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Is it ethical to ask students to proofread a textbook?
I will have a draft of a new textbook ready for the fall semester. It is an engineering class.
I very much want feedback from the students concerning the quality and usefulness of the material.
What are the best practices for getting this feedback from students? Is it ethical to give a grade (or extra credit at least) based on students' feedback?

Comments are not for extended discussion; this conversation has been moved to chat. Please read this FAQ before posting another comment, and please avoid answering in comments: if you want to oppose the idea of collecting feedback from students, write an answer.

In practice, you will receive great feedback from a very small proportion of the students (and this subset will consist almost entirely of students who will do well on the course regardless). But even the weakest students can and will make perspicuous observations, or point out gaps in your explanations, that will be helpful. And then many students will be hard-pressed to contribute anything.
If any credit at all is traded for feedback, you actually raise the threshold for students who are aware they are not among the top and hence afraid of saying something dumb. The "swots" might go into overdrive, which generally produces lots of great feedback, but you feel you are abusing the time and kindness. The majority who has no substantial thing to contribute might feel compelled to manufacture something.
The "extra" idea does not mitigate against the latter problem, since students will evaluate every bit of possible credit in terms of the relative effort. Any carrot being dangled is far play.
So: my answer based on experience over several books and years of teaching: do not skew or degrade the feedback you could be garnering with any of these extra credit arrangements (quite aside from ethics which has been well addressed in the other answers). Use the book-in-progress as lecture notes, make it very clear that you are aware it is still teeming with mistakes, and that any and all comments are hugely appreciated.
At the end, you will know the main feedback contributors by name. They will come to you for recommendation letters, career advice, and so on. And then you will be able to reward their kindness in kind. Such is not a bribe; the praises you have to sing about such a student are genuine!

Letters of recommendation absolutely are a bribe, and absolutely do affect students’ motivations and behavior. All professors see this. So yes, the praise may be genuine, but let’s not be naive about the effects of this gamified rewards system of academia on human behavior. Whether it’s grades, letters, fellowships, or other carrots and sticks, academia is full of bribes. (To be fair, I don’t have a suggestion for how to eliminate them, and don’t think this statement is true only for academia - the same could probably be said about most workplaces and industries.)

@DanRomik Sometimes they are a bribe, but there can exist genuine relationships and actions, which are not motivated by personal gain.

@axsvl77 of course. That’s true equally for grade-based incentives. This answer tries to draw a distinction between grades, which are supposedly a kind of bribe, and letters of recommendation, which are supposedly more honorable and not tantamount to bribes. What I’m saying is that this distinction is arbitrary and doesn’t make sense. Both reward systems are a kind of bribe. That doesn’t mean OP shouldn’t use them, though. And yes, in the situation OP is asking about, I believe the students’ motivation to help out will be primarily intrinsic and “noble”.

The use of the word "bribe" is problematic, because its definition is very much dependent on context. Mirriam-Webster defines it as "money or favor given or promised in order to influence the judgment or conduct of a person in a position of trust", which in theory could apply to any purchase or sale, except perhaps for that "position of trust" part. However, the general feeling seems to be offering or soliciting something that isn't normally up for sale, in this case a grade or future recommendations from a professor, that ticks that box. I'd say this is probably bad territory to play in

Horrible answer. The only reasonable solution is for the professor to pay the students. If you want professional work done, you pay for it. That's all there is to it.

@user91988 If you have a different solution, please post it as an answer, instead of repeating it in comments.

@MassimoOrtolano I was commenting on why I downvoted, which is what you're supposed to do. If I wrote that exact comment as an answer, you'd say it's not long enough and needs more details. There's no winning on this site. I'm giving the best advice I can in the best place for it. But thank you for your input.

@DanRomik It's the nature of a bribe that you give it or promise it before someone engages in the action for which you are bribing the person. Here there's no expectation that the student will give the book feedback after getting the recommendation letter and Deipatrous has nothing about promising people better recommendation letters if they provide feedback to the book.

Is it ethical to give a grade (or extra credit) based on student feedback?

I think the key question is, will reading draft material from your textbook help students towards their understanding of the subject of this class?
If yes, then it honestly sounds like a great exercise to me. Not only does it force the students to actually read some material related to the class (albeit in an unpolished draft form), it also could allow them to "check" their understanding by comparing the draft with the material they are already familiar with. Some suggestions:

It seems best if they are asked to read material that you have already covered in class and that there are other sources on; that way they are not just completely lost, but they have something to compare to and a way to reliably detect errors.
If this is part of the grade (extra credit or otherwise), I think it should be mainly based on completion, not on how many errors and typos they find. You could also ask them to write a "summary" of the chapter to check their understanding and thoroughness.

If no, then it is unethical. Your job as a teacher is to help the students learn the material, and using them as free labor to proofread your book is inappropriate.
This could be the case, for example, if the book is not exactly on the subject of the material that the class is covering, or if it is in such an unpolished form that it is difficult to get anything out of while still a student, and not an expert on the material.

+1, you nailed the essential points. I have done this with draft book chapters and course notes and it works to everyone’s benefit. My suggestion to OP is to make it an extra/bonus component of the grade rather than required. And don’t forget to keep a list of the students who have useful feedback and mention them in the acknowledgments section.

I worry that the OP could use this answer to justify optimizing for their book rather than for their class. I would agree if the question was changed from "Will it help their understanding" (ie anywhere >0 in usefulness) to "Is this the best thing to help their understanding"

@NathanCooper Good point -- I agree with your clarification, and I also agree with the now accepted answer.

It's not enough that reading the draft is arguably helpful to students. If it's helpful to you, and you would otherwise have to pay people to do this. It is very similar, though not identical, to letting people paint your house as an exercise in becoming a painter. It may be educational, but you're getting a free paint job (ok, imperfect metaphor, they might stain some places).

@einpoklum I see your point but I don't think I agree. Assuming it helps students (more than an alternative assignment) then it's a win-win. The fact that it helps the teacher is irrelevant. In the painting example, if painting the teacher's house is a great way to learn to paint, then what's the problem? Once again seems like win-win.

The real potential issue is that it might not really be the best exercise for the students -- the accepted answer points out why. The fact that it benefits the teacher is mostly irrelevant.

@6005: It is anything but irrelevant. When a teacher has pecuniary interests relating to how they teach a course, this is an ethical issue, and the course content may be inappropriately warped. What's more, it is usually very difficult to realize in hindsight whether this has happened and how.

It is ethical to ask students to proofread a textbook. It isn't (generally) ethical to grade students based upon their feedback having proofread (unless their is an agreed-upon educational basis).
Some students will read the draft of your textbook, especially if it is required reading. You can ask students that do read your book to provide feedback and you can offer to include any students that do with an acknowledgement.

"It is ethical to ask students to proofread a textbook." It absolutely is not. You have power over students, you should not ask them for such favors - ask them to do work which you would otherwise need to do yourself or pay for. If these are graduate "students" who are actually paid a salary or a research stipend to be part of and assist your research and/or teaching efforts, then it is more likely ok (depending on the details). The most you can do is say that you're working on a textbook draft, offer a link, and say that feedback will be appreciated but will in no way affect the grade.

@einpoklum The most you can do is say that you're working on a textbook draft, offer a link, and say that feedback will be appreciated but will in no way affect the grade vs. ask students

I have done this in one course (letting students proofread my lecture notes for extra credit) and might be doing it a few more times. A few caveats:

Keep the stakes low. This should be extra credit that can take an A- to an A, not a source of points that lets students max out their grade without writing exams. There are several ways to do this: You can make each correction worth very little, or you can cap the correction points per student, or you can let correction points peter out (e.g., the n-th correction a student finds is only worth 1/sqrt(n) points or so). I don't know what the best option is. Moreover, there should be a way to get the maximum grade without reporting errors. Rationale: There is generally a certain type of student that tends to find a lot of mistakes, while others just don't see them, either subconsciously correcting them in their mind or focusing on the "big picture" and reconstructing the details on their own. All else being equal, error spotting probably correlates positively with scientific success, but all else is not usually equal, so it is not a great measure of ability. Moreover, if you value corrections too highly, students will get too defensive about bad corrections for the sake of grade optimization.
Make sure you aren't only rewarding the "fastest gun in the west". Let students know they can still get points for correcting slightly outdated versions in reasonable time.
Prepare a few canned "thanks, but that's not what I'm looking for" responses for students "correcting" what are actually matters of style. In case of doubt, give out points, even if you don't correct.
Prepare a comfortable way to keep track of what student has received how many points. A specific tag in your mailbox is one option, but there are probably better ones around.
Including the model solutions in the "bug bounty" (i.e., giving extra credits for mistakes found in them as well) is probably a good motivator to make students read model solutions, which may improve their later homework quality.
As my lecture notes are open content and closely relevant to the class material, I have never found any conflict of interest in rewarding students for improving them. If the notes were to become a commercial textbook, I'd be a bit more conflicted, although I'd still say it is on the ethical side, if the students get to keep the notes. If the notes were unrelated to the class material, I honestly don't know; as a student I would find such a grading scheme somewhat bewildering.

This answer has great practical tips.  One more such tip could be to be sure to thank the proofreaders in the book itself, because the book is a project that goes beyond grading of the current semester and therefore any extra credit should not be the sole reward for participating in proofreading.

for extra credit Then this is unethical, because it is not testing your students' knowledge of the subject. If the grade doesn't actually matter to the students' outcome on their course, then it's not too bad. If this counts towards the grade of degree they get though, you very seriously need to be talking to your university's ethics board and legal team, because you're putting yourself in a real corner here.

@Graham: My reasoning is that as long as the errors found are in relevant course materials, error hunting does test the students' knowledge of the subject. (It isn't much different from homework problems, many of which are not really central to the understanding of the subject but rather can be viewed as brainteasers. Part of the problem is that no one really knows what helps students understand the subject.)

@JirkaHanika: The problem with acknowledgments is, as I understand FERPA it might require asking any single student who reported a typo for permission to include their name. It's more trouble than it's worth, alas.

@darijgrinberg - True.  If the students become collaborators, one has to treat them as collaborators.  There are ways to thank unnamed contributors, too, and if the primary author gets paid for the book, to pay collaborators as well.  All this is practical only if the number of actually collaborating students is reasonable.  In my limited experience only certain students tend to pick up the challenge in a meaningful way.

Agree with the "keep the stakes low" - in practice, zero stakes elicit about as much useful feedback as low stakes, and are much less of a headache to administer!

@Graham: Moreover, I can't imagine any course where "interacting with professionally written subject matter" (i,e., training wheels for future articles and reviews) would fail to be part of the discipline being shared.

@DanielR.Collins This isn't any kind of "training wheels" for the students.  Based on the numbers of textbooks written versus the numbers of students, I would bet that none of them will write a textbook and be reasonably confident of winning that bet.  Being able to write good documentation is a skill in its own right, and deserves to be taught in its own right.  Simply giving fake marks to favoured students, because that's really what this amounts to, is not teaching.  If it has not real consequences then it's no big deal, but if it affects the final course grade then it's a disastrous idea.

@darijgrinberg If you don't know what helps students understand the subject, then I suggest that finding that out would make you a better teacher!  I know from my own uni days that this is the case for almost every university lecturer, because they are selected for their knowledge of the subject and not their ability to teach it.  Teaching in schools is radically different today from what it used to be, based precisely on research into what does help students understand.  Universities still seem to be stuck in the "put students in rows and talk at them" model though.

@darijgrinberg ... Fair play to you for trying something new which might get the students involved, although I do have concerns about the marking.  But in all respect, there's a lot of theory of education which should be pointing you towards how students learn.

@Graham: And all of that theory is pointing in mutually opposite ways. I have almost never found any educational theory of use in a university setting that doesn't make unrealistic (and often unsaid) assumptions, such as "all students are roughly on the same level", or "all students have roughly the same amount of spare time", or "any two students can usefully collaborate with each other", or "all students will find any given task roughly equal in difficulty", or "there is a way to define a set of measurable and specific learning goals for each course". If education theory ever ...

... progresses to a point where it can give concrete incremental advice for improving a course rather than "actually, have you tried a completely different type of instruction?", lecturers will likely be a lot more willing go try it out. For now, we're just stumbling about in the dark, and our self-proclaimed guides are as blind as ourselves.

@Graham it sounds like you are not, and never have been, a university professor, unlike the writer of this answer and others commenting here. I’m sure you’re an expert on many topics none of us know much about, and you sound like a very logical and reasonable person. But you should know that, from the point of view of someone who actually teaches university for a living, your thinking on the ethics of grading expressed in this thread comes across as simplistic and naive.

Assuming the situation was the same as OPs, it was unethical for you to do this. You're lucky you kept it low-stakes so students weren't upset enough on principle to act.

It is ethically fraught in any case. It can be perceived as a bribe by some. It can be perceived as a requirement by some students that asks them to go beyond learning and demonstrating their learning.
Certainly you can ask students to proof your text books and you can solicit their opinions. I would do the latter anonymously, however. You will get better and more honest replies. You can still give an acknowledgement to the class, if not to individuals.
It is fairly common to pay grad students to do this sort of thing and to ask them to write exercises. But there are no grades involved.
My suggestion is to make it a side transaction, fueled by money, not by grades.

:s/money/other perks/

In practice, I'm sure that any financial rewards given to students will be a much greater headache (in terms of reactions and in terms of paperwork) than grade rewards. Moreover, the "go beyond learning" argument can be made verbatim for homework: Very few homework exercises are really "on the critical path" to learning the material; many are sideways explorations and digressions.

I agree with everything you've said, except that the last sentence should only be relevant for students who have already gotten their final grade for the course. Maybe even not for another semester or two afterwards (i.e. right now only for people who took it a year ago).

@darijgrinberg: It's easier to butter up students with grades because academic oversight is weak and employment justification is strong. But what you're suggesting is avoiding red tape by bending, or breaking, ethical principles.

@darijgrinberg Why would financial rewards be a greater headache? That's how business has been done for centuries. You want work done, you pay for it. There is no reason this would be a "headache" for anyone (except, of course, for a stingy prof who doesn't want to pay). Not paying them would result in headaches.

@user91988: Administrations tend to get stingy when there is money involved.

Proof reading is work. Pay them.
It's probably worth checking with your faculty if they have arrangements with any proofreading services for publications since these will already exist. If you want to reward students with work experience in academia then you should request a casual work contract that is managed by your institution's HR department (never engage in a contract by yourself). Though, it is still an iffy question ethically, particularly where this might take work away from professionals.

Why two times though near "Casualisation"?

What does "casualisation" refer to? Extrinsic motivation by means of higher grades? (1. (economics) The process by which employment shifts from a preponderance of full-time and permanent or contract positions to higher levels of casual positions. 2. The process of making anything casual.)

Why does this not have more upvotes.....

@PeterMortensen Casualisation is defined as described in the link you shared - employers favouring casual contracts to the detriment of worker stability. It was intended to refer back to the point of it being possible to employ students on a casual basis, which I was hoping to indicate should be considered a later resort than hiring professionals. As an example of this, the UCU is currently striking over the issue of casualisation in the UK.

In grad school I took a class where we test-drove a textbook draft (not the professor's, but a colleague's). We used a tool where the PDF was available online and students could highlight parts of the text and post comments or questions or feedback about it. Everyone could see and respond to each other's comments, including the textbook author and the professor.
I don't remember exactly, but I think students were required to participate by posting regularly on each week's assigned chapter, and constructive feedback was requested, but it was pretty much just a participation/effort grade. Comments didn't have to be feedback or constructive to get full points.
I don't know if this kind of approach would work for you, but I think it was very effective for students and the book's author and I feel there were no ethical issues with this setup.

Wait, the author was not the course professor? In that case, the scenario is completely different IMHO. Suggest you make this a comment rather than an answer.

@einpoklum the author asked our professor to test-drive the book, which was still in the drafting stage. So I feel the scenario was very similar.

One textbook we used was created, chapter by chapter with all the examples over several semesters at one university.
The author expressed his thanks to the students in the preface...

I see such acknowledgments in many textbooks, but this doesn't answer the question: is it ethical to give students grade credits for it?

@darijgrinberg that was not the only question...

That's just fine but it's not what OP asked about.

A long time ago, one of my professors used lecture notes that were intended to become a textbook. He offered a bottle of champagne to the student or team who reported the most errors in the manuscript.
This clearly removed the issue of a grades-for-services trade, and still encouraged us to spot and report errors. The bottle was good enough to try for, yet cheap enough that it wouldn't bother the tax authorities.

I would hand out a draft of the book to the students (or the relevant parts only) and  award bonus points towards the final grade for every valuable suggestions that helps to improve the manuscript. I did this several times already and the students appreciated this. Probably relevant: I used the bonus points only for a "pass of fail" grade, so the students could look for improvements to make up for fails in the homework assigments but not to improve a final grade.
To make sure that you only count every suggestions once, you can use a forum to collect them. I do this will all my teaching material for some years and it really helps.

In several universities, you could be brought up on disciplinary charges for doing something like that. And if I were in the student union when you tried to pull this stunt, you'd find your name in the local papers: "Lazy professor pays students for proofreading his book by artificially inflating their grade." Just don't. @Buffy's answer has it right.

@einpoklum can you cite the relevant policies and/or news reports involving your claimed “several universities”? Oh, and good luck trying to portray an academic textbook author as “lazy”.

No. We were required to buy a draft release of a new text book, written by the professor. Corrections were handed out on photocopies. The typsetting was bad. The binding was poor. The book was $250 back in 1997.
And we didn't get a 'new' copy with all of the fixes.
Just remembering this event... and we (as students) all made fun of the situation and how ridiculous it was as a requirement for the course.

I am planning to make the book open access.

It's your book. You are the one who should proofread it, not anybody else. You should take sole responsibility for it, but also, you should then receive sole credit for it.


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Can I do publish my paper without APC?
Now a days,I have no money to pay for Article Processing charge (APC) since I have no money support foundation.I want to publish my paper without paying any amount of money in an international journal .For this, I need the names of some international, prestigious physical journals in which I can easily publish my paper without APC in open access .I will be grateful if anyone can help me in this case.
Many many thanks.

Are all journals in your discipline open access?  In my disciplines, many journals are free to publish unless you exceed the page limit, in which case that will attract page charges.

Closing this for being a shopping question. What you can ask about here is how to find such a journal, but in physics, this should really not be a major hurdle – I know of only two relevant pay-to-publish journals. Things become a bit different if you require open access, but then you should first ask yourself whether you really require this in a field where supporting preprint publication is the norm. So, if you wish to ask about the how, please specify what your real constraints and difficulties are.

https://scipost.org/

@Wrzlprmft There are more than two gold open access journals in physics now:  https://journals.aps.org/authors/apcs#pricing https://publishingsupport.iopscience.iop.org/2022-iop-publishing-apc-prices/

Of course you can! There are two ways:

Publish in a subscription journal. Most of the biggest journals in physics are still primarily subscription. For example, the Journal of Cosmology and Astroparticle Physics says:

Subscription publication is free of charge.

If you can't publish in a subscription journal, you can request a waiver. Example from MDPI:

For journals in fields with low levels of funding, where authors typically do not have funds available, APCs are typically waived and cross-subsidized from fields for which more APC funding is available. For authors from low- and middle-income countries, waivers or discounts may be granted on a case-by-case basis. Applications submitted before article submission are assessed by the Managing Editor based on the quality of the research article and the authors’ ability to pay.

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Is there any added advantage to getting Presidential Postdoctoral fellowship (STEM) over regular postdoc appointment?
Is it more prestigious? Does it help to have it on your resume, if you are applying for faculty positions later on? How does a presidential fellowship compare to a regular postdoc appointment at a prestigious university? General pros and cons? What makes a good postdoc offer in terms of professional growth? I am about to defend soon and need to make a decision. Thank you.
This fellowship is based in the US, applicants submit a research proposal along with their choice of mentor or PI. Then the fellows are chosen from that pool. Similar to https://ppfp.ucop.edu/info/. In particular, I am in Electrical Engineering, working on signal processing and communication.

I think you need to tell us which country these are in, and what specifically these Presidential Postdoctoral Fellowships are/how one gets those.

Is this the fellowship you’re referring to?

This is in the US, applicants submit a research proposal along with their choice of mentor or PI. Then the fellows are chosen from that pool.

Dan Romik, yes same idea but different university not in the UC group.

Well, okay, but the answer could depend quite a lot on which fellowship exactly this is, so don’t expect a high quality answer if you won’t provide that detail.

Any answer would be better than no answer, and greatly appreciated, thanks.

I think knowing what field you are in would also help, as different fields have different cultures (and different levels of competitiveness for faculty position).

Thanks I am in Electrical Engineering, signal processing and communication in particular.

I don't know about this particular fellowship, and you'd like to not mention a specific one, which I think is fine - this site does not want to get into recommendations for specific graduate programs, journals, etc, and I think this falls into that category.
I will give a more general answer regarding postdoctoral funding:
It is an asset in future job applications to show that you are able to generate funding for your research.
A competitive fellowship application based on the merits of a research proposal you have submitted would be included in that. If it's just a fancy label assigned to your work under some PI, it probably isn't.
A fellowship that people are familiar with likely counts better than one no one outside a given institution would know: if they know how hard it is to get, say, a postdoctoral fellowship from NSF, then they know the value of having that on your resume. If it's some lesser known fellowship, it'll be up to you to make the case that it's important.
Just like applicants for graduate school, applicants for academic jobs will be evaluated on a broad basis. No one factor will get you or cost you a job, so you'll need to weigh funding sources versus all the other aspects of a post doc that will influence your success in publishing papers, etc.

Thank you, really appreciate your answer and its very helpful

I would also add that something to look at is that NSF and similar post docs often do not have benefits whereas a plain post doc through a profs funding does. Something for the OP to consider is what benefits they are trading. Also, begin Dr. Smith's post doc might be better than an NSF post doc with a lower Dr. not famous if Dr. Smith's network helps her post docs get better (in the eye of the bolder) jobs as the next step.

Thanks, that's exactly why asked this question.

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Being a co-supervisior of a branch proposed for Master thesis from my PhD thesis
I'm a PhD student, writing my project proposal and also a junior teacher in the same university. An ex-student asked me if i would like to co-supervise him in his master thesis and perhaps suggest him a topic of research. It comes in my mind to include him in a task of my PhD project, which might be further explored by him, being also helpful for me. The other supervisor would be my own supervisor.
Would this be ethical?

I'd consider that an excellent opportunity to get further into research, and gaining a pair of hands in your job (even more, as the advisor will also chip in). As long as everybody is happy with this, particularly the master's student (who clearly is on board, as you were approached in the first place), I don't see any possible ethical problems.
But you'd have to check carefully that this doesn't run against any local regulations.

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Extreme nervousness during exam period
I'm currently a master student in computer science. I study at a school where we have only one take for the exam. I study really hard, yet I am never able to feel confident enough when the exams approach. I am nervous that somehow things will go bad and it only makes me perform worse. I tried studying weeks in advance and really going over all of the materials to feel sure that I know it, but it does not help me. I feel I have no power over what happens in an exam and I feel that I only have one chance that could lead to an ugly mark on my resume. How do I reduce the stress and the nervousness?

This might be worth reading:https://academia.stackexchange.com/q/31195/72855

Nervousness in the face of uncertainty is normal. Ask any astronaut sitting on the launch pad. What you experience is pretty common. Overconfidence can also be a hinderance.
You seem to have good study habits ("weeks in advance"). But note that cramming the night before an exam is counterproductive for nearly everyone. If you are tired, so is your mind. And it will be focused only on what you studied last, rather than having a more general and nuanced sense.
One "trick" is to do something active in the last couple of hours before a big exam. Anything to get your blood flowing and let your mind rest. Even deep breathing as a calming exercise has benefits.
I also have a bit of a mantra that I use at the start of an important activity, such as an exam. "Some things are beyond my control. I can only do my best."

Reducing Stress and Nervousness

Begin to look at the exam as a game. It is a quiz and you like quizzes.
Try to answer as many questions from the previous exam papers. This will add to your confidence.
Pray for a calm and clear mind. Never underestimate the power of prayer.
Focus on an imagined object for a short time when you start to feel stressed. This will help you relax.

I can only tell you what works for me. My degrees were all in physics, nothing in any sort of mental health or self help. So take this for what it's worth.
Visualize yourself doing well on the exam. Think about sitting at the desk and blocking out all manner of distraction and disturbance. You can even build yourself little fantasies about the student in the desk next to you being fidgety and making a lot of noise, or some door somewhere is slamming constantly, or there is a thunderstorm. But your concentration bubble deflects it all. Practice this calmness in your mind before the exam. Then in the exam it's going to kick in automatically.
If you are allowed, go look at the exam room in advance. If not, then go look at a similar room. In your mind, picture yourself sitting in this room and being calm. Do it "movie special effects" style and add feature by feature. In your mind, add some other students. Add the prof or the TA's patrolling the space between the desk. Add the sound of the clock. Even go sit at the desk and imagine you are already taking the test. Imagine that there is a furious amount of distraction around you, but it bounces off your Teflon and you are all untouched and untroubled.
After that it all comes down to practice and confidence at the subject matter. You should definitely set yourself some problems to do against the clock. Get yourself used to doing problems under stressful situations. Try going to the cafeteria (or the Starbucks or whatever) where there is noise and distraction and maybe even people bumping your table or chair. Do your timed problems under these conditions. If you can stay calm and finish your timed problem while some barista is shouting "half calf latte with extra foam for Fred!" then you should not get nervous in the exam. But also try doing them in the library where everybody is supposed to be quiet.


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Online College Class Grades
My professor for my online class refuses to grade two late assignments because they were too late to grade. They were only two days late, and she has graded one that was later than that, but she won't grade these ones. Those two assignments tanked my grade to failing. I am freaking out, it is a college class that I don't have enough money to pay to retake it. What can I do to change her mind?

Probably not much,especially if this is the third time you hand in late. Deadlines are there for a reason.

I do not think anyone can answer.  However, it is possible that the online learning system does not allow your professor to input a grade for those assignments.  In that case, your task would be (1) to motivate your professor to change that; and (2) to grade the assignment.

She graded one by another student that was even later than you, or an earlier one that you handed in when it was due for four days already?

@MorganRodgers That sounds an awful lot like an Answer.

If the policy is that late assignments aren't accepted, then late is late. Just because you got a pass once, doesn't guarantee another pass (let alone two more). Next time, get your assignments in on time, especially if you are paying a lot of money to take the course.

Whenever you hand in late assignments, you are at the mercy of the instructor.  Certainly where I work there is no guarantee the instructor will mark these copies at all or without penalties.
It could very well be that your instructor graciously allowed you to submit a late assignment once, but that was it.  I can easily see that an instructor would not want students to habitually submit assignments late, quite frankly a hard line on this is not unwarranted.

I interpret the OP as saying the instructor graded another student's assignment who was even later, which is conceivable if there were mitigating circumstances.

@Allure you could be right but no third party is mentioned by OP.  Either way it’s imprudent to count on anything once due date is passed.


text:
Emailing a professor in another country for a feedback on a project that I'm working on?
I am a telecommunication graduate (Bachelors holder) and currently getting my master degree"completed one semester" .
I am working on a project and developed a new  original idea and constructed multiple algorithms based on it, however my professors could not provide me with a feedback about this new idea since they are not specialists in the field of my work, So I need a feedback from a specialist.
How can send a decent email to professors in another country for getting an answer on whatever my idea is valid and can be published.

Use an apostrophe ' rather than a backtick ` in words like "I'm", "I've", "it's", etc. Backticks are used in Markdown for formatting snippets of text as code.

Your question is somewhat unclear. Are you currently a student? Are you asking about emailing professors at your own university, or somewhere else? Please [edit] your post to clarify.

Related: How do researchers send unsolicited emails asking for feedback on their work?

First, assuming that you are in the US, learn to use professional grammar, spelling, punctuation, capitalization, and fonts.  Starting off with "i m a" will not get any professor's attention.  Try using "I am a".
If English is not your primary language, and you must communicate in English, then find someone to help you.
Next, just write up what you need, in detail.  Spell it out, like this.
Dear Doctor ______,
I am a student in _________ and I am working on an idea regarding algorithms.  Specifically, ___________.
I would like to get your feedback as you are an expert in algorithms.  May I stop by your office during office hours?
Thanks in advance,
_________.

I see the question was edited and looks much better now.   If they are not local, then leave off the stop by the office part.  Maybe suggest a phone call.

As i get from your question. The best approach is to compare your work with existing works. Read latest papers from reputable journals, related to your work. If there is some expert professor try to find his latest publications and see what direction is his work focused on.
Compare your algorithms with latest one in the same field say you are working on collision detection. So read whats the latest approach that has addresed the collission detection, remember collission detection and resolution are two different fields when you come to compare algorithms.
I dont think you should send your final work without publishing it to some one, as it is very easy that your hardwork may be stolen in such case.

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


text:
Would it be appropriate to mark down a student who selected all the answers in this exercise as "correct"?
I was in a library and by opening at random a book about university tests I crashed against this page

This is meaningless, a finite set of numbers can't define a succession and this is a multiple choice test that doesn't ask to justify the choice: the student can answer peacefully randomly. For example in the question 3 the book say that only E is correct, but we can answer A, if we consider for example the sequence

or B, if we consider for example the sequence

or any other answer. The authors of the test implicitly consider the simplest law the only correct: is this way of proposing the thing acceptable? Am I too pedantic? I only contest the fact that this kind of question is not compatible with the closed form. It would be correct to reject a student who provocatively check all the answers? Please note this is not a question about mathematics (things are simple about that), it concerns the right, or maybe the duty, of a student to respond provocatively to a question he deems wrong. Would it be inappropriate?

Edit
Of course strictly speaking this is not a university book, this is a book thought to admission tests. Anyway the target are men and women who are preparing to enter the university, decidedly not kids. I add that if "quickly" is the point, I could think to:

This is simple, quick, correct, but it would be marked as wrong. I didn't know the Stack Exchange room about teaching mathematics, is it possible
 migrate the question there?

Yes, you are too pedantic.

Clearly the exam question is not the best, as multiple answers could be justifiable (though, I suspect the intended meaning is clear). What exactly are you asking? Whether you should mark off for students who feel duty-bound to protest the bad question by selecting multiple answers?

I remember those kinds of questions from when I was a kid. After answering them all 'correctly' (using the simplest analysis) I then enjoyed figuring out various other more complicated ways of making the sequences. But, the 'simple' one was always the 'correct' one. Fortunately  I had a sympathetic math teacher who loved to talk about the other possible answers as well.

That looks as a practice book for some undergraduate admission tests in engineering. If it is, it would be better to specify it in the question, because it's otherwise misleading.

If you want to keep the question strictly about mathematics, we can migrate it there. If you want to have a broader context, it can stay here. Two other remarks: admission tests are graded by machines not humans, so trying to be "smart" may not end well; this kind of objections have been already raised at least some 40 years ago, I can recall several pop-sci journals and magazines discussing the issue.

You mention both the possibility of rejecting a student who marks all answers as well as a student responding provocatively. These are two completely separate issues. What a marker should do when a student has already marked all answers doesn't tell you what a marker would actually do and that answer doesn't tell you what a student should do when faced with such a question. It largely seems like you already know what the "correct" answer is and this is a rant more than something you want an actionable answer to.

I don't read Italian so I have no idea about the detailed content of the page, but engineers should be looking for simple solutions to problems not over-complex ones, and in that sense the test is a "good" one (but far from optimal, of course). Someone who ticks all the answers as correct may be better suited to a career in law or politics than engineering!

@alephzero wish I could upvote this more than once. I have worked as an engineer with people who looked for the complex answers, and it was Not Good.

@alephzero yes, it’s true that engineers should look for simple solutions, but that’s not the only way to frame this issue. For example one can say with equal validity that engineers should care about scientific truth and not choose which answer they give to a scientific question based on what they imagine would be more pleasing to their superiors. Psychological considerations of this type have no more place in engineering than they do in mathematics.

I don't want to pillory the authors or anyone else. I don't know the mechanisms by which this happened (often the world goes too fast and the quality of job suffers, probably there is a set of causes involving publisher, authors, university admission tests, etc.), but I feel sad when I see things like that. @Geoffrey_Brent I find it bleak that my professional skills are superficially called into question: in my job and in my life I look for the simplest solutions. This has absolutely nothing to do with the question.

I actually think this is a question about mathematics, or more precisely about mathematics education (and in the limited scope in which it is presented it would be a better fit on the Math Educators stack exchange), but there is a larger academic issue which is perhaps what you are “really” asking about.
The point is this: as educators we try very hard to instill in our students the values of precision, logical reasoning, and attention to detail. When they are sloppy in their answers to our carefully phrased exam/HW answers, we mark off points and wag our fingers at them. We go to great lengths to provide them with examples of well-written, thoughtful, precise, polished answers (and other content) that pertain to the topics being discussed, in the hopes that they will pay attention and seek to emulate that style of discourse.
Given all that, and especially in mathematics where that precision is an essential value that goes to the core of the entire discipline, we cannot afford to ask sloppy (and formally incorrect) questions ourselves. It is a terrible example to give students and undermines the very goal we are trying to achieve. A teacher who is sloppy cannot expect to produce students who are any less sloppy than the teacher.
Coming back to your textbook example, it may depend on the age group this textbook is aimed at, but for a university-level audience the problem you cite is indeed unacceptably sloppy. You are not being too pedantic; a student who answers that all answers are correct will have answered the question correctly (to the extent that the question is sufficiently well-posed that it can be said to have a correct answer) and deserves to get full points for the question and to not have anyone be describing their behavior with the word “provocatively”. Such a student will have shown themselves to be more thoughtful (unless they arrived at their answer by pure luck) and to have a better grasp of mathematical precision than the authors of this textbook.

Actually, the OP does not seem to be totally honest: for what I can tell, that's not a textbook, but a practice book for some undergraduate admission tests in engineering.

@MassimoOrtolano yes, I realized that how acceptable this way of presenting things is may depend on the target audience. It also depends on specific issues of wording that I can’t speak to since I don’t speak Italian. In any case I hope my answer addresses the larger issue I was extrapolating to from OP’s situation. Also, even for a practice book like you are describing, I think it wouldn’t be good practice to frame the question as being about finding the “correct” next term in the sequence (but I don’t know if that’s what’s done here). Even high school students deserve more respect than that.

I guess there is also the philosophical (but also practical) issue of whether one views mathematics as a particular methdological approach to finding out what is true, or as a standard for Xtreme certification of particular kinds of "truth". I myself am a bit fond of the latter, but in my later years far more interested in the former.

If this is indeed a practice book for admissions, there is little point scolding the authors of the book - if the admission questions are indeed that silly, the book needs to prepare students for that, otherwise it's not doing its job very well.

@xLeitix perhaps you have a point that the book isn’t a proper textbook and its authors aren’t really educators and should not be held to the same standard as educators. Fair enough. Nevertheless, I can imagine a way to explain to the readers how to “correctly” answer the question (meaning to get full points) while still managing to put the point across that the question is sloppily stated and has no “correct” answer, so I don’t fully agree the authors are beyond reproach. (And regardless, even if they are, I can still be unhappy that students are exposed to such poorly thought out content.)

Although not reliably explicitly made a part of the question, it is widely understood that the "correct" continuation of a sequence is the (allegedly) "simplest". There is still a problem with the notion of "simplicity", since it is relative to context. (The notion of "Kolmogorov-Solomonoff-Chaitin complexity" is a rigorous approach, but certainly not something that kids should be expected to know.)
Nevertheless, in the implicit context of school mathematics, for example arithmetic sequences are very simple, so if the initial segment fits into an arithmetic sequence, just continue it. Also geometric sequences.
Beyond that, it quickly becomes murky, because I don't think students are taught "polynomial interpolation" (also known as "Lagrange interpolation"), although I may be mistaken.
So for a student to check "all" as a sort of "protest vote" is not really justifiable, since a student who knows that any finite sequence can be interpolated arbitrarily will surely also know that that's not really the point... :)
EDIT: and, no, _of_course_ there's scant excuse for an awkward version of the question being posed, where there is no unique very-simple extrapolation. Yes, of course, in principle this could happen, and then we might imagine that a student is justified in a protest-response. In practice, in my experience, such questions most often really do have a plausibly-best response, while, yes, in principle, being ambiguous. The fact that, in principle, there's a problem, does not, in practice, create a problem.

What about cases where there are multiple reasonable interpretations, and the student chooses one which isn't the standard or expected one, but nonetheless makes sense? I find "that's not really the point" a very weak argument imho, and it does not make for a reasonable excuse for the question being set in an imprecise and unspecific manner.

Of course, I can understand your point for the questions specifically listed out in the OP, which are clearly arithmetic/geometric progressions. Even so, I don't think it is appropriate to mark a student down for putting down an answer which is technically correct, even if one might be tempted to write it off as pedantic. (Things get worse if the sequences aren't so obvious even if relatively simple, for example with sequences a(n) given by a quadratic in n but only the first few terms given.)

What @YiFan said. I've absolutely seen examples of this where there were multiple very plausible choices and which one comes to mind is just a matter of how your brain works. The protest here is fully warranted because, short of something like it to fight the entire practice of giving this type of question, students are going to be unjustly punished for it silently.

While a student at this level is unlikely to be able to prove it, I find it plausible that some students know that for any n points in the coordinate plane, unless vertically aligned, that a polynomial can be found to pass through them all. (1, 3), (2, 9), (3, 81), (4, k), for any value of k. It might even be mentioned as a "teaser" in a relatively low level class.

You say "The notion of 'Kolmogorov-Solomonoff-Chaitin complexity' is a rigorous approach" - and which Turing-equivalent machine do you use? k/s/i calculus? Lambda? Fractran? There is no "simplest" explanation unless you specify the language/machine. "Common sense" is not common either for such short sequences.

@CaptainEmacs, part of the point of K-S-C complexity is the result that changing the machine/language does not change the definition by much... Yes, of course this is only useful for some very large (or infinite) class of computations/descriptions, asymptotically, etc.

The fact that "simplest answer" is sometimes ambiguous does not mean that it's always ambiguous. I'm pretty sure that most of the folk who are hair-splitting here could in fact figure out what answer the examiners intended, if there was something of value at stake. Yes, there are poorly-written multiple-choice questions where it's genuinely unclear what the "correct" answer should be. No, these are not among them.

@paulgarrett Yes, with the emphasis of "asymptotically". Which above short sequence is emphatically not. A better answer in this case would be VC dimension or Rissanen's principle, but even then, you need to specify the class of approximators. I sympathise with OP, because, despite the relatively obvious answers in this particular case, I distinctly remember as a kid having argued with my quizzer in a similar test (IQ?) about the right solution in a quite ambiguous case. I remember having cost me points then.

Actually, it would be wrong to reject such an answer, but the student had better have evidence to back it up. This is the sort of thing that a teacher might be misled by if they haven't actually developed the question themself. Or worse if they are a "tester" rather than a "teacher". Worst, if they are teaching "by the book", keeping one day ahead of the students as is done too often.
I fear for the student in a situation like this. The "expected" answer is likely looking at only simple progressions and not sophisticated ones.
I once encountered a similar situation, though, thankfully, not on a test.
But if a student had an enlightened instructor they could answer outside the bounds similarly to what you point out here. But an uncommented "checking" of all the boxes will probably not be seen as provocative, but as unprepared.

Gauss was famously hated by his teachers for his brilliance. Or so the story goes.

Let me add, for people who aren't mathematicians here (taken from a comment elsewhere):
While a student at this level is unlikely to be able to prove it, I find it plausible that some students know that for any n points in the coordinate plane, unless vertically aligned, that a polynomial can be found to pass through them all. You don't even need to get to the point of "a unique polynomial of minimum degree".
So, consider (1, 3), (2, 9), (3, 81), (4, k), for any value of k. There is a polynomial, which is a simple sort of function, passing through all of those points. It might even be mentioned as a "teaser" in a relatively low level class. It shows how relatively simple functions can have great power and applicability.

Indeed, a good teacher should be able to come up with better questions. But it is usually a mistake to make a model more complex than necessary. See for example: https://en.wikipedia.org/wiki/Overfitting and https://en.wikipedia.org/wiki/Occam%27s_razor

@louic Overfitting is the very reason why all of these answers are potentially correct, though; it’s possible to construct a polynomial sequence that exactly matches any finite set of points, as long as they all have different values on the x-axis.

@nick012000 Sometimes the gap between "possible" and "advisable" is very wide indeed ;-)

Just curious: if you had received this as an answer to an exam question, would you have marked it as correct? https://www.gocomics.com/calvinandhobbes/1995/01/09

@Allure If the student can explain how this translates to an accurate description of Newton's First Law, they should have it marked as a snarky but correct answer. Of course that requires more interaction between the student and the teacher than is often allowed.

If a student is knowledgeable enough to recognize that all the options are correct, (s)he should also be knowledgeable enough to recognize which is the answer that's desired.
As the exam-setter, you can never exclude the possibility that there's something you aren't aware of which could make a multiple-choice question have multiple answers. For example in the 3rd series, even if you write "what is the next number in this power series", how certain can you be that in some obscure field which you've never heard of, "power series" has a different meaning? To illustrate, try this question, which is similar:

Q: Which of the following is a metal?
A) Bromine B) Oxygen C) Carbon D) Calcium

 Technically, all four of these elements are metals - by the astronomer's definition of "metals" as all elements heavier than hydrogen & helium. Of course, by the much more common chemist's definition of "metals", only calcium is a metal. If you had never heard of the astronomer's definition, you would never have dreamed of this objection. I'd actually venture that most astronomers would also never think of this objection and will happily mark (D) as the answer. Indeed, I first heard of this question as a gameshow question where the contestant got it wrong, then discovered via Google that there's actually a definition of metals where his answer was correct, and filed a lawsuit alleging he should be given the prize. Similarly, I will give anyone who tells me "none of the above, metal is a type of music" zero marks (sorry).

You can't rule out every possible objection, but you can say that anyone who's familiar with these obscure "other interpretations" of the question really should be able to recognize what you're trying to ask, and therefore get the right answer. In the absolute worst case, they should object during the exam. The student should know that marking one of the other answers and then objecting after the exam is asking for trouble, and that marking all of them is just as bad (I'm sure the instructions say to only mark one answer).

Sorry, but I don't buy the argument. You are just guessing what is in the mind of the instructor. "desired" answer in mathematics is repugnant.

I agree with @Buffy. Saying that an answer is “technically” correct but is not what’s “desired” may be acceptable for a physicist or in other areas (although I don’t think it should be), but it’s not acceptable in a university math class. See my answer for additional thoughts.

@Buffy It's not really "guessing" in this case, because the accompanying text gives some information about how these questions are supposed to be answered (quickly, without use of non-elementary operations).

The example is a bad one, imho. If the question comes up in a chemistry class, it is obvious what definition of metal is assumed. It's like taking a course on group theory and objecting that "group" can also be interpreted in the colloquial sense as merely a collection of objects. That's not really relevant to the discussion taking place here, which is about whether or not a mathematically correct answer can be marked wrong because it is not the desired one.

Another (far more elementary) question to illustrate your point: "We want to build a cannon, what material is required?" A steel, B wood, C plastic, D glass. You can build a cannon out of all 4 materials that sort of maybe works, but there is only one that should be used.

@Buffy Even if questions don't state the simplest sequence is wanted, it is implied in all such questions. Imagine question "which of these is a line" with a drawing of a line and a circle? I would accept both marked only if I believed that the person both knows enough about non-Euclidean geometry to know AND is dumb enough to not know ordinary geometry is implied.

@ZizyArcher, actually, you are creating an impossible dilemma. Suppose a student just happens to jump immediately to a formula suggesting answer (a). Now are they wrong because they didn't go through some analysis over all possibilities  (an infinite number) to find the "simplest"? And whose definition of "simplest" shall we use? Yours, mine, Gauss'? If a question isn't, itself, correct mathematically, how can you expect a student, relatively inexperienced, to figure out a "correct" answer?

@Buffy Well, I would accept all answers that show some reasonably simple formula how the sequence is generated. Say from example, 85n^3 blahblah that would fit A) has more terms than shown numbers in the sequence, while desired an-1^2 is pretty simple. So, I wouldn't accept such a complex sequence when a simple one is available.

I'll also note that multiple choice problems are hard to create in general. Don't blame students when you get it wrong. This may be more true in some fields than in others, but it is a general enough problem that schools of education spend some time on it. I once advised such a student who was told (among other things) that you shouldn't state such questions in the negative. The exercise was to create an example problem. Her solution was to use double negatives for every answer.

@ZizyArcher, then you would be wrong. Sorry. But wrong. But if the answer to the question requires a justification, then the problem goes away. But here it does not. That is the issue at hand.

The authors of the test implicitly consider the simplest law the only correct

Google-assisted translation from the text at the top of the page, emphasis added:

"...these are questions that intend to assess the candidate's ability to quickly discover the criterion by which numbers and letters are arranged within a given succession. Also in this case, no mathematical or linguistic concepts are required other than the ability to perform elementary arithmetic operations."

IMHO that text makes it pretty explicit that they are looking for quickly-discoverable answers which don't require the use of non-elementary operations. Of the two alternate answers you suggest, both require significantly more time than the obvious/expected answer, and one requires non-elementary operations (square root).
(Also: you mention that you opened the book directly to this page, so I guess none of us here know whether there's any further guidance earlier in the book on how to approach such questions.)

This is meaningless, a finite set of numbers can't define a succession

It's not so much meaningless as slightly non-rigorous. Yes, there are infinitely many different sequences with the same beginning, which cover all of the answer options given. But even mathematicians don't need to be 100% rigorous 100% of the time; it's commonly accepted practice to use "..." to mean "continuing this sequence according to the most obvious/simple rule", in cases where there is one rule that is much more obvious and simple than the alternatives.
In this case, I would suggest that 95%+ of competent high-school maths students could figure out what answer the examiners are looking for.
Insisting on absolute rigor in all circumstances is just a recipe for unreadable tedium, even for mathematicians - let alone undergraduate engineers.

You make a reasonable case to support your conclusion, but it’s worth pointing out that polynomials can be evaluated using just elementary operations. So putting the emphasis on that wording is a bit of a non sequitur.

@DanRomik I didn't say that the polynomial answer required elementary operations, and my answer doesn't assume that. The "quickly discover" is the part that excludes that one.

Well, why did you emphasize the part about elementary operations? I don’t see how it’s relevant to the discussion.

@DanRomik Because it's relevant to the other answer OP proposed. Square-root is not generally considered an elementary operation.


text:
Do you include your thesis on a "publication list"?
I am currently on the job market in an academic field (mathematics). Several of the jobs I am applying to ask for a "publication list," distinct from the CV. My CV of course lists publications, and lists my PhD thesis separately, in the "education" section, under my degree. (Per this question: Can dissertation be included in publication part in CV)
Is a separate "publication list" also supposed to include the thesis?

Well, was your thesis published?

I mean, it's in ProQuest...

I don't think there's a clear universal definition of what should go on a "publication list".  It's possible they only want peer-reviewed research publications, it's possible they want other works as well.
So the best approach, in my opinion, is to create a publication list with multiple sections.  Have one section for "traditional" peer-reviewed research publications, and one or more additional sections for other works of yours that have been made publicly available (hence "publications" according to some definitions) but not in typical peer-reviewed venues.  You might lump these all together under "other works", or if appropriate for your body of work, you could have sections like "dissertation", "posters", "preprints", "popular articles", "lecture notes", "technical reports", etc.
You can do the same on your CV.

@NajibIdrissi: Sure, they are reviewed by a committee of faculty / examiners / etc.  But regardless of semantics, the term "peer reviewed" is generally understood not to include this process for theses.


text:
Referee says the proof is wrong, but it is not, what to do?
About 3 months ago, my co-author and I submitted a mathematical paper to a journal. Yesterday, we got the editor's response and the paper has been rejected. The reason is that the referee thinks that our results are wrong or trivial.
However, we carefully read the referee's report and we conclude that the "errors" pointed out by the referee are not errors at all and that our proofs are correct. In all modesty, we think that the referee understood very poorly even the statements of our theorems.
Personally, this is the first time that such a situation occurs to me.
I already have four papers published in such journal and the reports I got from the referees have been always really accurate.
What do you think is the best thing to do?
Forget about and try another journal? Write an e-mail to the editor explaining why we disagree with the decision? Other ideas?
EDIT: Thank you very much for all your answers. At the end, we submitted our paper to another journal with only some slight edits we have already planned to do independently by the referee's report.

I agree with @jakebeal's answer below, but just want to voice my support as an author and a referee; sometimes referees make mistakes, and are wrong in their assessments. Nevertheless, I think the best practical solution is as jakebeal suggests, whether or not one thinks the original decision was just.

Is the paper on arXiv?

@Navin Yes it is.

Appeal to the editor (rebutting the arguments of the reviewer) and request another round of reviews. Alternatively, go to another journal.

"independently OF"

I must disagree with some of the answers.
Some assume that it is a problem with the person asking the question and giving suggestive answers with a very limited number of fixes ("I would strongly advise performing a major revision on your presentation of the proofs"; "two potential problems. One is that you may be in error, [...].
The other is presentation[...]").
If we are attentive enough, we all know well what the source of our problems are: The magic word is feedback. If people complain consistently that our papers are hard to read, the suggestion to work it over has a point. If again and again referees find errors in the manuscript, we will take much more care to avoid errors (proof-read, double-check, triple-check).
But if we get an outlier answer and cannot fathom what exactly should be the problem, it is very, very likely that we are not the source of the problem. Working the paper over in this case is a waste of time.
The reason(s) that a referee rejects a paper are virtually unlimited. He is wrong, she does not care, he is busy, she is right, but explains it badly.
Whatever.
But what you can do is to read very carefully the answer and ask yourself under what circumstances a person would give the answer. Is it aggressive, dismissive, bored, sad? It is rather short or more detailed? Does it look like the referee invested time or it is hastily written with boilerplate passages? From this you could often discern what the real reason for the rejection is.
Everyone will sooner or later have a paper rejected for inexplicable reasons, it is normal. Nothing to be afraid of.
That said, the best strategy already mentioned by other answers is to cut the losses and simply go to another journal. I would advise to challenge the decision if and only if the editor made it clear that the decision is not final and then if and only if it is objectively important to have it published in this specific journal. In that case do everything in your ability to check and recheck your paper and hone it to perfection because you will only get exactly one chance to convince the editor.

In fact, the problem with the referee's report is that being wrong with the mathematical reasoning, it doesn't suggest in any way how to improved the paper, even assuming it is necessary.

While you might be able to appeal to the editor, once you've been rejected, you're probably not going to get a change in decision.  I would instead recommend focusing on a new submission to another journal.
Before you do so, however, I would strongly advise performing a major revision on your presentation of the proofs.  Assuming that your proofs are in fact correct, you clearly did not convey them in such a way that their correctness and significance were obvious to the reviewer.  The reviewer may have been a sloppy or shallow reader, but so in fact will be many of your other readers after publication.
In short, take the feedback as an indicator of how your paper needs to be improved before you submit it to another journal.

+1 for the second (middle) paragraph. It's not enough for the proof to be correct --- it has to be convincingly correct.

Yes, that. If you trust the editor to make at least reasonable reviewer choices, then at the very least you can assume that the reviewer was a member of your audience, i.e. one of the researchers that you'd like reading, understanding, and building on your paper (and, in fact, one that was explicitly incentivized to scrutinize it in detail). If they didn't get the paper, that probably means that the text could be clearer.

I somewhat disagree with the second paragraph.  I would say that the report should motivate the author(s) to look over their paper again to be sure that they are stating things clearly and well.  But when it comes to math papers: a reader who is sloppy, shallow and trying to evaluate the results of a paper for correctness and importance will indeed often come to faulty conclusions, irrespective of the way the paper was written.  Math is hard; understanding it takes time and effort.  Most sufficiently good mathematical results cannot be written up in a way that overcomes that.

@PeteL.Clark While I agree with you in general, in this particular situation the OP wrote "the referee thinks that our results are wrong or trivial" which for me would indicate that some things weren't stated clear enough. On the other hand, if the OP already had a paragraph which presents a simple example showing why this result is not trivial and where the naive reasoning fails, then that is a very good argument why the reviewer did a sloppy work.

The sad thing about the referee's report is that her objections do not give us an understanding of what she did not understand. It is not that she said something like "the proof is wrong because f is not continuous..." so we just need to put more emphasis on the hypothesis that f is continuous. Her objection are wrong on the logical plan, something like (of course not so silly) "You proved that A -> B but in case X in turn out that A is false and B is true...".

@import.all: So at least put emphasis on why a beeing false and b beeing true is no contradiction int A -> B.

@PeteL.Clark Why would someone (anyone) be reading a paper and not constantly be trying to evaluate it for correctness and importance?

@corsiKa: The answer to that is not quick.  You can ask it on this site if you like.

On could moderate the second paragraph, taking into account @PeteL.Clark’s point. The referee’s misunderstandings don’t necessarily mean that the paper was unclear and needs improvement, but they do strongly suggest that it might be; so the authors should at least seriously consider whether the presentation could be revised to make such misunderstandings less likely.

@dtldarek As I understand the question, the editor stated that the results are "wrong or trivial", but the referee report simply states that there are logical errors. So it sounds like "wrong or trivial" is just a broad category of rejections, not a meaningful statement about this particular submission. OP is this understanding correct?

Appeals can work if written correctly. Even if they do not accept appeals, you can try something like: "We understand that you do not accept appeals, but like to point out that A->B is proven because of C,D, and E, and the case A=False, B=True is irrelevant because of F,G and H. Thank you for your consideration" - or similar. Often papers are reconsidered where there is a clear editorial/reviewer fault. Even if not, it signals to the editors that there may be a problem with their process if it is a decent journal (and you want them to fix it for your next submission, if it's relevant).

Consider this quote from Cantor Medal winner Yuri Manin: "A proof only becomes a proof after the social act of 'accepting it as a proof'."  Found here and here

The reason is that the referee thinks that our results are wrong or trivial.

This first caught my attention. Trivial and wrong are two completely different things. How did you come to that conclusion?

the "errors" pointed out by the referee

This leads me to believe that the issue is mainly about errors. But:

In all modesty, we think that the referee understood very poorly even the statements of our theorems.

has, two possibilities:

you are right. Math is quite hard and he did not invest enough time to understand it. Or maybe he does not even have the ability to. Which should not be "your" problem.
He is very good in the field you are working and sees your results really as trivial. He therefore did not read it properly and marked wrong errors (it may looked to him like a "trivial paper with errors"...)

In both cases, I'd really recommend, to

Write an e-mail to the editor explaining why we disagree with the decision?

That's the most "academic" solution in my eyes as problems should be discussed until you agree on the same conclusion (even dough this is surely not possible everywhere, it is in math). Regarding the second case, it is may even possible, that you missed a point. You know, we all make errors all the time. But submitting a paper where someone (who actually should understand the topic) spotted errors and just ignoring (not able to convince him otherwise) his opinion is quite, let's say, self-confident (especially in math), and in general not advised to do;)
Don't get this wrong; most probably you are right and he is wrong. Ok. But you surely don't want it the other way around. Better make sure it is not.
Instead of writing directly to the editor, it is may a good advice to let your paper check by a colleague in your field, who is neither the referee nor the author to check for a third opinion.
Others suggested to rewrite your paper for more comprehensibility. I would not conclude that already; too many other factors may play a role. Depending on the editor's answer (say he did not get the points as he find it confusingly written) I might rewrite the parts.
Another journal is surely a good idea if that somehow won't work out, but I don't think you are in a hurry, right?

"first write to the referee": this is almost never the correct thing to do with anonymous peer review.

It is indeed possible for a mathematical result to be "wrong or trivial"; for example, one might claim to be proving a non-trivial result A, but actually only prove a trivial result B. Thus, the proof is either wrong (if taken to be a proof of A) or trivial (if accepted as a proof of B). Being wrong and trivial isn't impossible, either: I am reminded of the oft-quoted review by Clifford Truesdell (Math. Rev. 12, 1951) that begins with the words "This paper, whose intent is stated in its title, gives wrong solutions to trivial problems. The basic error, however, is not new."

@jakebeal, there really seems to be some misunderstanding between the authors and the referee, right? Why do you think it is wrong to clarify things? I completely understand that it must not be a pleasing for publishing, but asking questions if you think someone may has "not done it's job right" (or found errors in your work which you did not) seems to be an acceptable step, don't you think? They should not argue about whether the work will get published but about objectively wrong statements.

@Mayou36 If you are going to appeal a decision, you need to talk to the handling editor not the referee.  Among a number of other things: 1) in academic peer review the referees are typically kept anonymous, and 2) it's not the referee who makes the decision, it's the editor.

@jakebeal, sorry, edited this, I meant the editor to contact (as it is written in the OP's question). But I am still not really convinced to let it go like that: there seems to be a misunderstanding somehow, right? Would you really suggest to just let this open without trying to resolve it? If the referee was bad, it is good to know for the editor (and the next submitter), don't you think?

The editor and the referee are not the people you need to be talking to in this situation. Their jobs involve managing many submissions and they likely lack the time or inclination to reconsider every person who's been rejected. For every paper published, many other papers must not be, so even when not making mistakes you can fall victim of being less novel than the most novel papers submitted recently.
You have two potential problems. One is that you may be in error, in which case the peer reviewer was correct to reject you and you really need to fix your paper before resubmitting it anywhere. Given your proximity to the paper, it's easy to get too close to the problem and become blind to such errors, so getting new peers involved to openly review the paper or leaving it for a period of time and coming back to it with a fresh pair of eyes after a break might help. Not knowing you nor the peer reviewer, all an objective observer should see is two peers of similar standing in disagreement with no way to judge who is correct without factual details.
The other is presentation. If we assume the paper is correct and novel, it may not have been sufficiently presented as such. Even if the peer reviewer was a lazy reader, their misunderstanding of the paper may have been helped along by lack of clear communication. The only real solution to this is further iteration and, again, external input. Open review is the best way to constructively improve your paper at this point.
If you want to double down on the paper being perfect in every way and just misunderstood, submit to other journals. This is a gamble, as they may just as easily accept it having missed what the peer reviewer saw or reject it for a variety of reasons out of your control. As others have stated, those involved in rejecting your paper may not be impressed if that succeeds, may not care or never find out, or they might recognize that they got it wrong because everyone makes mistakes.
One submission of one paper to one journal being rejected is not a big deal, it's normal, so don't let that demoralize you.

I've had this happen several times. These papers were all in a technical subject where it was hard to find a referee. I would get a referee report making elementary errors while accusing me of making elementary errors. Often the referee had poor command of the English language. In one of the cases I even had an email back-and-forth with the referee through the journal editor. This was a total waste of time, as the referee was simply not able to understand basic concepts as he was accusing me of the same.
I have found that it's best just to resubmit the paper to another journal. On one of these papers I did substantially revise the exposition, but in the other cases I did not. I will have to disagree with Jake Beal over the value of revising.. I don't think the exposition is usually the issue in these cases. As the asker pointed out, such referees often don't even understand the statements of the theorems.
In all cases the next referee behaved normally. That is not to say the next referee always accepted the paper, but the referee always understood what the paper was about and when a referee rejected it he/she always had intelligible reasons.

"Wrong" proofs may be wrong in the sense that

some small step is logically incorrect, or
what is written there is not a Bourbaki-style proof (Bourbaki-style = small-step, well-formulated), or
there is a typo, or
bad, incomprehensible English,

or a combination of 1.-4. holds.
Items of which kinds (1.-4.) does the referee mention? Strictly speaking, any reason 1.-4. is a valid reason for rejection. E.g., I really, really hate to read a paper with a typo in a formula which makes me ponder a whole day long until I notice that a typo is the culprit.  Regardless of the case, you should take the chance to improve the proof.  However, a strong rejection might be objectively too harsh a measure; it really depends on the case whether a weak rejection would be more justified. If any of 1.-4. holds, don't complain as it would not contribute to your reputation. Only if neither 1.-4. is present and the referee's report is bogus, you can complain.
A related aside: recently, some people started asking for a machine-checkable proof in a theorem prover (e.g., Isabelle, just to name one). If you want to immunize your paper against the "wrong proof" claim completely:

write a machine-checkable proof, and
make it available to reviewers somehow [put it online, supply a file, etc.], and
submit to another venue or resubmit.

Whether you submit elsewhere or resubmit would be the next issue; it really depends.
Notice that above, I abstained from speaking about "trivial proofs" or "trivial results": these would be too hard to formalize. Even trivial theorems might be published, but only if they are really genuine and are of great importance.

You should not revise your paper as Jakebeal suggests just because of the negative outcome of the review process so far. Revisions should only be done if upon taking another look, you think you can improve the paper, or if the paper has pretty much been accepted on the condition that you make certain improvements. In the latter case you may face the difficult decision of making reversion you don't fully agree with, you then have to balance the option of publication with such revisions against the possibility of a rejection.
I have had a mathematical physics paper rejected on totally flawed grounds once. I did appeal the decision, but this went nowhere. I submitted the paper to another journal, where it was again rejected directly by the editor. I later found out that this editor also worked for the journal I originally submitted my paper to, he had probably seen the appeal there. I then submitted the paper to another journal (with a similar impact factor as the original journal) where it was accepted without even a referee report sent to me to address problems.
The paper was not revised, the referee report did not contain any useful information for me to act on. The misunderstanding that led the referee to think that my paper was flawed was caused by the referee not being familiar with the jargon used in my field. It was also quite clear to me that the referee had skipped all of the sections about the physics and had only read the section where the results are derived. There the referee was misled by the jargon. If the referee had just read the entire paper the problem would not have occurred. Adding more explanations would in principle be possible but this has to happen at the start of the paper that the referee didn't read.
So, while you should always consider if the paper can be improved, and not hesitate forging ahead and make changes even if it inconvenient (e.g. if the paper is already under review), making revisions by guessing what an incompetent reviewer got in his/her head to try to get to a different decision the next time your paper is reviewed in that incompetent way, is not a good way to go about revising your paper.

... try another journal? Write an e-mail to the editor explaining why we disagree with the decision?

I would pick up on this.  I do not know how compact or concise or how deductive your proof is.  I don't know how concise and deductive (rather than inductive) it can be.  Let's suppose it is both concise and deductive, then spell out each step to the editor.  Make sure each step is undeniably justified and spell that out.
If the result is "unimportant", make the case for how it is salient.  What other mathematical work does this influence?  How does your result help some other mathematical effort?  If your result serves only your mathematical effort (like in previous papers of yours), then you have the problem of making sure those are salient as well.
I used to be a reviewer for the Audio Engineering Society.  There was a guy from Hong Kong that submitted and published paper after paper after paper on the topic called "Wavetable synthesis," but they were only continuations of his own work and quite self-referential.  Finally the editorial folks got tired of it, because it got to the question of "Who the hell cares?"  or "Who gives a rat's ass?"  You need to be able to answer that question.
Saying, "This work is important to increase my publication record so that I can get tenure" might not impress them.  (I'm not saying you're saying that.)

Please fix your shift key.

Sorry, but I think your answer is not relevant. The referee did not say that our work is "unimportant", but that the proofs are wrong.

import.all You did say that the result were wrong or trivial. You do later say that you think it is really just because they don't understand, but you misled robert with the inclusion of trivial (synonym for unimportant), and then ignoring it for the rest of the post and downvoting answers that pick up on it. If your paper writing is similar to your post writing, I can see how a reader would have totally missed your point....


text:
What can be done when my assignment's requirements has been so vague that it is jeopardising the grade that can be achieved?
An assignment spec was released but it was poorly written and vague to the point where the requirements of the software system is unclear. As a final year undergraduate this unit counts a lot to my overall grade. After numerous emails, phone calls and face-to-face discussions with: other students, lecturer, other lecturers and head of the course, they clarified the assignment with 2 weeks to go (was supposed to allegedly take 4-6 weeks which would have been a struggle anyway). The other parties all agreed that the spec was poorly written and interpreted it wrongly themselves.
I have been working on the solution but I am worried I cannot implement it to the standard of a 1st (70%+). The institution seems reluctant to offer an extension to the deadline and I don't know what else can be done. It is a sponsored degree so I study part time and work full time, so there is very little gap to pull all-nighters or power through whilst keeping a professional front for 9 hours a day.
Is there anything me and fellow students can urge the university to do, or anything our employers (sponsors) can do to encourage action?

Walk out and protest

I am not versed in software writing assignment but there are a few things I can think of:

Submit your work with a memo, detailing how each of the assumptions was made to the assignment components that were not clearly specified. If you're so keen, list a couple alternatives you have thought about, with pros and cons, and why you made that choice. I have seen students sometimes do that in written tests and exams, and I often considered their point of view a bit differently.
For all the communications, if you have paper trail, keep the paper trail. If not, at the very least, have a log of meeting and discussion, jot down all main points. Any conversation about this project from now on, if possible, should have a paper trail, and if it's a face-to-face meeting, follow up with an e-mail detailing the main points covered in the meeting. If all go south, having this record to demonstrate i) your due diligence to clarify, and ii) the lack of clarity among the teaching staff would help you make the case if you decided to complain or grieve.

Good luck!

You can only do what you can do. There is no magic here.
Perhaps the project was purposely left under specified, as often happens in undergraduate work, calling for creativity. I think that is sometimes (but only sometimes) justified, as long as the conditions are clear. But that's not the most likely situation here, of course.
Perhaps the people specifying the project just messed up and tried to complete the spec without thinking it through. That is less likely to be justified, of course, but it isn't that rare in the real world.
I'm not going to be one of the evaluators of your project, of course, but I would value more highly a project that correctly completed a subset of the specifications than one that had no results at all. Ideally, which subset would be negotiated before the end date, so you might explore that.
Maybe you are just trapped. If that is the case, then you won't be alone and all grades will come in lower than expected. The powers-that-be will need to deal with that somehow, maybe satisfactorily or maybe not. But it is out of your control.
But if you finish something, I think you have a stronger case for complaint after the deadline. And you may need to complain, of course.


text:
Creative solutions to convince research dean that I deserve PhD candidature
I need your help please to suggest solutions to a problem I am facing during my PhD. My story is detailed below with the important events that are related to the story:
I just finished my first year PhD at the university. It has been a difficult year for me because I had a supervisor who left and another supervisor who left again. My wife had home sickness and financially I had my scholarship fund cut by 30%.
Now, I came across another obstacle in my PhD. During our first year, we have to attend a generic research course and complete tasks to confirm our candidature. Although I attended all lectures and completed all tasks, the course lecturer who turned out to be also the associate dean of research at the university decided that I have not done them. Her proof is that there is an electronic feedback that I have never completed after each lecture which she used to confirm our attendance. She mentioned this rule at the start of her first lecture. Because I didn’t know about this rule and because also sometimes my phone was without battery, I was not able to complete many of these feedback. I may have completed two or three out of eight.
Later, I went to the make-up class and tried to talk to her to convince her that I have done them all but because of all the stress I had from my other PhD issues, I may have become angry in defending myself which I regret now. At the end, she decided that it is OK to leave and I can send her an email stating my story which I did. Later, she sent me an email telling that not only that I still have to retake all classes but also I have to re- do all tasks. I thought it was not fair because I have proof at least that I have done the tasks. So, I did not fulfil her request because at that time 1) I was partly not thinking straight , 2) I was also still hoping to convince her that I have completed the tasks , 3) I was thinking of switching universities and thought I do not need to do them
Later and after I got admissions from a couple of other universities, I found that my wife is pregnant and the doctor told us it is difficult for her to move to another city. So we took the decision to stay at my current university. So, I went back to the lecturer and sent her an email to inform me about any remaining requirements but she still insists that I have not completed them. In fact, she talked to my supervisor after my email and suggested to terminate my PhD. She told him that one day I came to class, ticked my name and left straight away. This happened when I tried to convince her once at the beginning of a class but I was not able to so I left the class in anger.
Now, I have to stay at the university and she said I will not accept you just retaking the class. She told my supervisor that  I have to come up with creative solutions to convince her that I deserve the PhD candidature. So, I need your help please to suggest some solutions to her so she can be convinced. She is meeting me in two days to listen to my proposal.
P.S. , I really enjoyed her classes and learned a lot from them. I thought they are really helpful. In fact, she taught us how to file a patent and because of her I got inspired and filed one. She also taught us how to write a proper paper and now I am writing my 5th journal paper. I also learned how to do a better presentation at her class which got me to present at conferences where I won two awards. However. she is still not acknowledging my attendance at the lectures.
I talked to other colleagues who attended the lecture with me and they all were happy to testify that I attended the lectures. Also, one time she brought three lecturers from the university in class to ask them about any problems we have with our PhD. So I told them my supervisor’s change story. I am thinking to talk to them to see if they would remember my question. I also have an email to one presenter after he finished his lecture to commend on him on his presentation which I can show her to prove my attendance.
I am sorry for my long post. Appreciate all the advice I can get.

(1) Your story is very long. I tried three times before I read it through. Please consider shortening it. (2) My creative solution is a conventional one: apology. My whole impression after I read your story is simple, you disrespected her although you admitted that she is a great advisor ( I was able to tell that in the P.S. section). It's your choice to walk away from a good advisor or keep your own ego. This is my opinion and your choice.

Good suggestion thanks. Yes, I think I have to apologize but I also think she might want other solutions.

One of the most important things is to learn to compress your research ideas into very short form so they fit page restrictions of a paper but still are clear enough to understand. You can practice this by trying to write shorter questions.

The word that the other commenters are trying to use - is "concise".  Using bullet points rather than pros would help.

I think you are focusing on the wrong part of the issue here. Trying to prove your attendance is not going to help you at this stage anymore. Bringing in others like the guest lecturers is only going to make matters worse.
Instead, here is the three main steps I suggest (plus a very important bonus step):
1) Apologize.
As you report having to leave a lecture due to anger after talking to her, I would almost take it for granted that your behaviour was problematic. Apologize. Do not attempt to justify your anger.
2) Express gratitude.
You mention that you feel it. Express it, and be sincere.
3) Detail (maybe in writing) how you have applied the lessons you learned from her.
While Steps 1) and 2) are just plainly proper behaviour, and will hopefully make her want less to fail you, this step is about showing that you actually learned what you were supposed to learn. Really go in depth here. This is the base for your case to be advanced to candidature. Be specific over what you learned and how you used it.
Bonus step: Given the overall dynamics of your story, it is completely unsurprising that the lecturer is female and you are male (that is making an assumption from having a wife that got pregnant). Examine whether you have an issue with female authority (the answer is probably yes), and search for ways to mitigate this. This will probably take you way longer than the two days that you have, but it is going to be a worthwhile endeavour.

Absolutely this. From the Dean's perspective the OP was very disrespectful, and it sounds like their behaviour was unprofessional and unacceptable.  On several occasions, it looks like the dean gave the OP chances and they didn't follow through, so I think all that is left is to suck it up, apologise and hope not to be kicked off the PhD.

I think step 3 should be done in writing, and should be written to the same standards of thinking, structure, grammar etc. as a good journal paper. That turns it into a practical demonstration of the OP's abilities, and shows effort.

@FooBar Apparently one cannot change ones mind from "unsurprising" to "expected" in the middle of the word without causing issues... Thanks.

While the answer is excellent and to the point (+1), the last paragraph is very speculative. I can imagine someone being (wrongly) mad at someone else and sex has nothing to do with the fact. As a matter of fact all the cases I witnessed were [someone] angry at [their boss or a figure of authority] for [something "unfair"], full stop. Instead of "issues with female authority", I would find it better if you speculated over "issues with authority"

@WoJ Given that the actors are gendered as they are, and given that this takes place in our society, there is no way that gender does not enter the equation.

@Amo While gender may (often) play a role in such situations, there is no guarantee that it does in this particular situation.

@Arno: seriously I cannot see any specific hints about "issues with female authority" in the OP question. About a lack of maturity, seriousness, etc. why not - but not with any genders.