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How to respond to my name being included in acknowledgements of incorrect/misleading paper whose authors ignored my recommendations?
My colleagues (grad student + their advisor) from my department approached me, a fourth year PhD student in STEM, for comments on a manuscript written on a topic related to my research.
In two iterations over email, I pointed out serious logical fallacies in their arguments, instances of misleading references and attempts to skirt crucial issues in the paper. Most of the issues in the manuscript are still unresolved but the authors have thanked me for my comments in the acknowledgement section. I'm uncomfortable with my name being included in the acknowledgement section of an incorrect and misleading paper submission.
Would it be wise to politely request for my name to be removed from the acknowledgements?

Not the answer to your question but very related: Do the authors need to ask for permission from institutes/companies for including their name in acknowledgement section of their publication? and Is it necessary to ask permission before including someone in the acknowledgements of a research paper?

Did I understand correctly that the paper has not yet been published?

I see nothing wrong with asking the authors to remove your name from the acknowledgments unless they address the concerns you have with the paper (I assume you're not worried about ruffling any feathers).

@Wrzlprmft, yes. The public preprint has been released but the work is yet to be submitted/published.

How acknowledgments work is always a bit of a judgment call, but to me the following principle seems reasonable.

You are free to acknowledge anyone in any paper as long as what you acknowledge them for is factually accurate.  If you have any reason to believe that the acknowledged party might take issue with the factual accuracy of what you write in your acknowledgments, it would be honorable to show them a draft of the paper and ask for their blessing on the wording of the acknowledgment.  If this causes them to ask to be omitted from the acknowledgments, then it seems reasonable to honor this request unless you feel that removing this acknowledgment compromises academic integrity.  (For instance, if you are including significant work of the acknowledged party, then just because they don't want you to mention that does not necessarily make it okay to do so.  This creates a sticky wicket that other questions and answers on this site have addressed.)

I believe it follows from the principle that whether acknowledgments are acceptable depends more on what they acknowledge you for than whether they drop your name or not.  For instance, suppose they thank you for "helpful conversations".  If you did in fact speak (or write...) to them about their work, then if they say the conversation was helpful, how can you argue?
I think that most savvy academics understand that just dropping someone's name in the acknowledgments does not mean that the paper contains their imprimatur.  Nevertheless it is shady to acknowledge someone -- especially someone very famous and eminent -- purely for the cachet that their name may convey to less than savvy readers.  Here is a famous review of Marilyn vos Savant's book on Fermat's Last Theorem that calls out the author along these lines: she acknowledged some very famous mathematicians, who when contacted by her surely did not say anything to indicate that the material in her book was correct (not only does it contain errors, but it contains errors that any practitioner or serious student of mathematics would regard as bizarre).
In the case at hand: I think the OP would be within her rights to mention that she would rather not be acknowledged in the paper.  Whether she wants to indicate that this is because she still finds the work to be significantly flawed depends on all kinds of social and political factors beyond the scope of this answer.  As to that I would only say: in my opinion, simply very politely asking for your name to be removed from the paper without getting into why is probably a higher percentage strategy than indicating that the work is still problematic.
Added: Let me add that the principle above is meant to be on the minimalist side.  In practice, if you think that someone is not going to appreciate being acknowledged in your paper for whatever reason, then unless there are academic integrity issues involved in omitting the acknowledgment it seems wise to do so.  Once I acknowledged a friend of mine in a preprint in a way which was factually accurate but nevertheless embarrassing to him: he simply did not want to be associated with something that he viewed as intellectually trivial.  I took his name out of the later drafts of the paper.  This incident has made me think more carefully about how acknowledgments will be received by the acknowledged party.


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What is the value of journal publications outside academia?
I am an economics PhD student; I'm seeking to wrap up my PhD and do something outside of academia.
If I don't plan on ever being in academia, is there any value (career-wise) for me to get any of my work published in economics journals?
Ideally I'm looking for answers pertaining specifically to economics; but information on other fields is welcome too.
To elaborate (following some comments):
The reason I do not want to stay in academic economics is that too much (though certainly not all) of it is bullshit I cannot believe in. (This of course is just my humble opinion.) If I wanted to stay in the game and do well, I feel I'd be forced to manufacture similar BS that I simply don't believe in.
In other words, doing this PhD was for me a mistake. If and when I do get my PhD, I will not even feel proud about it. But now that I'm near the finish line, I reckon I may as well cross it, if only for the credential.
Right now I'm looking at working for one of the MOOCs. I enjoy teaching and believe that teaching/education is important. But it is also possible that I might do something completely different; I don't quite know yet.
So now I'm thinking: Should I just try to graduate ASAP with the lowest quality work possible? Or should I invest a bit more time and effort to polishing my work up, so that some of it can get published?

The answer to your question may well depend on what "something" is.  Could you be more specific about your plans?

If your "something" isn't related pretty directly to the field you're publishing in, I suspect that publications in that field will serve mostly as evidence that you can write a decent English document. How much that matters will depend on the job.

Economics papers might demonstrate competency for things in the financial industry, investments, or consulting -- depending on topic of course.

Just to add that unlike many other disciplines, in economics, the norm is that most students will not have had a publication by the time they receive their PhD degree. Also, you can get tenure at a decent department with just 3 or 4 good publications. So the standards in terms of quantity of output may be quite different from other disciplines.

If you are planning to work outside academia as a specialist in your field, then you need to have academic knowledge. I don't see any value of having PhD papers publication while you are seeking non-research job positions; but, a wise employer will decide upon your CV.
As far as most of your time as a PhD student has been spent on research, so the employer is probably seeking the out put of the years you spent in university. These are the years you did not have enough freedom to work in industry, so the question here is what this candidate did at the university.
Nobody wants to hire a tired and depressed candidate who did not do well in his studies as a student and it may come to mind that he will be as tired as the years he was student, why to have him in company?!
So by having publications in your CV, you not make your CV comparative and comparable to the other candidates registering for the job; but also you will show that you are an ideal person in every situation. When you attend university, you did your best, finished your degree and have some publications; and the employer becomes more sure about choosing you. Percents bellow is my approximation of the need of publications in job market.
If I want to generally answer your question:

If you are going to be hired somewhere:

100% If it is a research job and related to your studies; then you absolutely need to show your research capabilities. So you need to prove that can do the research chores and then having paper publications is good idea.
80% If it is a research job and not so related to your field, then the title of your papers may have no significant value but you need to show your ability to conduct research and having publications shows that you have the ability and the knowledge to do research.
50% If it is a non-research job and related to your field, it seems that having publications does not make any sense but you have to show what you did in your education years, so if you don't have work experience in your CV, show that you have published something, show that you are expert in your field, have something in your CV!
10% If it is a non-research job and not so related to your fields of study; then you may not need that much publications (see my answer above).

0% to 100% If you are going to work on your own and do not have any plans to be hired somewhere, do some business, be an entrepreneur, etc., you are the one who wants to hire you, so having publications isn't significant. But keep in mind that having research publications gives you ideas to work with, opens your eyes as a specialist and opens many more job opportunities than a person who has not any insight to research. So having publications may give you many more opportunities than having no publications.

In my opinion, be firm in every step of your life, finish your PhD with most output and publications; and enter a job which is so related to your field and make use of the things you learn during your studies at the university. If you do not gain much from your education, then it seems that you have lost your time for a PhD. So what was the use to get a PhD?
By the way, I think that your question highly depends on answering to this question: What are you going to do after graduation? And, What the consequences of not having publications would be in your future careers and jobs. You are the only one who can answer these questions precisely.

Disclaimer: I know nothing about the research in economics.
Publications are useful when applying to a job closely related to their field of study, but are almost never a requirement outside academia. This being said, if you want to 'work for one of the MOOCS' you might want to reconsider, because they very often are made in universities. I never applied to a teaching position, but I suspect it's not irrelevant to have at least one publication (although again, not a strict requirement).
Anyway, regardless of what your plans are, if you think your papers are not worthy of being published (what you qualify as BS), don't submit them, you will only lose readers' time. People apparently forget that the point of publishing is to show your work to others thus contributing to the field. The CV part is a by-product (at least it should be).
In addition, publishing something you don't 'believe in' is going to be a long-lasting pain in the neck (that is, in reputable, peer-reviewed journals). It could take you month of struggling with a paper that you do not want to read again, but have to. If you made your decision never to work in academia again, then it's pretty much pointless.

The reason I do not want to stay in academic economics is that too much (though certainly not all) of it is [BS] I cannot believe in.

Exactly because you think there are so much BS there, you should publish your papers if they are not BS.
I would review my manuscripts to see if they are good if I were you. If I believe they are of good quality, i.e. non-BS, I would submit them to the journals for peer review. If they do not match good quality standard, I would improve them so that they are not the same as those BS I saw in some journals. I then submit them to the quality journals which do not publish BS.
P.S. In my opinion, your question really has nothing do with where you are going to be and I consider MOOCs is part of Academia.

I'm in a different policy field, but share the same sentiments as you about academia. Consequently, I'm in the same situation of wondering how much I should care about publishing.
Here's some of my observations to date:

You have to show that you did something with your time while in a Ph.D. program. Publishing shows that I worked productively with my boss (advisor) on something "important" while I was a graduate student. However, this has diminishing returns. Namely, I'm perfectly content pumping my work out to a mid-tier journal, where I'm confident most of what I do would be published with just some simple edits that come about from the peer-review process at that level. My advisor, on the other hand, has a "go big or go home" mentality to publishing, which suits this person well given his/her career, but doesn't particularly help me get through the program rapidly to get a job outside of academia.
The best part about being in graduate school, but also being certain that I'm not going into academia, is that I have all sorts of time to build skills on my resume that will help me land the kinds of jobs that I want outside of academia, but are skills I wouldn't otherwise gain through the formal experience of a Ph.D. program. For me, this is computer programming. I'm great at statistics, understand research designs very well, and plan on leaning on these skills on the job market. However, a perfect complement to those skills, for the positions I'm interested in, is to be able to hack my way around several programming languages. Now, I can build something tangible with the analyses that I was already quite fluent with. Aside from the basic work that I need to do for my lab, and the program requirements I need to fulfill to get out the door, I really focus on these tertiary skills while I have the time to focus on such things. This means I usually am less concerned about the conference deadlines that seem to loom over the other graduate students, or revising that paper for the 100th time to try and impress my advisor. However, I should say that I also get a lot of shit done for my lab, more than other grad students, and work in ways that are much more smart/efficient than other students in my department. So, I find it easy to find the time to focus on other skills that might be beneficial to me on the job market. So, I hope given your disposition about academia, and your career goals, that you are using the extra time that comes from letting go of engaging with the rat race in order to do something cool for your resume.
The hard part is getting your advisor on board with your goals, which are reflected in a lack of concern about publication. First, it's harder to get them to pay attention to you if you aren't publishing things that are going to help them and their career. Two, if you're dealt an unlucky hand in being advised by someone who's never done anything other than academia (which is my case), it's hard to get them to understand your position. He/she might support your longterm goal, but will not be able to provide a vision of the intermediary steps one needs to take to reach that goal. I'm in the midst of negotiating my publication path with my advisor (i.e., "this is a perfectly fine article that would get published in a range of mid-tier journals." Advisor: "I just think if you redo this, that and the other thing, and then do this other thing, and think about this stuff then you could get it in one of the top journals..."), you might find yourself in the same position.

I really could go into so much more about being in the position you are in, and the difficulties that come from it, but that would get away from the question at hand.

Disclaimer: I never worked in the industry, so I have no first-hand information and everything I write is what I picked up from old colleagues, ... .
That said, I think in economics outside Academia a publication is worth barely the space in the CV. When applying to positions in consulting you may have luck and someone recognizes the journal you are publishing in, but in large companies you rarely meet someone who even knows what AER or Econometrica are.
So publications might look nice  on the CV but (if you are not applying to a university or maybe a consulting firm) no one cares if you published at Econometrica or the working paper series of the university of nowhere.
However, your case is a little bit different: MOOCs (and most teaching jobs) are at a university, so I would consider them as part of Academia and there publications might be worth something. Maybe not much but something at least.
To put that in (pretty random) numbers:
100% For a research job (normalized)
50% For a teaching job at an university
10% - 20% If you are "lucky" and someone with a PhD in Economics makes the decision
0% Otherwise

Publishing takes a lot of time and effort, so, if you are sure that you do not want to stay in Academia (or work at MOOCs) graduate faster without polishing your papers too much (if you are getting some kind of grade: that usually does matter, so some polishing is probably needed).

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Should I switch to PhD or graduate with a Master's?
I am doing Master's in Applied Science in Civil Engineering. In my research I work with big data analysis which has gotten a fancy new name in past few years "Data Science". When I joined the master's program I didn't knew much about programming and had basic knowledge of statistical analysis. Over the period of about 2 years I learned a lot about data analysis in R language, developing data apps, creating interactive documents, etc. Although my research area had no direct relation with any of those things, I enjoyed learning them and using them in getting insights about data.
On the other hand, this journey has been very frustrating because I could get very little useful knowledge for my research study. My 2 supervisors have been very supportive and both have asked me to continue my work and switch to PhD.
One part of me long for getting out in the 'field' and have a 9 to 5 job with set amount of tasks everyday. But at the same time I am afraid to leave academia as this is all I've ever done in my career (worked as a Lecturer previously and now have graduate assistant positions). Money is another concern as I've not yet determined how much I would be able to get in scholarships/ grants during PhD.
I don't know how to keep myself motivated continuously during research, so there are always some days when I just don't do anything. I am really confused at this stage as to what should I do, complete my master's in next 4 months and graduate or go for a PhD. What are your thoughts/ experiences?

I am afraid to leave academia — This is a terrible reason to stay in academia!  Even if you decide to switch to a PhD, you really should spend a summer or two in industry internships.

While I really don't think you should do a Ph.D. if you don't actively want it, I have to say I doubt the jobs you will find as a Data Scientist with a Master's degree are going to be "9 to 5... with set amount of tasks." Why did you decide to get a Master's degree?

I forgot to mention that I love teaching and that was the prime reason I opted for a career in academia

If you're considering industry, now's a GREAT time to get into a data analytics industry position, though.

You shouldn't stick around for a PhD because you're afraid to do something else. A PhD is something that you should do because you're motivated to use the skills you acquire in the PhD in your later career (either as a researcher, or in a research-oriented field).
If you're not excited about being a PhD student, then it's not worth it in the long run to be miserable for several years of your life to obtain the degree. Moreover, because the PhD can limit your ability to take certain jobs—because of the perception of overqualification—if you're not motivated, don't do it.
In other words: Choose to do something because you want to be there—not because you're afraid to be somewhere else!

FYI: Big Data analysis and Data Science are two different things, that can certainly involve one another, but one does not have to involve the other.
Also, Data Scientists don't fully know how to define data-science (i.e., is it a singular person with specific multiple overlapping skills, or is it a team of people with multiple overlapping skills? How is it different from a statistician? How is it different from a programmer?)
Anyways, I'd take a job then come back and get a Ph.D. if you still want to go that route. It will be clear to you a few years into your job if your heart was really in academia or not, and if your heart isn't fully in academia you'll at least have a clear rationale for what the value added of a Ph.D. would be for you.

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Is there any systematic approach to select/find a research topic?
I was offered an opportunity to prepare a 2-page research proposal for a postgraduate research program in computer science.
I am searching for a systematic and step by step technique to select/find a workable research topic.
Is there any systematic procedure/strategy/approach/method that researchers generally use to select/find and narrow down a research topic from an ocean of topics that pops in one's mind?
Is this technique an standard in the academia?

Best thing to do is finding something in the frontier of the state of the art where you can make some progress, not too many people are trying to do so and has some economic interest. E.g. a problem not seen to open, an open problem to close or a limitation to solve. PD: actually, I'm going to make this an answer...

If there were a way to automate this, it wouldn't be legitimate research.

I think that most people just find something that looks like fun, go forth, and do science. Or am I doing it wrong?

@paulgarrett systematic and automatic are two different things.

@Trylks, I understand your point, but/and the question (in my opinion) touches upon the "desire to do research" while not knowing much at all. It's not just about "desire to do research", or "following up on one's ideas". Many people have thought about many things already. Scholarship plays a huge role in competent, useful research, and scholarship is not a quickly-acquired thing. Sensibilities, context, awareness, ... not systematizable except as "study, reflect". That's what I mean to say.

@paulgarrett I beg to differ. Scholarship is important to write papers in the same manner that authors in the area write them, but it doesn't help to find fresh and new ideas, in some cases it may even make it harder. «"What is the task of all higher education?" To turn men into machines.» However, reviewing the literature is absolutely necessary to find the research topics (the problems) that have to be addressed, and that certainly takes a lot of time.

@Trylks, again, I do see your point, but I do not advocate "taking classes" as a way to acquire awareness of what-is-known, for one thing. Quite the opposite, although I do try to make my graduate courses un-stultifying. In my field, mathematics, I find that there is a pervasive misunderstanding among novices both about the role of "schoolwork", and the role of experience/scholarship. Reinventing an unusable wheel is not a desirable goal, obviously. Thralldom to doctrinaire coursework isn't, either. Ignorance, however, is not an asset, is my point... and mere enthusiasm is not sufficient.

@paulgarrett you are right in everything and I'm personally concerned about the potential impossibility of progress in Mathematics soon, it seems to require deep knowledge about a topic (which cannot be acquired soon) and a "powerful" mind (i.e. a young brain). More progress would imply that the window for groundbreaking research grows thin. However, if we are able to build abstractions that are precise enough as to work with them without knowing all the details of what is hidden below them then scientific progress would be possible in a different holistic level, I continue.

@paulgarrett this would mean that young researchers could stand on the shoulders of giants without climbing all the way up, not even knowing what is below. I don't know whether this is possible, but sooner or later I think it will be necessary. If this was the case in some area (maybe computer science) then young researchers could find that it is not necessary to check hundreds of papers but maybe only a few dozens. This could save a lot of time (and even our lives, depending on the research topic). If this is not possible, I guess our last hope is teaching computers how to do all that.

@Trylks, yes, the "burden" of accumulated wisdom, in mathematics anyway, is a genuine problem for beginners. Some very good mathematicians have said to me that it is infeasible to understand all the "tech" that one uses to prove new theorems. I partly concede that, but I do not like it. The goals of (personal) "greater understanding" and of (collective) "progress" are not-so-subtly different, obviously. Things become "saturated" at some point, and we cannot move... I have no good advice for the future, sadly.

I don't know whether it is standard. there may be some standards, but probably not worldwide. I personally had to write a 2-page research proposal on a topic I didn't choose.
IMHO, it's a great opportunity to choose a topic that you can like, if the topic was imposed (or changed after a few years by your supervisor) you would probably hate that, since you have this opportunity, I'd try to make the best use of it.
Systematic approach to select/find a research topic (by trylks):

Make a list of the  areas that interest you
Make a systematic literature review (so the approach is systematic) for those areas
Find research problems in the literature review and at least one that:

has not been researched yet (it's "open")
should be done next. It's in the frontier of the state of the art
a) Without many previous requirements or they will become your thesis
b) it's interesting from a research perspective
not too many people are working on it (best is zero, but that could be for some reason...). The problem if there are too many people (and you are not a part of their team(s)) is that the frontier of the state of the art may keep moving before you are able to reach it.
you have the necessary knowledge and skills to advance the state of the art in that problem
you have the necessary resources to advance the state of the art in that problem (e.g. don't choose something that requires access to the data from LHC if you won't have access to that data)
There is some economic interest in the problem and the results of your thesis (you don't need this for the thesis, but it will make everything much easier, specially after the thesis)

WRT the frontier of the state of the art, it usually looks like:
a) Some limitation in current systems/techniques that has not been addressed (specially in engineering)
b) Some question that remains open (specially in science)
c) Some question that has not been addressed (in some particular way) (specially in philosophy)
But well, research in those areas is more than that and it will be done in different ways depending on the topic. Computer science is sometimes considered an engineering (software engineering), sometimes a science (and can be empirical with benchmarks or formal with proofs) and it can be as well philosophical (specially in AI, IMHO). The kind of problem should arise from the review of the literature.
BTW: don't try to rush, this is systematic, but it will definitively take very long.

Perhaps a sane suggestion is to get advice from an experienced, trustworthy person. Otherwise, one's very perceptions of the supposed issues may be far from the actual substance. Intuition for what is importnat, what is possible, what is impossible, although not "rules", are very, very useful guides, etc. Inexperienced people especially suffer from failing to understand the potential benefits of experience, etc.

Indeed. Almost everything is easier with a bit of help from someone experienced. In this case I see two main possibilities, either "a priori" to find your way in an ocean of papers or "a posteriori" to check those two pages and whether they make any actual sense.

I'd be concerned with this approach that unless the area(s) chosen in Step 1 are extremely narrow, the following steps will involve iteration over many thousands of published papers.  And choosing a sufficiently narrow yet workable area in Step 1 is almost tantamount to choosing a research topic.

@NateEldredge the topics can be narrowed down during the literature review, i.e. I'm interested in machine learning, so I check the titles of the papers in main 3-4 conferences in machine learning in the last year. Then based on the titles I continue with the abstracts and based on that I continue with the rest of the paper, if needed. If I'm interested in machine learning and I find a paper in that area that is clearly not interesting (for me, based on the title) then checking that paper in more depth can probably be safely and indefinitely postponed.

I'm not an experienced graduate student or post-grad (yet, to my great consternation), but here's my somewhat-educated guess to expand on Trylks point 2 above, and others, and create a short answer:
A. Do a 2-level review of Review Journals.  These are the literature that review the state-of-the-art research done in a prior period, such as the last year.  Do a high-level scan to get your bearings and then a deeper-level dig, as you might guess.  Here's one for your field, e.g., that was published up until 2011: http://en.wikipedia.org/wiki/Annual_Review_of_Information_Science_and_Technology
B. Combine that with the expert help of people senior to you in the field, as others have suggested, to find gaps in the field.
C. Pick an area in the gaps that interests you in which you can make a contribution appropriate to your level of expertise/skills, and go.


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Can I reference the abstract?
I finished writing my internship report for a master degree. Now I am writing its abstract. Is it possible to mention a statistic study on the abstract and reference it in the bibliography or is this something bad to do ?

I'm not sure if I understand your question correctly, but if your report doesn't talk about X, then the abstract wouldn't mention X - it's just a summary of what is in the report; the report should have more information and detail than the abstract, but not the other way around.

I suggest changing the title to "Can I put references to other works in the abstract?". Your original title, "Can I reference the abstract?", suggests the exact opposite, namely whether it is acceptable to add a reference in another work that points to your abstract.

I voted to close as a duplicate, assuming the OP meant "Can I put references to other works in the abstract?" as the title of the question. To the OP, please clarify If this is not what you meant.

If this is just an internal document that will never be seen outside your own institution, it doesn't really matter.
For a document that will be distributed outside your institution, the abstract should be fully comprehensible even if that's all you see. It's quite common for databases to include only the abstract or for it to be much easier for people to see the abstract than the rest of the document. (For example, on ArXiv, each paper's "home page" includes the abstract but you'd have to download the whole paper to see the references.)  For these reasons, an abstract that says something like

We build on the statistical analysis of [5].

isn't very useful.  This isn't so bad with a long reference style:

We build on the statistical analysis of Smith and Jones (2005).

is better, especially if that is a well-known paper in the field but not everything builds on well-known papers and the reference is potentially vague if Smith and Jones wrote multiple papers together that year.
The best way to do this is to give a full citation in the abstract itself:

We build on the statistical analysis of Smith and Jones (J. Interest. Res., 3(1):41–59, 2005).

Some journals forbid citations of any kind in the abstract but that seems to force people into the suboptimal "Smith and Jones" style.


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How to become a whistleblower?
I used to work in a company that has close ties with the academia.  One of the professors ("Dr A") wasn't/isn't using his funding properly by hiring his long-time girlfriend as his research assistant.  He and his girlfriend showed up at company events as a couple so there's no doubt about their relationship.
After I left my previous company, one of the profs ("Dr B") in the same area of research who works in a different university pointed out to me that the government's funding agency prohibited the researchers from hiring relatives and partners using the money.  At Dr B's department, a prof had been fired by the university for violating this rule.
No one from my previous workplace and the circle of researchers bothered to report to the funding agency about Dr A's violation.  I was temped to be the whistleblower after leaving that workplace, but was taken back because it's obvious who was the reporter: There were not that many of us in the circle.  Even if the funding agency had a whistleblower policy in place, I doubted if it could protected me as someone who worked in the industry.
I'm not seeking any heroic stories about penalizing the profs.  Instead, I'm wondering if anyone has encountered a similar problem.  In addition, I'm also interested to know how the universities and the departments deal with this kind of issue as peacefully as possible.

@BillBarth Canada.

Why do you assume he is breaking the rules. How do you know how this person is being paid? Professors often have multiple funding sources and even if they only have a single funding source, there is often some discretionary overhead which can be used for anything. Potentially his long-time girl friend doesn't qualify as a partner or maybe he got permission from the funding agency.

@StrongBad Then no harm would be done even if he reported him.

@StrongBad Thanks for the benefit of the doubt.  I no longer have access to the docs so I don't have solid evidence on his sources of the funding or the fundings' policies.

@user8001 If an investigation were launched and there was no harm to him at the end of the day, it would be obvious on who reported him.  I need to protect myself.  I asked this question here just to see if the academia can be accountable with the taxpayers' money.  (The universities I dealt with are funded by the government.)  In addition, I wonder if it's possible for the universities and the funding agencies to implement a usable whistleblower policy.

@user8001 - actually some harm would be done if the OP reported the prof and it turns out that no rules are violated. The harm is that taxpayers money would be spent for the investigation. Even if they find that the ruleas are violated and the GF and/or prof are fired, it might do more harm than good if their contribution to the project is valuable.

@lacampane11a, why do you want to report this? Are there any personal reasons involved? Do you dislike the prof or the GF? Do you think the GF does an inferior work? If you are just concerned about the taxpayers' money, see my comment above. And how can you actually prove that they are a couple? What if they became a couple after starting the project? If you have said that the GF doesn't do what she is supposed to for the project, it would be another matter but wanting to report that 2 people who work together also have a sexual relationship sounds distasteful, imho.

@greenfingers You raised a good point on why such an incident would be reported. In addition, you're absolutely right on the money spent on the investigation. :) The profs who was fired in Dr B's department made some enemies indeed.  At least one of my former colleagues who have worked with GF questioned her credentials: Her accomplishments and advance degrees sound great on paper, but she had problems solving some fundamental problems in the field and had trouble understanding English. I wonder what she actually did for the projects.

@greenfingers While I do in principle agree with you in that starting a fight over this matter seems petty, I want to point out that the reason you should not hire your girlfriend is similar to why quotas (gender etc.) should never be used: It is not obvious that the hired person is the most qualified, or qualified at all. Now it might be that they are good at what they do, but this is often not immediately apparent and the hiring process probably was not transparent. If your collaborators have doubts (like the OP does), then a re-evaluation of hiring criteria seems to be in order.

I know about two situations like this one (actually husband-wife at this moment, both) in two different countries. At least in one of the countries this doesn't seem to be illegal because it's very common with all types of relatives. I'm quite certain any action on my side would have only had negative consequences for me, so I did nothing. For context sake, I'm currently doing my best to move to a different country (an English speaking one) and to the data analysis area (and out of academia if possible).

Thanks all for commenting. I'm surprised that so many readers who are interested in the topic!

Good things rarely come to whistleblowers. Most of the time, absolutely nothing happens [to the accused] and occasionally really bad things happen to the whistleblower in the forms of retribution, blacklisting, defamation/slander lawsuits, etc.  Laws protecting whistleblowers tend to be ineffectual at best.
You need to evaluate the benefit/risk ratio yourself.
That being said, if you were to whisteblow, there are several levels you can do it at:

University office of research integrity/ethics. For example:  http://research.ubc.ca/ethics/british-columbia
** While this involves a private company, the PI may  also have an affiliation with a university
National office of research integrity. For example in the USA: http://ori.hhs.gov/
**  In Canada: http://www.acaho.org/?document&id=164
Funding agency whistleblower hotline
** Canada: http://www.rcr.ethics.gc.ca/eng/policy-politique/framework-cadre/

Good luck.

[That all being said: the situation you describe is likely to yield at most a   reprimand from the funding agency if the girlfriend  was actually  working while receiving a salary (and thus it wasn't embezzlement only nepotism). I'm assuming the company already knows -- private companies tend to be more lax about these things compared to public (and even private) universities which receive a majority of the funding from the state.]

The first phrase is absolutely golden: Good things rarely come to whistleblowers.

Yes, golden as in "black gold" - coal... Valuable, but very dark...


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Criteria for choosing undergraduate school to prepare for graduate study: "focus on undergrads" & "extensive rigorous curriculum" mutually exclusive?
I'm trying to figure out which undergraduate colleges are most conducive to graduate school applications, but it seems to me that (with few notable exceptions) my two main criteria that lead to this sort of success are mutually exclusive. Are there any schools in the U.S. that have both an extensive mathematical curriculum and a focus on their undergraduates?
Schools known for being strong in math (such as MIT, Harvard, and Stanford), seem to be very heavily focused on their graduates, with comparatively less attention payed to their undergrads. I'd like to avoid classes taught be TAs and be able to learn from and get to know my professors, both for the improved learning experience and the improved graduate school recommendations that will inevitably eventually result. Perhaps even more importantly, it seems that research as an undergraduate tends to improve students' chances at graduate schools; thus, colleges that have significant research at the undergraduate level are most appealing.
However, schools with the above desirable criterion tend to be less mathematically rigorous, especially in pure math. I've found a handful of schools that will even keep a math major occupied for a whole four years if they've taken only introductory multi-variable calculus, linear algebra, and differential equations. I don't want to have to sacrifice an education for attention -- I also want to go to a school considered highly for graduate school that has extensive course options.
Is the first criterion a fair voting system and the second a dictator? Is there any intersection of the above specifications? My own rudimentary research suggests a few options, but these hardly make a list even the best students can expect to be comfortable applying to.
I want to make sure I have the best options for graduate school in the future, both in being a qualified applicant with the opportunity for stellar recommendations and in having learned the extensive mathematics required to give me a head start for future research.

I voted to close as an undergraduate question (which are out of scope here), but I am willing to admit that I might be wrong - as there is also an aspect about how to best prepare for applying to grad school.

If it better fits the site's content, I can change the focus of the question to more largely reflect the graduate school preparation aspect (that's the reason I chose the two criteria, anyway).

Since the question is partially motivated by admission into graduate school (e.g., recommendation letters) I think this is on-topic here.

I'm unsure that we want this site to have "America's Top Colleges" shopping lists like this. Perhaps a  meta discussion is in order. (In the meantime, it sounds like you might be interested in a liberal arts college - there are quite a few with excellent reputations in mathematics. Keep looking.)

@NateEldredge I'm pretty sure we don't.  To the OP: I think your concern about big research schools are over blown.  Assuming you're taking calculus in high school (I hope you have if you're considering a math major), you'd take at most a couple classes with TAs even at the biggest R1.  On the other hand, there are lots of liberal arts schools with good math programs.  Williams is probably the most famous.

You'll need to decide for yourself which sort of school is the best fit for you educationally (this is a highly personal decision, and a school that's a wonderful fit for one person might drive another crazy).
However, I don't think a focus on undergraduates matters much regarding preparation and admission for graduate school.  Not even in the ways you'd think it should, like getting good letters of recommendation: there are disproportionate numbers of students in top graduate programs who attended institutions nobody would describe as focused on undergraduates, so this is clearly not keeping them from being admitted.  In particular, faculty at universities with strong math programs know what it takes to be admitted to top graduate schools, and they provide what's needed.  You might have to put in some effort to make sure you don't fall through the cracks, and this could be a hardship depending on your personality, but for many people it's not so difficult and in any case it's a valuable life skill to develop.
If you're looking to judge universities by how well they will prepare you for graduate school, the main factor I'd look at is how many students they send to graduate programs you might like to attend.  If the number is large (relative to the size of the undergraduate program, of course), then that's a very good sign.  Clearly they're doing something right, and you'll have the benefits of a strong peer group already as a undergraduate.  If the number is small, then you should worry.


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Some advices regarding the first research paper
I am an undergraduate student in Mathematics and I think that I have discovered something significant in Mathematics. My friends and some professors to whom I have sent my ideas also confirmed its significance. They suggested me to write a paper on it.
But the problem is that being an undergraduate student in Mathematics, I don't know how to write a paper. Besides, the professors to whom I have sent my ideas weren't experts in this field and they have asked me to send my works to some experts in the field. But unfortunately I don't know anyone such and I see no point in assuming that even if my work is significant, they would give time to read it without dismissing it beforehand as a work of some crank.
So what should I do? Can some suggestions be provided?

Hi there! There're some thoughts in: http://academia.stackexchange.com/questions/8121/how-to-write-a-white-paper-for-a-non-academic

Ask your professor to introduce you to a suitable expert.
If some of your professors think that your work is of substantial quality and probably novel, then they are surely fine with introducing you to some suitable researchers in the field. Note that, for example, a postdoc in the respective field may suffice. They should be willing to give your work the "badge" that in their oppinion, your work seems to have potential by writing that to the suitable researcher themselves. This should get rid of the problem that you describe in your second-last sentence:
"But unfortunately I don't know anyone such and I see no point in assuming that even if my work is significant, they would give time to read it without dismissing it beforehand as a work of some crank."
Note that an experienced academic in the respective field can add a lot of value to your paper, including improving the accessibility and providing a more comprehensive literature survey.

Thanks for your answer. I have already tried to send my ideas to a professor (who is an expert in this field) as suggested by one of those professors who are not expert in the field but to whom I first sent my ideas. But the professor was silent for quite some time and so when I inquired whether he had gone through my works, he replied that he hadn't given time to verify my works for he thinks that it is fairly improbable for an undergraduate to make some significant advance in Mathematics, simply because his training of Mathematics isn't complete yet!

That only means that the professor did not invest the time to look into your write-up (yet). I would say that you can inquire again in two weeks or so. If after three inquiries, she/he still did not read it, ask for the task to be delegated or for someone else to contact instead.

I don't know anyone else. Besides I am afraid that I will get a similar response from that person too!

@user170039 That's too bad. I see two options here (after the third inquiry) - (1) go back to your initial non-expert professor and ask for help, and (2) making a "sales pitch" to the expert professor during his/her office hours such that she/he actually wants to read your paper.

First of all, Im not a mathematician but I am in a closely related field (CS)
I work in the machine learning domain and sometimes I read mathematical papers to find hints of my problem so I think I may able to provide a little help.
According to my experience, the most different part in Maths to the other domain is that, their main results, are always a collection of theorems or properties instead of experiments / methods.
In most of the cases I saw people organize their paper in the following way:

Formulate the problem, provide some minimum facts that is nessasary for the readers to understand your contribution.
List out your main results in layman terms.
Write all the necessary lemmas and theorems that finally lead to your main results.
QED!
If available, some application examples.


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What incentives do professors have to increase the PhD completion rate in their department?
In other words:

How do professors profit if a larger (rather than smaller) proportion of entering PhD students in their department complete their degree?

(At my department at least, it seems like the only benefit is "warm-glow altruism". A professor gains no more from having more students at her department complete their PhDs than I do by having fewer stray dogs in my town getting killed by traffic. A professor's career prospects does not seem in any way affected by whether 80% rather than just 50% of PhD students complete their degree. Not surprisingly, the completion rate, at least at my department, is closer to the latter.)
Note:  I am not asking whether it is a good idea to give professors stronger incentives to increase PhD completion rate. Neither am I asking for suggestions as to how PhD completion rates can be increased. Rather, I am asking what the incentives at present are (granting of course that this varies from place to place).

In my country (Europe) the number of PHDs awarded per professor is considered during promotions, since it is indication not only on professors' capability of doing research but how he helps other people (his students) to become researchers themselves.

Usually what matters is the number of completed PhDs (not the percentage), and this matters a lot. However, given the resources that you have available (funding for PhD students, time to supervise them, etc.), if you want to maximise the number of completed PhDs, it usually makes sense to try to maximise the percentage of completed PhDs. So there is plenty of incentive to make sure that your PhD students complete their studies  on time.

Are you asking what incentive I have to increase MY completion rate or my colleagues completion rate?

A bit ambiguous about whether it's external incentives, or internal.

Your question seems to emphasise "department-level" completion rates. This is a performance metric for a head of department or head of research. However, for an individual professor, the relevant performance metric is the completion rate for the professor's PhD students.

Yes, my question is precisely that - about "department-level" completion rates. To use the same analogy: My question is "What incentives do people have to make sure fewer dogs (in general) are killed by traffic?" rather than "What incentives do people have to make sure their own pet dogs are not killed by traffic?" Whether one should care about dogs or PhD students that are not one's own, is perhaps a question to be asked separately.

In the United States, the National Research Council (http://www.nap.edu/rdp/) regularly ranks university departments. One of the criteria by which departments (and thus universities) are ranked is the "Average of Median Time to Degree" with the presumption that lower is better.
In my university, this results in the provost's office putting pressure on us to reduce our time to degree through a number of measures, some coercive and punitive. Most of the time, the coercion and punishment is directed towards the graduate students (i.e., after the sixth year they lose their rights to certain fellowships, they have to pay more for their gym and library memberships, etc.).
But the department as a whole gets some attention. Our chair has been regularly sending out lists of our orphaned and missing ABD candidates (some now in their 12th year) and asking us to find and terminate them (either through graduating them, or formally asking them to leave the program).
I've also been putting some pressure on my peers through the admissions system by suggesting (since they are my colleagues, I have no power) that people with many students on the books should refrain from taking on new students until they clear their backlog more a bit.
I should note that I'm in anthropology where: 1) students tend to go into the field and disappear for quite sometime; 2) doctoral students are mostly useless to faculty for slave labor as most of us work individually and not in labs (with the exception of some of our archaeological / biological colleagues).

If an advisee leaves without completing a Ph.D., then the advisor can end up feeling like the whole process was a waste of time, since the goal of strengthening the research area by training a future contributor was not achieved.  That's not fair or reasonable: the education and experience may be useful for the advisee despite not culminating in a Ph.D., and the opportunity to try was itself valuable regardless of how it worked out.  However, these feelings are relatively common, and the advisor's investment of time and effort becomes an incentive towards higher completion rates.
This personal investment begins only when the student chooses an advisor, so the corresponding incentive is not relevant before that stage.  On the other hand, spaces in graduate school are a limited and therefore valuable resource, so there is still an incentive for faculty not to waste them, even at the coursework stage.
What makes this issue tricky is that nobody can agree on what the ideal completion rate should be.  To a first approximation higher is better, but this isn't a universal principle, and a 100% completion rate would arguably mean you're doing something wrong.  Over the course of a difficult five-year program aimed at a narrow career, some people will legitimately discover that there's something else they'd rather do instead, and others will be prevented from finishing by factors beyond their or the university's control.  The only way to enforce a perfect completion rate would be to refuse to admit anyone who seemed like they might not finish and then bully all the students into finishing regardless of whether or how their circumstances had changed.  For example, you would never take a risk by admitting someone who seemed like they deserved a chance, and you would never gracefully accept a student's change of plans.  Ultimately, the fundamental difficulty is that we can't necessarily distinguish between reasonable attrition and inappropriate attrition caused by unsupportive practices, and this makes the whole issue contentious.

In France, labs are assessed by the AÉRES (mirror)  (~= Department of Evaluation of Research and Higher Education).
The evaluation criteria (mirror)  show that the AÉRES prefer labs where PhD students don't drop out too often.
Since the AÉRES evaluation has an important impact, e.g. to get funding, professors have an incentive to increase the PhD completion rate (and they also have an incentive not to turn PhDs into some ever-lasting position: labs typically to try to graduate students in 3-4 years).

In the US - at least in my university - I'm not aware of any incentive, except that new PhD students will avoid professors who have the reputation of taking a while to graduate their students.

I'm going to answer the opposite question. What disincentives do professors have to increase the PhD completion rate in their department? I'm looking at the opposite of what you asked because I feel it will give us insight into your question.
In some fields, which I can only talk directly about the one I am familiar with - Compute Science, having students complete their PhD in a timely matter isn't a focus unfortunatly. Professors who are already established may already have a little army of PhD grads out there citing their work and growing their PhD empire. Which means that current or recent crops of PhD students under that professor sometimes get stuck. Why? Unfortunately one thing that PhD students are is cheap(ish), reliable labor.
A PhD student is going to work on the tasks or research set before them by their PI. They are going to do their best to complete that research - not just because it benefits their career but because failure in that arena may lead to disfavor or even being removed from their program. A professor can be assured that PhD students working under them will focus on their research of choice and will invariably cite or reference previous work done by the professor. Incidentally the PI is almost always an author on any paper that student publishes.
That's a bit cynical, I'll admit. But even beyond the pure cynicism of authorship farms and indentured servitude is the basic truth that it takes time to train someone to do research work at a high level. If I have been researching creating artificial butterfly wings out of volatile polycarbonates(or whatever) then it's going to take at least a year, if not more, to get a student enough information, enough skill and enough confidence to wind them up and let them go on important research.
Right now some of the other Academic posters are rolling their eyes. This sounds both incredibly cynical and a little bit tin foil hat ish. But the thing is... these are real problems that have been identified in at least a few schools I know of. You get some old, cranky, tenured professor who has dozens of students out in the world and who has gotten used to his or her status as king of the research mountain and all the sudden students start taking longer and longer to graduate. All the sudden that professor forgets what it was like to be a PhD student, trying to make a difference with your research and trying to get the heck out and graduate and only remembers that it's annoying and expensive to train a new PhD student and, btw, this student's producing pretty well and... well it would be more convenient if this trained student would stick around for a while.
What is done about this? Some programs tie tenure positions with completion rates and timelines. This is problematic and, to be honest, I've heard people talk about it but I've never seen or heard of it in action.
Some programs have a soft cap on the length of time a student can remain as a PhD student. I have seen this in action and I'm conflicted about it. On one hand, PhD students need to either graduate or leave the program eventually. But different fields can take different amounts of time to get results. Additionally, sometimes life just happens and the student who is moving along their degree runs into a snag(changes PIs, has a health emergency, just needs more time). The hope is that these soft caps are flexible enough to deal with these situations. The ways I have seen these soft caps(for lack of a better word) implemented is by having a fairly strict timelines for course work completion, having a deadline for committee selection(generally very early in the process) and having regular meetings between advisors(academic style advisors, not research advisors) and students.
Although your answer states that you're not interested in what could or should be done in these situations I think it's valuable to say that: I think low PhD graduation rates are signs of an unhealthy department and unhealthy academic culture. They should be taken very seriously and the fix should never be the 'warm fuzzy glow' of graduating someone.

There's a bit of an inaccurate presumption in the question itself, or anyway ambiguous wording. That is, some assumption of causality...?!?
As a mathematician, I do not think of PhD students individually or collectively as assisting my research program so much as doing teaching work that I don't have to do. Even my own PhD students, while stimulating to talk to, do not "help" my research program. Perhaps this is contrary to mythology. Although more-experienced TAs (teaching assistants, in the U.S.) are generally better at their job due to that experience, that level of proficiency is attained within a year or two of beginning the role. That is, in my sort of situation, there is absolutely no motivation for faculty to delay completion of PhDs. Indeed, as @roboKaren comments, there is some pressure from higher-ups to improve "stats". (That is, in terms of TAs, we cycle them through at a certain rate, so there're always roughly the same number to do the TA work. Shortening or lengthening the cycle time would accomplish nothing, and we have no motivation to do so.)
Is the supposed issue about people leaving the program? This is a very complicated question, considering that it might be entirely reasonable to leave a program if/when one discovers it's not what one thought. Should we brow-beat people to stay? Bribe them? True, being nasty to try to "drive out weaklings" is incivil, but I don't address that possibility.
If the question is about the "drop out rate", then it is probably impossible to answer usefully. If it is about time-to-completion, some useful things can be said.
This simplifies the question to two very different ones: about my interest in colleagues' students finishing faster/slower, and about my interest in my students finishing faster/slower. Apart from general humanitarian/professional-ethical concerns, I have no interest in the arc of other peoples' students, as it is really not my business. It is true that my perception (based substantially on two stints as Director of Grad Studies in Math) is that some PhD students and their advisors devolve into an unproductive, uncommunicative relationship, with "blame" not clearly assignable, but which creates enormous difficulties in completion. E.g., if either party is naturally non-verbal (despite the seeming ok-ness of this in math, ... which is not the case, actually), there is a potentially fatal problem. If there is a misunderstanding (from either side) about the context, origins, degree, and sense of the alleged "novelty/progress" of a thesis, this can be a huge obstacle.
For my own students, I try to arrange a thesis project that will optimally
use the talent, energy, background, etc., in the time fully-funded by the department as TA (not counting on RAs (research assistantships), fellowships, etc). My thinking is that one's clock really, really starts once one is "out the door", so taking a sixth year instead of just five may be well worth it. But if/when someone says they want to finish more quickly, a suitable project can be chosen, up to a point: usually, there is a misunderstanding, a misguided prior belief that, indeed, somehow, faculty or departments are conniving to delay degree completion. :) "If only they'd get out of my way so I could do my research...!?!" ... overlooking the point that all the "required" stuff is meant to assist that (nevermind the common stylizations and distortions and misunderstandings).
So: incentive for quicker completion than the funded period? None, on scientific and educational grounds. On bureaucratic grounds, there's an ever-hardening soft cap on funding, which is a good reason to get people out the door... even though this soft funding cap is meant in practice primarily to avoid funding "eternal grad students" who make a bit of progress but either can't finish a PhD-worthy project or who are unhire-able for some reason (e.g., inability to speak in English, in the U.S.).
So, while my experience as Dir Grad Studies in Math made me unhappily aware of others' foibles, I don't think there's much motivation in mathematics for faculty to delay PhD graduations, and only a little to accelerate it. But faculty aren't the obstacle, in most cases. It's just that the U.S. undergrad system under-prepares people for grad school, so there're two or so years of basic coursework necessary to be even marginally literate, and then becoming aware of the basics of any fragment of modern mathematics can (obviously... though people in CompSci seem to have a radically different epistemological mythology) take a year or two. Unsurprisingly, quite a few people discover that "math" is not what they thought it was, given that U.S. coursework typically is at best very-early 20th century stuff, giving no inkling of mid-to-late 20th century stuff, apart from the not-really-contemporary-research, somewhat delusional (inevitably fairly contrived) "REU" (research experiences for undergrads) episodes. Given the popularity of REUs in the U.S., I'll not comment further on the alleged virtues-or-not... apart from agreeing that, yes, it is good to spend some time hanging out with other same-age kids who really like math, and not being in the usual stodgy classroom situation...
So, if "completion rate" means completions-per-admission... well, that's a can-of-worms, all the more for programs (such as ours) which try to be imaginative in visualizing the success of some students who do not necessarily have the traditional trappings of "success", but seem to have sufficient interest and talent. Gambles! If we'd be taken to task for not gambling on sure things... ?!? And a similar analysis applies to length of time to completion: pressuring people or limiting them to finish more quickly could induce more "failures", rather than "coerce" faster success.
Again, I feel that the question itself is predicated on a misunderstanding of why it is not so easy to get a PhD... but maybe I'm just old-and-tired. :)

This depends very much on your discipline. In many experimental sciences, for example, experienced PhD students are a lot more useful to the lab then newbies.

@ff524, indeed, I know, but/and the question's context was not clear to me. Even in math, there seems to be a traditional mythology among grad students in which, somehow, faculty "keeping down" grad students mysteriously benefits the faculty...

@paul garrett  Like you, I'm a mathematician, and I have always wondered if we're producing more Ph.D's than we need.  On the other hand, I don't want to discourage, or remove the opportunity, for anyone who really wants to pursue mathematics deeply from doing so. Solution? I don't know.

@paul garrett (to continue) I agree that US undergrad doesn't prepare students for graduate work. I work at a less competitive liberal arts school so I see the problem first-hand. But then again, US high schools are apparently not preparing their grads that well for college either. It's a vexing problem for which there is no easy solution.

PhD is largely depend on the individual effort and skill of the graduate student, much more than the result of a student in lower educational levels. Therefore it is questionable how much credit should be given to the supervisor and the individual.
Indirect intensives of being a good mentor is numerous from tenure track level, as it is mentioned in the comments. A strong prof-grad students relationship is also a very strong basis of future research networks for both the students and the professors. I saw several examples how a successful former graduate student can raise the reputation of a prof, and help in new cooperation.
Direct incentives (head money? ) to the teacher to improve that rate would be counterproductive. PhD is not elementary school: it is not like pass or fail. Just because someone passed it, the career prospects doesn't get much better if it is not coupled with actually skills, good publications etc. So just pushing someone to pass when it is not deserved doesn't do any good to students neither. Even if the reason of failure is beyond the student, or the prof is unreasonably demanding, changing the lab and / or institutional level of protection of the student is much better solution i believe.
Imagine this scenario: top notch laboratories can (should) have really challenging research topics. Big part of the research is however carried out by graduate students. Do we offer direct intensives to the professor to lower the level and bet on safe projects, just to have higher pass rates for his graduate students? Easy trick, yet at the end the student ends up with poor publication record and the once-prestigious lab lower its quality, too. It is not good to anyone.

Do we offer direct intensives to the professor to lower the level and bet on safe projects — Heh. You mean aside from grants?

I don't think that the grant system would perfect, but this imperfection is not good reason to make more poorly designed incentives.

Oh, yes, I totally agree that we shouldn't make things worse.  But if you think academia doesn't offer numerous direct incentives for faculty to bet on "safe" projects, you're not paying attention.

If you want to discuss grants and other elements of science policy, you may want to open a separate question or something. These comments are rather limited spaces for off-topic conversations.

"PhD is largely depend on the individual effort and skill of the graduate student" While I would agree that the WORK and OUTPUT of a PhD is the result of the individual effort and output of the student I think this misses the actuality of the post graduate education system. Professors has a real effect on when a student can propose and defend and many programs will not allow a student to move forward unless their professor gives the OK. This removes a large portion of the autonomy of the student when it comes to the time line on which they graduate.

@Nahkki Well, that would be said if the prof had no effect on the process, and the student would be 100% autonomous... Then the whole thing would make no sense. If the prof is abusing his administrative power or just using students as free slaves that is a problem of internal regulation and should take care off, similar to harassment cases, not some incentives.

@Greg But that's the point. There are a lot of (academic)cultural and systemic incentives, unstated, to slow or low graduation rates. To pretend that it is as simple as using students as 'free slaves' misses the point that such things could be(are) problematic at a system level. Simply put I don't think the responsibility for a student's graduation speed or rate can be placed largely on the student's skill or effort level.

@Nahkki Then how about directly deal with the "cultural and systemic incentives" instead of overpaint everything with another dubious one?   Anyway, we discuss this mater without much specifics, so makes not much sense.


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Splitting a relatively long paper into two shorter papers
I have recently submitted a 40 pages paper to a journal, say (A). After about 6 months, the editor let me know that several reviewers have declined to review my paper, and so he decided to reject the paper. He suggested that I submit my paper to a more specialized journal. Journal (A) is already a specialized journal and I only know 1 journal more specialized than (A), let's call it journal (B). So, one of my options is to submit my paper to journal (B) and accept the risk of a similar feedback from the editors of journal (B), of course after several months.
In the mean while, I think the main reason several reviewers declined to review my paper is that (1) my paper is relatively long, (2) My paper consists of two parts and each part addresses a different subject. Therefore, the set of reviewers who have expertise in both subjects and are willing to read and review my paper is very small. Due to these facts, it is very likely the editors of journal (B) face the same problem. So, as the second option, I am thinking of splitting my paper into two shorter papers each consisting only one subject of my original paper. Regarding this option, I can think of the following pros and cons:
Pros:
(i) There are a good number of experts in each subject and it is fairly easy to find a reviewer for each one of my shorter papers.
(ii) This facilitates the referee process of each paper and hopefully reduces its time period .
(iii) Two papers (each approximately 20 pages) look better than one paper (approximately 40 pages) in my CV.
Cons:
(a) The second part of my paper depends on the notations and results of the first part. So the reviewer of the second part may prefer to read and review the whole paper at once, or even worse he/she may call the paper containing the second part incomplete.
(b) Part of the motivation of the developments in the first part of my paper comes from my work in the second part. By separating these two parts, the reviewer of the first part can complain about the lack of enough motivations and justifications for my results. In my opinion, it is not a serious problem because I will explain the application of my works which is going to appear in the second paper. But I am not the person who makes the final decision and the reviewer may blame this and reject the paper.
(c) I can imagine that it would be a difficult path to follow the referee processes of two related papers simultaneously, because of the following reasons: It is possible that the opinions of reviewers of the shorter papers differ significantly. Or it is possible that these papers get refereed in two very different time periods. It is also possible that one of the papers gets accepted and the other one doesn't, which is a pretty ugly situation.
Unfortunately, I have faced each of the above difficulties ((a), (b) and (c)) in my previous submissions and I know how they can ruin my papers. In fact, the main reason that I organized my results collectively in one paper was to avoid the above issues. But now that my paper has been rejected without any peer review, I am considering the option of splitting my results into two papers. So, I have the following questions to ask from people who have more experience and have been involved with similar situations (for instance as an editor or a referee):
(1) What do you think about the above pros and cons? Do you know any other pros and/or cons? And, is it a good idea to split my paper into two shorter papers?
(2) If it is advisable to split my paper into two papers, should I submit them to the same journal, (maybe same editor), or should I submit them to different journals according to the best editors who can handle my papers?

Why did you include two different subject in one paper? If reviewing them requires different expertise, as you suggest, it sounds they are not much related. Also, have you tried to verify your assumptions with the editor? The reason of rejection may be completely different than what you think.

@Greg: The answer to your first question has already been given by the OP: "(b) Part of the motivation..." It certainly does not follow that two parts of a work that require different expertise are unrelated: much of intellectual work involves making connections between previously separate things.

@Greg: As I explained in the above, the second part of paper depends on results of the first part and the first part is motivated more convincingly by the second part.

It seems like (a) is easily fixed: in paper 2, spend a page or two to restate the notation and necessary results from paper 1.

One more pro comes to mind: as a reader, I'll more likely read one or two shorter papers with one specific topic than a long paper with two different topics. I'd assume the two separate papers will be easier to find by someone searching for a specific topic later on.

To add to @NateEldredge: it will also help to contact the editor to make paper 1 also available to the referees of paper 2, if it is not already on arXiv.

Your concern (c) would be more easily handled if you submit the articles to the same editor at the same journal.

Well, in my opinion, the following fragment of your question outweighs everything else:

(2) My paper consists of two parts and each part addresses a different subject. Therefore, the set of reviewers who have expertise in both subjects and are willing to read and review my paper is very small.

I appreciate that you are able to imagine the problem that will be faced by the journal editors. So, splitting into two is certainly not a bad idea in this case.
I can mention some instances where this has been done in the past. In each of these cases, the problem wasn't as acute as yours (i.e. both could actually be reviewed by the same expert), but perhaps the authors chose to do this because of length considerations (or some other reason that I can't imagine). Also, in these cases, it wasn't a case of two different journals A and B - it was two sequential papers in the same journal. So, that creates an additional option for you, if you find it appropriate. (The context here is Physics, but I'm sure this can be generalized to Maths, if I'm right!)
Example 1: R. P. Feynman was a charismatic Nobel Laureate (Nobel, 1965), as you probably know. Here are his two significant contributions to QED, appearing back to back in Physical Review:
Paper1, Paper2 (both are free pdfs officially, given their landmark status.)
In particular, he began Paper 1 by writing:

This is the first of a set of papers dealing with the solution of problems in quantum electrodynamics.

and started Paper 2 with the sentence:

This paper should be considered as a direct continuation of the preceding one ...

He had developed the formalism in the former and applied it to the problem in the latter. That makes a candidate for splitting into two.
Example 2 Here are two papers by Sidney Coleman which form the backbone of phenomenological effective Lagrangian method in low-energy Nuclear Physics. (These aren't free and I'm not sure you will be able to get past the paywall here!)
Paper 1, paper 2.
Notice again, that they are consecutive papers in the same journal. The second paper also has an extra author, and that could be one reason for splitting into two. But once again, from the point of view of content, the general method was devised in paper 1 and applied to some context in paper 2. But here, the authors spent a section of paper 2 in explaining what they developed in Paper 1.
Thus, long story cut short - it should be possible to go ahead and split into two parts. If they are consecutive, you can carry over everything directly, if not, spend a few sentences explaining your notation etc.
PS - Congratulations for doing this sort of work which could put the editors into this type of a fix. That smells like a significant contribution to Maths, having applications elsewhere (other branches?), which is probably why you insist that it would be rare to find a referee who can ably judge both!

I know it would be immoral to pick up things from Greg's answer now, but I wish I had added that ''consult the editors'' note. Sounds sensible.

This problem sounds either:

bad editorial choice and poorly structure paper or
two papers that were not split in time

Generally a research program is not just growing like a blob, but follow some strategy, planing. If you split the two parts, you can briefly mention this strategy (even if it is retrospective) and the results of the other paper. It can be in the introduction and in discussion as well.  Most journals allow to cite manuscripts under revision. If not, you can try to describe without citation that you had this and this motivation, and the results will be published soon.
If you don't want to split the paper, you can restructure it as one part to subordinate to the other. Eg. if you you have some important technical detail in the first part you use in the second, but boring in itself, you put the details in an appendix or SI. It is pretty common practice, especially in older paper, and it helps the reader orient themselves around.
Two notes:

Again, I would consult with the editor at first place. They are busy, but generally nice people, so he may comment more in detail about your worries about size and structure. You may have completely different reasons of rejection.
You always can try to send out another journal (not necessarily more specialist) without much re-editing. Different journals have different expectations for length, structure, scope.

(b) could be a serious problem, because the referee reading the first paper does not know how legitimate the promised application in the second paper is.
If so, one option is to just follow the editors' advice, resubmit to the more specialized journal, and move on.

Allow me to quote from the code of practice of a journal in my field, which (IMO) should apply everywhere:

Fragmentation of research papers should be avoided. Authors who fragment their work into a series of papers must be able to justify doing so on the grounds that it enhances scientific communication.

The practice of splitting papers up into "publons" (or minimum publishable unit) is a scourge. Get rid of the "two papers looks better than one" adage in your mind. It's not necessarily true, and can be detrimental to the science.
As it stands, you present no valid reason as to why splitting the papers up will improve how your work is communicated. Therefore, you shouldn't do so.

I disagree. Having two papers that are easier to read, understand and review is a perfectly valid reason for splitting up content. I do not at all get the gist from the OP that he wants to split up his papers into publons.

And, yes, for better or for worse, two full papers usually do look better on the CV than one.

@xLeitix I agree that easier to read papers are better. But the impression I got from the question was that there might be too many dependencies for the split to work. If multiple publications will be easier to read, then of course the large paper should be split. The decision to split or not to split should be based on what's best for presenting the science.

20 page papers aren't usually anywhere close to publons, but the desire to have more papers on your CV should be left out of the decision of how to publish your research.


text:
Is it advisable (or even possible) to get a second masters in a similar field from a higher-ranked instution?
In May, I will graduate with a Master's Degree in Mathematics from a school ranked #201 in the U.S (for undergraduate education). It is unranked in graduate school rankings (for my program).
I am excelling in my current program with research focus in mathematical biology.
My goal: I would like to get my Ph.D. from a top-5 institution.
Assuming I don't succeed in my goal directly, is it advisable or even possible to pursue a second Master's degree in mathematical Biology, from a second-tier institution, and then apply for a Ph.D. at a top-tier institution?

My goal: I would like to get my Ph.D. from a top-5 institution. — Why?

Can't you apply a PhD program with your current masters degree? Why do you prejudge and assume you don't succeed? First apply for one or two PhD programs; if you see something wrong with your resume, then try to fix it.

@JeffE - Haha. Well, it is always lucrative until you get there, isn't it!

To expand on @Jeff's comment above, your question asks whether something is advisable. Advice can only be dispensed if we know your goal. If your goal is simply to have a PhD, then anything that leads to that end is advisable. If you have a different goal, the question is too vague to give good advice.

It is possible to get second masters degree in a similar or related field. Doing so might even help with getting into a top PhD program.
That said, where you did your master(s) degrees is not the key to the kingdom or even the most important thing in your PhD application. Demonstrating that you are smart, hardworking, and excellent at research should be your goal. Another masters from a "better" University might help toward that end but it's hardly the only or best way.
Focus on doing excellent research, publishing that work in excellent scholarly venues in your field, and getting excellent letters of recommendation from people that are known and respected in the field. If you do those things, and if you also have good grades and test scores, you'll be a strong candidate for any PhD program. I have seen people build that portfolio as an undergrad, in a masters program, as research staff at a university, or even in industry. What you do matters at least as much as where you do it.


text:
Do mathematics researchers regularly solve problems like the ones from Project Euler?
I'm not sure that this is the right exchange for this question. It asks about the possibilities of research in mathematics and computer science.
Extended Background
I am very interested in mathematics and theoretical computer science. Over the past few years I've gained lots of experience from math competitions, programming competitions, software development internships, and talking to professors, and I've learned that I do not enjoy writing code; I enjoy writing "beautiful" and elegant code in practice, just as I enjoy beautiful and elegant proofs in mathematics, but I do not enjoy writing hundreds of trivial imperative lines of code to make some company money. I've learned that I like to think critically about problems, and I like finding the quickest, most efficient, most elegant solutions. I enjoy the mathematical (or theoretical) side of computer science.
So, recently, after coding only with imperative languages my whole life, I discovered Haskell, a functional programming language. It is extremely close to mathematics: Everything is a function. Ideas are defined rather than executed; instead of giving a computer step-by-step instructions, the computer is given a definition. This discovery reaffirmed my passion for mathematics and the mathematical and theoretical side of computer science.
Minimal Background/Question
I've also been frequenting a website called Project Euler, which is filled with 450+ mathematics-based programming problems. This is essentially the epitome of my passion. I love solving these problems with Haskell (and sometimes, when I'm clever enough, with merely a pen and paper).
I know that many of the questions (if not all of them) have already been solved and researched in both the field of mathematics and the field of computer science, and hundreds of their variants have been as well. However, many of these problems were initially proposed and solved hundreds of years ago by mathematicians (such as Euler and Gauss), and most of the relatively newer problems were all proposed and solved by the 1980s.
So my question is, are there still problems like this that I can think about for a living? If so, which field and sub-field is closest to this type of research? If not, would I be involved in these problems by teaching and then introducing them to students of mine, or hosting competitions?
TL;DR

Can I solve problems like this one as a career?
If this research isn't viable, would I be more involved with this type of problems by teaching and hosting competitions, etc?

I assume by research you mean paid research rather than just a hobby. If so, this probably makes sense mainly in an academic environment. So it would be useful for us to know whether you have any relevant academic background.

@Bitwise I am still only a senior in high school, though I have been actively involved in mathematics and computer science for quite some time now. I have explored my passion for academia over the past few years and have firmly decided that I want to be involved in it for the rest of my life.

Have you considered doing research in theoretical computer science, for instance on programming languages?

Functional languages are closely linked with Artificial Intelligence - an area of science with a lot of problems to be solved in a beautiful and elegant way.

Most code isn't trivial. If you are spending a significant fraction of your time writing trivial code, something has gone wrong. Automate it.

Your enthusiasm will serve you well in any career that you choose, but I would caution you that it is increasingly difficult to pursue a career as a tenure-track mathematician. There are many software companies that solve difficult, math-intense problems; it's not all writing line-of-business software for medical records automation. If you're interested in learning about the sorts of problems that professional mathematicians solve, go to your local university library and take a look at some journals; the librarians will help you find what you're looking for.

One field that comes to mind is classifying combinatorial objects, which often involves computer searches. Do the publications in, for example, this, this, and this list sound interesting?

You should look into category theory. It is the mathematical underpinning of type theory.

This may be a better question for Math.SE.  That said...
These sorts of problems fall in the category of contest math.  Sometimes they are related to active areas of mathematical research (most often number theory, combinatorics, and geometry), but more often, current research deals with problems that are considerably more complex and can't be solved (or even stated) in a page or two.
Note also that, at least in the US, there are very few people who get paid to do mathematics research full-time and exclusively.  Most professional mathematics researchers are professors at colleges and universities, and their duties also include teaching and administration (to varying degrees).
There is a recognized subculture of mathematicians interested in contest math.  They may get involved in creating problems, organizing contests, and coaching students.  At some universities, such activities may be considered a significant part of their research or "scholarship" duties, but they would normally be teaching regular math classes as well.
Edit: Actually, there is a category of careers I had forgotten: intelligence. The NSA and its counterparts (GCHQ, etc) employ many thousands of mathematicians. Of course, it's hard for an outsider to know what goes on there, but it could be that their activities have more of a problem-solving flavor. At least they are not bound by the requirement that their work be publishable! The NSA has a well-known (and highly competitive) summer internship program for undergrads, the Director's Summer Program, so that could be one way of testing those waters relatively early on.

Well put.

"in the US, there are very few people who get paid to do mathematics research full-time." But I think it's worth noting that there are a substantial number of people who get paid to do mathematics research for a substantial fraction of their time.

@David: Well sure, I happen to be one of them. :-) The asker seemed interested in doing math more or less exclusively, by my reading, so I wanted to address that. Though I just thought of something to add.

@NateEldredge I know you know that but I also know the asker doesn't so I think the clarification is helpful.

I believe @Mangara's comment is very relevant here:

Number theory, combinatorics and geometry (the areas Project Euler mainly draws from) actually have lots of accessible problems that are still unresolved.

Accessible here means that the problem can be easily explained.  However, unresolved problems that anyone can understand tend to be extremely difficult.  If they weren't, then someone would have solved them!
Get a copy of Richard Guy's Unsolved Problems in Number Theory.  There you can find some problems that constitute "real mathematical research" but are more or less in the vein you describe.
You can usually only (get paid to) do this research in a university, you have to be very talented to get a tenured job in these areas, and it's a long road.  Also, due to the highly interconnected nature of mathematics, the techniques used to solve these problems are often vastly different from what you might expect -- for a famous example, see the proof of Fermat's Last Theorem via algebraic curves.  So if you want to work in (say) number theory, you'll still need to learn deeply about and use other areas of mathematics.

I prefer his Unsolved Problems in Geometry.

As @NateEldredge already explained, such easily-apprisable questions, most often arising in math contests, or as puzzles, are mostly not what could allow a person to make a living as an academic mathematician, except in cases of ultimate-extreme talent, perhaps.
At least as idealized, academic mathematics aims to develop and validate viewpoints that clarify fundamental issues. "Problem solving" is significant, but is at the extreme end of the phenomenological aspects of the business. As Nate E. noted, most "active" questions in mathematics will not be easily understood by amateurs, or perhaps even by non-specialists. These questions are mostly not of the easily-apprisable sort...

Number theory, combinatorics and geometry (the areas Project Euler mainly draws from) actually have lots of accessible problems that are still unresolved.

@Mangara, I have some reservations about "accessible problems that are still unresolved". That this is usefully so is a pleasant optimism, but I doubt that it is matched "in the fact".

I can only really speak for "the fact" my own field (computational geometry), but if we define an accessible problem as one whose problem statement can be easily understood by amateur mathematicians, many of the problems we study are indeed accessible.

What @Mangara said. It is constantly surprising to me just how many accessible questions are open. The fact that a question is easy to understand is no indication that it is easy to solve!

@Mangara: Still, even if the problems look similar to contest problems, the experience of solving them is very different.

Here's the view from my vantage point:

The kind of interesting problems you can solve in 30 minutes to 7 days each (as found in mathematics olympiads, competitive programming contests, and which, by the way, have tremendous value by being fun for whoever gets into them and being accessible to large numbers of high-school students, as well as developing their mental capacities and practical skills), are typically  not of interest to most professional mathematicians because they are considered too trivial. Research publications require more substance than a couple of observations and a direct application of some 100-year-old theorem. Also, you would drown in the task of citing the relevant literature.
Therefore, as a professional research mathematician, if you want to keep your job, you will be effectively forced to find a frontier somewhere in some field and publish results which are very likely to be novel and well-received by journals. You can expect to meet lots of interesting sub-problems, but also lots of questions that frustratingly don't have easy answers. Also, the chances of this type of work making impact on some field external to mathematics are not great.
Interesting sub-problems come up all the time in all sorts of other research, not just in mathematics. Even in programming jobs that are not considered research — sometimes a requirement says that certain aspects have to behave in a certain way and meet certain constraints, and naïve solutions turn out to not be good enough.

Putting it all together
To alter the question a bit, I think there is a wide selection of jobs where 10-30% of your time will be spent on solving interesting sub-problems. These are not restricted to research in mathematics. Very few jobs where this figure will be 100% (people do this on a volunteering basis, verifying problems for Codeforces, TopCoder, etc., not to mention actually competing just for the fun of it).