text:
What does it mean to "succeed" in mathematics?
I don't know if here is the right place to ask this question but I would be glad if you could help me.
I am currently a first year PhD student in pure mathematics, and I have some issues that seem like are preventing me to try to become a mathematician, and come in my mind every now and then.
I start with my background, when I was in high school I tried a lot to be in our national IMO team but I didn't even get close to it, after that I tried a lot of university math books and almost finished undergraduate material in my high school, but after getting to university I didn't have any success in my first years, and after that I got to some "CV-filling" places, that I used to get to a rather good university in math for my PhD, but when I see young great mathematicians, almost all of them have had some of the great successes in their high school and undergraduate, and seems like everyone is looking at them like a great mathematician because of that, and they do not need to put a lot of effort on what they're doing, for example, one of my colleagues got to one of the best universities in math without trying to learn a lot of mathematics - even those that I knew from high school- but has a lot of "success" in mathematics.
In my undergraduate I tried to continue my way of reading mathematics, and learned a lot in my undergraduate studies (from books not courses, and for that I didn't have the best GPA in class), also worked with some professors and other things that not so bad undergraduate students usually do.
My questions are the following:
1) What is a mathematical success?
(for example, I know that in PhD working on good things and having great ideas about core problems in mathematics is a success, but it seems that I'm doing something wrong because it seems that I will not get good things in math by just doing what I'm doing)
2) how can I have motivation to become a great mathematician and be sure that all my efforts are not in vain?
(for example, in my department, everyone talks about having some number of papers published to get to a better place (which I think is something bad to be someone's goal in math) , and when I see former graduate students of my department, almost all of them are in big data analysis and stastics and these non-pure mathematical jobs, even after having a good understanding of some part of pure mathematics)
I would be happy to see other questions similar to this, if there are any in this website, but I would be happy to not put duplicate to this one, if there are duplicates, I would be happy to see answers in my case.
Regards,
Sorry to put anonymous, I'm a little insecure when asking these questions!

What level of success are you looking for?  Fields Medal or bust?  Good enough to have prove some theorem that is worthy of publication in Annals of Mathematics?  Good enough to get a job at a top math department?  Good enough to get a job at some research university?  Good enough to prove some theorem someone else is interested in?

Good enough to be the best mathematician!

Life is not a competition, and neither is mathematics.  (Unfortunately, the job market is a competition.)  If your goals are based on comparisons to others, you're pretty much doomed to a sad life.

You should measure success by having measurable, reachable goals. Being "the best mathematician" is not such a benchmark, and setting that as your goal, as Alexander Woo mentioned, will almost certainly guarantee you will be unhappy in your mathematics career. Moreover, not pursuing a career you want because you can't be "the best" in that discipline seems shortsighted.

If success requires being the best mathematician, then everyone on this site is a failure.

What is a mathematical success? — Results that you are proud of and that other people like.

'Good enough to be the best mathematician'
Not to be cute, but the set of mathematicians is not well-ordered!

@Charles E. Grant: +1 --- Good point, but you probably mean "linearly ordered".

@DaveLRenfro The set of mathematicians isn’t even partially ordered.

@JeffE: Yep --- transitivity surely fails, which incidentally reminds me of my tennis playing days.


text:
Correcting professors' lecture notes
One of my profs in college has (after years of students asking him to do so) put forth a syllabus with all the material for the class he is teaching.
With the help of 3 students from previous years (who did most of the writing), he made a neat 90 page syllabus covering what is taught during lectures.
My year is the first year that'll benefit from this as it was finished early September 2017 (currently in October 2017). However, as is to be expected, some typos still exist, and some little mistakes in formulas do too. I read through it and compiled a Word doc containing all the typos and mistakes I could find and was wondering if it would be badly received if I sent him an email with those. He has asked his students to tell him if they found mistakes, so I know I should probably let him know about those, but I'm not sure as to whether fixing typos will be seen as arrogant or even remotely relevant, since I'm probably the only one getting triggered by them because of my OCD.
Thanks !

Just FYI, I wouldn't usually call this a "syllabus" in the U.S. I would describe this as comprehensive lecture notes or a lecture guide.

I have less than 90 pages of typed notes/instructions/examples and I offer a bonus point or two to any student that finds an error of any type - typo, actual error, dead link, etc - in the content.  Granted, a couple of points really doesn't change a final grade (unless it was so close that I would round up anyway) but it does give some motivation to report errors instead of ignoring...

When he asked for mistakes, did he mean typos? Or logical / factual mistakes?

Please don't send an MS Word document. Send plain text or a PDF.

@corsiKa He didn't specify but I'd assume both

@UTF-8 I'll edit it in LaTeX ;)

@Peiffap: You can simply export the MS Word document to PDF. No need to duplicate the work done.

As the others say, I doubt these will be looked upon unfavourably. Especially given that the document was written with students and is new, I would expect the lecturer to be quite happy to have received corrections. (Especially of typos.) It makes me think back to statistics in my maths degree where we got an explicit warning that the document contained typos which got fixed along the way - because it was rewritten too. - Over time, the document will then become perfect.

Frankly, I'm surprised anyone would hesitate to send in corrections to lecture notes (because that is what they are). In the worst case scenario, they'll simply be ignored (unlikely). The professor will probably reply and thank you (very likely). It's very very unlikely he will hold it against you, and if he does, he's nuts. And given that he's actually asked for corrections, a negative reaction is vanishingly unlikely. And no need to apologise or explain. You're doing him a favor. Personally I find typos very annoying, but maybe it's my OCD too.

Why not approach him face-to-face about it?  Tell him you've been keeping track of typos in a separate file, and if he'd like it, you can send it to him.  Then you can discuss the format, etc.

Give him a diff.

I'd recommend pushing typos to the end. They are far less important than other errors.

@DetlevCM ... "become perfect"... :) Yes, it is comforting to believe that all our writings will eventually become perfect, but unless we stop writing, our rates of production of flawed documents will surely vastly exceed our corrections of them. :)

@paulgarrett I've found that the number of typos in an all-but-finished document is a strange creature: it is (hopefully) monotonically decreasing, bounded below, but nevertheless doesn't converge!

I can only speak for myself, and I'm just a postdoc.
I would be indifferent if someone pointed out one or two typos; on the one hand that's helpful, on the other a bit pedantic.
However, if I received a "Word doc containing all the typos and mistakes [you] could find" in a 90 page document, I would be delighted and grateful.
As an aside, I'm currently working through a textbook to brush up my statistics skills. I'm trying to collect the mistakes that I stumble upon in order to send them to the author once I've finished the book, so he can correct them in the next edition.

Thanks, I know it might sound pedantic but given that he asked for it I think I'm gonna go for it.

@Peiffap I would only consider it pedantic to point out one or two typos, but having a 90 page document proofread is really nice.

I do not know any professor who would think "How pedantic!" when a student points out even a single typo by email. We all want our material to be flawless while spending as little effort as possible.

I cannot speak for all professors, of course, but I'm my case I'd be delighted and I'm fairly sure that such would be the reaction of most professors.
Over the last two years I have circulated some lecture notes among my students and a few other persons, and I'm really frustrated by the lack of feedback on typos (or anything else, for that matter).

I would talk to them in private and, if they don't know about your ocd, let it come up during the conversation as you explain why you made the effort - they are sure to ask...
I once spent a whole weekend doing a massive differentiation based proof to see the result was as stated ( you've seen those in maths / engineering where it says : it can be shown that xyz from abc). Well the proof as shown was incorrect so after doing it several times and getting it checked I took it to the Prof and said I thought I was making an error and could he check it.
Next lecture I nearly fell of my chair when he started with "the proof you were given last week has an error in it, been like that for 5 years, anyway the correct proof is now available thanks to" and gave my name... Not asked for, not expected but a real surprise as he had not warned me either...

Yes, you should send the errata. (But, as others said, use a format that the authors can definitely read without going extra steps. PDF or text, for example; not docx.)
I have been recording errors in notes, books, papers and even forum posts since forever (I tend to read things very thoroughly, sentence by sentence, as my mind is otherwise tempted to skip the actually important parts and dwell on the easy bits; the list of errata comes out of this rather naturally). Most of the time, as long as I've discovered any mathematical errors (as opposed to just typos), I've notified the authors, and the notification has been either received positively (authors thank and often correct the errors) or ignored (i.e., no reply). In my experience, it gets ignored the more often the older the work in question is; after all a paper you have written 15 years ago could just as well be a paper by a different author to you. But if the work is recent or even currently in class use, then the authors are likely to be thankful and highly responsive. (Out of maybe fifty authors I've contacted, only 1-2 have been defensive, and one of these two was outside of academia.)
Mathematics isn't quite like open-source software where bug reports and community patches are actively encouraged, but it's getting closer (unsurprisingly, given the noticeable social overlap). That said, as an algebraic combinatorialist I am probably closer to computer science than the average mathematician.

"as opposed to just typos" Typos should be reported too. They're errors.

As a professor I always welcome suggestions for improvement like these, as long as they are presented politely and respectfully.
If your professor has already made the effort to write down and publish his class notes then your should expect him to welcome whatever helps him improve the material. This is real work and any help is welcome (after writing, rewriting, reading and re-reading, it becomes harder and harder to pick up your own errors).
In addition, I would like to suggest that academia is a place where you should be more concerned about truth (and therefore quality of class notes) than personal feelings, be it of professors or of students. What matters is that the quality of education keeps improving and you can help make that happen.
Having an OCD student willing to do that work for you is a godsent for a professor, so go ahead and expect him to thank you for it!
(of course if he reacts negatively just let it go: that would only reveal a flaw in character...)

Thanks, the part about truth being more important than personal feelings makes sense, and it's a point of view none of the other answers have raised.

You need to stay firm , send him the doc state that's it's unaceptable for a university profesor have typos in any text he sends his students and offer to corect/mantain the document in exchange for creds

I would have some typos to point out for you.

You should probably also expand the answer somewhat

This is not accurate/appropriate/relevant. (Plus, gosh, you have an "incorrect" space before your first comma.)

Is...is this a serious answer?

source: Stack Exchange

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

sort: votes


text:
How are GPAs from different universities evaluated for admissions to MS programs in the USA?
I am about to apply for a Master program in U.S. as I am about to graduate in Bachelor of Engineering. Though I heard that all my grades during all my academic life is taken into consideration (GPA). Here in Brazil is very common to have a huge gap between universities both in teaching level and avaliation process. So, holding a degree from a weak college may be much easier and thus helping you to get a higher GPA while a well-known college will be much more difficult and probably your grades will be lower. Even though you have a degree from the very best college and you do have a good knowledge of most subjects, the GPA from the person who came from the weak college may be higher.
This also extends to the outside world (comparison between GPA's from different countries). So, how is it really done in practice? Do I still hold a reasonable chance of getting into a nice college with not a so high GPA?

Also see: Is it ethical to apply different criteria for graduate admissions based on country of undergraduate study?

You can add a note in your statement or supplemental materials that "At my university, ____, the mean GPA was 3.5 with an sd of _ and in my department, the mean was xyz with an sd of __" so that it's clear that you are two sigmas above average, etc.
That assumes that you are above average. You should be able to get this info from the university registrar or office of institutional research.
But you should know that GPAs as a whole are deprecated in the application process. Individual grades (how well did you do in computer science, for example), some test scores in some disciplines, and your statement is much more important. As well as your letters of recommendation.

If your university is not well known, being "above average" at your university does not carry much meaning either.

It at least gives some context as to where you are in terms of your peer pool.  You can also add a note in your file that "University of ____ is ranked 3rd in my country according to the survey of universities conducted by so and so organization." But I wouldn't worry too much about this. If we're seriously looking at you, we'll contact you and try to evaluate you via criteria non-dependent on your institution -- by telephone interview for example.

In my (US, research university, engineering) department, we don't do phone interviews for any MS students (the volume of applications is just too high). I guess YMMV depending on the department.

In general 3.4 or 3.5+ is considered a good GPA, and you won't need to explain why it isn't higher to any reasonable admissions board no matter where you graduated from.  Well know schools want a diverse grad student body, and will look to pull students from prestigious schools as well as smaller state schools and international schools.
No matter the GPA, I would apply a prestigious "dream" program or two and see what happens.  This is especially true if you can line up excellent recommendations.  While it might be a longer shot, $50 application fee isn't much, and you will not be left playing "what-if" with yourself.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
What is expected of a postdoc?
What do different people in the department expect from a postdoc?
By different people I mean the advisor, graduate students and PhD students.
I know it mainly depends on the job description but there are few basic things that a postdoc must be expected to do. How aggressive (proactive) must one be? This question is important since a postdoc cannot just wait for the adviser to give him/her inputs. Rather the postdoc must take the project(s) as another PhD research of his own but be completely accountable to the adviser in terms of what he/she is doing and how is he/she doing that.
The above are my thoughts. My question is divided into the following sub-parts:

What would you as a professor expect from your postdoc?
What preparation one must do to rise to the expected level?
Is the preparation merely restricted to having sound academic record and experience?

This question is a possible duplicate of this http://academia.stackexchange.com/questions/2173/who-actually-is-a-post-doctoral-fellow

By now the answers here are so useful that I'd be against closing this question as a duplicate.

@DavideChicco.it the link your provided is essentially a list of questions. The final question is clearly a duplicate, but the answers focus on the other questions in the list. I therefore say not duplicate, but relevant.

You'll very quickly learn that being an academic involves more than just writing research papers. Your time as a postdoc is when you can start learning about these other aspects, while building your own profile.
A postdoc needs to do the following:

Build a publication record. This will involve both what you are paid to do and your own line of research.
Get involved with supervising students. Help with the PhDs in the lab, and get involved in supervising masters students.
Get involved with obtaining funding. This can either be by helping your employer or (ideally) obtaining your own funding.
Build an international reputation.
Start collaborating with external parties.
Gain some teaching experience. This is absolutely crucial if you want a faculty position.
Learn how to manage projects and a lab. This includes overseeing the progress of projects, allocating your time (and others), presenting results at meetings and  writing deliverables. If you are in a lab setting, you will need to learn how  to fix/calibrate/maintain critical equipment and software so that you can start your own lab some day, and you will need to become proficient in teaching more junior members on how to use that equipment.
Start to devise a strategic research plan. While it is fun to do opportunistic research, solving a problem that comes along or investigating any idea that pops into your head, a better long term strategy is to formulate an interesting long term research plan and follow it, building result upon result.

Be as proactive as humanly possible, without being annoying. Talk to everyone in the department, especially people whose research interests are close to your. Go to conferences and sit down and work with interesting people (not necessarily the superstars).

To the manage projects I would add how to fix/calibrate/maintain critical equipment and software so that you can start your own lab some day.

I am going to print this answer and hang it above my monitor for the next three years.

As for managing project, I feel it also include overseeing the progress of the projects and how different people (mostly students) are taking it further.

Speaking from personal experience, I would emphasize the importance of gaining teaching experience. During my PhD and postdoc years, I was not offered any opportunity to obtain teaching experience - nor was it even considered a possibility. This has made it extremely difficult for me now when applying for lectureship positions.

I consider most of these activities necessary for senior PhD students, and some of them (like "Build a publication record") even for junior PhD students.

Great answer, I wish I'd been able to read that before I got started.

I like this answer. +1 for that strategic research plan and ...building result upon result.

Let me add one item that Dave Clarke omitted, which I think is actually the most important:

Separate your research reputation from your advisor's.  Congratulations!  You have enough of an independent research record to land a postdoctoral position.  Unfortunately, that reputation is almost certainly deeply entangled with your PhD advisor's; deep down, many people in your research community still wonder if (or simply assume that) you've just been riding your advisor's coattails.  Your primary job is to convince them otherwise.  Do not work with your advisor, and do not work in the same subsubsubfield as your PhD thesis.  Make a name for yourself as a truly independent researcher and scholar.

And a secondary corollary:

Do not just ride your supervisor's coattails.

Is /that/ why a post-doc cannot be at the same place as a PhD? I've been wondering about that.

"cannot" is strong (because it happens) but "probably shouldn't be" is true.

+1 for Make a name for yourself as a truly independent researcher and scholar.

+1. The whole point of the "changing institutions" custom, at least as I understand it, is to act as a replicate measurement of your abilities as an academic using new variables. There will be a higher degree of confidence from the point of view of hiring committees if you can demonstrate that you consistently obtain papers and funding even with different advisors and lab environments.


text:
Compressing figures for paper submission
I recently submitted my first paper to a journal and had some trouble with the figures I uploaded. Specifically, the journal required vector graphics figures to be exported at 1200dpi, grayscale at 600dpi and coloured at 300dpi and I could choose between tiff and eps formats. The problem I faced was that there was an upload limit of 30MBs and I had to submit each figure separately. Keeping the dpi guidelines produced images that had a total size more than 200MBs and the only way I could upload them was by exporting them to 200dpi. Has anyone faced a similar issue and if so, how did you solve it?

What format are the images? I guess .eps
If you have access to a linux machine, you can use the command ps2pdf or gs to considerably reduce the size of your files.

How did the editor answer when you asked them this question? (You did ask the editor, didn't you?)

I did answer but no reply yet.

Are you really sure that the journal requires you to convert vector graphics to pixel graphics? If yes, they are stupid. If no, just use vector graphics and your size problem should be gone.

In my experience, Matlab is very good at compressing figures in *.eps format(I have also used SciLab, Mathematica, R, but the best compressed images are produces with Matlab - 2D, 3D images, 3D histograms, density  contour plots, 3D object reconstruction, etc).

I didn't know that @Mikey Mike. Thank you very much!

I am assuming that the OP already is being careful to make the bitmapped images approximately the size that they will be printed (that is, the image should be 600dpi (or whatever) at the printed size, not the original size it was created just in case that was some default large format

The upload limit is clearly a stricter requirement than the image resolution threshold since you can't submit a paper over that size. As you have done, I suspect most people would compress the images to meet the file limit.


text:
Is it appropriate to ask a student I tutored how their exam went?
I tutored a student in math for two weeks to help her prepare for an exam. I expected her to inform me how the exam went, but she did not.
Is it appropriate to ask her how the exam went?
We are in Ireland.

What are you planning to say to her if it turns out it went badly? You might be embarrassing her.

@ElizabethHenning, actually, I would want to follow up with a discussion about how "we" can make it better for the future. What needs to be done on her part and mine so that the outcomes improve.

Is it appropriate to ask a stackexchange user, in case that the conclusion of this question was to actually ask the student how it went, how the student did?

hahahhaa @Nanne, She did so so.

I expected her to inform me how the exam went

I'm not sure why you expected this. While it's certainly not unusual to follow up with a tutor (or thank them), it's not a requirement.

Is it appropriate to ask her how the exam went?

I see no reason why not.

Not a question about academia, but of general interpersonal interaction. It's good manners of the student to inform the tutor, but not outright bad manners not to do so. Many students are either thoughtless or worried about more imminent things. Whether or not to contact depends on rapport with the student.

@CaptainEmacs True, but you only know it's not a question about academia because you already know it's not about academia.

https://academia.stackexchange.com/help/on-topic specifially lists "requirements and expectations of students, postdocs, or professors," as an on-topic question. It's at least tangentially on-topic, IMO.

You might also ask this in the context of how you can improve your tutoring.  No matter how it went, you might following up with "is there anything I could have done to help you more?"

As a tutor in undergrad, we were taught to ask "how did the exam go?" and not "what did you make on the exam?" The idea being that the tutee gets to project their feelings onto their score (some are happy with a 75) and gives them a way out ("ehh ok I guess").
It's implicit in these instructions that asking "how did the exam go?" is appropriate for the tutor.

Well, the are two sides to the answer. It's either the exam went well or it didn't. If it didn't, I am not sure your tutee will be comfortable to tell you about it. Another thing is that your tutee may also expect you to ask how it went, to show you care. So it depends. Regardless though, it's not a bad thing to ask a student how the exam went.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Does gold open-access with article processing charge (APC) really help access to science and save taxpayer money?
I value the reputation of the journals to which I submit articles. Mostly, I wish to confront my work with the most competent researchers in my field through peer review, in order to have an expert opinion on its quality. In my field, the best ranked/most reputable journals are dominantly subscription-based (although all offer 3'000$ open access (OA) options, that not many researcher choose). So I give priority to reputation/quality over OA policy. On the other hand, I'm well aware that subscription journals are a big weight on universities budget.
So, does OA* really help access to science and save taxpayer money?
The arguments I know about that suggest it does:
I'm aware of the arguments (very efficiently publicized by big OA publishers like Frontiers) that OA is good karma because it gives access to science 'for free'. People argue that when the taxpayers pay for research, they should also get to read the results without paying a subscription.
Reasons for which I'm not sure it does:
I believe that if every article costs 500-3000$ just to publish, and the total number of article explodes, taxpayers (or private scientific funding agencies) are not winning a lot in the change. I also think that people can go to the library to get access to research.
Isn't it reasonable to use the options that we have to freely give access to our work (self-archiving, sending preprint to people who ask politely, etc.).
ps. I published in both OA and subscription-based, and I will gladly submit to OA journals if they end up being the highest quality ones in my field.
*I'm talking about OA journals with article processing charge. I'm aware of the existence of completely free OA journals (funded by universities I presume), but they are only relevant for a few research topics. And not mine.
Edit apparently the science funding agencies of the UK think that gold OA is not that good of a strategy.

Not all open access journals require author fees.

There is absolutely no reason every article should cost $500 to $3000 just to publish. By the way, you may want to look at the example of the Journal of Machine Learning Research.

Can we call "OA with processing charge" "pay-to-publish"? I feel that the expression "open access" is used to mean too many things and it would be better if we phased it out completely.

There is one reason: copyediting.  As far as I know, no journal does copyediting and also costs less than $40/page.  I don't think that copyediting is worth the price, but it is a reason for the cost.  Also outside of the mathematical sciences some significant typesetting costs are inevitable.

@FedericoPoloni The established term for this is gold open access.  See http://en.wikipedia.org/wiki/Open_access#Implementation_practices.  I've edited the title accordingly.

@NoahSnyder: http://theoryofcomputing.org/ does copyediting and costs nothing.

+1: What a great question.  It's questions like this that make me want to be a part of this site.  (You know you've asked a good question on academia.SE when "Ask your advisor!" is not a plausible answer...)

I feel this question might be mostly about hybrid OA rather than gold OA in general. Fully OA journals are very different and they work in various ways. Hybrid OA has tons of problems: http://rossmounce.co.uk/2017/02/20/hybrid-open-access-is-unreliable/  http://bjoern.brembs.net/2016/04/how-gold-open-access-may-make-things-worse/

Sounds like an unsustainable system. Taxpayers pay a lot to support research, much of which never benefits them directly, yet publishers provide added value and that's not paid for by taxes.

I also think that people can go to the library to get access to research.

You're assuming that libraries can pay for access. That's not the case anymore. Even Harvard univerity, one of the richest in the world, can't pay for all the journals its researchers need. I think none of the Universities I know have access to all the journals it needs. So, you can imagine a public library won't grant access to all the existing literature.
That's even worse in developing/not too rich countries. In this case, you can notice that most Open Access (OA) journals adapt the cost of publication to the wealth of the country the article comes from (for example Plos).
It can also be a problem for small enterprises, that aren't very rich, so they can't subscribe to journals and have to pay "per view", but need access to the latest research in order to innovate. So, non-OA journals are an impediment to the technological progress too.
And I will also add the fact that, even in rich countries, it is not always that easy to go to a library. For example, when answering here on Stack Exchange, I try to add links to research articles which can be more precise than my own answer. If the OP is really very interested in a complete understanding of the answer, he could go to a library. But in most cases, if he doesn't have access to an article through the Internet, it will just waste an opportunity for him to learn.

I published in both OA and subscription-based, and I will gladly submit to OA journals if they end up being the highest quality ones in my field.

However, you're pointing to a real problem here. If the "best" journals are not OA, do you have to compromise your career (or your students') to publish in an OA journal? In fact, some people would answer that the Impact Factor-based ranking of journals doesn't make much sense (see for example this article). And it is one of the reasons for the creation of Plos One, a "mega-journal" accepting articles only based on their scientific value, and not on an estimate of the interest its conclusions might have in the future. But for sure, this is a hot topic.
And another real problem here is money. If the Universities have to pay both for keeping access to non-OA journals, and for publishing in OA journals at the same time, it will be even more expensive. No university can afford it. A proposed solution is green Open-Access, where the articles are just put in repositories, and nobody needs to pay neither for publishing, nor for accessing. With a good post-publication peer-review system, this could work. But it also implies a huge paradigm shift, with new problems.

Isn't it reasonable to use the options that we have to freely give access to our work (self-archiving, sending preprint to people who ask politely, etc.).

That is in fact kind of green OA. But, depending on the license you agree with when you publish in a journal, that's not always possible.

You are raising important points, just to clarify, when I say reputable, I do not strictly speak about impact factor (in my fields, top journals have an IF of about 3) but journals respected by the community. As for not so rich countries: I think that OA publisher are well aware of the huge potential in article-processing charges in these areas.

In each of my past jobs I have occasionally run into papers that I cannot access given the databases the university has subscribed to. Sometimes, I ping colleagues elsewhere and find it, which is a real hassle. Other times, if the article was only a "nice to have," I just skip it. In this way, not being freely available will affect the impact of your work (all else being equal). In some quite indirect way, this seems to lower the value that taxpayers are getting.

@EricMarsh 'not being freely available will affect the impact of your work' It may very well be, but this is not the original topic of my question.

As far as I know, Elsevier does not send take-down orders for pre-prints.  They allow those (see http://www.sherpa.ac.uk/romeo/search.php?id=30&fIDnum=%7C).  The actions you've linked to involve cases where authors posted the final journal version.

'A proposed solution is green Open-Access, where the articles are just put in repositories, and nobody needs to pay neither for publishing, nor for accessing. With a good post-publication peer-review system, this could work' Agreed, but how do we fund this? Managing high quality publications and hosting the data for ever securely, with a back-up strategy etc, is obviously not free.

I actually see a shift in favor of green open access, e.g. the new German UrhG. As for gold open access, I haven't done it yet and I'm not likely to do it - instead I use the self-archiving policy. IMHO besides the huge costs the big publishers charge for their gold OA, I do think that this myriad of spamming gold OA journals really threaten the concept - hopefully not the concept of the other OA versions.

'Even Harvard univerity, one of the richest in the world, can't pay for all the journals its researchers need' Or with this statement, they used their position as an influential institution to bring publishers to negotiate subscription fees. I work at Harvard and 2 years after this announcement, I have access to most relevant subscription journals.

(Edited to address Anonymous Mathematician's great remark)
Well, my understanding is that you asked a math question: is it better for the tax payers to have academics publishing in Gold Open-Access, compared to the standard journals? Neglecting the fact that the tax-payer won't have access for free to articles published in regular journals, this could be answered by a comparison between the current closed system (all the costs are concentrated in the library subscriptions of journals) and the open system (all the costs are concentrated in OA journals processing costs).
It is hard to have good figures, so I will make a number of approximations... Feel free to correct/adapt these as you like. I also consider only Harvard - other institutions may give very different outcomes.
So, trusting this link, the total library expenditure for research purpose is 3 750 000 $ /year for roughly 20% of Harvard's collection - in other words, the total yearly spending of Harvard's library for science publications amounts to the mind-boggling 19 000 000 $ / year (!)
Knowing that Harvard has roughly 2000 faculty members cf the Wikipedia page, the total expenditure per faculty is between 9000$ and 9500$ per year.
Given that the typical faculty publish maybe 3 papers per year (depending on the field!), any cost lower than 3000 $ per publication in OA journals is worth the money for the tax payer, as this means that the overall cost per year and per faculty is below 9000 $. Furthermore, according to this article from Nature the true average cost of OA publication is around 2300 $ (with some good journals well below), making the open system a better value for tax payers.

My reading of the $3.75 million figure is that it covers only 20% of the journal Harvard subscribes to ("In 2010, the comparable amount accounted for more than 20% of all periodical subscription costs").  In that case, the spending is more like $9375/year per faculty member.  That would fit pretty well with the $3000 figure.  My understanding is that it is not based on actual costs, but rather is an attempt by publishers to re-capture all the current spending if the model switched from subscriptions to gold open access.  (Fortunately, competition would presumably drive the price down.)

@Anonymous Mathematician: the sentence I based my reasoning on is "Harvard’s annual cost for journals from these providers now approaches $3.75M." - which does not let any room for ambiguity. Also, The Guardian reported exactly the same figure and no comment under that article suggests that it was wrong (here: http://www.theguardian.com/science/2012/apr/24/harvard-university-journal-publishers-prices ).

The key phrase is "these providers".  It refers only to the "certain providers" mentioned in the previous sentence, while the next sentence says that "all periodical subscription costs" are five times larger.  Similarly, the Guardian article refers to "many large journal publishers, which bill the library around $3.5m a year" without saying anything about the total budget (not limited to these particular publishers).

For comparison, http://www.provost.harvard.edu/institutional_research/Provost_-_Harvard_Fact_Book_2009-10_FINAL_new.pdf says that library collection costs were about $35 million/year in 2009.  The Faculty Advisory Council memorandum broke it down the collection costs as 50% journals, so 20% of the journal costs would indeed be about $3.5 million.

@Anonymous Mathematician: You are absolutely right. thank you for correcting me :) I edited the response.

@AnonymousMathematician & Jealie, thanks for your valuable contributions. In fact we could simply trust a company like Elsevier to have done the maths for us. If their APC is 3000$ it's for a reason...

@Jigg: "In fact we could simply trust a company like Elsevier" must be the most ironic thing I've read on this site. :-)

@Shree: I'm not sure if ironic is exactly the word I'd use, but it is certainly "one of the lines I am most glad I did not have a hot beverage in my mouth when reading", yes.  Or: we could trust a company like Elsevier and unfortunately we largely do even though by now it is painfully clear that we shouldn't trust a company like Elsevier any farther than we can throw it.

@ShreevatsaR and Pete, ironic is the word. My point is that if Elsevier charges 3000$ it's because that is more than the average it makes per article with subscriptions. It was a way of saying they did the calculations form this post long before we did.

@Jigg: I stand corrected.  Your use of the term ironic is in accord with the dictionary definition of the word (which I know by heart since it occurs in song in my favorite episode of Futurama).

Of course, there are many subscription journals (notably those published by mathematical societies) with much more economical subscription costs, so that they are a much better value than typical gold OA.

To expand on JeffE's comment: the diamond open access (free for both authors and readers) certainly does benefit the taxpayers while for the golden open access (the author-pays model) it is less clear, as detailed in the answer by AlexIok. A detailed discusion of differences among different kinds of open access can be found e.g. here: http://www.jasonmkelly.com/2013/01/27/green-gold-and-diamond-a-short-primer-on-open-access/
EDIT: To make things clear, this answer was written for the original version of the question that dealt with OA in general rather than with the author-pays model.

Isn't it reasonable to use the options that we have to freely give access to our work (self-archiving, sending preprint to people who ask politely, etc.).

Many academics don't self-archive, especially for non-recent work, and consider the idea of sending a pre-print out - first, this implies that the reader knows that they can ask for this (given you're talking about the general public, I don't think it's a great assumption to make), and second that you'll do so in a timely fashion. Consider the circumstance where you're a faintly scientifically literate family member trying to make sense of what the doctor's are telling you about a loved ones medical condition - it's very possible that sending out a preprint, or a PDF, if you can even find a corresponding author, the email address is still current, etc. will come only after several weeks, which can be extremely frustrating.
Beyond that, if they can't get past the paywall, how do they know if it's worth reaching out to you?
I also think "Will save the taxpayer money" is a little bit of a red herring. The argument I've always heard, and advanced, is not that it will save the tax payer money, but given they have already paid for the reseach, Open Access gives them access to what they paid for.
As to whether or not it will save them money, I think that's a question that changes based on the dynamics of the journal publishing industry. Right now, I'd say the answer is no - in addition to authorship fees, I have yet to see a library be able to drop a major publisher because there's sufficient OA coverage in a field (or group of fields). I suspect the cost savings for individual users not having to pay $50 or whatever it is for access to an article pale in comparison to library subscription fees, mainly because per-article readership is fairly low.
Someday, perhaps, but I think cost is one of the weaker arguments for OA.

Can I rephrase the question "Will OA save the taxpayers money?" to be "Under an author-pays OA system, will the public pay more for the same amount of, or less, research?" I think it is a given that taxpayers deserve access to research they have funded, but the trade off may be that less research gets done - is this trade-off worth it? I'm genuinely curious for a response from someone who has thought about this more than I have, because I'm still trying to form an opinion. Thanks! :-)

@darthbith I'll add some thoughts on that shortly.

Thanks for the comments. I agree that in the short term, cost is not a great argument for OA. The far better argument is the moral one, that the public has already paid for the research and they deserve access to it. It will be interesting to see how the field changes now that the new rules in the UK are in place, or whether there will be much change at all. Thanks again!

'Many academics don't self-archive' well, they should.

Let me add a slightly different point. It's slightly off-topic because this is not OA in any of the colorful meanings, but it is on topic for possibilities to lower costs and get the taxpayers access to published papers:
Here in Germany one reaction to the library subscription costs is that now the DFG negotiates nationwide (not only university libraries) subscriptions with some publishers. I believe the DFG is a big enough player to stand their ground when haggling with Springer, Elsevier & Co.
I found some numbers:

total costs for scientific libraries (Germany-wide): 793 M€ / a
therof infrastructure costs for buildings and staff: 548 M€ / a
for buying books and journals:  245 M€ / a
the Nationallizenzen cost ca. 110 M€ / a (according to the text linked above they started with much less)
I did not find numbers on how much subscription costs the libraries saved. All in all, I assume that the total costs probably stayed roughly the same (at least that's what I hope) but the availability is increased.

The nice thing from taxpayer's point of view is that everyone can access these papers without the need even to go the next university library (need to get a login, though but that's not difficult).

On the topic of save taxpayer money, I think it is important to consider the question - where does the money to pay the publisher come from, in an "author-pays" system? Presumably, PIs will have to add the cost of publishing into the budget they submit in grant proposals. This may increase the amount the grant giver is required to give PIs, or perhaps they will be able to do less research for a given grant. Either way, the taxpayer may end up paying more for research, and it may be research they are not interested in, so even if they can access it all freely, they may not care to.
Now the counterargument to this is that if universities are no longer required to pay subscription fees, the amount they take from a grant should be reduced, and so the PI will end up with more or less the same amount of money as under the old system. I think this may eventually be the case, but the transition time will probably be somewhat difficult, and I would imagine that universities will be loath to give up a very steady source of funding - they will just find some other use for the money if not subscription fees.

In the UK, PIs are no longer allowed to add publishing costs to research council proposals. Instead, universities are given block grants for this purpose. In my experience these grants can run out towards the end of the year....
It's also worth noting one of the downsides of the author-pays model that hasn't been mentioned thus far: that it becomes unaffordable for somebody to publish research if they are not part of a university.

There're two completely different aspects to your question. "Help access to science" is completely different from "save taxpayer money", as will be apparent in the following.
Help access to science: this is relatively straightforward. The answer is yes, as you can see from Wiki:

OA articles are generally viewed online and downloaded more often than paywalled articles and that readership continues for longer. Readership is especially higher in demographics that typically lack access to subscription journals (in addition to the general population, this includes many medical practitioners, patient groups, policymakers, non-profit sector workers, industry researchers, and independent researchers).

Save taxpayer money: this aspect is much more complex, because where all the money in publishing goes to is itself complex, but I'll go ahead and venture the answer "not really".
The reasoning is pretty intuitive. Publishing involves lots of things, and those things cost money. So to actually save money, you need to either do the same thing for less money, or don't do the thing at all.
So the question becomes "is it cheaper for the publisher to publish an OA article than a subscription article?". Drawing on my experience doing editorial work in academic publishing, I am quite confident that the answer is "no". The production process is 100% the same, except that at the end, one bills the author for the APC. Things like the editorial management system, the journal's website, the indexing - they are all the same.
Hence any savings come from other aspects of publishing, like marketing or distribution. Here OA definitely saves on distribution, since OA doesn't involve print journals and therefore doesn't need to be distributed. But then again, it's generally already possible to subscribe to electronic journals only (i.e., you do not request the print journal if you don't want it), which would also eliminate distribution costs. Marketing is a different animal and I am not an expert on it, but my impression is that it really isn't that different. You have $X in budget (in turn this is indexed to the journal's revenue) and you use all of it. Sure you might do something different when promoting an OA journal, but ultimately you still use all the budget.
One thing that isn't complex is whether the publisher gets less revenue if all the journals convert completely to OA. This can be easily calculated by taking the journal's subscription revenue and comparing that to the expected revenue if every paper paid the APC. Here the answer is usually "no"; the publisher does not lose revenue if everything converts to OA. In fact they probably gain revenue. This differential is a big part of the reason why publishers are able to waive OA fees for some authors.
So the answer is not really - gold open access simply shifts the money around. To actually save taxpayer money, one needs to do what I alluded to in the second paragraph: either do the same thing for less money, or don't do it at all.


text:
Preserving ownership of authorship in the period after leaving a position and before journal submission
Background:
I am currently working on a paper as a first author with 3 other members.
My tenure with the research institute ends on the end of this month and I have no intention to continue any working relationship due to the very complex political environment and "back-scratching" among upper management in this research institute I am in, plus my observations of other ethical issues.
However, I intend to submit this paper to a journal after the end of my tenure. This journal has an associated conference that has deadline submission on the 15th July 2018. For this particular conference, an acceptances of a paper for this conference would enable a direct proceeding to its associated journal.
I have a valid concern aimed at the senior research fellow (No PhD), whom I report to and who is also the last author of this paper, due to strong corroborated anecdotes (credit stealing included) from multiple employees. As far as facts is concerned, he comes from industry after 20 years, without a PhD, and sorely lacks technical skills in my observation.
This further cements my concern and I am aware that there exists a possibility that my concerns may be misguided.
Measures taken:
1) I have created an official email confirming the roles, responsibilities and order of authorship of each team member involved in this project. The email has been acknowledged by each individual team member including aforementioned senior research fellow/ programme director (without a PhD).
His role is to review to review the draft before my submission (possible and probably potential red flag?).
He has not acknowledged nor mentioned anything in his reply about getting back to me with changes to the draft.
2) I intend to submit my paper to an open journal arXiv before submitting any draft to this senior research fellow.
3) 2) is followed by a submission of a draft to senior research fellow with a co-correspondence to the integrity office, worded in a diplomatic manner.
Are these three steps sufficient? What more should I be aware of?
Edit: The email also serves as a centralised communication where any work done by must submitted to that email.

re 2) I tend to think it is neither wise nor ethical to submit anything to arXiv without the consent of all co-authors, so that is probably not an option.

@Alice I am close to completion of paper, not close to submission; journal's call for paper opens in October.
How do I say 'No' when I will not be in the research institute to ensure control? I see no reasonable way to put a pristine draft in his hands, leave the research institute without an iota of doubts when the research fellow in question has at least 2 isolated case of hijacking paper?
Edit: I have stated that that his lack of technical skills are from my direct observation.

This only makes sense if the guy could bully you into not bringing up formal complaints if he striked you from the authors list. But you are leaving, so how would he do that? He could falsify a lot of records, but that brings him into jail if it fails, as it will if you sign your emails and keep copies. Unless he's a mad idiot, he's not going to risk that.

In the world of patent, researchers establish priority in the following way. They keep a bound notebook (no loose-leaf) so that pages can't be added between other pages. Whenever they have a good idea for which they want to establish priority they make a dated complete note of the idea. They then get a colleague to date and sign their note. At some companies most employees always have this patent book with them so they can record ideas as they occur.
Then, if another person somewhere tries to patent the idea, they can present the patent book as evidence of prior art. The other person in this case may be completely unknown to you, but for patent, priority is pretty much the whole game.
You can do something like this yourself, if you are unsure. It needn't be confrontational to your co workers. Make a signed and dated (paper) copy of each version of the paper that you work on and have a non-involved but trusted colleague sign and date it. You can even leave them with a signed and dated copy so that you each have one.
The existence of these copies protects you a bit from being excluded. But in the absence of a problem, they are just private notes and so non-confrontational.
For your future, you are likely better off with cordial relations with your co-authors. It may even turn out that they are proud of their association with you.

Hi Buffy, your method appears to be similar to what I propositioned.
I created an email, indicating the role, responsibilities of each member and their corresponding authorship.
The email also serves as a first - stop "depository" for any work progress - no matter how minute - done by co-authors.
It appears that my proposition is in the right direction.

@Physkid, get a neutral third party involved: the signer. Make it non-alterable: paper. In an extreme case, use a lawyer as the third party, but you need to be pretty convinced of problems before you need that.

I am afraid there is no neutral party I can count on.
This is an Asian-oriented working environment with people not willing to risk prospects or livelihood; the political relation on the upper echelon is also very complex.
I have sent all email attachment to the integrity office to have a general discussion about how my work can be protected and be advised of any necessary steps that should be taken.


text:
Reporting a student who cheats
Firstly, I do not believe this to be a duplicate of the related recently posted question due to the key fact that that user was anonymous to his class and I am not.
This has happened 3 times now. While taking standardized tests, someone cheats. These aren't just classroom tests, but rather officially proctored, nation-wide tests. The first time, some students had significantly more time, both starting before the official call to start, and ending after the official end. The Proctor was pretty relaxed, and either didn't notice / didn't care. The second time, someone's phone went off twice, and on full volume (the student in question had to stand up and manually turn the phone off). The Proctor did not alert his superiors, although many students had lost a significant amount of time and the incident negatively impacted our scores. We were told beforehand that any distractions during would be an immediate invalidation of the test (we even had to keep our phones in a box), but this seemed to go unnoticed. The third time was similar.
I complained to my peers afterward, and they all told me not to tell anyone or do anything for fear that it would cancel or negatively impact our scores (most of them did well). I didn't feel comfortable with this, but I didn't report anything both for fear of both my reputation being impacted, and for fear of my scores being cancelled on a test that I studied significantly for and potentially did well on. If I were to report any of these incidents, most people would immediately know that it was me who had filed the report, and I would be severely socially ostracised. I did/do not desire this at all. In hindsight, I should have kept it to myself, not expressed my worries to my friends / acquaintances, but unfortunately this did not happen.
In a situation like this, what is the appropriate course of action post-disclosure? Report the student in question and risk negative reputation, a cancellation of scores, and hard work put in (but do the right thing and have fairness reign), or keep the cheating to oneself (and preserve reputation but carry a dishonest weight)?

"The first time, some students had significantly more time": Do you know that they might have been allotted more time because of a disability?

They started while the proctor was reading instructions, closing their book when he looked around. It was clear that they were cheating. They worked through the 'please close your test books now.' The proctor also asks at the beginning if anybody has extra-time needs etc.

Based on your comments, this is a question about college admission exams (which are nominally off-topic here), However, given the nature of the question could still be applied to exams at all educational levels, I'd leave this question open.

Yes, sometimes students are assigned more time because of some disability. A few years ago, when teaching at a university in Canada, the university notified me that a student provided a medical letter proving that he has some issues with concentration, and that I should give him extra time due to his disability. It is quite possible that this happened here and in that case, the university will not tell the other students.

I know for a fact that is not what happened, but anyway, this discussion is beside the original question.

Simply that the ramifications are the same.

If you really wanted to do something then you should have voiced your points to the relevant authority (head proctor, Dean whoever) at the end of the exam.
Speaking to your peers after - in the canteen , bar wherever, is just a discussion / rant that is not productive in reducing / controlling cheating, but dooes allow you and your colleagues to relieve stress after the exam.

I don't know in which country you live. If a phone ring, this is not cheating because a phone that rings does not provide any information to a student. However, if a student is using his phone to look up at information on the internet, take phone calls or send messages, or look at answers stored on his phone, this is of course cheating. So if the phone just rings, I don't think that it really matters.
About ending after the official end, if it is just a few minutes, maybe that the professor just decided to give a few more minutes to give a chance to those who could not finish the exam on time. I don't know about your country, but in my native country (Canada), it is not something unusual that a professor will give 5 more minutes to students if he sees that many of them have not finished the exam. In that case, this would not be called cheating, as long as every student can have this extra time.
So, if you think that it is cheating, then you can report it (if you think you are OK with the possible consequences). But from your description, I am not sure that we can really call this cheating.

Having your phone ring during a high-pressure test situation will break concentration for others. Especially when you have been told to not bring your phone (and/or mute it), this is an obvious case of "I don't really care about anybody but myself", which can (and probably will) negatively impact the score of other students.

@janh   A "high-pressure test" is a test where you are not well-prepared.  The best way to succeed in an exam is to prepare yourself well and sleep well.  If a cell phone ringing for a few seconds bother you in a perhaps 1 or 2 hours test, I think that it means that you are not well prepared.

We were specifically told beforehand to silence our phones and place them in a common box. As janh said, this disturbs everybody's concentration and will affect scores. As for the extra time, these are nationwide tests. Millions are taking it on the same time, and 5-20 extra minutes has a significant impact.

Sorry, I live in the United States. Massachusetts.


text:
Applying to PhD programs in mathematics: would a letter of recommendation from my department chair at the community college be of any advantage?
I finished my MS in mathematics 5 years ago.  Over these years I have been teaching at a community college (primarily calculus 1,2,3 with analytical geometry and Ordinary Diff. Eqs).  When I was in my masters program I was having trouble narrowing my interests and decided to stop at my masters and start teaching. During this time as an instructor I have become very interested in some applied mathematics (biology in particular).  I plan to apply to several PhD programs in the near future.   With that said, I didn't keep in touch with too many people from the university I attended.  I did stay in touch with a couple of my professors (on a minimal basis) and plan to ask them for letters of recommendation.
My questions...
Would a letter of recommendation from my department chair at the community college be of any advantage (and even suffice as 1 of the 3 required)?  Or should I call a professor from 5-7 years ago that may remember the grade they gave me?  To me the latter seems very generic and I feel my department chair could say more about my dedication to mathematics and teaching.
Thanks!

Does your department chair have a Ph.D.?  That could make a difference, since the admissions committee may wonder whether someone without a Ph.D. really knows what is needed to succeed in a Ph.D. program (so if you have a choice between several colleagues to ask for a recommendation, I'd choose one with a Ph.D.).

I was accepted into a number of Computer Engineering PhD programs with recommendations from the following people:

My then-current department chair at the high school where I taught physics and computer science.
A professor from the graduate education program where I got my Master's degree in teaching.
A professor who taught "how to teach physics" courses at another university, where I had been taking a series of the courses in order to become a better physics teacher.

I would have loved to get recommendation letters from professors from my undergraduate engineering curriculum, but my degree was from 15 years prior, and no one would have remembered me, nor been able to write anything substantial.
The letters I did get gave detailed information about my work performance from a teaching perspective for technical classes, and from a learning perspective in (somewhat) technically-minded classes.
Bottom line: get letters from people who can comment on your ability to do research, if possible, but more importantly from people who know you well and can add information to help a committee decide on whether or not to accept you.

As a "non-traditional applicant," you will be evaluated more on your work experience, and less on your coursework than most. So a letter from your department chair where you teach would be very helpful.
Fortunately, your work experience is very germane to your graduate study aspirations. I (and most others) can see how an interest in "applied mathematics (biology in particular)" grew out your your teaching calculus, analytic geometry, and differential equations. (And there's the old saying, "those that don't want to practice, teach. Those that don't want to teach, do research.")
Even in a research-oriented graduate program, teaching ability is a "tiebreaker." In your case, with your heavy experience, a potential "deal maker." Graduate students are expected to do research first, but teaching, second. You already offer the teaching "bird in hand," and if someone has doubts about your academic background, the likely thinking is that since you can teach this stuff, you're not likely to be bad.
While research earns the advancement, teaching "earns your keep." You may take particular interest in programs where there are tenured associate professors, people who can't get promoted to full professor based on research, but get tenure based on teaching ability.


text:
Is it better to have a single-author paper or a joint-authored paper?
I am a new graduate student and I am about to start writing my first paper. Some of my adviser's other students have been working on similar topic to what I have been working on and he has been pushing us to combine our results into one paper. However, I feel my results could be a paper on their own. I want to start beefing up my CV so that I can get extra funding and, hopefully down the road, a research position but I am afraid that if I am only a coauthor on a paper it won't look as good as if I am the sole author (especially since I worked completely on my own for my section).
So my question is: would it be better to try and publish a paper in which I am the sole author or would it be better to try and publish a slightly better paper in which I have 2 or 3 additional coauthors? Do funding selection committees and the like give precedence to people with papers that they are sole authors over ones who have coauthors?
Edit: My field is math, in case this matters.

Have you already asked your advisor?

Why not do both?  You write a paper with them as a co-author and they write a paper with you as a co-author.  Win-win situation.  The paper has some common grounds but your specialities hopefully vary enough so you can focus on different topics in-depth, thus having enough material for two papers.

You should really listen to what your advisor says. "...he has been pushing us to combine our results into one paper." That about says it. Your advisor knows what works and what doesn't work as a paper in your field. He also knows (presumably) about the scope of your work and how it fits into what you and the other students have been doing.
There is little downside to this. The importance of the paper to your career has far more to do with how well received the paper is than with how many authors there are. Having more authors means the paper is stronger, means you have a network of people to help rewrite and deal with any negative reviews you may get, and (as suggested in Peter's answers) it shows you can collaborate with others.
It would not hurt to bring this up with your advisor, make your point (ask your question), and see how the advisor reacts.

That last line (either you trust ... or not ... get a new advisor) is perhaps a bit extreme. There is room for some disagreement with an adviser being you need to find a new one.

The way authorships count varies substantially between fields. You therefore need to figure out how things are in yours. Multi-author papers are commonplace in most fields today and in some (mine included) there is almost a negative to be sole author (it seems as if you do not collaborate). This view strongly depends on what kind of paper/study it is.
Anyway, benefits with co-authorships is that your name becomes associated with others. If it is only with your fellow graduate students, the value may be somewhat limited but if you are co-authoring with someone who is well known and respected, the value is much larger.
In your case, the way you have described it, it seems silly to put your research into another paper if it can stand alone. If the joint paper is likely to become a benchmark paper and get lots of attention, then being part of it may not be a bad idea. So you see that it really is a problem of assessing how you can optinise your gain from it as well as how much the science will gain from a colaborative paper where all parts are present. One way to resolve such issues is sometimes to write several papers where the group is present on all but where the first author varies so that your own work is accredited you but the joint effort is also acknowledged.
These kinds of decisions are always tricky and, in my opinion, depend on how the work can be divided up without losing strength and impact. You should definitely bring this to the table and discuss the options with your peers.

but if you are co-authoring with someone who is well known and respected, the value is much larger — This is not necessarily true.  If you only publish with people who are well-known, you may develop a reputation for riding other people's coat-tails.  (This is why I insist that my PhD students publish at least one paper without me before they finish.)

True. In this case it is from a graduate students perspective which of course deserves to be emphasized.

The relevant questions should be: What have those other people done regarding your own research? Are their contributions worth adding them as coauthors? These are the questions that you should be thinking about. From what I read from your post, it seems to me that the other people did not contribute much to your research, and you feel that you should publish the paper on your own. What confuses you is "the dark side of the force:"
"Do funding selection committees and the like give precedence to people with papers that they are sole authors over ones who have coauthors?"
The thoughts that surround this question are very serious issues (c.f. the current ethical standards of academia), and you should think about it. I think the answer of the paraphrased question above should never be a determining factor on whether you should publish that paper on your own or with coauthors. You have to first form your own ethics depending on what you think is true/right/just, and pursue that direction regardless of the monetary/fundetary/titletary disadvantages that it brings within.

Although, you have a valid point, it does not quite pertain to the question at hand, which is what the pros and cons are of combining results in a joint paper.

It is better to have a single-authored paper than a joint-authored paper. But it's better to have a joint-authored paper than nothing at all. Given the difficulty of getting papers published, joint is probably the way to go here.

I do not subscribe to single authorship. No man is an island. I strongly believe that there is power in team work (co-authorship) than single authors. You need to bring in different reasearchers from different faculties for you to have a QUALITY ARTICLE for publication.

Steven Weinberg's A Model of Leptons turned out to be pretty important too...

I guess I’ll just toss out 20% of my papers then.

OP is in math. In math at least there are a lot of single author papers of very high quality.  There are also others with other authors. There's no special reason to think that coauthors are necessary. Is it possible that you are making this conclusion because this is the norm in your field? If so, what is your field?


text:
Is it desirable to compliment a seminar speaker before asking a question?
Some people, when asking a question at the end of a seminar, make comments on the talk first along the lines of "great talk," "really enjoyed this talk," or similar phrases. Is this a desirable thing to do? I've noticed that most people don't do this, but some of my favorite scientists do.

Great question, @AnonymousPostdoc.

My personal preference is not to offer a compliment in this setting.  It often strikes me as less sincere (off-handed or perfunctory).  If I really want to compliment someone, I tend to catch up with them later and start with something like "I really enjoyed your talk.  If you have a minute to talk, I have a question for you about..."  On the other hand, I know that some people feel like asking questions (especially if they are critical of some aspect of the work) can feel hostile, and so they find the compliment as a good way to off-set that.

Totally agree. I groan inwards every single time somebody does that. Usually, after conferences, my inner voice is sore.

If it's your honest opinion, then I would compliment the talk. However, I wouldn't do it just to be polite. There is no need for false kindness.

I would only do this for a talk I liked.

When asking a question, it is desirable to explicitly establish a non-confrontational tone.  It is natural and common (though of course not correct) to interpret even well-meaning questions in an antagonistic way.  If the speaker feels threatened, they will be less able to focus on the content of the question and may instead become defensive.  A question that is interpreted as non-confrontational is therefore likely to get a better answer.
Complimenting the speaker is one way to make your subsequent question non-confrontational, and is a good idea as long as you are sincere.  Other ways include saying something nice about the topic itself ("you're studying a very interesting question"), smiling, and carefully controlling your tone of voice.  These are especially important if your question amounts to a criticism of the presented material.

Yes, and tone of voice and body language matter enormously. The relative status of the speaker and the questioner matter enormously.

I think if you reason why you compliment the person, like "I really enjoyed your talk because [state your specific reason here]", it will always be warmly accepted.

The one drawback is that insecure, literal-minded people may worry that it's an implicit insult (the talk wasn't good to praise for its own merits, but at least the subject is worthwhile).

@AnonymousMathematician My guess is that, depending on your country, it may or may not be seen as an insult.

I have edited the answer because it was too ambiguous. I meant that you should state specifically why you like the talk.

I agree with the other posters.
Personally, I try to make my tone of voice, attitude and choice of words respectful when asking a question while the conference is in session (and of course otherwise). I try to indicate indirectly that I enjoyed the talk (if indeed I did), without offering a direct compliment.
You note your favourite scientists being complimentary to speakers. I expect that these scientists are well-established, well-regarded and that they know that any praise from them would be a particular boost to, in particular, more junior scientists.

It is not desirable, but you can do it if you want. But do it shortly, because there is not a lot of time for questions after a talk.
Personally, I think that saving the compliment as a way to start a discussion later with the speaker is preferable.
To tell the truth, I also think that, except for clarification requests, questions are better asked in a discussion with the speaker, after the session. This is the only way to have complete and clear answers.

Somewhat like @Dan C suggested...
If you really felt inspired and got something new from the talk you should offer verbal appreciation. If you very much liked the presentation and is relevant to your research, it would be a good idea to talk in person.


text:
Extending a result submitted to a conference before acceptance/rejection notification
I recently submitted a paper to a conference whose notification of acceptance/rejection is due to 3 months from now. However I realize that I can extend my results in such a way that it gets much more general and such that the results of the previous paper follows as a special case. The generalization however is non-trivial, in the sense that I will need much more advanced and esoteric techniques, and somewhat more 20 pages to write it properly. It also fits in the scope of a conference whose deadline is in 2 months.  Here are my options.
1) Put the first paper at arxiv. Write the second paper citing it and showing where things get different. Submit the second paper. But then the second paper doesn't get self contained enough.
2) Put the first paper at arxiv. Make the second paper self contained by rewriting all results that I need from the first one, but specifying that it is a generalization of the first one. Submit the second paper.
3) Write the second paper and wait for the result of the first conference. If accepted, write the second paper as an independent extension of the first one. If rejected, merge everything into a new piece of work and resubmit to a new conference whose deadline is in 5 months.
Problems:
a) There are two groups working in a very related subject, and I'm afraid putting the first paper in arxiv would lead them to a similar generalization before me. So I wonder If I should wait to put the first paper on arxiv until having finished the second one.
b) If I write the second paper and put it at arxiv before the notification from the conference, could this make the first paper be rejected because the program committee would argue that there is a possible generalization of it? Even though highly non-trivial?
c) If I submit the second paper to a new conference but don't put it on arxiv, would I fall in the case of double submission?
What is the best way to proceed in this case? I believe several researchers might have faced similar situations.

My preference would be for option 3)

My preference would be for option 3 and put the paper on ArXiv.  And why aren't you just collaborating with the other two groups?

@OneMoreAcademic Is the conference fine with you putting your results on ArXiv before/during/after the conference? What conference is this, if I may ask? I have had this thought about several conference papers that I submitted to the ASME but I could never find information about whether or not I could submit a preprint to ArXiv.

Firstly, this question is relevant to your considerations.
In my community it is quite common to publish a (possibly extended/revised) submitted work as a technical report or a pre-print right after, or before the conference submission. The idea is to get a useful reference for future work falling exactly in the period between submission, notification and hopefully publication. ArXiv, or a TR with ISSN is fine for that.
Having said that, the option 2 is something I myself often resort to. Also to consider with this option, if the publication date of the "generalization" is after the submission deadline, such a rejection would be baseless.
As you yourself note, option 1 leads to a non-self-encapsulated paper and option 3, even though fine and correct, prolongs the period between invention and publication.

Researcher does not just stop because you submitted a conference paper. In many fields arxiv is not an option. Waiting when you do not need to is not an option either. But you have another option. Incorporate enough of your first paper in a second one for it to be understandable, and cite the unpublished work for the details. By the time the second paper is published, the first one should be out and the full reference can be included.

cite the unpublished work for the details — Do not do this without putting the first paper on the web.  If the second paper relies on results or techniques that are only described in an unpublished manuscript, the reader has no way to verify, even in principle, that those results are correct, relevant, or even described correctly.  That's sufficient reason to reject the second paper.

I had the same situation where we proposed a method and then generalized it later.
What I did (not the best option though) is wrote two papers (yes they overlap in almost 30% of the content) then submitted them for two different conferences.
still waiting for the feedback.


text:
Are there studies testing whether academia rewards researchers based on number of publications?
I would like to know whether any scientific study has tested a hypothesis relating number of publications to career advancement.
It is often suggested that hiring and promotion decisions at research institutions are based heavily on the number of publications produced.  That is, one is more likely to get a tenure-track position and subsequently to get tenure if one has a larger number of publications (independent of quality).  One could also introduce an opposing argument that large numbers of publications are negatively correlated with quality of work and therefore negatively impact career advancement.  Are there any studies supporting either of these views?
Some remarks: I understand well that even if there is correlation it would not imply causation.  Also, I suspect that the relation between publication quantity and career advancement is very different between disciplines and between world regions.  I would be interested in studies that address the question globally or among some subset of academe.
I believe this question is different from Whether to publish one big paper or many smaller papers for a given research project?, since I am asking for general scientific studies rather than opinions.
I am aware that, for many reasons, reaching valid conclusions may be impossible.  I am interested in whether it has been attempted.

Note also the reversed causality effect. Since successful researchers tend to have long list of publication, it is often falsely assumed that it is the explaining variable.

Interesting question. However, I assume you should make sure to think about survivor bias here - if having a bad publication record during your PhD makes you inelligible for TT and postdocs, and hence those people quit after a PhD, you will only see good track records when looking at tenure stats.

This will be hard. How do you operationalize "quality of work", if not through some publication-related metric like citations? If your success in obtaining grants is partly driven by your publications (because that's how people hear your name), then grants acquired will also be correlated with publications, without necessarily being a measure of "quality of work". Bottom line: I'm afraid there are so many issues with measurement and confounding that I would take any results of such a study with a large grain of salt.

Is this relevant: http://academia.stackexchange.com/a/3155/929

Do we need studies? I've had several tenure and promotion committees outright state a needed number of publications.

There's quite a bit of this sort of thing in economics. One early and now classic study, Katz 1973, performs a regression of salary on the number of books, articles, "excellent articles", and other variables associated with a faculty member, and finds what seems to me to be very low impact of publication on annual salary even in 1973 dollars: an article is worth $18 and an excellent article worth $102 in annual salary.
A later study Diamond 1986, estimates the marginal value of a citation on lifetime salary: somewhere in the $50 to $1300 range (!!).  Note that is in economics where citations are somewhat stingy, back before people started gaming citation rates as much as they do today.
Since there has been a huge volume of publications on the determinants of faculty salary within the economics literature. For some reason, this particular labor market has been of exceptional interest to academic economists.

It's interesting to imagine oneself as distributing money when citing other people's work.

In biology, there was a recent study relating publication metrics (including quantity of publications) to odds of becoming a PI.  A summary of the article is here and the full article is here.

Can you provide a bit more of a summary of this article in your answer please?  Answers that depend almost entirely on an external resource have a tendency to decay badly over time.


text:
Money as a factor in PhD admissions
I'm wondering to what extent money is a factor in phd admissions?  For example, does an admissions committee limit the number of students admitted in a year depending on how much the department can afford that year? and approximately what percentage of the departments funds go to graduate funding(I am asking mostly in regards to US universities that rank in the top 20 for math.)?
And also, are qualified students who are less expensive more likely to get admitted because it wont cost the department much, if anything at all, since at many institutions certain groups receive their funding from the central administration rather than the department(such as women and minorities)?
Below is a source where the writer says

Even as faculty members on committees expressed philosophical commitment to diversity, Posselt observed financial motivations at play. Some universities offer extra funds for minority graduate students, so that a fellowship might be paid for from general university funds and not departmental funds. Where such incentives exist, they appear to have a strong impact, Posselt writes.

and in What do admission committees look for in a diversity essay?, Paul Garrett says:

being a woman in a STEM field (Science, Tech, Engineering, Math), or of ethnic origin other than northwestern European . . . opens certain money-pots to both the department and to the individual.

You have too many questions and most of them depend on the country and/or university. There are also a few misconceptions in your post regarding funding and costs of a PhD.

I sort of deliberately asked many questions in my first paragraph not to elicit a response to each question but to get a better general understanding of how money factors into phd admissions.  What misconceptions?

"... since at many institutions certain groups (women and minorities) receive their funding from the central administration rather than the department." I have never heard of this practice, could you name such an institution?

I edited my answers with credible sources where I got the information from

@johnfowles For example, where funding comes from (it is not always the department) and costs associated with a PhD (math students also need various equipment).

@astronat I know of a couple of situations in the US where a few grad student slots are either reserved for URGs or URGs are given preferential admission. In these particular situations I don't think there is additional funding coming from above the department, but it's possible. I do know this happens for faculty hiring.

Anecdotally, I don't think "cost" enters too much into US graduate admissions decisions, with the possible exception of international students from certain countries. The additional "money-pots" might refer to designated university fellowships for URGs rather than standard grad funding.

@ElizabethHenning Are the slots that you mentioned for specific groups or general URGs?

@johnfowles The ones I know of are for general URGs meaning gender and/or URM ethnicity. That is, they are not specifically earmarked for Latina women or somesuch. Fellowships OTOH are often specifically designated for Latina women, etc.

Top-ranked schools generally commit to offering accepted candidates a certain level of support during their graduate candidacies. Therefore, finances must play a role in how many students they can afford to admit: if you only have sufficient financial resources to support 30 students, and 40 enroll, you're in for a bit of trouble. Thus, the students who are most desirable are those who can provide their own funding, in part or in whole, via external or internal fellowships or "matching funds" from the department. This frees up money that can be used on other students. (I would imagine that in math, much of this funding is awarded in the form of teaching assistantships rather than RA-type positions.)
This makes deciding how many students to admit a difficult challenge. Top students will have competing offers, and thus universities need to admit enough students to make sure they fulfill their research and teaching needs, but need to not be overly generous in making offers, in case yields exceed expectations.
As far as diversity goes, I agree with the assessments in the article you linked to: diversity only comes to play after candidates have cleared the qualification bar.


text:
What should I do if I realize there is a minor error in a paper I submitted?
I have submitted a research article and later realized that it has a slight error.  The paper is now under review. I have proposed a few theorems; one theorem contains a slight error that can easily be removed. The methodology is correct. Would this cause the rejection of my paper?

I would contact the editor and point out the problem. The editor might be able to convey the issue to the reviewers. If the process has come too far you might get a reject but you could still contact the editor explaning your problem and ask if the paper could be reconsidered.

@PeterJansson Is there more chances of getting rejection? Will they not consider my other contributions and idea presented in the paper?

Everything depends on how serious the problem is in terms of affecting any of your conclusions. If you do not do anything, nothing might happen, so it is a judgement call. If the correction helps anyone understanding the paper better, I would say you should make the contact. If it is on the level of a typo and does not affect results, it should not be grounds for rejection. Clearly it is impossible toprovide clear distinct recommendations without knowing the details.

@PeterJansson It will not affect the result. More specifically, I have constructed an iteration method of second order where I have given the expression for error estimates. There is one typo in the final error estimate expression. Although it will not affect order of the convergence.

It does not sound like a big problem to me. My original suggestion, however, still stands. You could send off a mail to the editor pointing at the error and making clear that it is of no significance for the peper. The worst that can happen is that you do not get a reply. I would think any editor would be happy to receive an upfront letter like that. I would, however, also like to see others comments on this.

@PeterJansson Thank you very much sir for your valuable suggestions.

In order to answer this question, we need to define some magnitudes of errors.
A small error does not affect the conclusions and if the manuscript was accepted as is could be fixed in the proof stage before the manuscript goes to press.
A minor error does not affect the conclusions but requires too many changes to be made that it could not be fixed in the proof stage.
A substantial error affects the conclusions and would require the manuscript to be re-reviewed.
If you have found a substantial error, you need to contact the editor and request the manuscript be pulled from the review process. You do not want to waste the time of the editor and reviewers. A small error can either be ignored or reported to the editor if you think that the correction will help save the reviewers time. Minor errors are the real problem. There is no easy way to tell the editor/reviewer what is wrong, but an unclear manuscript is likely to get negative reviews. I would suggest contacting the editor and explaining and apologizing for the problem.
The real question should be how did you find the error? What are you doing looking at a manuscript after it has been submitted?

Dear sir it is a matter of small error. It will not affect conclusions. There is one typo in writing the expression for the error estimate. Although it will  not affect my conclusions.

I would then let the editor know. You don't want the reviewers scratching their heads trying to figure out what is going on.

Dear sir wouldn't it will leave bad impact on editor?

@srijan this is not really a discussion site. If you want to discuss the issue, you could try our chat room.

wouldn't it will leave bad impact on editor? — Not as bad as if the reviewer finds the error, or worse, if the error is only discovered post-publication.

"What are you doing looking at a manuscript after it has been submitted?" -- I hope that's sarcastic. If you mean it, the imho obvious answer is: check that you did not make any minor or substantial mistake during the overnighter preceding the deadline. Or prepare your arXiv upload. Or polish some more for the final version you are optimistic enough to assume you'll need.

@Raphael I am serious. I think you should incorporate into your submission process the extra day, or three, to allow you and a colleague to look for mistakes to avoid exactly these types of issues. I also think when you submit something to peer review that if the reviews come back as "publish as is" (not that that happens frequently), that you should not have to tell the editor "I want to do some "additional polishing". As for ArXiv, I don't use it, but I think I would probably prepare both submissions at the same time to keep everything in sync.

@StrongBad Point taken. But then, we all know that there's always another mistake.

What if you have submitted a[n]... article ... that has a slight error?

You're answering your own question. If it's slight, then it's slight, and should not matter much.
Still, to be more practical: If

The error, despite its slightness, means a significant claim is invalid, and
The "distance" from the submitted version to the corrected version is small (e.g. replace a sentence, change a couple of numbers etc.), and
You've just now submitted the paper (i.e. not weeks ago)

then I might describe a correction, in at most one paragraph of text (hopefully much less), and would write the PC chair to ask whether that can be passed on to the reviewers.
In all other cases I'd just wait it out and see.

Would it cause the rejection of my paper?

If the error is indeed slight, then this is very unlikely. But if your theorem says "P = NP" and you typed "=" instead of "!=", then maybe it will be rejected :-)
Seriously, though, the only cases I think this could have any weight is:

Clueless reviewer who loses track of the flow of the paper because of the slight mistake, and thinks you've derailed yourself with it
The slight mistake being accompanied by several other mistakes, slight or otherwise, so the submission is perceived as having numerous mistakes (regardless of their severity).


text:
What does a US university expect of a student applying from the UK?
How understanding are American Top-10 universities of different expectations abroad? In the UK, nearly  nobody publishes anything before they start their PhD. The master courses are much shorter and usually include mostly courses instead of research. We are not expected to do any teaching. I am therefore wondering whether all of this will count against a UK student applying to the US. Personally, I have a very good profile for a UK student (Top of my class in undergrad and masters), but I only have 2 research internships outside of my courses. Is it expected of UK students to achieve the same things as US students applying to the same universities?

Applying to what? Graduate studies? Post-graduate studies?

Applying for a PhD.

Are you at a well-known university? If so, then people at the US universities are likely to know and trust your letter writers.

The same as for any other country, I suppose.

One of the requirements is obviously English. For you, it would mean not to blush when somebody says, "Neat pants!"

This may vary by field; my experience is in mathematics.
Most US students start a PhD program immediately after finishing their bachelor's degree, so they apply during the last year of their undergraduate program.  It is less common to complete a separate master's first, especially in the sciences where PhD students are funded and masters students are typically not.  The first couple of years of a PhD program are usually coursework similar to a masters program (you would probably be able to skip some or most of these courses, if they are comparable to what you have taken).
Therefore, the US students with whom you are competing are mainly undergraduates in the last year of their bachelors program.  At this level a few of them may have published papers, but most will not.  They may have research experience from summer projects, summer internships, independent study or lab work, but it is not usually comparable to graduate research.  Very few of them will have any formal teaching experience; at most they may have worked as teaching assistants, which usually means grading homework.  Some of them may have taken a few graduate-level courses at their undergraduate university, but not to the full extent of a masters degree.
So I don't think you need to be concerned about your level of preparation or experience in comparison with US applicants. If anything, you should be ahead.
As mentioned in comments, at a major US research department there should be people who have either come from UK universities or have experience with them.  If they are not already on the graduate admissions committee, the committee members will consult with them if they have questions.
Good luck!

If you are literally talking Top-10, you will be on equal footing with American applicants, especially with your research internships.
Below that threshold you may well surpass American applicants, as you haven't spent any of your time minoring in side subjects since school.
This may not relate to how well your applications fare, but the larger universities will be well versed in taking on Eurasian applications, and you should expect fair judgement on UKish criteria.

@Gavin, you might even find some professors at those schools whose Alma Mater is your own. There's a lot of crossing the pond in academia, especially among the higher ranked schools.

To continue on @JonathanLandrum's point, if you do find such profs (a) from your university, (b) within your field (biology, right?), anywhere in the US, you could approach them and ask how to best frame your UK experience in your Ph.D. application so that would be easier to understand for the US colleagues. (Addressing the US graduate admissions in their language would also signal that you have done your homework on preparing for the course of the Ph.D., is aware of the expectations, and ready to tackle the challenges.)