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Paper or doctorate thesis?
I have completed some work that I believe could well be worth a Ph.D. I have been working completely in private, with no affiliation with any academic institution.
I would like to use this work to start a career in academia. What should I do with it next? (In case it's relevant in any way, I am a mature professional in business and IT and 53 years old).
In particular I'm wondering about the following options:

Attempt to publish it as a paper (a fairly long one, around 50 pages).
Use it as my thesis for acquiring a doctorate degree.

My questions are:

Can I do both? If not why not?
If not, which of the two is preferable and what are the pros and cons?
Are there alternatives from the above two that I could pursue to achieve my goal?

What is your scientific area? In many scientific areas 50 pages would hardly qualify for an undergraduate thesis. Also, where are you located (Greece perhaps)? Rules vary by places

See Can students finish much of their PhD thesis before applying to a PhD program?

Unfortunately, (2) will likely not be an option. I do not know of any university where you can just show up with a dissertation and get your degree. All require that you do your work in collaboration with the university.

Starting a "career" in academia does not really work that way. Many, possibly most, universities do not offer IT degress, and while business degrees exist, it is a pretty broad field. To get a job in academia you ideally need references that can speak about your teaching and research abilities.

What is your goal? It's not clear. At your age the best shot is to make it to the C-suite, then potentially find a teaching job after the retirement.

A thesis is only one part of a doctoral program.  Generally, there are also classes, qualifying examinations (to make sure you have sufficient breadth and depth), and general apprenticeship as a researcher.  The goal of all of this is to prepare you for a scientific career (whether in traditional academia or elsewhere), which requires more than just the ability to produce a single project once.  In my experience and observation, life as a practicing researcher typically involves producing another Ph.D. worth of work every year or two---a Ph.D. thesis is just the capstone demonstration that you have been educated enough to be capable of doing it at least once.
As such, I think that it is unlikely that any good institution will allow you to skip straight ahead to using a completed project as a thesis, no matter how good the material.  If you want to use the work as an entry-point into academia, I would instead recommend publishing it as a paper paper and simultaneously using the work as a springboard for admission into a good Ph.D. program.  If your field supports use of preprint archives, this is a good way to put your paper formally out there even while it is going through peer review.
If this is truly the direction you want to go, don't worry about rushing to the end-point.  As other questions on this site indicate, age need not be a bar to an academic career.  Instead, I would recommend that you take the time of graduate school as an opportunity---if your independent experiences give you a head start, so much the better for being able to do even more awesome work during graduate school, and also better positioning yourself for what comes after.

This might be true in many/most countries and/or for most doctoral degrees, but it is not universally true (see longer answer).

"classes"? Not in the UK, not in Germany... - And to be honest, the only place that seems to mention actual classes in what is a degree awarded for research is the US.

In US you we have classes but it's because you go into PhD right from the undergrad.

@DetlevCM This is not true for economics. In Germany the better PhD programs have classes and I think in the UK there are no PhD programs without classes.

@TheAlmightyBob I am in the UK - no "classes" for the PhD for anybody in the department - and that's in Engineering.
A PhD is a research degree, not a "teaching degree".

@Aksakal The same is possible in the UK (and not in the rest of Europe) - you can start a PhD directly after a BSc but do not need to attend any "classes".

@DetlevCM Even if there are no formal classes, I believe that in most European programs there is still an expectation of the student being educated in the practices of scientific research through the course of their program by their advisor.  Except in unusual cases (e.g., Sverre's example below), I believe that the rest of my answer still applies.

Partly as a comment/correction to jakebeal's answer, this largely depends in what country you're considering getting a doctoral degree. In some countries, like the US, the thesis is normally just one part of the requirements for the doctoral degree. This is why the first page of the submitted thesis typically contains a phrase along these lines (taken from my Ph.D. thesis):

A dissertation presented by [Name] to The Department of [X] in partial
  fulfillment of the requirements for the degree of Doctor of Philosophy
  in the subject of [X].

But in other countries and/or at other institutions, you can indeed get a doctoral degree by just showing up with a thesis ready in hand. In Norway this type of doctoral degree is called "dr.philos. (doctor philosophiae)". There are only three requirements for this degree:

A dissertation.
Two trial lectures.
A public defense.

I won't go into more detail about this, since you're unlikely to be in Norway (more detail can be found in the University of Oslo's overview article and regulations) for this type of degree.
In short, you need to check if such degrees exist in your country and/or at your preferred institutions. Otherwise see jakebeal's answer.

That's fascinating --- this is the first I've heard of a Ph.D. being awarded in that way.  How much do people distinguish between this type of degree and a standard Ph.D. in Norway?

@jakebeal They're distinguished only by name. "ph.d. (philosophiae doctor)" vs. "dr.philos. (doctor philosophiae)", although they clearly mean exactly the same in Latin. The Ph.D. was introduced as late as 2003. Before that, the doctoral degree in the humanities was the current 'dr.philos.', i.e. a non-supervised dissertation+defense. Supervised doctoral degrees were introduced earlier in other disciplines, but they were also not Ph.D.s, cf. e.g. 'doctor scientiarum' in the natural sciences (introduced in 1977 until it was replaced by the Ph.D.).


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Checking with co-authors on status of a not-yet-submitted paper?
In the spring, I briefly helped with a decently sized project. Shortly after it wrapped, I was asked if I wanted to be co-author on the paper being written on the project. I agreed, and subsequently haven't heard anything back. It's a database project so there will be a long list of co-authors, and I don't want to be a bother, but I also don't want to be left off.
Is five months a reasonable time to wait before asking after status?

Are you sure the paper was sent out to a journal or a conference?

When I last spoke with them it sounded like a done deal. That's part of what I wanted to check on.

I usually have more problems with co-authors who fail to check in with me.  I say check once a month, and if you want it to get done, offer to help.

Publications plans can end up going into limbo for a long time.  In my experience, this can be especially true for publications with lots of authors, because you can easily end up in a situation where nobody's really stepping forward to get it written, or where everybody thinks somebody else is the one dealing with the current road-block.  One paper that I am an author on spent three years in un-submitted limbo for such reasons.
As such, checking in every few months is totally reasonable, as you may in fact provide the stimulus to keep it moving forward.  Be warned, however, that if it's ended up in limbo and if you actually care about the paper, that you may well find yourself one of the ones getting handed tasks for actually writing it.

I agree with Jake Beal that too much nagging might result in you doing all the work. So I would suggest asking a rather innocent question related to the paper, e.g. about the content of a section you had little to do with, some formulation questions, or whether you can give a small talk about your work somewhere (e.g. the local seminar, not a conference). Chances are pretty high that you will get the information you want without taking over too much obligation.

I'm not sure I'd put the same value qualifiers on the situation that you do.  If one pesters without wanting to do the work, then yes, it's nagging.  But if you're willing to end up doing a lot of the work, you might end up in a more prominent authorship position, having a really interesting experience, and learning a lot in the process!

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What is the decision on my paper?
I submitted the revised version of my paper to a journal. after two weeks the paper status changed from under review to reviews completed. and still remains in this state about 10 days. What do you think is the decision on my paper? Reject or accept?

What do you think is the decision on my paper? Reject or accept?

Decision pending. Likely, this means that the review phase of the paper is finished, and is currently awaiting a final verdict by the associate editor or editor-in-chief.

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How to get feedback from my supervisor about me
I'm a first year PhD student in mathematics. One day I was having some conversation with my supervisor and we got to a point where he casually mentioned about his other students and said that one of his student is quite "weak" and one of his other student is "strong". Since then I've been wondering what does he think about me.
An obvious way is to just ask him directly, but the problem is that this country is Canada and here people are very polite (most of them). So, if I ask him directly, I think he will just say nice things about me and so, it wouldn't really answer my question. I would really like to have an honest answer, even if it's bitter, because then I would know what skills to work on and try to improve.
Can you guys suggest some better way to get honest feedback/constructive criticism from my supervisor?
Another vague question I have is:
How can I know what he thinks about me? Does he think I'm a weak, mediocre or good student?
Little background: I have been working with my current supervisor since my Masters and I decided to have him as my supervisor for my PhD as well. We meet weekly to discuss about my progress/ideas and other administrative stuff (if there's any).

Is your supervisor Canadian?

@astronat yes, he is.

Wow, that's incredibly unprofessional. To say nothing of a violation of academic privacy of those other students.

@ElizabethHenning my supervisor didn't mention any of their names. Also, I don't know any of his other students

Since your supervisor talks to you this way, he most probably thinks that you are doing OK. Note that you are a first year PhD, so you are not expected to do something outstanding. The fact that you already have a supervisor is good enough.

Actually I have been working with him since my Masters and I decided to have him as my supervisor for my PhD as well.

OK. The fact that he knows you and has agreed to be your supervisor answers your question. Doesn't it?

I'm sorry, but I'm not sure how does it answer my question.

He clearly think high of you. I think it is obvious. Of course you have a few years to prove that he is right.

"The fact that you already have a supervisor is good enough." In many places, that a prerequisite for enrolling in the PhD program at all.

@N.I.: What you wrote is not true in math

@MarkSapir I'm a mathematician... Once again, this is something that has more to do with location than discipline. Not having an advisor when you start is common in the USA. Not in Europe (or at least the European places I know).

@N.I.: The OP is in Canada.

I suggest that you ask them directly. Being polite doesn't imply not being honest. It certainly shouldn't imply misleading you to believe you are doing well when you aren't.
But the way you ask can influence the reply. Asking whether there are things they would suggest to help you improve is quite different from asking "How am I doing?". There might be other, more effective, formulations, of course.

First, ask yourself why you want to know. Comparing oneself to others (or to an external scale of weak or strong) can be incredibly demotivating, and as a rule you should only do it if you need the information for some useful purpose. For example, if you're considering dropping out and changing careers, it may make sense to solicit blunt feedback about how you measure up to the average student. But if it's just morbid curiosity, I'd encourage you to try not to think about it. Put your head down and channel that anxiety into doing good work.

It doesn't need to be a comparison with others. And it probably shouldn't be.

@anon I agree with your advise, but it's not about comparison. It's just that I wanna know what skills I need to work on and try to improve.

Also, ask yourself what you want to know. Feedback shouldn't be about "me", it should be about actions, problems, outputs, ways to improve etc.

In pedagogy it was found (sorry I can't find the reference to the study) that when a feedback in the form of a mark or a comment like "Good" etc does not lead to improvements.  Rather, what would be a better line, and one that would be ok with cultural sensitivites, would be to ask what should I be working on?  What do you think has went well so far?  Of course, you could do a lot worse to ask yourself this question too.  Try to be SMART about how well you have done (specific, measureable, achievable, relevant and time limited) e.g. to say I produced a 20 page literature review after 6 months would be better than I wrote about some papers I read.

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Why do pure mathematicians tend to start publishing good papers a bit late?
Why is it so common for pure mathematicians to start publishing "good" quality paper a bit late? Maybe towards the end of PhD or start of Post-doc. Whereas in some fields people start publishing research papers as early as in their masters.
I know there are some undergrad research programs, for e.g.- REU, but only in some cases do  they get published; but not in some good quality journals. Most of the times they maybe just arxived or in some cases not even that.
I know some people, from different fields, who had 2 or 3 publications in their masters itself, while some of them are in their 2nd/3rd year of PhD and already have around 10 publications.
Maybe such a thing is also possible in mathematics, but there must be some good reason why mathematicians or graduate student, along with their supervisor, agree to publish good results in good journals, a bit late.

"End of PhD" is not a later stage of a career.

A big issue with mathematics is that it is a very old field. For most courses we teach/take in undergraduate, the theory was  developped in the 1700s or 1800s, and in the last 2-300 years these subjects have been studied soo much that there is not too much left for a student to do... For most mathematicians, to do reearch you need first to familiarize yourself with the newest theory, which is done in graduate school either via classes or most of the time via reading (note here that many if not most undergraduate students do not have the background needed to do this).

A lot of math grad students don't even have a thesis advisor until their 2nd or 3rd year.

Some other factors not yet mentioned (which depend on country/school): in math masters work is often focused on learning rather than research, math grad students often have to spend a lot of time teaching, and the publication process is slower in math than many fields.

One reason is that it typically takes a while to learn the theory which is necessary to write (or be a co-author) on a good paper.  If you don't know that theory, you can't really make a contribution which allows you to be an author, whereas in other fields people can and do get on the author list for much smaller contributions or contributions which don't require a huge amount of theoretical knowledge.

Also, much smaller publication pressure in math than in other fields. Much fewer people would focusing on fast publication in other sciences, if that were not a basic necessity to survive.

Does this answer your question? Is it common for an undergraduate thesis in pure mathematics to prove something new?

@Mehta Not having a thesis advisor for several years in grad school seems fairly exclusive to the US. In the UK, for example, you have a supervisor from the very start.

Honestly, it takes a looong time to learn enough in one area of Mathematics to be sure that you are beyond previous knowledge...  And then to find something new and publishable out there.

Also bear in mind that it typically takes a while to have a paper published, so a paper which is being published in 2021 might basically have been finished in 2020 or even 2019.

One fundamental distinction between mathematics and more-obviously experimental scientific and engineering disciplines is that, in math, there is no analogue of "reporting on several months of experiments". There's no analogue of "keeping experiments running, and whatever turns out, is a paper".
That is, while there is in fact a large experimental aspect to mathematics, it is not the same sense of "experiment" as in other sciences, and the conventions are such that this does not generate papers.
Yes, the ambient pressures do push PhD students in math to try to arrange at least one or two publications prior to PhD completion. Not entirely a bad thing, but definitely not a convivial atmosphere.
Edit: and it may be worthwhile to observe that most of prior mathematics does not become obsolete or wrong due to new discoveries, unlike sometimes happens, and is always possible, apparently, in more experimental sciences/etc. Thus, mathematicians cannot too much disregard prior work... of which there is a great deal. Many excellent (and not-so-excellent) results known prior to 1900 are rediscovered on a regular basis, and do indeed show evidence of insight!, but are not "publishable".
This "problem" is the reason I tell myself, and my research students, to not even think in terms of "verifiable novelty", because it is just a mess, for mathematics. Better to follow a good, natural line of inquiry, and leave the appraisal of "novelty" till later. (It is admittedly hard to ignore academic-administrative pressures... and, yes, this is corrupting academic mathematics, among other disciplines...)

Thanks for your answer. What about a field like computer science?

@FreePawn, I would not claim to really know the current conventions in CS, but/and I suspect that there is a large range, from the theoretical end to the engineering end.

@FreePawn Yes, and even on the "theoretical end" it's probably easier to still come across a publishable idea than in pure math (albeit far from trivial). Benefits of a younger field.

There's big variation within math, in particular, combinatorics (one of the most CS-like fields in math) is reasonably similar to a lot of computer science in terms of people publishing shorter papers more often and often doing so earlier on in graduate school.

@NoahSnyder, yes, indeed, there is a sort of gradient pushing many students in the direction(s) of lower start-up cost. Understandable.

I don't think it's just age of the field.  Physics is as old as mathematics but (speaking only in absolute terms) I personally think it's easier to publish a physics article than it is a pure mathematics article.

@freepawn, my company has a program where CS students can work half with us, and study the other half of their time. There definitely are unis (at least in Germany) where at least some part of their contents are current (e.g. modern topics like cloud security, CI/CD, blockchain etc.), and if the students are lucky, their profs are interested in driving technology forward. In this case, all possibilities are open I guess - while most progress is probably directly driven by companies (and open-source), there are plenty topics of theoretical nature which those will probably not tackle much.

@fourierwho, increasing expectations of students can communicate something positive to them, yes, but it can also expand the range of ways-to-fail, etc. Plus, "publication" is at least superficially in conflict with study and scholarship, so increasing emphasis on publication can back-handedly have a negative impact... And, I think significantly, in the days where one's "clock" (for publications, etc.) did not start till the PhD was obtained, there was less stress in grad school.

@FreePawn CS has both a practical ("applied") research aspect and a theoretical research aspect.  The practical/applied side has new areas opening up all the time and has publishable experimental aspects (and is funded/employed by industry).  The theoretical side is more like theoretical math, but since it is a few hundred years newer, it's not as hard to find the frontiers.

This is related to the issue where you have a result but it is not clear whether it's known to the experts, but you can't find it anywhere in the literature. Is the result new, or is it "well-known" (known to more than a dozen people for more than two years) (MR 50:2128, Roger Howe)?

A key difference between pure math and many other areas is that there are typically only 2, maybe 3 authors. The papers you cite with Masters students are often in larger collaborations wherein the Masters students do some of the menial tasks: data collection, data analysis, but not necessarily theory development that require more years of training. In pure math, these sorts of papers are quite rare: You have to understand the theory if you're writing with just one or two co-authors, because otherwise there is nothing for you to contribute. As a consequence, there is just no opportunity for students in pure math to be part of authors earlier in their career.

I've seen some stark examples of this.  I went to a talk by an undergraduate student who was included as one of many authors on a experimental physics paper and she was unable to answer basic questions about the experiment or seemed to have no knowledge of any of the workings of the experiment on which the article was based.

@Tom yep, typically with experimental physics collaborations it's simply "if you're in the collaboration you're on the author list". I'm an author on a paper about a laser system that I haven't even looked at the optics table setup of (if I can avoid being in a room with an extremely powerful pulsed Ti:sapph I will), because I worked on the other end of the experiment. Not ideal but it avoids a lot of arguments and potential discord within the group

@Tom: Same with some of the stuff I did in what might be called computational biology.  I could have done my end without knowing anything about the biology (though I learned a good bit just out of curiousity), but the work couldn't have been done without someone with my computer expertise.

Also I had a friend who was one of five authors on a journal article.  When I asked how much of a contribution they had made or how much of their MSc thesis had been used, they said they didn't know as they hadn't read the article!  I would at least want to have read the actual article all the way through if I am classed as one of the authors.

Folks (@Tom @llama), it's not necessary to disparage other disciplines here. Good science is done outside mathematics as well, they just have different strategy of who is included in the author list.

The other answers do a great job explaining why math is quite different from experimental sciences.  But I don't think this is the full answer, as computer science, statistics, and theoretical physics are "mathematical sciences" and it's less clear why they should be any different than math.  In fields where there's substantial overlap (e.g. there are people working on tensor categories in math and in condensed matter physics) I think there's also different publishing conventions in terms of what level of originality is expected of publications.  For example, working out an example that any expert could do and writing it up is much more acceptable in physics than it is in math.  There's advantages and disadvantages to both approaches (in particular, math ends up with far too much "folklore" that is hard to learn without social connections to experts), and I think a lot of this difference is cultural.  For example, the culture in math departments is that the main goal of a PhD is to have a substantial result, while in CS the expectation is that you will have multiple less substantial papers.  There's similar cultural differences within mathematics, e.g. combinatorics is more amenable to short papers and homotopy theory or Langlands number theory are more amenable to people who publish more rarely in larger papers.  I think these cultural differences (like many inter-departmental cultural differences) are going away as there is increased pressure for mathematicians to publish more and publish earlier even if that means not doing as substantial work.
Finally, I should point out that most of the humanities is even more extreme than math in terms of focusing on a large substantial work, and the expectation is that your PhD should be a publishable book which you will still be editing several years after graduation.  Again, I'm not saying this means math is "better" than other mathematical sciences, or that history is "better" than math, there's advantages and disadvantages to both approaches.

Thanks for your answer. Shouldn't quality be preferred over quantity? Isn't publishing one paper with great, general results better than publishing 3-4 papers about some specific cases of the same bigger, general results?

@FreePawn, unsurprisingly, quantity is easier to determine (by administrators) than quality. Even for hiring committees, the number of entries is vivid... while the quality of each is most likely completely obscure except to experts.

@paulgarrett is that why people in other fields win more awards/scholarships than people in mathematics? Or, is that a whole different topic?

@FreePawn, in my observation, yes, when the decision-making committee for awards has many people from high-publication-rate fields, the math people have a hard time competing on paper-count basis. Not that there's a conscious bias, but just that it's somehow inconceivable (to some people) that grad students wouldn't publish 3-4 papers each year, etc.

Another related convention which keeps down math publication numbers is the convention that advisors not typically coauthor material from their students thesis (even if the advisor’s contribution is substantial enough to merit coauthorship).  I don’t think that convention is sustainable.

It's interesting to compare REU students to first and second year graduate students, the latter are more mathematically mature and know more but the former are more likely to publish.  If REU students can publish then so could early grad students if we thought it was a good idea.

@NoahSnyder I guess as soon as you become a graduate student, all of a sudden the expectations become high. People start expecting more from you and they want you to do good mathematics. Maybe that's why.

CS and physics apply maths, they don't have to advance maths, they use them as a tool. You don't have to understand everything, you have to know your tools. Many physicists don't even understand the proofs or the limits of their tools, but get great results anyway.
I even know applied math works, that are more programming and developing a clever numerical scheme then real maths work in the sense of finding a theory and proving it.

@NoahSnyder The convention of advisors not coauthoring material from their students' theses in mathematics goes back more than a century -- I'd say it's fairly sustainable.

@FreePawn Not quite.  The point of an REU is to do research, but the point of your first couple years of grad school, in the US at least, is to learn more mathematics.

@Carl-FredrikNybergBrodda: Just because something has been done a certain way for a long time, that doesn't necessarily mean it's sustainable going into the future (no matter what fossil fuel fans might tell you . . .).

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How can you get to do a Short Oral Presentation at the International Congress of Mathematicians?
I am wondering, how hard or competitive is it to obtain a slot for short oral presentation(20-minute talk) at the International Congress of Mathematicians?
Generally, how many slots are allotted for such presentation?

Short answer:  I don't know, I've never been on an Organizing Committee.
Long answer:  You likely can look at statistics for attendance versus
capacity of venue.  At the last few  International Congresses I have attended, usually there are about 2000 or more from the host country, and anywhere from 1000 to 2000 from other countries.  There are about 20 plenary lectures, about 150 invited lectures,
about 1000 Oral Communications and not quite as many posters.  Also some interesting
prize lectures, roundtables, and a few other items.
(I am doing this from memory.  I don't think attendance has surpassed 5000 lately,
but I won't guarantee it.  I could be off on any of the numbers by a factor of 2, but I don't think so.)
I have submitted abstracts for short communications since 1994, and have had them
accepted in all but one case (and in that case there were facilities for last minute "impromptu" sessions: the organizers kindly let me have a slot for one of those).  My unscientific guess is that the rejection rate is determined mostly by capacity, and that about half the local attendees and more than half of the non-local attendees submit abstracts, which would lead to about 2500 petitions for 2000 slots.  My estimate of the population whose desire to satisfy vanity overcomes their fear of public speaking  would suggest that 2000 petitions are for oral communication, and so roughly half are filled.
FUZZY DATA:  I submitted two abstracts this year, one a week or so before the first deadline and one a few days afterward, possibly after the first and before the extended deadline.  They were given designation numbers below 1900;  this supports my guesstimates.
LESS FUZZY DATA: at this writing, about one month before the 2014 Congress, registrations are pouring in and number near 2900.  There are almost 500 posters accepted and a little over 700 short communications, with some designation  numbers reaching over 2300.  Not substantive, but if the code numbers reflect submissions, this would imply an acceptance rate near 7 out of 24 for oral
presentations, and a little less than half for all presentations.  Off by less than an order of magnitude.

See Short Answer above.  I imagine the committee has as a goal to satisfy both speakers and audience, and the truth is that both quality and popularity play a role.  If you are attending the one this year in Seoul (I hope to), you might ask for a moment with one of the Committee Members to get a face-to-face response.  If you are satisfied with email, you can also try asking them through their interface.  Now that they have sent out abstract status letters, you might get a answer based more in truth than political expedience.

Also, at most 1 out of every 20 (roughly) of the Short Communications I attended had a quality level that I considered unacceptably low.  My opinion is that they are able to meet their goal, or at least have a reasonably low failure rate.

Can you give a general idea of the quality of the talks?  How low is "unacceptably low"?  Not worthy of Annals?  Routine results?  Boring results?  Time Cube ramblings?

For Short Communications, all over the map.  Rather than name names and cause embarrassment, here are two characterizations which fall into the "unacceptably low" class: 1) the speaker may as well be a Navajo codetalker, because I cannot read anything on their slides or understand any spoken word (literally, meaning I can't even tell if "the" or "a" is being used), and also refuses to give up the mike two minutes after time is called;  b) the enthusiast with enough math and counterculture to be dangerous (I've no time to argue about whether x and its power set are equipollent for finite x.)

@NateEldredge, another characterization which is personal but likely shared by you and me, are those talks where I have afterwards thought "Can I have those twenty minutes of my life back?  I didn't deserve it being used that way."  This in my opinion transcends a talk on boring results or even some ramblings.  Fortunately, that has happened to me perhaps twice in my ICM journey, no more.


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What is a good method to assign topics to students?
I will be conducting a course with 10 students and will provide about 12 topics. Each student shall work on one topic. I will meet with the students and present the topics to them.
What is a good method to assign the topics to the students?
I would like to give them the option to choose their own topic, but I foresee problems when some topics are very wanted and others are not...

In my experience, with only 10 students and directly in class, things work out rather well if you let the students assign topics more or less peer-to-peer.

That is, as long as it is not the case that a small subset of topics is widely preferable for the majority of students. But in that case you have a different problem anyway.

Have each student rank the projects in desirability and apply the stable marriage algorithm. This will guarantee no pair exists who would both prefer the other's project.

@xLeitix: I actually did as you suggested and it worked extremely well. So if you would write a formal answer I accept it.

I have seen instructors/advisors assign the topics by random chance, followed by a brief 'trading session'. Students pick the topic out of a hat, but they then have the option to trade with other students. Of course, some students may be stuck with a topic that they didn't really want, but they should also have the option to work with you to tweak the assignment into something that they can be passionate about. Since you say that you will have more topics than students, you could also have the option to put their draw back into the hat and try again (after everyone else has drawn at least once). This method seems most likely to avoid the problem of a student feeling as though they were forced to take a 'very much not wanted' topic.


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Importance of my PhD research for my post-doc
I'm a first year PhD student and my research is related to Quiver representation and recently I have been looking at semi- invariant rings in the context of Quiver representation.
Sometimes I feel like nobody cares about this particular topic that I'm working on. I recently attended a conference where many eminent mathematicians from this field of representation theory were present and I felt like nobody really cares about semi-invariant rings for quiver representations.
My question is:

Will this make it difficult for me to find a post- doc position?
Will it make it difficult for me to do research in the future, because people might not value what I'm doing

One thing that I would like to add is that I find this field and semi-invariant rings for quiver representation interesting and I like studying about it.

https://academia.stackexchange.com/questions/11765/how-to-effectively-deal-with-imposter-syndrome-and-feelings-of-inadequacy-ive

There are at least one or two dozen professors at research universities who are interested in semi-invariant rings of quiver representations.
That's as many as you will find for almost any specific research topic in mathematics.
I wonder if you went to the right conference.  Representation theory is a big area, and of course most representation theorists won't be interested in semi-invariants of quiver representations - but that will be the case for almost any topic in representation theory.
In addition, there are another several dozen professors (including me! - but we don't have postdoc positions) who might be interested in your research if it has implications in their area (using known connections between quiver representations and their area).
Now if I were your advisor, I would indeed be worried that I was leading you into some dead end that no one was interested in.  Hopefully your advisor is a better mathematician (in this regard) than me and has some good reasons to suggest the problems you are working on, including some good reasons to believe connections to related areas might be uncovered.
How geographically mobile you are for a postdoc also matters; some countries are more interested in this stuff than others.

I'm not 100% sure that there is no one interested in semi-invariant rings for quiver representation or that it is a "dead end", it's just that I feel that way sometimes. As I said, I'm a first year PhD student, so my knowledge is very limited, not only in mathematics, but also in other generic things in the world of mathematics. For e.g. I'm really surprised to know that there are at least one or two dozen of mathematicians interested in this particular topic.

It will matter what specifically you work on.  For example, trying to figure out the semi-invariant ring of some moderately complicated random quiver of wild type is probably a dead end (but maybe there is something special about that specific quiver of wild type that makes it interesting or important?)  Other problems might be more promising.

The more tightly you focus the search for a post-doc tied to any specific research thread, the harder it will be to land a post-doc, just because there are fewer opportunities in narrow areas. You need to be flexible in the short term. You can use mathematical skills and insight to do many things.
To get autonomy you need to first have a secure position. Tenure track is probably secure enough in most fields, but in some, you really need tenure before you are free. (Fields that touch on political questions, for example.)
To keep your interest in your current specialty alive, spend some time on it periodically while you are doing things to please some PI. Take a lot of notes. Especially notes about questions that might later be explored. Once you have the needed autonomy, the world is yours to explore.

I finished my degree in the era before ubiquitous post-docs, but my field was so narrow that there were only two or three people outside my working group that were qualified to understand my research or interested in it at all. And, I wasn't interested in moving halfway around the world anyway. Had I been too narrowly focused at that moment, I'd have failed to move forward. But I had deep insight that I could apply to other things.

Thanks for your answer. So, are you suggesting me that I should research on other topics as well, as a part of my PhD thesis, other than semi-invariant rings? Maybe find a connection of these with other topics.

I disagree with this answer.  Some postdoc opportunities are indeed very specific, and will only hire someone who is tied to that specific thread.  So specialization can win as well as lose.

No, not at all. Doctoral research is necessarily very narrow. But don't make post doc applications contingent on being related to your dissertation. Best to focus closely on finishing. But a broad search for a post doc later.

@AlexanderWoo, yes, and if you hit one that matches it is pure serendipity. But the closer you focus, the less you see. I don't understand why you disagree with that.  Being inflexible lessens your options.

@Buffy - the question isn't about being flexible or not - it's about being ultra-specialized or not.  You have to be ultra-specialized to produce a thesis.  Whether this leaves you with enough time/energy to learn other bits of mathematics depends on your abilities.


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Using same text in different papers sent same time?
I study on a topic with different algorithms. Can I send two papers to different journals that include same texts. Same paragraphs in introduction or literature review?
You can think first paper: "solving problem a with method x".
The second paper:"solving problem a with method y". Is it self plagiarism?
Also I can't reference the other paper because I will send same time. Should I wait the first paper until published?

This is impossible to judge without a lot more information. The examples you give would not be self plagiarism, since there are so few ways to say what you mean. But note that plagiarism (including self-plagiarism) isn't about words, specifically. It is about ideas. Copying words is about copyright, though using the same words can also imply the same ideas in many cases.
If you write about ideas you've written about before, you need to cite the old work even if none of the words are reused. This lets a reader trace the complete context of the ideas back to the sources, including those you cite in the older work.
But, from what you write here, I think you are worried about minor things.
You can actually cross-cite papers that are "work in progress", especially in initial submissions. Since the first version submitted will almost always be revised over time, you have the opportunity to update those citations. The editor will provide guidance for the final copy if changes are needed.
There are some other situations in which non-published work needs to be cited - even never-published work.

I didn't know about citation for work in progress paper. Thank you for this information.


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How to maintain your professional status and not get troubled by the junior lecturers
A new senior lecturer, say A has been assigned to work in doing some tutorials with a set of assistant lecturers. These assistant lecturers, say B1, B2, B3 etc. don’t know some of the theoretical concepts properly.
Sometimes, in the middle of the tutorials they try to ask and clarify things from each other. Since, there is a group of lecturers per class, usually they do the tutorials by taking turns. The subject X is A’s specialized area, so that when classes from that subject are going on, A even teach the other assistant lecturers some easy techniques in teaching them too.
There is another subject say Y. It is not A’s exact area and actually when assigning A to that, the management has mentioned that A will be working under "on training" mode. There is a one assistant lecturer, say B4 who has passed out from the same university, and so she also has done it during her undergraduate program. But B4 is also sometimes not very clear about some theoretical sections and for some questions, what she says is not exactly logical. But people have to accept it.
A, B1 and B4 are doing a class on Y together. Since it had been bit difficult for A and also because of some other works, A couldn’t catch up at once and so for about 3 weeks, A has kind of stayed in the background, looking at B1 and B4 doing the class. Actually, sometimes B1,B4 also get stuck at questions, and also, what they basically do is letting the students do the tutorial questions by themselves and explain the places they get errors only. They don’t explain anything on the board or anything. So, there wasn’t anything much A could catch up from being there and observing them either. In the 4th week, however there was a theoretical part that A is familiar with, so that A explained it while B1 and B4, now stood at the back. A’s explanations were good and so B4 was feeling kind of remorseful, it appeared like that.
After a few days, another assistant lecturer, said “Oh, it’s not good if people are not taking turns to do the classes. B4 said there’s someone in her class who is not taking turns with them” as if to hint at A, loudly so that A can hear. It kind of hurt A, because, B1 and B4 could have directly told A, if they wanted to take turns and also A was just put as on training person, so A didn’t think about it much, that it’ll be a problem for them.
Is there a way that A can respond to this situation (may be in a lighthearted and bantering way) but still defend herself and gain her a good respect?
I mean, many people, when others say something, defend themselves. What can A say to imply that it's not A's fault and even B1,B4 is not doing things properly, so why would B4 try to point a finger at A like this...

To me, this question is unclear. It would be improved by shortening the back story and clarifying the question you want addressed.

The story does not sound to me like "being harassed by junior lecturers".

@BryanKrause if A don't react to this situation, she'll be having to hear more and more such comments, and eventually they'll start harassing her

Okay @Ian I've made edits as mentioned. Can you please see now?

I have serious difficulty following questions like this one that include unnecessary placeholder names for individuals.

from what you've written I'm guessing this is culture dependent, you appear to be from a high context society ( https://en.wikipedia.org/wiki/High-context_and_low-context_cultures ) which may mean you are skirting around the question you want to ask, making it impossible for us to answer. You are also a woman and depending on culture this might be important to understand your story. It would be good to include your culture (and where you work) for context. Re-writing this as being about you and stating your concerns first before providing the background story would also help readability.

As a side note, I'm wondering if the high context/skirting around what you want to say (very useful in face-saving environments) might be part of the reason you had issues in the past with papers being misunderstood. Computer science/maths is more low context/explicit, and I know European/North American Countries/Australia all have cultures more on the low context side of things.

What can A say to imply that it's not A's fault

It's not clear to me that it's not A's fault or that A should try to defend themselves. Rather, it seems like there is a conflict of expectations among the various parties that needs to be resolved.
B4 is going about this in a bit of a passive aggressive way but perhaps they don't feel like they can address A directly due to seniority. If B4 were asking for advice I'd recommend they take a more direct communication approach, but it seems A is asking for advice so my advice is: A needs to pull their own weight in the course and needs to be an adult about dividing responsibility. As the senior party here, even if A is not comfortable with all the material they have to at least be comfortable with coming up with a reasonable division of labor among the instructors that is mutually agreed upon.
I don't think lighthearted or banter will look good for A: this just belittles a colleague and will make A look like a jerk. Instead, I'd recommend being open about what appears to be a conflict: "hey team, I'm getting the impression that you're expecting me to do more for this course than I have been. What division of responsibilities would seem more fair to you?"
You're not required to accept whatever they suggest, but it will start the conversation and hopefully everyone can move forward with shared expectations.
I'll add that there seems to be a lot of contempt by A for their colleagues and a feeling of superiority by A. In this story, A seems egotistical and insecure. I'd recommend a broader reassessment of A's attitude towards junior colleagues; a professional therapist might be useful in this, therapy isn't just for "illness".

Hi thanks @BryanKrause you mean that B4 is feeling not like telling A to share work, because of her seniority? And also, if B4 and others have been doing the lessons right, A could have gotten the training she needs and would have developed herself to face a shift by herself too? But they are not sure about what they teach, they don't answer some questions and so on, and that's why A is unable to get trained and then what can be done?

A is learning by herself @BryanKrause but that's why it had taken a bit of time.

@Hasini It's not normal for an instructor of a course, even an "in training" one, to need to learn so much of the course content from the other instructors, and especially not to blame others for not understanding the material. If you need more guidance about the direction the course is going (upcoming topics, reading lists) you can certainly ask your colleagues for it but it's very immature to just say "oh they didn't teach me so it's not my fault that I can't contribute". That's lazy and unprofessional.

If I was B4 I am not going to mind that A is not taking turns with me, as it was the class lead by me, before A came (A joined newly in the middle of the semester).  So that's why I think I don't understand why they did such a thing at once, without discussing with A. @BryanKrause then it means that them not knowing the subject is kind of ok? If it was a class lead by A and B4 joined later and B4 observed that A didn't know the subject, usually what type of action will a passive agressive person like B4 will follow? If you guess or have observed from such a similar person?

I'm asking that just to find out the behaviour

@Hasini If you're not B4 you don't get to decide what they do and do not mind. You need to have a conversation with your colleagues about your role and take some responsibility for yourself rather than blaming everyone else.

Yeah will be taking responsibility but am reluctant to give free knowledge like before when they don't know as I don't understand their behaviour @BryanKrause If you were B4 who came late and if it was A's class and A didn't know properly what will you do?

And I didn't know they were expecting me to contribute. I'm not saying that "oh they didn't teach me so it's not my fault that I can't contribute". They didn't talk about shifting. If they did I would have speeded up my self learning this semester itself.

@Hasini What do you mean "free knowledge"? It's okay if you didn't know what they expected before, you should have asked rather than assumed but nothing can be changed about the past; now that you've learned differently it's time to have a conversation about it.

I mean for subject X, also they don't know theories and concepts properly. They come to the lecture and sometimes they get stuck. Then I'm the one who is teaching the correct stuff... To students and also to them.. But I don't feel like doing so now, if I didn't know I think they will go ahead and do something passive agressive rather than telling me. Yeah now anyway I'm going to teach the sessions to students whether they tell or not as they have gone and put a show in an indirect way

Isn't it part of your job to contribute to teaching this course? You've been assigned to work there. That's not free it's your job.

Teaching teachers is also my job? When it's their class in the subject X? They have not been put as under training under me...

That's a conversation to have with your supervisor. I'm not going to contribute further to this conversation, good luck.

Hmmm, okay. Then if it was B4 who came late and have seen A not knowing the subject, B4 would have gone to the supervisor? And also when it's a circumstance related to a subject like X?

Do you want advice or do you want to complain until someone says you're right and everyone else is wrong?

Hmm, does this comment look like it suggest like a complaint? I'm sorry about that.. What I was trying to see is that how these people act as that's not how I act. I would rather have had peaceful conversations, and I also have helped. Using my help only they were able to teach the subject X properly, and they get paid. And I was trying to learn Y also by myself. And I didn't know that such a problem was going on and their views. So I feel curious to know if there was a switching of places how they would have acted...I want to know how they think and understand because like

I told before, my way of thinking is different @BryanKrause Sorry for the trouble though. Thanks a lot too!!! I would have talked with them before too if I knew. On the other hand as I'm peaceful and had been helpful, I kind of feel why they didn't present their problem to me directly eventhough they have enough evidence to see my nature. I've always expressed friendly and humble cooperative conversations to them. That's why I want to understand their behaviour. I've to stay with them in the future too.

If they just said "can you take the next week session" simply, if they wanted these sessions also to flow like normal sessions even though it was training, I would have taken it. I always have talked like a friend, otherwise, usually people can't come and take advises from another person while teaching you see, but they take from me. Anyone else, would have condemned them I think if they go to ask that many basic questions while working as a teacher, that's what I think they would have done if it happened the otherway round


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Is there an optimum time to leave between writing and self-proofreading?
Having read a number of guides on tips to do when proofreading as well as some questions on this website. They all refer to leaving some time between writing and proofreading. This time can vary from 5 minutes as per Purdue online writing lab

Even a five-minute break is productive because it will help you get some distance from what you have written.

to

Put the paper aside for a few hours, days, or weeks. The writing centre-UNC

My question is has there been any scientific work/papers done that gives a result on an optimum time to leave between writing and self-proofreading?

I wonder if this would get better answers on [writers.se]...

In maths, I have seen somewhere (can't recall the reference...) the suggestion to leave a freshly written paper aside for at least a month but I am quite certain that no research supporting this was cited.

From my own experience I would be very surprised if the effect of proofreading is not monotonically rising with the length of the break. Thus the optimum break length is infinity – unless there is some other constraint or effect of your break length that forces you to compromise. Though such constraints undoubtably exist in reality (e.g., deadlines), they are usually very individual and thus do not allow for making any general statements in my opinion.

Also, as a (hopefully helpful and probably well-known) aside, in my experience switching from the computer screen to the printout (or even just to another device -- e.g. a tablet)  considerably increases the efficiency of self-proofreading even though the time required for such a switch is usually small.

@just-learning: To add to this: It even suffices to see the text differently rendered. E.g., it is more effective to review one’s Stack Exchange post in the preview than in the edit field.

Also, reading the text aloud is useful for proofreading. Because it is tedious to do more than once, I save it until near the end.

It appears a number of factors come into this, such as what point proofreading should be done, familiarity with the text and length of time away from it.
According to Jane Cogie, Kim Strain and Sharon Lorinskas

It is important also that editing [proofreading] be done at the appropriate stage of the writing process, that is, as the last step, after issues of organization, coherence, and flow have been addressed.

In a study, The generation effect in reading and proofreading, the authors Meredyth Daneman and Murray Stainton conducted the following experiments in which;

Subjects spent 30 minutes composing an essay on student life; after a 20 minute interval (Experiment 1) or a two week interval (Experiment 2) they proofread their own essay, another subject's essay after being familiarized on an error-free version of it, or another subject's essay without the benefit of a preview. Experiment 1 showed that subjects were less able to detect errors (e.g., The best part of student like is socializing.) in self-generated essays than in unfamiliar other-generated essays; on the other hand, they were better able to detect errors in familiar other-generated essays that in unfamiliar ones. Experiment 2 showed that the disadvantage for proofreading self-generated text is likely a by-product of extreme familiarity rather than any special quality of self-generated knowledge per se

Commenting on the above study, Maura Pilotti, and Martin Chodorow (doi:10.1007/s11145-007-9110-x) state that;

The difficulty experienced by proofreaders with their own writing occurred even though the proofreaders were warned that errors had been added to their writing prior to proofreading. Interestingly, the impairment uncovered by Daneman and Stainton turned into an advantage after a delay of 2 weeks between writing and proofreading. The researchers argued that the ‘‘excessive’’ familiarity afforded by one’s own text, which is likely to decline over time, is detrimental to proofreading because it promotes a less thorough processing of written material.

It would appear from the above that 20 minutes is too short a period, and that something like two weeks is more optimum, but if possible leave it as long as possible.


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Using others' figures, illustrations, and diagrams
I am writing up a chapter of a literature review and I thought to add two figures to illustrate the theory of that subject of my research. These two figures are available in the literature and they are well known. My question is: if I used these figures with complete references to the authors, would that be acceptable in the APA style?

There are two distinct issues at play here: copyright and intellectual honesty.

From an intellectual honest point of view, it is entirely acceptable to reproduce a figure provided that you clearly credit the original source.
Copyright, however, is an entirely separate legal issue, and the figures that you wish to use may or may not be available to you under a license that will allow you to use them (or use them cheaply).

If this paper is being written for a class project, copyright probably isn't an issue you should worry about.  In anything intended for publication or even an MS thesis or PhD dissertation it would normally be necessary to get permission from the original publisher.  For example, the graduate office at my institution demands signed releases for any material in a thesis that has been taken from other publications in this way.    Another option would be to redraw the figure and cite the figure as "based on figure xxx in (Jones 2013)"


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Student asks for letter of recommendation: I can't remember the student
I have already had this issue a few times. I just received an e-mail from a former student of an undergraduate course, asking for a letter of recommendation to apply for graduate studies. This course took place almost 5 years ago. I don't think I had any contact with the student after the course, although it's hard to say: I can't remember the student, and I don't even work at the same university anymore, so I don't even have access to grades, etc. He sent me his transcripts but can I write a letter only with that?
What do people do in this cases? Write a standard letter quoting some of the grades (from the transcript)? How can that be useful to anyone?

If you can't even remember the student, just politely decline to write the letter.

You should decline the request to write the recommendation letter. As you said, a lukewarm letter is useless, if not detrimental, to the student's application.

Ask if he can provide any of his work that your graded/worked on with him (be honest and note that you cannot quite remember him) - I had a professor do this and he said reading my particular coding and writing style jogged his memory and he was able to write me a good recommendation for a job because of this.

Here is what I tell all students about letters of recommendation: http://bbrown.kennesaw.edu/recommendations/index.html

If you cyber stalk (I use that lightly) the name/e-mail, maybe you can find a picture of the person (on facebook or linkedin, et al), and that might trigger a memory of the student when you see their picture pop up?

@BobBrown that's actually very useful, thanks

Request the student to forward you "ghost-written" recommendation.  - If the recommendation looks like something you would write and the information is correct then the recommendation is written and you are close to done.

If something looks wrong then politely decline.

Could you ask him which aspects of his undergraduate study he wants to emphasise? - might jog your memory. I did a similar thing to two of my lecturers - after 15 years - trying to get a copy of the reviewers' report on my final year honours project. They couldn't help me - those records are disposed of with a 7 year horizon - but I was a bit surprised that they both remembered me.

@Agriculturist: Don't get how this would fit any purpose?!

Assuming that the student had good grades, I'd explain that I couldn't remember the student and that I could only base my recommendation on the transcript.  I'd still be willing to write such a letter, but I'd encourage the student to find someone else to write a letter if possible.
If the student had grades that weren't very good, then I'd simply decline to write a letter.

Brian, how could a letter that's based on just a transcript have any value? If it just takes the same information that's written in the transcript and repackages it in letter form, it seems completely useless to me. Am I missing something?

I've written a few like this.  I can say things like: "I have no particular recollection of Joe from the freshman calculus course that he took with me in the fall of 2009.  However, I can see from Joe's transcript that he has a GPA of 3.99.  His A grades in difficult senior and graduate level courses like MATH 439 and MATH 567 indicate that he should be well prepared for graduate study.  Very few of our undergraduate students perform at this level."  This isn't a very good letter of recommendation, but it's better than nothing.  Unfortunately, there are many students like this...

@DanRomik The letter might also contain some information about the content of the course (if it's not a universally standard subject), its level, and the grading policy.  If the transcript says that this student got an A+ from me, it can be useful to point out that I almost never give that grade.

I ask such students to tell me which course(s) they took from me and what major projects they did for those courses (where appropriate). I also ask for a current résumé. That's usually enough for me to write an acceptable recommendation letter for a job or award.
I turn down requests to write Ph.D-program recommendations, as I neither have a Ph.D nor make the kind of assignment that differentiates the Ph.D-ready. (I teach in a professional program and my courses are pretty hands-on.)


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What is the best way to tell a professor that my research interests are not limited to a specific topic?
I want to write to a professor and tell him about my research interests. What is the best way to say that my research interests include, but are not limited to X?
Is the following sentence a good choice?
"My main research area is X, but I am open to other subjects as well. "

I guess the answer depends on what kind of information you want to convey, and for what reason you want to make it clear that your interests are not limited to X area. "My research interests include X" is already non-exclusive - just because you say that you are interested in X doesn't mean that you aren't also interested in Y and Z, and most professors realize that students (and all their colleagues) have more than one small narrow area of interest. So you can just say that and be fine.
Basically, my point is that it's absolutely fine to tell a professor that you are interested in one specific area, as long as that area is sufficiently broad in your field. The goal is to find a professor whose interests match or are complementary to yours, so when you say "I am interested in X" he thinks "Ah, I have always wanted a student who would study X!" or at least "Hmmm, it might be good to have a student in my lab/group who studies X."
However, I would not say "My main research area is X, but I am open to other subjects as well." That makes it sound like you would be willing to change your area of interest if the right PI came along or to get into a specific program, and you don't want to convey that, as counterintuitive as that may seem. It makes you sound wishy-washy. You want to be regarded as a serious scholar with a deep interest in a particular area.

" and you don't want to convey that, as counterintuitive as that may seem" That definitely depends on the context / programme. When we hire in Switzerland, this is very much what we want to hear, because usually we have a concrete project that needs to be done, and rarely is what a student lists as research interests exactly what this project is about. You say "wishy-washy", I say "flexible".

By this comment I meant a very broad change - aka, "I currently do HIV research with humans but I would be willing to do obesity research in animal models if only you would let me in!" That would make me skeptical about a students seriousness. But related interests within a specific area - that's different. Actually, that's what happened to me - I specified an interest, and my eventual advisor had a project within the same general area but not exactly the same and was intrigued by my background.

Well I think telling profs that you are only interested in a very narrow research field may seem like you are not flexible, and in conduction research you sometimes need to be flexible since your specific research area might be eliminated or replaced according some new findings! But telling them I'm interested in X, but I am open to Y as well seems like all you want is the D*mn fund and admission. ;) (And yes we're are looking for that, but there are better ways to ask for it).
You can make it seem more exciting and show yourself as an adventurist to them, not someone who has not made his mind yet. So if you send them the herald that I have made my mind but as I am an adventurist and researcher I am ready for dramatic shifts if necessary you could use some statements such as this one :
I am very interested in X, but science has been always full of surprises for me and I will welcome new exploring options during my graduate studies as I have always done about previous opportunities.
just check out the syntax and grammar ;) since English is not my native language.

I might go with:

Right now, I am very interested in X and Y, but since I'm still a [undergraduate / masters] student,  I'm sure that might change, and I want to be flexible and keep my options open for now.

if you are already working professionally than replace * student with early in my career.
This conveys flexibility while admitting adaptability.


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Online courses in standard university curriculums
Does anyone know examples where online courses (or other similar eLearning methods) are currently used effectively in the curriculum of a university?

Maybe this question is interesting for you: Can I include the completion of Udacity and Coursera classes I have attended in an academic CV?

Fully online or semi-presential? (aka, can I do it from the other side of the world, or I have to go to a regular class/exam at some point)

if there are functioing examples of online exams I would also be interested in that

What does "effectively" mean in the context of this question?

@50k4, perhaps you should ask that as a new question.

There are several types of online learning. Some practical considerations you seem to be wondering about are meeting times, delivery methods, and best practices in online learning.
The time of meeting could be described as synchronous, asynchronous, or a combination of both. Synchronous refers to the practice of the students and instructor meeting online on specific days at specific times. Asynchronous means that the students and instructor do not have to "meet" or connect online on specific days and times. Most online courses are asynchronous.
The delivery methods of online course content is as varied as the universities, majors, and faculty involved. Nearly all of them will use an LMS, or Learning Management System, to deliver course content to students. Some of the most popular are Blackboard, Brightspace by D2L, and Canvas. The content itself may be text-based, video-based or audio based and may include interactive elements, whether simply utilizing the discussion and quiz tools in the LMS or more complex learning interactions such as simulations or gamification.
You can get started in finding some of the best practices for online instruction can be found by searching academic research using keywords such as: elearning, distance learning, online, best practices in online learning (or elearning, or distance learning), and postsecondary (higher ed) educational technology. Another research topic that might be of interest to you is instructional design models. Many of the best practices in online teaching and learning have much in common with F2F best practices. The delivery method is simply the means, not the end.
Additionally, there are universities offering bachelors, masters, and doctoral degrees in instructional technology, instructional design, or educational technology where one can make a study and subsequently, a career, in online learning. There are also many national and international organizations devoted to the continual improvement of distance/online learning/elearning in both K-12 and higher ed.

Online master's programs are quite common in Library and Information {Science|Studies} schools/departments. Sometimes there is a (very limited) requirement for face-to-face attendance, e.g. an opening orientation bootcamp.
As far as I know, no online LIS program has lost accreditation merely for being online. Admittedly that's not the best way to measure effectiveness, but it's hard to know what is, exactly.
Some working professionals still maintain a hiring bias against students from online programs. To the best of my knowledge that has diminished over time (though not to zero), and in my experience most of their objections (when they can be bothered to articulate them) are either mistaken or specious.

Could you please explain more about the practical aspects? How are exams carried out, is there live interaction (videochat or similar), video lectures or lectrue notes? Are there any best practices?

Few exams on the master's level (it's usually project-based work), but we can either use the learning-management system's quiz function or do a timed release of an exam paper. Live interaction level varies; where I am, some require it and some (like me) prefer wholly-asynchronous. Video lectures are common; most of us post our lecture slides for students also. Best practices -- large literature on this, check it out. :)

could you give sime hints how to search for the literature on best practices?


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Is it inappropriate to decline presenting paper on behalf of someone else (outside my expertise)?
I have been requested to present a complex paper outside of my own expertise at an upcoming conference. I have rejected this invitation on two occasions stating reasons such as:

Not my expertise
My first Conference
I'm not an author on the paper
I don't understand the paper
and so on...

Apparently people present other people papers in Computer Science all of the time at conferences, but surely these people are knowledgable on this subject? Would it be inappropriate for someone to present a paper, for the reasons listed above? I'm not feeling like a team player right now.

Who is asking you to present the paper?

I tagged this with CS, since I think that's what you're talking about; please correct if I am wrong.

"Apparently people present other people papers in Computer Science all of the time at conferences" Hmm, if that's true I find it interesting.  Is this because if the paper is not "presented" then it cannot be published?  Actually, I'm not sure I even understand the motivation behind that: you submit the paper in advance, it gets refereed, and people think it's strong in both the absolute  and relative senses (in particular, better than other papers), and then if you don't show up to speak for at most one hour on your work no one gets to read about it later?  Why is that?!?

@PeteL.Clark Yes, a couple of conferences won't put the papers into their proceedings unless presented.  I can't really answer your final question. It seems bad to me if you or none of the authors know you can't present it. I just happen to be published in the same conference.

@WolfgangBangerth My PhD supervisors. I specialise in language, whereas the paper is in vision if that adds more context.

@PeteL.Clark Exclusion of non-presented papers is standard IEEE policy, as explained on this page.

@jakebeal: Thanks.  I was asking about the motivation behind it, which I still don't really understand.  It says that they want to "encourage attendance".  I don't really get that: either the conference is valuable to attend or it isn't.  Having the requirement makes it sound like people don't want to attend the conference...in which case I don't understand why they have the conferences.  They certainly don't need them in order to publish the papers.  I understand that cultural questions from outsiders can sound weird, and I'm sure my question sounds that way...

@PeteL.Clark I'm afraid I'm not a good person to explain the IEEE hard-line position here, since I find it somewhat dubious myself.

@PeteL.Clark: One reason may well be that if 80% of the prospective conference visitors find the conference valuable to attend, 20% no-shows can still seriously disrupt the planned schedule. Furthermore, as a paying conference attendee, part of what I pay for is the opportunity to watch presentations on up to 100% of the published papers, not just a random selection by those authors who bothered to travel there. These are only subjective reasons, though, and I think this warrants a separate question of its own, which might also attract more authoritative answers. ...

... However, as I cannot resist adding a bit more speculation here, note that what a researcher sees as "valuable to attend" and what their funding agency sees as "valuable to attend" may be two very different things. Getting a refund for a compulsory travel can be considerably easier than getting a refund for an optional travel. The same may apply to invitation-based visa and other administrative hurdles. Lastly, the Q&A round at the end of each talk can serve as a means of quality control. In that light, looking exclusively at what the authors of the paper want would be counterproductive.

@O.R. Mapper: There are some interesting issues you raise.  I should probably ask a question about it if really want to learn.  Just one thing: I certainly wasn't saying that people should "no-show", just that the people who speak at the conference could be a proper subset of the papers that get published.  The idea that there is value subtracted here seems totally subjective: the other way to look at it is that there's value added in these additional papers!  (Also travel that you need to do to get published in a proceedings is not what I would call "compulsory".)

Are you actually going to the conference and presenting your own paper as well? Or is this request your ticket to the conference?

First of all, I think that in your particular case, it was a right course of action to reject the "invitation".
To answer the general question

Would it be inappropriate for someone to present a paper, for the reasons listed above?

let's look at the single reasons one by one:

Not my expertise

A somewhat valid point. You probably shouldn't be talking about something way outside of your area of expertise. However, if the topic is at least marginally connected to yours, it could also be argued that you should not enclose yourself in your personal bubble, but try to get somewhat acquainted with as many other topics as possible. In general, despite researching specific questions, an educated person should have some wide knowledge, and maybe knowing about such another topic even provides you with opportunities for expanding your own research into unforeseen directions.

My first Conference

This. In my opinion, this is the strongest point in this list. You don't have any conference experience yet, not only giving talks, but also listening to how conference talks work at all. As so often, it is advisable to start out somewhat simple, and presenting a paper you are not fully knowledgeable about yourself is probably not a good way.

I'm not an author on the paper

That is not a valid reason. As you said, people present on behalf of others all the time, and there are various reasons why the actual authors might not make it to a conference personally1.

I don't understand the paper

Acutely, that is a severe issue, though it could be said (also referring to the first point) that in that case, you just need to spend some more time trying to figure it out (and having the original authors help you understand it!). So, it is a somewhat valid reason, but given a little more time, it is an issue that can be mitigated.
A word on your statement

surely these people are knowledgable on this subject?

No. Sometimes, not at all, which is unfortunate, as like that, the Q&A session degrades into nothing but: "Next question, please." - "... ?" - "Sorry, I didn't write the paper." However, if the presenter is at least partially knowledgeable, in a way that they prepared the presentation well (together with the original authors!), it is fully acceptable if the presenter cannot provide an answer for every very specific question, as long as they can sufficiently describe the gist of the research.
1: Scheduling conflicts, visa issues, illness, or restrictive travel funds come to mind.

"I'm not an author on the paper" - "That is not a valid reason." I disagree. Of course it does not mean that the OP can't present a paper just because he is not one of the authors, but the OP is certainly under no obligation to present a paper that he isn't the author of, even if he is experienced and understands the topic and paper well. It's maybe not the best reason, but it is hardly an invalid reason to reject presenting a paper.

@xLeitix: Well, I answered the question "Would it be inappropriate to present the paper?", not "Would it be appropriate to reject presenting the paper."

Outside CS it would be highly unusual for the presenter not to be an author (@xLeitix)

@ChrisH That is interesting. Thank you for sharing :-)


text:
How to decide about the university to stay for the future after facing some troubles
In our country working in a state university is regarded as a priviledge. Even when we consider the degrees offered, people accept the state university degrees more. Usually first preference is given for that. And when we consider the payment for academics, the academic freedom allowed, facilities etc. are better in state universities.
I have been working at a state university as a lecturer on contract basis, an opportunity which I got I think also because one of my supervisors (A) specially recommended me, by thinking to help based on my hard work while working with him.
I've applied to get permanent there too, but later I found that there were some internal politics, and even though the dean has listened to my supervisor's recommendations, the head didn't like it and she purposely tried to create trouble for me. I actually got in to some unjustifiable and unreasonable situations created by her and some of her friends, I couldn't understand what was happening at the beginning. So I explained the situation to my supervisor, and he had checked through some of other seniors working there and found that there is some biased situations happening.
As they were troubling me and trying to sabotage my work, I gave resignation and soon afterward, I got an opportunity at a private university.
Now (after about a month) I’ve got an opportunity to go to another state university. After resigning from the previous place, I actually put applications to every advertisement I saw, and my supervisor was put as my referee. Actually two of my supervisors as referees. So at this state university, the department head is a friend of both of them and when she was asking they both had recommended me for the post and had put in good words on my behalf.
With respect to the salary I will be getting almost same amount as the private uni I'm at now. But at the interview I found that this state university has several centers located in far way regions as well. They asked if necessary will I be able to go. It will be about for 1 week but I have several issues with respect to my family such that I’m unable to travel to outstation areas like that.
During the interview, I replied ok (because I couldn't think properly and it's usually embarrassing to say no, negatively at an interview), but after coming home I told my supervisor (A), that I have a reluctancy because of this travelling issue. However, his friend has also called him and told him that “Hasini did the interview well. She might have gotten afraid about the travelling issue, but tell her not to worry as, so far I also haven’t travelled, I’ve been here for about 10 years. But such a necessity never came”.
But when I inquired from several others, some people had come across situations where they had to travel.
I’m also looking to go to a state uni, but as the private uni I’m currently at is not very bad I would like to go if the place is really matching with my capacities and interests. There is a high competition to go to the state uni’s, I know that and also I got the opportunity because my supervisors also spoke. I don't know whether I'll get such opportunities always.
But on the other hand it’s only a month since I started at the private uni (so they will also get upset when I say I want to leave), and I didn’t think the state uni will call me for an interview this fast, because they usually take time, and this particular place, I just put the application by thinking that: based on the situations I’ll decide.
I didn’t think that all of a sudden my supervisors will speak by hearing about my application from their friend.
Actually A specially, as he knows what happened at the previous place, which was also recommended by him, as I told you, I think he feels sad that I got in to trouble without a reason there and wants to help me.
If I choose to stay in the private uni, with the hope of going to a different state uni in the future, I have to explain the supervisors in a strong way,

Because they have already spoken here on behalf of me and they think I really like this state uni and that's why I applied

As everyone thinks it’s a higher priviledge to work at a state uni and there is a high competition, they will be getting surprised when I try to refuse this chance I got. So I will have to explain and overcome this barrier, and keep the supervisors in a good mood too as they are going to be my referees in the future too.

But still there is no point in going to the state uni if I can't travel if they ask me to by any chance... I'm worried about that. But I don't know how to say it and also am I making the right decision by refusing?
Please advise me.
Thank you very very much!!!!

That's a very long question :-) May I ask why you can't travel?

Hi @WolfgangBangerth thank you for the comment. I have some family issues, which make it difficult to travel. Need to take care of parents, no one to take care of some things at home, etc. Because of this, I did my studies also at places where I can travel to at least by taking 1 to 2 hours of travelling even.

Have you asked your parents about this opportunity, and whether they have any thoughts about how they can be better taken care of, just in case you need to be gone for a week here and there?  They might not want you to pass up a job you really want? If you need to be gone for a week, would there be any way for you to find someone else to take care of your parents for a brief period of time? I imagine there might be other family members, significant others, etc, who you might be able to recruit to do so?

Thank you for the comment @Parever like I said it's not just taking care of them is the issue. There are several. And also this is going to create a risk to my safety as well, because some of such areas have terrorist problems, racial issues. From parents side, they are worried about my safety. And I didn't think exactly I want to go to this particular state uni itself. I just applied by thinking I'll go and see their conditions and agree if I'm really ok. I didn't expect that the supervisors will have a lot of words put in like that.


text:
How to face some tough academic superiors who give undermining comments in the academic environment
If a group of Computing undergraduates ask to explain why 3 is greater than 2, what is the best way to explain it?
When I asked the above question in the Math SE, one of the Mathematicians said this answer: "You have 3 apples. Is that more apples than 2 apples? "
This was a question asked from me at an interview, and that's exactly how I explained it. I told about cattle actually instead of apples. But one professor said we could have used the number line, in a kind of an undermining tone. This actually he did to kind of show his superiority I guess.
I said, yes, if we try to explain it using a mathematical way, we can use the number line too, I thought you were asking for a more detailed explanation, that's why I said like that. So, I know some say such comments to show their superiority. How to face such questions and comments to my answers in the future? Any suggestions please.
I mean, I don't like to feel undermined just because of he wants to show his superiority in front of everyone. I'm feeling bad that others who are not doing Maths might believe him more and have a negative feeling about me. I have the second interview soon.
So how can I use and show my Mathematical knowledge and defend myself in the future. I know there are such Mathematicians so any practices the you'll follow as academics to face such situations?

A fairly common interviewer strategy is to challenge whatever answer you give - they want to see how you react, and whether you can justify/defend your views.

Personally, I think your answer (and the one that QY had suggested in his comment) was aiming too low. In your place, before answering, I would have asked about the level of these undergraduates. In my experience, many CE majors take classes with rigorous math proofs. For such students, your answer would be a bit insulting.

one professor said we could have used the number line --- I don't know what I would have said in reply to the question (maybe "doesn't this depend on the order defined on the underlying set"), but in response to "could have used the number line" I would ask what if we're considering 2 and 3 as complex numbers?

I'm not sure why you should feel "undermined". Your explanation was fine. The professor's was fine. They may just have been giving an alternate explanation, not necessarily a superior one. In some courses I might have reminded you of alternative ways of looking at some (any) issue. There is nothing inherently wrong or demeaning about that.
Having written a book that includes things like the axiomatic treatment of the Natural Numbers (Peano's Axioms), it is pretty clear the the "number line" concepts evolved from simpler concepts like what you expressed (the "successor relationship"). Then later the definition of the "greater than" relation based on it.
The different explanations are really just rooted in different insights, one more complex, perhaps, but a complex explanation for a simple situation isn't necessarily "best" and using a simple explanation shouldn't reflect badly on you. If the professor thinks it does, they have a problem IMO. Especially so if they used an "undermining" tone.
In particular, the "best" way to explain anything depends on the context, including the audience.
I suggest you relax. It might be benign. But if the professor is a jerk that is their issue, not yours.