agency and how well your advisor is at selling and justifying the idea to the agency.


Should I ask for permission from the journal before making available publicly the (anonymised) text of the evaluation I received from peers?

Unless you signed a very peculiar publication agreement, you are under no obligation to keep the reviews your received confidential.  Moreover, there is probably no issue with copyright infringement either.  Publishing a modest amount of text, for the purpose of critiquing it, almost certainly qualifies as "fair use" of potentially copyrighted material.  (This could, however, vary from jurisdiction to jurisdiction.)

So I think there is rather little legal risk of doing this.  However, it sounds to me like a very poor idea nonetheless.  In most academic contexts, the dangers of doing something wrong come less from formal legal repercussions than from the damage that may be done to your professional reputation.

Presumably everyone who has published in these journals understands the relatively lax nature of their peer review (having gone through the process themselves).  Unless one or more of the journals has an undeservedly high reputation (which seems doubtful, since you describe them as "national"; prestigious journals typically have international contributors and audiences), publishing accusations of laxity against the journal are not likely to affect the journal at all.  On the other hand, doing something like that can definitely get you a reputation as an obnoxious troublemaker, which can be extremely damaging to your career.


How to search for list of papers citing both papers A and B?

Just get the citations of each document from the Scopus database, export the results into two files, and write a Python script that does a set intersection. You can generalize this to any files.

You can export the Scopus results to .csv files, and then use the csv python module to read the files. You can then have the set operation based on the title of the articles (even though I would also export the DOI and use it). If you know how to program in Python, writing this script shouldn't take you more than one afternoon.


How can I join/volunteer a research group for short term?

If you want to do it as a hobby you should look for "citizen science groups" near you or in your area of interest. See the Wiki article to get an idea.

  Citizen science (also known as community science, crowd science, crowd-sourced science, civic science, volunteer monitoring or networked science) is scientific research conducted, in whole or in part, by amateur (or nonprofessional) scientists.

If you want to participate in research at universities and research institutes I would just try to contact the group(s) there that work on the topics of you are interest in.
I guess plenty of groups would be happy to have someone to do some research assistant work and for you it would be a possibility to get to know them and their work.


How to add DOI to the published version of an article in arXiv?

The arxiv has a dedicated field where you can add the DOI.  (Note that this will not create a new version.)
In addition, most journals will allow you to upload the final accepted version (that is, the version with the corrections you did following the referee comments, but without any copyediting done by the journal), so you can additionally upload that version when you add the DOI (and potentially clarify in the "comments" field that this is the accepted version).


Professor reviews proposal as a favor, should I send a reminder

Send an email suggesting you don't assume he will offer any more help, but leaving the door open in case he offers some:

  Thanks so much for your help with my proposal. I believe your suggestions have really improved it. Attached is my current version; I will submit it tomorrow evening. Let me know if you have any last-minute suggestions before then.


sharing ideas for collaboration or working on them individually?

As a PhD student you are not usually required to have significant collaborations outside your school or department, although it does happen. So, if you are thinking about external collaborations, the first think you should do is talk to your advisor about it. Your advisor almost certainly has many connections in the field. Thus, they might be able to recommend someone to work with. But, they might also discourage this. You are (at least in theory) being trained by your supervisor. This gives them a greater responsibility for helping you develop your research abilities. Working with someone externally can put some of this burden onto them if your advisor isn't also involved.

For instance, I have a current PhD student that is part of an external collaboration, but I do some work to ensure that anything that we do that goes to our external collaborators is high enough quality that we aren't wasting their time. My colleague does something similar when his students work with me.

When I receive an unsolicited research request from a colleague's student, the first thing I do is contact their supervisor to see if they know about the request. I don't want to be seen as going behind their back to work with their student, and I wouldn't want someone else doing this with students I'm supervising.


How to get through the rigorous phase of PhD?

Take a (short) vacation immediately.

By working 15-16 hours a day you are making yourself too exhausted and tired to be effective. That is also probably why you make mistakes. You should take a break that is long enough to reset, and when you come back aim at reasonable working hours (depends on a person and circumstances but for most people this is 40-60hrs/week).


I think the best way to deal with this as an instructor is to set the tone right from the first day.

Make it clear you want an interactive class room, and that includes the students asking questions and even challenging you as well as having the students answer your questions.
Make sure your questions are worth answering. No one wants to answer an obvious question that was in the book they read for the day ("How may valence electrons does an oxygen atom have?"). Students like questions where they have to think a bit or interpret a bit.
Conversely, make sure your questions are not too hard, and that they are not unclear.
If all else fails -- and it often does the first time you ask an interesting question on the first day of class -- this is what I do. I wait a moment, then smile and acknowledge the awkward silence. And then I let the class know that I want an interactive class and that I'm perfectly happy to stand at the front the room through the awkward silence for as long as it takes. From my tone, I make it very clear that this not me being strict and judgemental, but that I want to work with them and that's why I am doing this.


Do you have to accept a postdoctoral position if the university has paid for accommodation and international flights for you to come and present?

If you are getting excellent treatment, that likely means they are fairly keen to hire you.  They are working to recruit you.  Accepting nice accommodations and amenities from them during the hiring process places no obligation on you--none at all.  That being said, this sounds like it might be a really good place for you.  Use your judgement about what will be optimal for yourself.


What qualities are organizing committees looking for in a reference letter for a summer school?

I once served as secretary for a summer school like this.  I wasn't directly involved with reviewing applications (this was the scientific organizer's job), but from conversations with him, my understanding was that the recommendation letter was intended mainly to verify that the student is a real person, is genuinely working in the field, and is at an appropriate level to gain something from the summer school.  Other than that, admission was not competitive (something like 90% of applications were accepted) since we didn't have any particular space constraints.

I believe there were a few "junk" applications from people who were not grad students, or were in unrelated fields, or otherwise didn't seem likely to benefit from the summer school.  Some may have been confused about the summer school's target audience, or were cranks, or were not in the field but were trying to use the summer school as a way to get a visa to our country.  The recommendation letter served to filter out these applications.

(We also had some travel funding available, but it wasn't competitive either.   The funding came from our government and would only let us fund our country's citizens and residents, so we essentially just divided the available money equally among all eligible participants.)

So I would say the letter should include:

Obvious stuff: student's name, your name, institution, fact that you are the student's advisor (helps if the institution is well known, and/or if you are known to be working in this field).
Brief description of what the student is working on (e.g. thesis topic).
Explanation of why the student is interested in the summer school.  If it is not obvious, explain how the topic of the summer school will be relevant to their research.  If there are specific connections, mention them.  ("One approach to Student's problem involves reticulated splines, so he/she is particularly interested in Professor Foobar's lecture at the summer school."  "Student has been recently studying Professor Barqux's papers on cromulent blobs.")
How far along is the student (just started in the program, several years in, about to graduate?).
Do you believe the student is adequately prepared for the summer school, in terms of background knowledge?  If your program offers basic courses in the relevant field or subfield, has the student successfully completed them?  Give some assurance that the lectures won't be way over his/her head.
If you think the student is especially strong and their work is particularly promising, you could say so.  But I don't think the organizers are looking for a detailed account of the student's academic strengths and weaknesses, or comparisons with other students.


What is the etiquette for repeatedly emailing questions to an author whose work I'm building on?

Although your intentions are probably good, you seem to take advantage of the creator of the source code. He is not your personal debugger nor he must be the one writing the code for your thesis (especially for free). He has written a paper and he has given you his source code. That is all the information you need to know. Read his paper (or his paper slides if they are publicly available) a hundred times, till you know every little detail of it and then look at his code (another hundred times) until you correlate everything between the paper and the code. Of course this will be slower than sending him a couple of emails but it is YOUR thesis not his. Only when you do all this and still there are unanswered questions, then collect all the possible questions you might have (including queries about his code and his paper) and then send it him ONE email, with all your questions. Anything more than that is exploiting his kindness. This kind of back and forth emails with questions is one of the many reasons why many people are unwilling to share their codebase.

Since he is probably a nice guy, you should consider that in the future you might collaborate with him or need his help. Being pushy or lazy (and delegating your work to him because you do not want spend 1-3 weeks refactoring or studying his code more carefully) is a sure way to burn bridges with him. And you really do not want to do that.

On the other hand, if after giving you access to his source code he understands (by your email) that you did everything humanly possible to understand his code and paper and just want some extra help, he will be willing to assist because: a) you seem to appreciate his work b) you seem to understand his time constraints c) you are also a smart, hard working guy worth collaborating with. And this is the message you need to convey.


What is the difference between publications and pure publications?

If this is related to the Max Planck Institutes, it might be this: https://www.biochem.mpg.de/878470/pubman

PuRe is a repository. In that case, "PuRe Publication" is just a special form of publication. Your capitalization in the question doesn't give much of a hint, however.


Does it make sense for the professor to write a recommendation letter that is directly readable by the student?

Is this a cultural difference between continental European and British/American system

I cannot surely speak for all continental Europe, not even for a small portion of it and not for all fields, but speaking with a few European colleagues of mine, it appears that the expectations that we have on recommendation letters are completely different from the typical US expectations.

In particular:

We mostly consider recommendation letters as a mean to discriminate between those that are not able to provide any recommendation letter and those that can provide at least a couple. That is, we expect most of the people not to be able to get one (in a distant past, I wouldn't have considered one who just attended one or two classes with me eligible for a recommendation letter).
We don't expect recommendation letters to be more than one page long, and half a page is ok (you just have to tell me that you had worked with this person and that they are not that bad).
We don't expect the recommendation letters to be sent directly from the reference to the application board.
We consider the writing of recommendation letters as a favour to the applicant, and not as a duty of our profession.

Actually, all the recommendation letters I wrote but one were handed directly to the student (or former student). For the exception, I've received a direct request from a university to submit the recommendation through their online system: the uploading procedure, with questions to answer too, was such a hassle that I've decided that in the future I will probably decline any request for recommendation letters to be uploaded anywhere.

To answer your main question:

  Should I ask the professors to write and hand me recommendation letters directly, or should I try to communicate with the university and let the professors email them the letter/give me a physical letter sealed within an envelop, which I will send to the university by mail later on?

I understand your reasons, but I'd consider this an odd thing to do. I'd simply ask the student to provide the recommendation letters.

In case the professors were reluctant to hand the letters directly to the student, I'd write an email explaining the different traditions.


Reference for use of name@math.univ.edu for mathematics department email addresses?

I don't have a reference about this. The split in email addresses is often because mathematics departments were among the early adopters of computing. I don't know whether this applies to your own institution, but it applies to several I have been at, of different sizes from 5,000 to 50,000 students.

When computing technology began to be available, mathematics departments were among the first adopters. Computers and mathematics go together. At quite a few schools, the computer science department is still part of the department of mathematics; at others, the two departments started together (when the math department began to hire computer scientists), and split apart later.

In the period before PCs became ubiquitous in the 1990s, mathematics departments often found funds (often via grants) to operate computer labs, web servers, and email servers on their own. At this time, especially in the 1980s, university-wide computing services were often quite primitive, and often consisted of terminal servers instead of PCs.

Over time, as computing became ubiquitous, universities hired their own IT staff, and began to run their own web servers and email. This is how, at several institutions I have been at, I had two different email addresses (one for the university and one for the math department) and two web pages (same split)

Now that email and web servers are viewed as a basic service that the university provides to faculty, it is more difficult for mathematics departments to justify having their independent systems. Administrators correctly look at the separation as an inefficiency, asking why the department can't use the same system as everyone else.

In my opinion, math departments that want to continue to have separate systems will need to present a very strong case for why the separate systems are necessary, beyond the historical developments that led to the separate systems coming into existence. As email and web services become more and more of a staple commodity, this argument gets more and more difficult.


Are there any good statistics on students who are second generation in higher education?

What you need is studies that control for parental education. If none of them have a university education then they are the first generation, if one of them has a university generation then they are not the first generation. So the "effect" of that variable makes the comparison you are after. Parental education is a fairly standard variable in this literature, so you should be able to find such references quickly enough.


How to tell my co-advisor I am leaving for PhD?

Tell your co-advisor. If he doesn't react well, take your advisor with you and have a second meeting. Maybe they can work it out colleague to colleague rather than professor to student. Withholding a good letter of recommendation because you want a promising student to stay and work with you is extremely selfish and borderline misconduct.


Having followed a few new journals from birth to quick success I can see the following steps:

Make sure you identify a scope that has long-term interest (pretty obvious)
Make sure the idea is supported by your scientific community; that they see a benefit in yet another journal. Community involvement really helps.
Assemble a group of enthusiastic and well-respected scientists in the field of interest to form a group to plan for the journal and who may constitute the nucleus of the editorial board (equiv.).
Create a proposal including a description of your goals and target audience for the journal.
Decide how the journal should be published. Open Access seems like a safe bet and initiate discussions with an Open Access Publisher. It is possible to publish on your own but using a publisher may provide access to other types of support so a careful assessment of the options are important.

----Now we assume the journal has passed the planning stages and will be launched

Make sure the community knows about the journal. This ground work can be continuous throughout the process but has to be realized by this point.
Try to attract as many prominent authors as you can and have them submit high quality work. This will help make the journal attractive. One goal, like it or not, is likely to get an impact factor (if that matters in your field) and that means publishing papers that get referenced. Attracting good papers in under any circumstances a good start.
Maintain high standards in your review process and make sure to maintain high publications standards. Good papers attract other good papers when people realize the journal is to be counted.

Only the contributions you can attract determine the success of the journal. Although some of the points above may seem obvious or even trivial, the more effort you add early on the higher the chance for success. In the cases I have seen, having the community on the train from the beginning and following the development has proved to be fruitful.


How to motivate myself to do more than the bare minimum that is required of me?

Wow.

While I was reading your question, I was thinking "did I just wrote that myself and erased it from my memory"? I just started my PhD in Mathematics, having obtained my Master's Degree last semester..

You pointed several problems we face as students of Mathematics who are trying to become researchers. One of them, which has drawn most of my attention, is this 'repugnance' from the details of something you already been through. I usually deal with this situation as follows: some of those details (in a proof, in a exercise, etc) are either too boring or too hard. If they're too boring, I usually make sure myself that I can remember them should I need them (in a exam, for example). If they're too hard, I usually try to convince myself that it won't be in the exam of the subject I'm studying for (this does not mean that I study only for exams!).

Whenever I am done with some subject, I choose another one to keep studying. As a PhD student I usually feel that there are a lot os subjects I should have mastered and a lot other which I should have some knowledge of. I usually use those 'confliting states' to switch to another subject which I have chosen by myself (not related to the lectures I'm attending). For example, I'm now having Several Variables Holomorphic Functions and Riemannian Geometry courses, but also reading a textbook of Theory of Foliations since I'm sure I'll need it next semester. It's not my priority though.

Now, keep in mind that you're not striving for the minimum at all times. Reaching a PhD course after obtaining your Master's degree is a really big deal. Are you really sure that A's and B's are the minimum that keeps your advisor satisfied? My advisor complimented me on my grades from Master's Degree Courses once, and it was full of B's, two A's and one ugly C!


Why does a UK university need to know my sexual orientation and religion?

The employing professor will not have access to this data.
You can omit anything in this form.
The data from this form goes to HR and is aggregated there so they can prove to auditing bodies that the staff distribution is not skewed (i.e. that they are not discriminating on basis of whatever)


Is there a default license for code libraries that accompany scientific research papers

In the copyright law that most countries sign onto (e.g., Berne Convention), copyright is assigned upon creation. In other words, if there is no explicit permission, you are not allowed to redistribute it. This is why licensing is so important.

However, if the code is publicly available and you reuse part(s) of it to create your own creative work, you are the copyright holder of that new piece of code. If the original copyright holder is of the opinion you violated their copyright (i.e., they think you copied too much of it directly and made too little additions/changes of your own), you have to substantiate your claim on how you deviated or added sufficiently from the original work to get copyright yourself.

In other words, take the risk or ask for explicit permission/a license to be added (e.g., MIT, GPLv3; see also here).


How to decide whether to publish masters project in computer science alone or with supervisor?

As a master student, or even Ph.D. student, there is nothing wrong on writing a paper with your supervisor(s). In fact, it shows your group work ethics. You should be delighted an experienced academic put his/her name next to yours on a publication. It adds value to the publication, because your supervisor is more well known than you and others will discover your publication faster.

You should think about being an independent researcher; at the later stages of the research (e.g., as a postdoc or an academic).


How to rate my level of proficiency in statement for graduate application

This sounds to me like a good place to follow the dictum of "show, don't tell." Giving a numerical or qualitative judgement will be useless, because they can't tell how your rating scale relates to their own.  What you can do meaningfully, however, is talk about what you have actually done which demonstrates facility with the concepts by putting them to use in classes, projects, or real work.

For example, if one of the concepts was "algorithms," then you might talk about a piece of software that you wrote that required understanding and applying complicated algorithms, or an undergraduate research project in which you created and analyzed an algorithm, or something of the like.  This will then give the evidence that the reader needs to assess you accurately, however they calibrate their scale.

If you don't have strong examples like that, then just say whatever the truth is about what you've done with the concept, e.g., "I got an A in my algorithms class."  It's not very satisfying, but in a case like that you really don't have much facility with the concept (peopler generally understand a concept much more deeply once they have applied it outside of the classroom).  Better a less than satisfactory truth than trying to guess what somebody who you've never met would think differentiates "pretty good" from "expert."


I feel like my mathematical competence is fading

First there’s no magical “being good at mathematics,” so it’s not something you can suddenly lose.  If you want to get better you can practice more and get better, and if you practice less you’ll get rustier, but neither state is permanent.  Your anxiety around your math skills may be due to this kind of black-and-white thinking about math skill.
In terms of practical advice, one thing that really helps keep you sharp on the basics is teaching.  Maybe try signing up to do a little tutoring, or do something with the undergrad math club.


How to show special respect to a famous PhD advisor?

I don't know what field you're in, but in mine, writing such a paper would be viewed as unnecessary and perhaps a bit strange. You seem to feel that you don't deserve your place with this supervisor, and so you need to prove your worth, or impress them, by writing a paper. This is unecessary, as you have already impressed them with your project idea and PhD application. They would not have taken you on as a student otherwise. Along these lines, you might want to search the term "impostor syndrome", both on this site and on Google.
"I am exhausted...". The last thing you need to be doing right now is writing an unnecessary paper with no help from anyone. A PhD is a several-year-long marathon, and you will need all your energy and stamina to complete it. Take a break, rest and recharge before you start. This will have a far greater benefit to your PhD, and accordingly to your relationship with your supervisor, than writing a paper.
Once you have started the PhD, show your current paper draft to your supervisor and work on it together. The paper will be much better for it. Again, this is field dependent, but in mine it would be extremely rare for a beginning PhD student to be capable of writing a publishable paper entirely on their own. You may be underestimating the challenge. This is something that your supervisor will help you with.
But for now, have a holiday, and celebrate your success at being accepted for a PhD with a great supervisor!


How much theory should be given in article?

Besides the already given hints I offer another guideline:

Give as many background as you yourself would have needed to get the idea and method before you have developed it.

In other words:

Write the paper to your former self (before you knew about what you've found out).

If you would have been happy with a paper that described the idea and references a lot to standard, readily available books for the background, then go for that style. If you had found it awkward to work through a paper that has a lot of references to papers/books that are hard to find, then don't do that. Note that different principles can apply at different places in the same paper.

These hint is in some way a simplified form of the general hint

Know your audience!

Oh, and also discuss this with your advisor.


Postdoc supervisor's impact when applying for a follow-up job

If you need to list references, you will almost certainly be expected to list your current boss—in this case, your advisor—as a potential reference. At the very least, if you do not, there is a non-insignificant chance that at some point in the interview process you'll be asked at will ask why he wasn't listed. You should have as good of an answer as possible ready.

Note that stating "I'm ready to move on, but he wanted me to stay on" may raise flags for a potential employer, as they could wonder whether this reflects a lack of loyalty on your part.


Is Research Fellow a gender-neutral term?

Yes, in your reference, the third definition is the one being used, rather than the first:

a member of a group of people who have shared interests, activities, etc.

Of course, we should look to how the word is actually used rather than solely to its dictionary definition, but in this case I think that actually makes the argument even stronger, since academics use the neutral form quite a lot and nobody else (at least in my part of the world) seems to care for the word.


Listing (peer reviewed) software article on CV

I don't think this should be treated any differently from any other peer-reviewed publication on your CV. There is still some standard of quality that's applied before a manuscript will be published in JOSS. In practice, there isn't a huge gulf between "major revisions" and "rejection" - both indicate that the manuscript needs to be changed significantly before it can be published. The category of "rejection" just indicates that the journal editor does not want to be involved in that process. Even though you can't be "rejected" from JOSS, that doesn't alone indicate that the papers which are accepted are of lower quality. A low quality paper could receive a label of "major revisions" every time it's revised and submitted if it's still low quality - it never gets outright rejected, but it never gets published either. The fact that it's not rejected speaks more to the patience of the editors than to the quality of papers they choose to publish.


A bad feeling about first published papers

You should do nothing other than continue growing and learning. The most common reason would be #1. I can't say the most likely reason is #1, not having seen the papers.

But a lot of authors, even poets, look back on their early work with a sense of wonder about how they could have been so naive. It is a sign of growth.

Yes, #2 is probably also a factor to some extent as CS has been a fast moving field overall, not being much over 60 years old, compared to, say math and such.

And you haven't said that the papers are actually wrong, just a bit naive. Hopefully we all learn some things as we grow older. It normally happens because we are actively thinking about things.

Others at the time (reviewers, editors, advisors) thought that the papers were fine for the time. They were fine.


How Can I Get a full scholarship to a University by my Skills | as an International Student?

You seem to have some misunderstandings about undergraduate education in the US. A bachelors here provides a general education along with a specialization. The general courses are about 40% or more of the total.
For example the CS program at UIUC seems pretty typical to me. Note the wide variety of courses, including the humanities. UIUC is a highly ranked research university.
Also, undergraduate admission is generally not controlled by individuals, but by committees who may only get involved in non-obvious cases.
The situation of scholarships, especially for people who don't stand out academically, is probably even harder. And especially for an international student who can't claim historical discrimination by race or ethnicity as can some citizens here. But in particular, contacting an individual professor for this is probably going to be fruitless.
To get accepted you need letters of recommendation from your current teachers, as well as an "acceptable" academic profile. The letters need to be from people who know you well and can speak highly of you.
Some people can arrange funding from their home country or some institution there.
My guess is that you can probably get admitted to a good US program, but funding will be much harder - especially "full ride" funding. Some discounts might be available to you, as they are to many. But much of Europe has much better funding for higher education.


How to grade students' lab worksheets to prepare them for a final lab exam?

While I don't TA physics, but Geology, our labs tend to have the same structure. Luckily the labs are small enough that I can get to know the groups ect, So I can determine how hard they are working on the labs ect, so I generally grade 70% effort and 30% correctness. The difference is though, that you are teaching engineering majors, where I tend to teach non geology or STEM majors. Getting something in the lab 100% correct for my students isn't as important and following the scientific process, but, for a class of engineers, I would have higher expectations since the content they are learning is helpful for their careers later. IE, they should have a vested interest beyond the grade.

My experience with the Lab exams is that the students either do very well or very poorly. I would be somewhat lax on the labs, especially on first time mistakes. But there isn't much you can do if they aren't working hard and aren't completing the labs correctly and they will likely fail the test if thats the case anyway.


How to learn about a department's culture?

I don't see a problem with contacting him, though his reasons for leaving may not be relevant to your situation. There seem to be a lot of red flags here, but it is possible that they are false alarms.

I would send him a note saying that you are under consideration for a position at the given department and asking if he has any advice he is willing to share with you. Give a sentence about your own experience or situation (recent graduate, associate professor, or whatever). Any response will probably be useful to you in figuring out your dilemma.

However, 20 days doesn't seem terribly long and might indicate some turmoil that is being resolved. Don't jump to conclusions, but stay aware.

If you have any good feelings about any of the people you interviewed with, you might send a similar note to them. "Any advice...?"


What should be included in a disclaimer about the omission of gender-neutral language in a bachelor's thesis?

I am going to respond to various parts of your question step by step.

For those unfamiliar with German, I am going to add a brief description of the gender-neutrality issue at the end of this answer, because things are quite a bit more complex in German than in English.

  German universities are very sensitive when it comes to gender-neutral language. Some professors mark it as a mistake if you use gender-specific terms instead of gender-neutral ones.

I am not convinced that statement is true for German universities in general, especially as there still is no single true agreed-upon consensus on what is a good way to navigate around the issues. Much rather than that, I can imagine that certain professors make it a point to enforce gender-neutral language (just like I could imagine some other professors to make it a point to enforce what they perceive as stylistically and grammatically correct language, even though it is in turn not considered gender-neutral by all).

  While I don't want to be sexist, most variants of gender-neutral language in German are (in my opinion) verbose, disturb the text flow and make the text harder to read.

While in your Bachelor thesis, your stance on this issue carries little weight, this is by far not a rare opinion, and exactly one of the reasons why some people (including professors, see my paragraph above) vehemently oppose some variants of gender-neutral language.

  This is why I want to put a disclaimer in the introduction of my thesis stating that I will not use gender-neutral language for the reasons mentioned above.

In my opinion, a disclaimer is a good idea, as it kind-of puts you on the safe side by making your intentions explicit. In fact, I would see the following benefits:

It gives you some freedom to pick the style you'd like to write in.
It might satisfy even some of the readers who would personally have chosen a different writing style.
The mere existence of the disclaimer shows you care about the document as a whole, not only the specific technical aspects of your Bachelor project.
It defines something that will be used later. In technical subjects, or at least subjects that are somewhat related to maths, choosing definitions in a convenient way, explaining them first, and then using them accordingly throughout the document, is a good practice.

Now, there is no guarantee these points will be picked up positively, but at least, there is some chances for it.

This notwithstanding, you should ask your advisor for their preferred style, if any, or check past theses (successfully) written for the same advisor.

  Is such a disclaimer generally acceptable in a bachelor's thesis (or any scientific text)?

As meanwhile shown by the other answer, yes. In fact, most things that clarify the contents are acceptable in Bachelor, Master, and Doctoral theses.

  If so, are the three points stated above both adequate and thorough to state my intention, or what should I add/remove?

The three points sound fine. I would indeed advise against expressing you are "not using gender-neutral language". You could try and focus on stating that some terms "can be understood in a gender-specific way".

Remarks on issues with gender-neutral German

At least according to my impression, gender-neutral language is a much more controversial topic in German than in English (for some further illustration of this, also have a look at a related question on German SE):

In English, a large part of gender-neutral language is replacing exclusive uses of he or his. In German, in contrast, gender-neutral language primarily tackles any noun describing a person, because these usually come in a male and a female form, the latter of which is usually formed by adding the suffix -in to the male form.

This opens up two issues that make the topic so controversial in German:

On the one hand, there is no general agreement that the male form is, in fact, not gender-neutral. It has commonly been (and still is) used when both genders were meant, and (as noted below) there often is no synonymous noun that is gender-neutral.
On the other hand, there is no commonly agreed-upon solution for how to express things in an explicitly gender-neutral way:

For a start, truly gender-neutral nouns for persons are really rare in German. Replacements such as the English steward/stewardess -> flight attendant do not produce gender-neutral terms in German. (Curiously, the terms are sometimes copied from English nonetheless, so Germans have replaced Stewards und Stewardessen with Flugbegleiter und Flugbegleiterinnen.)
Offering both alternatives every time a person is mentioned can make a text hard to read (imagine a text about actors and actresses, or actors/-resses, or actorsResses, and imagine that split happening for every single noun referring to a person). Hence, this variant is opposed by some native speakers.
There is also the suggestion of using the neutral gender for all gender-neutral nouns. (In English, this would be akin to generally referring to persons whose gender is not specified as it.) While this sounds logical, it can also be perceived as disrespectful, as (unless the person noun specifically calls for neutral gender) using neutral gender on a person is like treating the person like a "thing".
Another approach is, as mentioned in the question, using a grammatical form that is (for many words) not normally used as a noun, but that does not change by gender, and that arguably has the same meaning as the role name - the present participle. If we transfer this back to English, a sentence such as "Participants pay attention to the instructor before their conversation with the student." becomes "Participatings pay attention to the instructing before their conversation with the studying." This is opposed by some native speakers as featuring abysmal style and bordering on being ungrammatical.

Therefore, a disclaimer expressing the author's intentions can be seen as preferable compared to any of the "gender-neutral" variants, all of which are controversial and cumbersome in some way.


Transitioning: PhD to Postdoc and Productivity

The main difference I noticed when I began a math postdoc is that postdocs are expected to act much more independently than graduate students. Math postdocs are viewed as (young but) full members of the research community, not as apprentices. You will need to choose your own goals and set your own deadlines.

One important change to make quickly is to develop (additional) professional relations with established researchers from other institutions. Some of these relations may turn into research collaborations, but others may just be discussions at conferences that lead to other discussions or to invitations to speak at other conferences or departmental colloquia. Keep in mind that you will need to ask for letters of recommendation when you apply for jobs again, and that others in your field will be reviewing your grant applications when you submit them.

In terms of research, as a postdoc you should also expect to always have multiple research projects underway, whereas many grad students only work on their thesis.  You should also aim for projects that have a high chance of giving positive results quickly. Don't spend too long on famous open problems or on results that would take a decade to complete. If you apply to research positions, you will be judged on your productivity in the time since you earned a PhD, and you only have a few years in your postdoc.

The "clock": in an important sense, your vita begins when you finish your PhD.  If possible, decide what sort of employment you want to have after your postdoc is over. Find well established colleagues you respect who took the path you are interested in, ask them for advice, and try to emulate them.   You want to leave your postdoc with a vita that will make you as competitive as possible for the type of job you plan to apply for. A generic vita is unlikely to be competitive in the current job market.


Why are degrees in Business Administration (and similar) considered Science?

Somee University's have found that they actually had no policy to differentiate why some degrees were only offered as a BA or as BS and decided to create (or at least formally define) a difference, like this story:

  BA/BS, Difference Between Degrees

  Background: in 1984, the Academic Senate Curriculum Committee was
  asked to prepare a policy statement which would differentiate between
  Bachelor of Science degrees and Bachelor of Arts degrees at California
  Polytechnic State University, San Luis Obispo. The need for this arose
  when some departments at Cal Poly proposed to change their B.A.
  degrees to B.S. degrees. The requests were refused by the Chancellor's
  Office in part because Cal Poly, SLO, had no campus policy which
  specified the differences between the two degrees.

This one University created this type of distinction:

  Bachelor of Arts Degree:

  is usually less specialized than a Bachelor of Science degree.
  requires a minimum of 180 quarter units for the degree; 36 units are
  required in the major, of which at least 18 units are at the 300-400
  level.
  is normally awarded in such majors as the languages,
  literature, other humanities, and history.

  Bachelor of Science Degree:

  typically involves technical fields.
  requires a minimum of 180 quarter
  units for the degree; 54 units are required in the major, of which at
  least 27 quarter units are at the of 300-400 level.
  is normally
  awarded in such majors as the physical and biological sciences,
  engineering, and agriculture

Here's a different take on the same issue:

  The BA is a liberal arts degree intended to develop skills and talents
  essential to succeeding in a global society. It combines study of the
  arts, humanities, historical perspectives, and the natural and social
  sciences with advanced critical inquiry and an in-depth knowledge in
  an academic discipline (major). The program develops cultural, social,
  and political literacy, including the abilities to communicate
  effectively and clearly in writing and in speech, and to understand on
  a basic level a world language other than one’s own.* In so doing, it
  fosters the ability to understand and actively participate in
  discourses both within and beyond the field of your major (such as a
  minor or second major), and it promotes engagement with cultural,
  social, and political difference.

  The BS is a liberal arts degree intended to develop skills and talents
  essential to professional work. It combines study of the arts,
  humanities, historical perspectives, and the natural and social
  sciences with advanced critical inquiry and an in-depth knowledge in a
  specific academic discipline (major). The program develops an
  understanding of empirical analysis, scientific methodology and
  protocols, and mathematics and quantitative techniques. In so doing,
  it equips you for continued engagement in professional research within
  your chosen field.

What's the actual difference in terms of coursework, other than the choice of major itself? The BA requires a foreign language (2 semesters) and a few extra humanities classes, while the BS has no requirement for foreign language but adds an extra natural science lab and extra math class. It's mostly a nonsense differentiation that means nothing, but it sounds fancy and gives the illusion of choice if you don't know why you want to go to college - so it's an effective part of the marketing to some audiences.

But in all of these note that no mention is made of the scientific method, math, or any classically recognized type of 'art' (such as painting, literature, etc). The words art and science are not well defined in this way across academia, and so in the end they are used in whatever way the school decides they want to use them.

There are some other classifications in use as well, such as bachelors of: music (BM), applied science (BAS), fine art (BFA), and even a Bachelor Of Business Administration (BBA).

One final note is the classification sometimes ends up purely as a result of what 'school' or 'college' within the University grants the degree. Some schools define themselves as liberal arts/humanities schools and only offer a BA, some define themselves as technical/technology schools and only grant a BS, business schools are more likely to offer something branded as a BBA/MBA, schools of "letters and science" often offer both, etc. In such schools the difference is who is in charge of that particular degree, more than it reflects a genuine difference in what the classification means to students or other community members.

And all of this is just in the US system!

TLDR; The difference in a BA/BS and how "business administration" will be classified (as BA, BS, BBA, etc) means something only within the context of a given school, varies widely between schools, and sometimes means nothing. Each institution generally chooses for itself what, if any, difference there is, so you'll need to refer to each school for reasoning on why they do things they way they do - and sometimes the answer will just be tradition. 'Art' and 'science' in academic degrees don't necessarily mean the same thing as they do in the vernacular.


In a mathematics publication, is it preferable to state all definitions immediately, or as they arise?

There is no general rule. Different authors have different opinions about this. To my knowledge no mathematics journal has guidelines about this sort of thing.

A rule of thumb could be that if your notation is going to be used throughout the paper, then it should be introduced at the beginning in a special section called "notations", "conventions", "background", or however you want to say this. If the notation is only going to be used locally in some section or even one proof, then I would introduce it at that point.

Another possibility is to make a categorized table of notations at the beginning or an alphabetical list of notation with references to where the object is defined, if your paper is long and complex enough to justify it. This can of course be combined with the previous rule of thumb.

I would recommend against making the "background" section as part of the introduction. The introduction is supposed to be something that can be read by almost everyone slightly interested in the paper, to know what the main results are and how they fit with the general literature, and in case of stars aligning, whether the paper is worth reading. (The abstract is to decide whether you'll even glance at the paper at all.) Keep it short and simple and avoid introducing too many things at once. In my opinion it is a mistake made by many younger, and also more experienced authors to make the introduction way too technical.


Which could be considered an appropriate number of self-citations?

If the self-citations are pertinent and useful to the reader, no amount is excessive. If they are not pertinent or not useful, any amount is.
Use judgment when assessing whether your readers will find references to your own work more useful than possible alternatives, if there are any.