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How is grading by curve fair at all? Are there any arguments in favor of it?
Per definition, grading by a curve usually means that the students are assigned grades based on the statistical distribution of the test/exam results. No matter what, say 20% of students will always fail, and only say 10% will get a perfect mark.
I see a number of serious problems with this, and I fail to see anything in favor. In my view, for a fair system, the following are necessary; and neither are fulfilled by grading by curve:

A test/exam should have clear and absolute rules and requirements. Here, the students do not know what are the exact requirements to get the result they desire, as the point limits are, obviously, only known after the test/exam.
The grade of the test should directly correspond to how much of the course material did the student learn and understand. The fact that the same ratio of comprehended material can give an A in one year, then a C in the next year,  tells that the requirements of the course itself are also very unclear.
Similarly, the grade should directly and absolutely reflect the knowledge of the student. An A+ should worth the same every time in the same test. But here, the grade only reflects the student's knowledge relative to class members. It can't be correlated to the amount of learned knowledge.
The grade should only be influenced by factors under the direct influence of the student. Here, the mark depends on factors like how "bright" are the other students, how much effort they put into preparation, and even on whether they cheated. Hence, the student's mark is influenced by circumstances completely outside of his control, and unrelated to his knowledge.
No matter the collective results, a given number of students will always inevitably fail. If almost everyone is a genius, there will be the same number of failures as if everyone did poorly. Good students may fail, and bad students may pass. In a similar way as the point before, a student shouldn't be faced with the negative, possibly serious, consequences of failing, just because by chance there were a lot of very bright students in the class.
Also, it creates and encourages an unhealthy and harmful class dynamic. Ideally, the students help each other in preparation. If an otherwise smart student doesn't understand some part and is roadblocked, others would explain. If a student missed a class due to valid reasons, classmates help to give and explain the missed material. But learning by curve creates an artificial race situation, where the students are actively harming themselves by helping others. Decimating the collective amount of obtained knowledge, this goes against the very spirit of education.

All these problems, and I'm struggling to come up with any argument in favor of grading by curve. In fact, I see only two cases where it may be used, and both of them are a fault of administration:

The department expects an exact number of students to pass the course. This is against the spirit of education IMO. If a student is good enough, he should pass. If not, he shouldn't. Regardless of others.
The responsible teacher failed to set exact, absolute, and clear requirements, and/or is lazy or unable to do so. Because of his fault, the students are exposed to an unfair grading system.

Am I missing something here? Are there any objective arguments in favour of grading by curve, and what are these? If not, or they are weak, what are the reasons it's still used, apparently widely?

"The department expects an exact number of students to pass the course": alas, this is exactly what many departments expect, because virtually everywhere nowadays having more students who complete their studies in a reasonable short time means more funding for the university (whether from student fees, government funding, improvement in the international rankings etc.)

@MassimoOrtolano I'm aware of this, but there has to be some arguments in favor of it to tell the angry students, university scoring institutes, and media possibly. If not, it would be more reasonable to decrease the number of passing students by raising their exceptations. Othervise, something fundamental is broken in the system.

"No matter what, say 20% of students will always fail, and only say 10% will get a perfect mark" - this is not a form of "curved grading" I have ever seen; usually the curve is only to increase and never to decrease the grades. It sets the top grades to the top scores in the class presuming that scores lower than perfect are more due to the difficulty of testing or inadequacy of instruction.

Does this answer your question? Why do educators use curve to adjust the performance?

No to both of your questions.

Many people writing about education--notably Alfie Kohn--have made the observation that a lot of educational practices are intended to sort students by "ability" rather than to educate them. Curving is one of those unfortunate practices.

@BryanKrause This exact form of grading was applied in 1-2 courses at my - othervise good - university. These were "en masse" courses, with around 200 students. The subjects were easy and totally irrelevant (like EU history, for physics/CS students), but they were a requirement for graduation. It always  bothered me, even though I except the results wouldn't have changed much from an absolute grading, given most of us didn't take them seriously... Anyway, AFAIk there were complaints to student council because of the grading and irrelevance, and eventually, the courses were made non-required.

@AnonymousM My question, I think, is fairly objective already. It's "What are the usually accepted arguments that support curved grading as a fair system?" But I can remove the last question which I only added for emphasis, it is indeed a bit misleading.

@BryanKrause The proposed duplicate doesn't ask for whether curved grading is a fair, it concerns why it's used at all, and doesn't concern whether it's fair. I'm aware of the usual reasons, but I find it hard to argue for it should a student question it's fairness.

@Neinstein The first answer there explicitly references fairness, and the second one does so implicitly, imo. I'd summarize those answers as saying that professors grade on a curve specifically for fairness.

@BryanKrause My impression from the answers in general is that a version of it may be fair in some circumstances, but more often than not it isn't. I'm still not convinced that it can be fairer, or even as fair, as an absolute grading system, in any circumstances, unless modifications are employed. After a while I accepted cag51's answer as it specifically listed arguments that in some circumstances support it.

Making new tests every year which are of the exact same difficulty and would yield the exact same grade distributions is a fairly intractable problem. There is no unambiguous way to precisely determine education outcomes (and many other things as well) despite our seeming desire for exact 1 to n rankings.

I've never heard of a course setting 20% to fail, that's absurd

@AzorAhai-him- That was just a number I put there, I don't know what's common. Anecdotally, we had some courses with absolute grading and almost 50% fail rate. Rightfully, I must say, freshman course and most students didn't get yet what university is about apart from carpe diem.

I agree with you for two types of courses:

Very small classes with fewer than, say, ten students. It is very possible that these students all deserve As or Fs and we should not try to impose a bell curve where there is none.
Very large classes like calculus I and physics I, particularly when there are multiple sections of each class. These classes are taught so often that it is very possible to design a sensible, static "absolute" grading scheme. Such a scheme will also give highest grades to the students who know the most, without regard to their instructors' competence or peers' ability (among the other advantages you list).

But for classes that do not fall in either of these categories, I submit that "curving" and setting "absolute" standards are just two ways of framing the same practice (and "curving" is more honest). It is a statistical reality that most medium-sized and large courses have students that master, partially master, and fail to master the material, and the instructor naturally wants the grade distribution to reflect this. So "absolute grades" in this case are somewhat disingenuous -- if everyone is failing or getting an A at midterm, for example, the instructor is likely to make some changes (e.g., making the final exam easier or harder than anticipated) in order to force the desired histogram. In this regard, explicitly curving is much more transparent; we are simply admitting that we will make changes as needed to ensure the desired curve. Further, even "curving" does leave some discretion to the instructor: if I feel that I have a great group of students that has learned a lot and is working hard, I might curve such that the average is a B+ rather than a B. Similarly, I would always consider the tails of the distribution manually.
Given that they are equivalent, I agree that "absolute" grading gives a healthier class dynamic.  As a student, I recognized that both grading schemes were effectively the same thing, and always find purportedly "absolute" grades to be somewhat disingenuous (unless the professor had actually taught the course often enough to be able to say that the exams were already written and nothing would change under any circumstances). But as a teacher, I learned quickly that most students do not realize this, and that they tend to respond better to the purportedly absolute system. In the same way, a very hard test with a massive curve is mathematically equivalent to an easy test with an unforgiving curve, but students respond much better to the latter. Irrational, but there you are.
Personally, I used both. When I was teaching a course for the first time, it was difficult to predict what grade distributions would look like so I would curve. But, I would also make adjustments to the curve based on my observations. When I was on surer footing, I would say things like "900 points is a guaranteed A, but I might give As for fewer points, we'll see how it goes"; I found that this was both honest and led to a healthy class dynamic.

Actually, I'd be incredibly happy to give all A's. Sadly, I never found it possible except with doctoral students.

Well, I am assuming the class is more-or-less typical; of course I’d be delighted to have a genius class that universally masters the material and all deserve As...I would also like a friendly pet dragon :-)

If everyone is getting an A or an F by the midterm, the instructor seriously needs to look at whether the course objectives are clear and whether the assessments are aligned to the objectives. Yes, it can happen that a whole class is awesome or horrible, but it's much more likely the instruction is off track and should have been fixed before the midpoint of the term.

I don't think we disagree...as I wrote, if everyone is failing at midterms, the exams are probably too hard, and the professor needs to change future exams. It may be that the scores are lower than expected due to issues with the teaching or course design, but this question just asked about marking schemes.

+1 for healthier class dynamic.  I once gave an exam with a range of scores from 10-100 and median of 55.  I chose not to curve because I thought it was a weak group (though I made future exams easier).  Punchline is that students turned on me; I still shudder at the venom.  I honestly believe I got students to work much harder and learn a lot more, but it was ugly out there.  Looking back, I needed to soften the blow to avoid demoralizing some students.  The ongoing relationship between class/instructor is a reality that can make curves "legitimate".  What is "fair" is another conversation.

"we all want to have a nice bell curve that separates the top, average, and weak students" ...ehh, no? I would like to have students that are each, individually, able to demonstrate a certain level of understanding and/or skill.

With typical class sizes, I'm skeptical that you can expect a "nice bell curve" of student ability, whatever that means. Even if ability were distributed like that, exam scores might not be because they are not iid: there are "correlated" errors: one rough lecture might make everyone under-perform on a question, differences between TAs or prior classes might stratify the class.

OK, my use of the term "bell curve" seems to be causing problems for many readers. Rephrased to hopefully sidestep this: the point of this answer is not really to prescribe a particular distribution, but to explain that there is usually some "alignment" between the actual and desired grade distributions, whether it's an explicit curve or a more subtle maneuver like adjusting the marking items and rubrics.

@Buffy If everyone in the class is getting As, the course is too easy. If you have a class full of very capable students, you can be more ambitious about what you expect them to achieve, set higher standards and have the best of them learn more.

I think that the argument for "they are equivalent" is wrong and also the claim itself is wrong. I also think that many people do not have "a desired curve" at all. I have standards that I would like the students to reach. That's it. No curve.

My firm belief and policy is that a student's grade should depend on their own efforts and nothing else. In that case, curving the class is actually just wrong.
But my grading policy is pretty different from most. First, I use (used, actually, as I'm retired) cumulative grading. Every student task was assigned a point value and those added to, say, 1000. If you did a 100 point task, you might get 90 points based on assessments of quality. The breaks between grades were defined, say 900 to earn an A.
Second, I permitted rework if a student earned less than they expected to earn, but rework only got you back part of the lost marks. Therefore, I didn't get complaints about strict grading. "If you want more points on this, do a better job of it". This also allowed me to encourage students to do better work and rethink poor assumptions.
Third, I assumed that I wasn't perfect and that I occasionally was overly strict, so a student never missed a final grade by what I considered an infinitesimal amount. 899 points didn't mean a B.
When I came time to assign final grades, I'd look at the earned distribution and make a decision whether that represented what I thought they had actually learned and I might adjust all grades upwards (only upwards) a few points if I thought that, at that point I'd been too strict along the way.
I had the reputation of being very demanding, and I was, both in the quantity and difficult of work. But I was just a bit less strict than my reputation. Students after the last class were never disappointed when they saw their final grade. They were able to compute it along the way, and they might learn that they did a bit better than their expectations.

No student should suffer in a class simply because, just by chance, there are a number of genius level other students.
Curving, is, I think, an admission of failure of the admissions system itself, which tries to predict that admitted students will be successful. If the system is set up so that some are guaranteed to fail then something is extremely wrong.
Expecting that the distribution from one year to another should be the same in an individual course is also foolish. The students aren't randomly selected from a known distribution in large enough numbers (for a single class) that statistical assumptions have any validity. Some years the students just work harder than in others. Some years they have to deal with things (pandemics, say) that make their work much more difficult.
Grade individuals, based on their performance. Make it possible that the performance can be good or can improve. Don't assume that the students in your class don't really need to be there. Be a teacher, not a grader.

Also see this question and my answer there.

Note: To make rework possible and not overly burdensome on the grader, students turned in work on paper. For rework they also turned in (in a folder) all of the previous versions that had been commented by the grader. They also highlighted, in the new work, changes to the most recent version. It was easy and quick to see if additional points should be awarded and easy to mark up the latest document with suggestions, etc.
This may not scale beyond 30 students per grader, I realize. I know that at 40, scale starts to be an issue.

"... a student never missed a final grade by what I considered an infinitesimal amount.  899 points didn't mean a B." But that then means an A is from 899 not 900, and then your rule becomes "899 points didn't mean a B" which then means an A is from 898. And so on.

I don't agree with grading on the curve in most cases and I agree with most of the criticisms highlighted in the original post, but that doesn't mean that there aren't any arguments in its favor. Generally these arguments can be summarized as "No human is perfect and students/employers* shouldn't suffer because its impossible for a professor to be perfect".
(* delete as your biases see fit)
No exam can test every single thing on a syllabus, so no two exams are likely to test exactly the same selection of material. Further, no two questions on the same material are of exactly the same difficult. Its not just that the setter failed to generate two questions of identical difficult, but that having two questions of the same difficulty is impossible.
So we must conclude that no testing systems fit all the criteria you set out above once you get above trivial knowledge-recall or mechanical-process application based tasks, which shouldn't be what university level education is about. For example, two of the Learning Outcomes on the genomic module I teach are:

"Be able to construct a convincing argument using evidence from high-throughput/genome-wide/genomic experiments"

"Create reasonable, testable hypotheses from genomic science research questions and design realistic experiments to test them"

There is no fully objective test of these with a precisely defined difficulty. For the first one there will always be a judgement on whether an argument is "convincing", but also some judgement of the extent of which an argument uses high-dimensional data. While for the second one can imagine an answer that does or does not make the criteria (although actaully designing one is much harder than you'd imagine), its impossible to come up with two questions of precisely matched difficulty.
So all systems of assessment are compromises between different priorities. What compromise you will settle on will depend on where your priorities lie. The design of valid and fair assessment is an entire academic discipline of its own.
To decide on the proper priorities for assesment design, this we must consider what the purpose of assessment is. I can think of three possibilities:

Guide the student as to where their strengths and weaknesses are, help them focus their efforts
Ensure to a "consumer" (e.g. an employer) of the student that they meet a certain minimum standard on some task
Measure the "ability" of students, either for this particular subject or just in general.

So at one end of the spectrum you have things like a driving test, where a person must demonstrate they are capable of performing a predetermined list of skills - its not about whether you are a better driver than your friend, just whether you meet the basic safety standards. And on the other end, NASA wants to recruit the best candidates for the space program. It will spend years training them, so what they actually do now is not as relevant as just selecting the "best" people.
I, and I like to think most educationalists, don't particularly care for reason 3. But many employers do, and because the employer does, students do.
Curve grading prioritizes measuring "how good" a student is, over whether they can perform a predetermined set of tasks. It means, for example, if the teacher is ill one day and performs the lecture poorly, the students from that class will not loose out to students from a different class when they come to apply for a job. Or students that take hard classes will not see their grades suffer for that choice.
It relies on the assumptions that your sample size is large enough that a change in mean test score is a more likely explanation than a change in average student ability. Thus, it was originally implement in massive, standardized tests, like the GRE in the US, or the nationwide GCSE (General Certificate of Secondary Education - a set of exams taken by all 16 year olds in the UK). These exams are taken by 100s of thousands of students at a time, are generally marked by more than one person, and are used to decide which subset of students gets access to some limited resource. They may well be appropriate in these circumstances.
To come back to the actaul question - how is it fair?
It is fair under two possible conditions:

If the aim of the exam is to sort/filter students. In particular if the student wishes to be compared to students from other classes/universities when applying for a job.
You believe that variation in test difficulty is greater than the variation in average student ability year-to-year.
You believe that the variation in teaching effectiveness varies from year to year more than the ability of students.

Note that the final two reasons are the fault of the instructor. But this immaterial. Given that instructors will be imperfect, what is the best way of negating the effects of this for students.
All that said, I am not particularly convinced of the arguments for curve grading in university class type situations.

One example where a curve could not only be warranted, but also beneficial is in cases where the course/exam is purposefully designed to be extremely difficult or 'discriminatory' towards 'worse' students.
In my graduate school experience we had exams that were designed to be extremely difficult. So much so that almost all the students would score an F. But then these were placed on a curve. One of the underlying purposes of the course was for the professors to figure who the strongest students were in order to offer them acceptance into the PhD program. At the end of each semester the professor basically ensured everyone passed the course and got a degree. But he also was able to discern who the brightest students in the class were.

Professors sometimes forget how difficult their material can be. As a student, my professors sometimes say after a particular exam that they "probably over-did the exam," or "made it way too long by mistake," etc. If almost everyone taking the exam requests extra time, it is likely that the exam was overly difficult, and the professor can correct their own mistake by curving the exam.
For smaller classes, the professor can use students that they are familiar with as a baseline: "student X is the best in the class, and even they couldn't solve this problem...I should probably give that problem less weight."

I can understand a retrospective positive-only correction on an exam that turned out to be more difficult than it should've been. But I encountered GBC as the per-syllabus method of grading several times, two times at my university and many times reading about it, here or elsewhere. I'm more confused about that kind of application. This, sure, I can support it.

@Neinstein To be fair, the question asked was "are there any objective arguments in favour of grading by curve." This is one. I think I agree with you that many exams are curved that shouldn't be; however, I don't think it's as detrimental as you suggest in the question.

Check out the four publicly available Physics GRE practice exams.

8677
9277
9677
0177

ETS have provided the % of students who get individual questions right. If you examine that statistic, it should be clear that two of the four tests are relatively hard because there were more questions which few students got right, and one of the four is noticeably harder still.
ETS got around the different difficulties by grading on a curve. To score 990 (the maximum score) in these exams, you need to get 84/100, 76/100, 67/100, and 85/100 respectively.
If you don't grade on a curve, how do you propose to accommodate the varying test difficulty? You could tell the students beforehand "to get 990 in these exams you need to score 85/100", and then 0% of the students in three of the four years will score 990. That makes the exam useless as a standardized test.
Some responses to your arguments as well:

The exact requirements are clear: answer as many questions correctly as you can. This is the case regardless of how the exam is graded.
The grade can be correlated to the amount of learned knowledge. If you know more you get a higher grade (for that class). Comparing students between different classes doesn't work, but then it doesn't work without curved grading either, as you can see from the Physics GRE practice exams. You can't easily compare students who took different exams.
Curved grading usually sets the top grade; it doesn't say "10% of students get A's and 10% of students get F's". Hence curved grading does not a priori cause students to fail if there are lots of bright students in the class.  For the same reason it doesn't a priori cause student vs. student competition.
Curved grading eliminates grade inflation. It handles both "exam too easy, everyone getting A" and "exam too difficult, everyone failing" situations. This maintains value for the grade, since you can reasonably e.g. say someone who fails did not understand the material as opposed to simply had a very difficult exam.

Edit: here's a link to an article explaining how curved grading is implemented in practice. It also explains why curved grading is used. Relevant part of the article is:

Setting such an exam [for a large group of students] is, by no means, easy. Pitch it tough, most students will fail. Set it too easy, and many will score very high grades, and the resulting scores are hardly differentiated.
Differentiation is necessary for CAP purposes, and for Honours classification, and these are here to stay for the foreseeable future. Most if not all major universities have variants of degree classes or GPA scores.  And because of the need for differentiation, many institutions from North America to Asia, use the bell curve as a mechanism to moderate marks.
Module requirements may encompass different modes of assessment such as tutorial presentations, laboratory reports, projects, essays, as well as mid-term and final examinations.  Grading may be based on absolute performance, relative performance, or a combination of the two.  Higher-level modules with small enrolments typically grade a student based on his absolute performance; larger lower-level modules take into account a student’s performance vis-à-vis the other students in the same module. Where necessary, the final grade which a student receives for a module may be subject to moderation.
One important reason for grade moderation is that examiners come from diverse academic backgrounds and may be accustomed to different marking regimes.  While we do make every effort to make sure modules are designed with clear learning outcomes, and professors are responsible to ensure their exams are pitched at the right level, grade moderation will prevent grade inflation or deflation, and helps to achieve consistency in assessment grading across modules.

The GRE is not at all the same thing. The numbers of people taking the exam are large enough that statistical assumptions are valid. That is hardly the case for course exams.

Curving can't undo "exam too easy, everyone getting A" in a remotely fair way. At the most extreme, if everyone gets 100%, there is no way to assign different grades. But even if everyone gets between 90-100%, are you really going to give the 90%-scorers anything below an A-?

@Buffy Whatever the value of the GRE, it is also much more consistent than any course exam because questions are tested large-scale to ensure that the GRE is consistent.

It's not really true that the GRE is "graded on a curve." It's designed so that the scaled scores year to year are supposedly comparable, at least within a few years. Using the publicly available tests to draw conclusions about the scoring is misleading, because they're old and they span 15 years.

It handles both "exam too easy, everyone getting A" and "exam too difficult, everyone failing - This is a scenario where the teacher failed his responsibility of construcing a fair and good exam. The solution is not curved grading, but to have an exam that is fair and well-made. If such a case happens with a good exam, that means all students deserve their A-s or F-s.

@Neinstein how would you know if a question is too easy or too hard before it's asked, especially if it's the first time you are setting the exam?

@Allure It should be excepted that the teacher knows his own syllabus well, therefore it can also be excepted that he has a good idea whether his own exam question is easy, hard or impossible to answer for someone who obtained all knowledge from the syllabus. Even if it's the first time (s)he set up an exam. Sure, lack of experience can make it harder; but the solution to lack of experience is not implementing an unfair grading system, but research, consultation with more experienced collegaues, etc.

@Neinstein what is obvious to the exam setter might not be obvious to the exam taker - see the curse of knowledge. I remember one such physics question: the question describes a physical system, and asks which of the following wavefunctions is the solution. The exam-setter thought that students ought to know that physical wavefunctions go to zero at infinity, which immediately identifies the answer, except it (unsurprisingly) didn't work out that way in the exam.

@Neinstein here's another question in classical probability I've encountered with the same issue. If you want to try it yourself, read only the quoted text in the question before looking at the rest of the question/answer. https://math.stackexchange.com/questions/3166661/does-probability-make-sense-when-the-prior-is-unknown

@Allure Sure it happens a lot, examining is hard! But it's still the fault of the exam setter. And such cases can be fixed by the students complaining, the exam setter admitting the fault, and compensate in the othervise absolute grading system accordingly. No need to implement an unfair grading system just because the teacher may make mistakes...

Let us continue this discussion in chat.

@Neinstein you are asking people to do the impossible. I have been teaching for many years and still am occasionally unable to predict how well students will do on an exam question I design. Friends of mine who are senior professors have complained of the same difficulty. Sorry, your expectations of what professors are able to do when they are experienced are grossly unrealistic.

"Learned damage", I think you meant "learned knowledge"? Both definitely implies a mark is left on students after their education :)

@Nuclear241 thanks, fixed.

Suppose that students can choose to take either course A or course B. After the exams have been sat, the results for course A are significantly higher than course B. Now there are two possible reasons for this (and, of course, they could both apply):

The exam for course A was (unintentionally) easier than the exam for course B.
The students who chose course A were generally stronger than those who chose course B.

Now if you adjust the grades ("grade on a curve") and 2 applies, you unfairly penalise students who happened to choose the same course as most of the stronger students. However, if you don't adjust the grades and 1 applies, you unfairly penalise students who happened to choose the course where the instructor set the harder exam.
So it sounds like the arguments for and against more-or-less balance out, with maybe a reason for preferring the status quo (that you shouldn't intervene unless you are confident your intervention is an improvement). However, there are a few reasons why I don't agree with this.

Actually, 1 is more likely to happen than 2, simply because it only depends on the actions of one person and not a group of people (and getting the difficulty level precisely right is hard).
If you do, by prior arrangement, adjust the grades, then 2 becomes even less likely, since you remove the incentive for weak students to choose "easy" courses.
You can get an approximate idea of to what extent 2 applies, based on previous grades for the students, and take that into account. When I was examining in an institution that required adjustment of grades, each course was given (in automated fashion) a target average score based on the predicted strength of students enrolled on that course. If the actual average result was significantly higher (or lower) than this, that suggested the exam was too easy (or hard).
Adjusting grades is important if you want to be able to compare courses from very different fields, even if the average marks in those courses are comparable. This is because STEM subjects naturally produce a much wider spread of marks than humanities subjects.


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Deciding between a pure math grad program and linguistics grad program with (potentially) mathematical bent, advice needed!
In undergrad I did a double major in math and linguistics, and I really fell in love with both fields. To be honest, I can't imagine ever fully giving up either one. I have a strong desire to go into academia, and my ideal situation would be to work at intersection of these two fields to some degree. There is a small body of pure math research that is motivated by questions from linguistics, and there's a larger amount of research that uses applied math in computational linguistics and adjacent subfields. My plan, since finishing undergrad, has basically been to try to pursue a PhD in (pure or applied) math, and then eventually get involved in these math-adjacent areas of linguistics in some capacity down the line. This seemed like a good plan for the general sort of work I was interested in doing.
Anyway, this year I applied to graduate programs in both fields. In math I got into a few masters programs, none especially highly ranked (though certainly not bad schools). No PhD programs. In linguistics, to my extreme surprise, I got into a very prestigious PhD program with full funding. I feel like I'd be a fool not to take the offer. However, I am still somewhat conflicted, because I really do want to be involved with math, and I fear that there is far less permeability across fields in the linguistics -> math direction than in the math -> linguistics direction.
I have talked with the person who would very likely be my advisor at said linguistics program; he works in math adjacent areas, and he told me that there would be opportunities for me to take relevant math classes if that's where I ended up. With this in mind: if my academic credentials say "linguistics" on paper, but I end up with a reasonably strong background in (certain areas of) math as well, will it be prohibitively difficult for me to get involved in mathematics research in some capacity (e.g. publishing in a math journal)? If I take the linguistics offer and then decide I'd really have preferred the math route, what are my options? Etc.
If anyone can speak to any of this in any way it would be hugely helpful. I have to decide by the 15th, so any thoughts or advice as soon as possible are very appreciated!

"There is a small body of pure math research that is motivated by questions from linguistics" In my ignorant, opinionated, subjective opinion, I would put it this way: there is a small body of pure math research that claims to be motivated by questions from linguistics, and then there is a truly miniscule body of math research that actually is motivated by questions from linguistics. You need to be aware that a lot of the claims that a certain math problem is "motivated by linguistics" are simply propaganda. There is, however, probably plenty of space for applied math work in linguistics.

@AdamPřenosil, ha! Indeed so. Perfectly true. (But: sooo cynical for a young person. :)

@paulgarrett Well, I should know since I have done the "ritual nod to linguistics in the introduction" myself. I have a brief paper on "pregroups", where we say that they were studied by so-and-so "with linguistic motivations in mind". This is perfectly true, but the paper itself doesn't have the slightest connection with linguistics. The OP should be aware that much the same applies e.g. to a large part of the work on Lambek calculus. (Although certainly not all of it!)

@AdamPřenosil, indeed. :)  I'm similarly aware that there are even "more-purely academic" (supposed) applications of math to music... using group theory and/or other things. Knowing a bit about music myself, I view all that stuff as really "purely-academic music theory", in the sense of having no genuine interest or use to music or musicians or audiences... And so on. In fact, in general, people who style themselves as "applied mathematicians" really mean that they're dealing with PDE's... with or without actual applications, and with or without talking to people about applications. :)

I'm doing an interdisciplinary PhD (I've taken graduate level courses in both math and linguistics), and I plan for my dissertation to be about linguistics topic-wise but with ideas/methods from math. Let me know if you want to chat.

In the "as soon as possible" vein: in my experience, in the U.S., at R1 state univ for some decades: (Edit: and in math, to be clear...)
Publication in math journals would not be influenced by your degree or departmental affiliation.
But perhaps that's not the salient question. If you got a degree called "linguistics", even "mathematical/statistical/whatever linguistics", so far as I know very few math depts would find you a high priority for postdocs or tenure-track hiring. Especially with the economic problems and tight job markets these days, nearly all math depts in R1 and R2 places would have higher-priority candidates than someone with your background.
There was and is certainly an analogous issue with "mathematical biology" and/or "mathematical neuroscience" and such stuff, but this resistance was overcome by exterior priorities aiming to emphasize and fund the practical importance of the applications. I don't know that any form of linguistics could acquire a comparable sense of urgency...
There certainly is the whole industry of trying to make computers understand and use natural language. This seems mostly not to be in math depts, but in computer science depts.
But/and, again, if you have a job that you like, even if you're not officially "a mathematician", there is no serious obstacle to your publishing mathematics research in refereed journals. Or putting it on arXiv... or on your homepage... :)

+1. I suspect the situation is not so different in the math -> linguistics direction too. People with degrees in STEM subjects sometimes seem to think that their STEM subject is "really" hard, that the less rigorous subject like linguistics will be easy in comparison, and that the linguistics community will be overjoyed to hire such a smart person even without much relevant experience. But the reality turns out to be quite different.

@cag51, hahaha. Indeed. :)

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text:
Dialogue in Master's thesis
In some works, as
What the Tortoise said to Achilles,
GEB or Invariant Risk Minimization, some ideas are conveyed by a dialogue. I find this both informative and entertaining.
I would like to use a dialogue to introduce the main ideas of my Master's dissertation, however I am unsure how this would be received in the academic community. I know that jokes should be avoided and I'm not sure whether this would be treated as such.

Can I use a dialogue in Master's thesis introduction to sketch the main ideas?

What does your supervisor say?

It seems like an interesting and novel idea - making your results available for a wider audience is one of the pillars of academia...

Why do you assume the academic community cares about your master thesis?

Do you have homepage? If yes, you could put the dialogue there with links to your master thesis or other places where to find out more about the material. People would more likely come by chance across such a document than a master thesis.

I try to understand whether the thesis committee will like this solution or not, hence I try to collect your (academic community) opinions on this.

There will always be some people who do not like this. A plain boring thesis is surely the safest bet.

@user111388 I see... Thank you!

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Told my professor something in confidence
I am in a bit of a pickle here.
I am in a course, and a student that I know quite well asked to collaborate with me on a project. I agreed. We started working on the project for 30 minutes, but I was the only one that continued (it took roughly 10 hours of work). Whenever I was working on the project, and asked the student to join, he never joined. I finished the project independently, but the student asked me to add him to my submission. To save face, I told the student that I did not finish the project, and added him to the version that we had worked on, and emailed the professor asking if I could submit the project over email instead so I would not have to add the student as a collaborator on the project.
The professor just reached out saying that he emailed the student for clarification, which puts me in a very sticky situation. I know the student quite well, and as I mentioned, I told him that I had not finished the project. Must my professor respect confidentiality in that matter? He did not ask before escalating the situation, but I do not know if he had to at all.

I'm very confused. It sounds like you sent the student your 30-mins-of-work version (with their name) and told them that this was the submitted version. But then you sent the 10-hours-of-work version (with only your name) to the professor. Is this correct?

Your behavior seems a bit dodgy to me, actually. Both in your actions with the student and the professor. The "pickle" is of your own making.

Also, is there some reason you expected the professor to treat your communication as confidential?

Was the project assigned/agreed upon as joint work? If so, do you want the other student to get a lesser grade then yourself? As faculty I would always get both students’ sides of a story.

@Dawn, and I seldom reward a student for "taking over" a joint project.

@JohnDoe Sadly, interpersonal "pickles" tend to be the consequence of focusing on making sure that other people fail rather than focusing on making sure that you personally succeed. By doing this, you've put your professor in a "pickle". He's entirely right to try to get both sides of the story, and will probably get annoyed with both of you once he gets to the bottom of things (particularly you, I suspect, since going behind someone's back is worse than laziness). I suspect the situation in which you'd just shared the credit with the lazy student would have ended better for both of you.

I get that. I did indeed send the 10-hours-of-work version to my professor, but the content of my email was saying that I did not want to share work that I had stayed up all night to finish with someone who was pestering me to finish it with no contribution. I explicitly told the professor no plagiarism occurred, since the joint submission is the one with both of our work, but the submission only to the prof. is entirely completed by me. I also agree that just sharing the credit with the student would have been better for both of us, it's unfortunate.

You should have gone to your professor with your problem, rather than your solution.
Your problem is that you were having trouble getting your peer to contribute, and felt like you did all the work on the project.
Your solution was wanting to clandestinely submit the finished version while lying to your peer.
I'm guessing your email wasn't particularly clear, but even if it was clear I don't fault your professor for reaching out to the other student on this. This is not the sort of "confidentiality" that relates to you personally, this is an interpersonal conflict between two students that you have implicitly asked your professor to solve. It's not reasonable to expect them to leave the other student out of it completely.

Must my professor respect confidentiality in that matter?

Usually no.  Information is only kept confidential if you make an agreement in advance that it be confidential.
Where applicable, FERPA requires that certain information be kept confidential.  This does not mean a faculty member cannot ask a student if they contributed to an assignment.  The grade would be confidential, but sending "requests for clarification" would be okay (depending on the content.)
https://www2.ed.gov/policy/gen/guid/fpco/ferpa/index.html


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Book recommendations for a PhD supervisor
I will start mentoring my first PhD student this fall, and I would like to read some books to have it start the best way possible.
I have already supervised some Master and undergrad students, but I was not always happy with the way it went. I would thus like to improve my "managing" skills to help my student become a good researcher. I looked online for book recommendations, but couldn't find anything useful (tailored for mentors, and not students).

So what did you, or they, do wrong in the previous situations? How would you avoid those pitfalls next time around?

@SolarMike I have analyzed the last bad situation, and I plan to work on that. However, I am looking for a more systematic approach (how to plan successful scientific meetings, more HR-like meetings, how to deal with a student that is not well organised, ...). One finds plenty website giving tips for students, I am looking for the supervisor's version, if it exists.

@Buffy I thought on-topic book recommendations were allowed on SE. This meta answer seems to agree https://academia.meta.stackexchange.com/a/3860/96729
I can always try to rephrase my question, but in the end, it boils down to "are there books for PhD supervisors", in the same that there are book on how to write science, and so on

@Adam see https://academia.stackexchange.com/help/dont-ask especially the bit that says : " If you can imagine an entire book that answers your question, you’re asking too much."

Since you only asked for books, you won't get answers from people here who know how to be successful at it, but haven't written books.

@SolarMike you misunderstand, it does not take an entire book to answer the question "is there a book on X".

As a current PhD student thinking about what I'd like a supervisor to be aware of, I can think of a few book recommendations which might be useful. The challenge of doing a PhD which I've noticed is learning how to be efficient and happy in the face of a really different kind of challenge than my previous studies were. These books offer models for that, which might help you make more concrete suggestions to your students when they (inevitably) struggle or at least help you understand them more.

Deep Work by Cal Newport. A really good advice-filled book about how to get productive, creative work done by relegating distractions and creating the right kind of time/space.
Becoming a Successful Scientist by Craig Loehle. A general book about the sorts of things a scientist in training might need to think about and adapt to.
A book about depression and other mental health struggles, for example Curse of the Strong by Tim Cantopher. This is very likely to be a challenge that your students may face, and knowing a bit about it will make you better equipped to help them.
A book about how to communicate when difficult things are happening. For example, NVC offers an interesting model, as in Nonviolent Communication -- A Language of Life by Marshall Rosenberg.

Hope that's helpful and good luck! And remember that your students can probably tell you a lot about what you need to know to help them if you can get to a place where you can listen and they can share.


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Using "we" in mathematical reports
Recently, I have submitted an early draft of a report summarising the results of a year-long project at my university, to my advisor for review. We have met up for a review of the paper, and he pointed out my frequent use of the word "we" in the paper. He considered it a mistake and asked me to change everything to a third-person view.
Personally, I found this incredibly strange. I am in the field of mathematics, and based on other papers and publications in math, it is very common and even considered "good" language to use the word "we" in writing, especially in proofs and discussions of results. For example, instead of

This proof demonstrates Theorem 3 to be true

it is considered desirable to instead write

We have thus proven Theorem 3.

The reasons cited for this preference, I have seen, is due to both convention and to avoid dodgy writing (third-person wording may suggest that the authors did something, but it could have been taken from somewhere else).
I have seen different questions on this site pertaining to this issue. This question, for example, has answers which suggest to take reference to the style guide provided by one's university, which unfortunately mine does not have. The accepted answer deals with economics, so I am unsure it applies in mathematics. This question suggests it is good to use "we" in mathematical and scientific writing. A quick search on Google, however, apparently suggests it is always undesirable to use first or second person pronouns in academic writing (see this site).
Thus, I am asking this question for my specific scenario for clarification. Should I follow my advisor's advice, or should I discuss with him further? Again, I find his advice rather odd and I definitely prefer to be able to use the word "we" as I please when appropriate.

"This proof demonstrates Theorem 3 to be true" sounds awkward to me. "We have thus proven Theorem 3" sounds better. "This completes the proof of Theorem 3" sounds better yet. I often use "we" in mathematical writing, even when I'm the only author, and my impression is that globally eliminating "we" would make my papers unpleasant to read.

Any advice that supposedly applies to all of academia is wrong.  Writing mathematics in the first-person plural active voice, even when the author is singular, has been standard for at least a century.  The standard explanation, possibly due to Paul Halmos, is that "we" is short for "the author(s) and the reader(s)"; after all, the target readers for any math paper are actively engaged participants, not passive spectators.

In the end it doesn't matter. I like to write "we" as well (and people around me don't). When I was in Leeds, someone who I believe worked for a journal suggested that you can write "I" if it is truly only your work. Other people will tell you that you never ever write "I" ... I think in the end, write how you want, reasonably formally and just make sure the science is clear and accurate.

@JeffE I have heard the term of "we" for "author and reader" too. Maybe because I started in mathematics? - I also find that active voice is often easier to read than at times contorted passive voice. Passive voice has its place and uses - and most definitely is not universally beneficial.

If you are a sole author and still want to write from a plural frst-person perspective, you can just add your cat as co-author.

If you were writing for a journal, you would want to check the journal's style guide. If it doesn't cover that issue, then the next step would be to check previous publications and see what the norm is.
For an internal report with no applicable style guide, one should write for the intended reader/s. If your advisor is going to be the main reader for this document, then write it in the style that he requests.
To me, this change seems unnecessary, but it may help to consider this story from the development of the computer game Battlechess:

The producers of the game were known to demand changes to the game, presumably to make their mark on the finished product. To this end, one animator added a small duck around the queen piece, but made sure that the sprite would be easily removable. Come review, the producers, predictably, okayed everything but asked for the duck to be removed.

In my experience, this is a very broad tendency among managers/advisors, and now that I'm a manager myself I understand the temptation to micro-manage. Even if a document is quite good enough as-is, if we don't suggest changes we don't feel like we're doing our job.
It may be that your use of "we"s is the sacrificial "duck" shielding you from more annoying change requests.

Reports and proposals in math often have different style than other mathematical writing.  For example, in NSF grant proposals you would usually say "the PI" instead of "we".  Similarly, in a document going to a broad science audience, conventions of science might be more appropriate.  I'd suggest following up with your advisor to better understand where he's coming from, maybe he just means "we" is inappropriate for this particular document.

I have a bit of overview over the fields, having my MSc in mathematics, prolifiely working in computer science, and having some contacts to medical research.

As someone mentioned above, "mathematics is for eternity". When I wrote my own texts in that field I was very, very wary of using "I" or "we" or anything. I think, I have overloaded my texts with passive voice then, and "we" should be Ok in mathematical texts in my opinion.
In computer science it is perfectly Ok to use "we".
In medicine "we" is actually frowned on, use passive voice. "The operation was performed in order to ..."
In liberal arts, when you express your opinion and your position, you use "I". Have seen few such papers, completely alien to me, but obviously an accepted usage in that fields.

And yes, "we" does not really mean "the authors of this paper", thus forcing you to "I" in a thesis or a solo paper. "We" means "us, the reader and the writer".

Think of it as follows: you are a guide at a museum and show people around. You would say things like "Here we see an example of ..., from which we conclude that ...", which is perfectly fine. What would sound wrong is using 'I' in this way. You don't say "Here I see ..." because you the visitors are also seeing this with you and you guide them through it. This is a different scenario from when you give a talk about some personal accomplishements, as in "Here I dug out this specimen on a trip to ...". In a mathematics paper you are reporting on a result, and not on your personal experience and circumstances in getting there (though you can, of course, choose to do so, in which case I would be fine). This is also why you find different advice for single author papers in other scientific disciplines, where you document how you arrived at your results.

I'll make two points. First, it is always good advice to a student to follow the advisor's advice. He or she has more experience and is supposed to look out for your interests.
But second, if you are writing mathematics or most other things, you aren't writing a blog or a diary. You are, in fact, writing for the ages. What you have found to be true is true, and has always been true, independent of your action. The writing should be about the it not the who.
When you present the work at a conference, you can be more informal and talk about your contributions and what made it challenging and/or rewarding for you. But in the writing, focus on the math itself.
I'd have to think about whether I'd give the same answer for Computer Science, which is an act of creation, not discovery. I'd need to think about it for a while first.

We don't all accept your creation/discovery dichotomy.

"He or she has more experience and wants to look out for your interests." - Well, I'm not really sure about the second part... - And experience does not necessarily mean it is helpful, for example when a supervisor tries to promote research in a direction which is under the present circumstances pointless. (E.g. using CFD in a chemistry problem where the chemistry is not fully understood...) So in conclusion: Do listen to your advisor, but also do question him/her if appropriate, they are not without flaws.

@DetlevCM, sadly, yes. I should have said "is supposed to be looking out for your interests." Too many questions here imply there are too many exceptions out there.

@erstwhileeditor, I thought that might be the case. Is mathematics "created"? Only in the sense that concepts/ideas are created. The Circle existed before humans did. So did the Natural Numbers. We named the concepts and explored the consequences. But we didn't "create" them. Think about it. The fact that a circle maximizes contained area for a given boundary length also was true pre-thought. That is all I mean. I don't mean that mathematicians aren't "creative", of course. It is my training, actually.

@Buffy That sounds better to me. We generally all hope that our supervisors want our best - but too often this is not the case which then leads to people being unhappy/disillusioned/depressed/etc.

@Buffy. Pure assertion on your part. We are not all naive platonists.

@erstwhileeditor, from a constructivist (or other) viewpoint, would you give a different answer on "we" v "it"? If yes, please offer it.

I agree with following the advice/guidelines, but strongly disagree with what is ideal.
Especially since we are talking about mathematics, it is obvious that the matter is not one of opinion, so the distinction is unnecessary, the use of it v we does not convey any non-trivial information. Therefore it is better to use whichever results in better style in terms of ease of reading, which is in my opinion mostly "we".


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Should I use the recommended environment in a programming course, if it's not mandatory?
I'm a first year Physics  MSc student. This semester I'll attend to a practical course where we learn to use Python for scientific computing. The course is beginner-level. We will work on our own laptop, not institutional devices, and are expected to install all necessary software.
Yesterday, at the first lesson, the teacher informed us about the recommended environment and code editor (Anaconda and Spyder). He also told us, however, that, if one wishes to, he's free to use any other environment of his choice - only the teacher will have a harder time helping him.
The thing is, I already am a somewhat experienced Python coder. Of course I still have a lot to learn, but e.g. part of my BSc thesis was writing (and debugging) a 1500 line complex data processing Python program. While I wrote this, and other codes since, I got really used to a different environment (bare Python installation with Pip, and VS Code). If only for my convenience, I'd use this.
On the other hand, this is a beginner level course, and I'm sure a measurable deal of time will be spent learning the environment itself – so it's a good opportunity to learn something new. Also, if I get stuck and need the teacher's help, it'd be more convenient for him to use the environment he knows. And it's not my aim to get him frustrated... On the other hand, I think I'd be faster and more powerful using the editor I got used to, and that would be an advantage in time-critical tasks (like tests). Also, though I never used Spyder, from what I found online there's nothing it can do that VS Code couldn't – actually, VS Code seems to be the superior to me – so there may be no advantage in learning this environment.
Should I use the recommended environment, or is it okey if I use a different one? I'm sure the majority (maybe all) of my classmates will go with the recommended one, as they have no former experience with Python.
I'd like to get some point of view from educators. How big a trouble does a wayward student like me cause, may it annoy the teacher in the long run, even if he doesn't believe it now?
[I'm not really familiar with the tags here, I'd be grateful if someone more experienced could check them.]

You have pretty much listed the pros and cons. What do you expect we can add to that? If you are uncertain, just talk to your teacher. (S)he is probably the only person who can add something meaningful.

Is there an in-class final test? What is installed on the computers in the classroom where the test will take place?

By the way: this would get better answers at https://cseducators.stackexchange.com/, I believe.

@Maarten Buis It's actually the teacher who did this listing. :) The reason I asked this is to get some point of view from the educators. How big a trouble does a wayward student cause, may it annoy the teacher in the long run, did anyone have an experience with this, etc. You're right, maybe this didn't really come across in the question.

@Frederico We will write that "test" on our own device as well (with supervision, of course). Good point on the sceducators SE, I forgot about it. I ask for migration, if this can be done.

After using dozens of different languages and dozens of computer architectures, I'd say the easiest thing is to go with the flow - consider being ahead in Python to compensate for the time learning the new environment. You might even like it better.

As a personal anecdote, I once had a C-programming course where the program you did the programming in was ostensibly irrelevant, but all compiling for grading would be done with gcc in a Unix environment with specific settings.  And you could get very different results if you were compiling in visual studio. In my case, I made this mistake, and found out the hard way that in VS code that was completely unused wasn't compiled or checked, but the gcc ran everything, so an otherwise irrelevant missing semicolon wrecked the gcc compile but not the VS one.

As a faculty member who has taught data analytics classes, one thing I hate to do is provide "tech support" to students in class.  (In office hours is fine.)  I would recommend a standardized platform to my students because it minimizes (but doesn't eliminate) the amount of technical problem solving I have to do.  At least, if I solve a problem once* for the class I don't have to solve it again.
So the real question is: are you a complainer?  If you can't make something work in class time, are you going to be calling on the professor to help you fix it?  Or will you just muddle through, watch/help your neighbor do the lab on his computer, and figure out how to configure your own machine on your own time after class?  If the latter, I as the professor would be fine with you doing whatever silly thing you want.  If the former, or if the professor needs you to complete the lab during class time, I'd use the tools he recommends.
By the way: Spyder is to Python what RStudio is to R.  In addition to being a code editor, it has window panes or tabs to explore datasets currently in memory, and to view and format any data visualizations generated by your code.  So it's different than using a typical Python editor like PyCharm; it's a tool specifically well suited to data analysis.  I can understand why your professor has chosen it, and I recommend you give it a try.
*Actually, twice: once for somebody with a Mac and inevitably also for someone with a PC.

PyCharm has added a few panes recently to give these kinds of views.

The biggest difference you're likely to see if you use your own set up is the level at which your instructor will be able to answer questions. With the recommended method you might be told "Find and replace the string using control/command + R", whereas with your own setup you're liable be told "replace the string". Providing you already understand things well enough that you can make the translations in your head, then for a beginner's course and a mixed group you aren't likely to miss that much.
It's worth pointing out that it's perfectly possible that the teacher is more used to using yet another setup when coding themselves. Anaconda + Spyder is a good choice in this setup mostly because it works cross-platform in a reasonably consistent manner, rather than because it's a high productivity environment.

The choice of editor probably doesn't matter so much, although I would lean to using something with the IPython console (default in Spyder, add-in for VS Code AFAIK) as it easier to work with. Spyder has features useful for data science, such as quick access to variables and an image pane to show plots. PyCharm has these too now.
However, I do think you should use Anaconda, as it provides a distribution of the common python libraries using versions that are supposed to be compatible. If you submit code for assignments or to share with classmates, this will ensure they run on everyone's machine. It will also ensure that your code doesn't have some weird bug using some half-baked release that no one else has.

I would suggest you start by "going with the flow" and using the recommended tools. If nothing else, you will get the chance to explore them, with help on hand if you hit any problems installing them and learning how to use them.
But if after a while you feel you can work more efficiently a different way, then change horses. After all it's your time that you are investing in taking the course and (you hope!) the course is supposed to be teaching you "Python programming", not "how to use one particular IDE."

I would suggest to use whatever you like as long as you are willing to invest the needed time and energy to get it to work.
For example, when I learned to use Anaconda for Data Science, I first wanted tot code in Atom, just to learn in the middle of the course that Atom (or rather the script plugin to run code) isn't able to work with the pandas package included in Anaconda...
Yes, you might be able to fix such issues with enough experience and time to google for fixes, but there is a real chance that it will take you a lot of time that would not be needed if you follow the prescribed steps.
Furthermore, there might be (homework) exercises that you have to do in the demanded environment for the teacher to be able to grade it.


text:
My professor and chair of the department traced back a supposedly anonymus course evaluation to me. How to proceed?
At my large American university, we have the opportunity to fill out course evaluations. They are not mandatory and are allegedly anonymous. I wrote a negative review for Dr. Smith's course. I stand behind what I wrote and it is all true, but it was scathing and lengthy (over 1500 words) since I listed in detail almost every thing I didn't like and why, with specific examples. If it matters, my main complaints were that I consider his class to be too easy, his standards were too low, and that he took a long time to grade our assignments.
I received an email from the chair of the department asking me to meet with him to discuss the evaluation. The content of my evaluation is all true, but I am embarrassed that my identity was revealed (or correctly assumed) since I would have been less harsh if I was aware the anonymity wasn't guaranteed. It wouldn't surprise me if they guessed I wrote the review, since I made by far the highest grade in the class and had actually complained about Dr. Smith in the middle of the semester to the chair since Dr. Smith allowed something unfair to happen during the midterm. (I was advised by other faculty to bring that specific complaint, so I hope it doesn't come off that I like to complain.)
What should I do and can anything negative happen to me over this?

Stylometry now claims to identify 80% of writers given 5K words. (http://www.smh.com.au/technology/sci-tech/why-hackers-should-be-afraid-of-how-they-write-20130115-2csdo) Not saying that was used here, but the basic concept is the more words written, the easier it is to identify the writer. A year back a student made a complaint in class, then that exact complaint showed up later in the day on RateMyProfessor. I mentioned it in another class as amusing, and some students were shocked that I could tell who had written it.

As a general rule, faculty do not engage in discussion of the shortcomings of other faculty with students.  So it seems unlikely that other faculty who told you to take your complaint to the chair were agreeing with you.  They probably only meant that it wasn't proper for them to hear your complaint and that if you wanted to pursue it, you should take it to the chair.  But what you've now learned is that when you complain a lot, you will get a reputation and people will figure out who you are even on an anonymous survey.  Deal with it.

But you should have known your identity you be correctly assumed.  If you wanted it anonymous you should have toned it down.

You say that the course was too easy. But it was too easy for you, probably not for the majority of the class. Hence, your criticism is  probably wrong.

@NajibIdrissi I guess I was just taking my frustration out on him since I had a lot of negative experiences with him. I regret it now, obviously. My main issue with him was that one time, he was proving something on the board, and I asked him for clarification on how he justified the logic. It turns out it was actually incorrect and it prompted him to a more complicated proof. Then every class meeting later, he'd say something to the effect of "I have to do this the hard way now since [me] will see the handwaving." I felt really alienated by those comments.

@Dilworth His course was a senior level math class and completely duplicated material seen in a standard freshman level class, and was actually a lot easier than the freshman level class. I guess I am upset by it since regardless of what we did in our class, I am responsible for the material we should have covered since it is a prereq for other classes I need.

Different universities have different standards. I still think your criticism is probably false.

Are you sure that they traced your evaluation back to you? "We would like to discuss the evaluation with you" could also mean that they just want to discuss the evaluation in general (since you previously voiced your concerns) rather than your evaluation in particular.

Most probably nothing negative will come out of it.
And there is also the chance that they want your opinion, independent of the evaluation (i.e., they did not necessarily guess that it is YOU who wrote these comments but given the fact that you talked to the chair about these issues, then the chair wants to discuss these with you.)
True, it shouldn't have happened the way it happened (to make you think that the evaluations are eponymous or that they have guessed the writer behind these comments and want to talk to you about that)  but most probably the chair and professor would like to discuss the issues for potential improvement. Just politely explain all these issues and make some suggestions on how they could be resolved and it should be fine.

-,,-, and during the discussion, I'd also express my discomfort about the review being traced back to me, while guaranteed to be anonymus.

Hmm, the questions strikes a chord, given I’ve been there (a long time ago), and later on the other side. So this is going to be a long answer. ;-)
It’s probably easiest to split the question into the different issues raised, and the perspectives involved.
Anonymity
As you have found out by now, anonymity is really difficult to achieve online. My guess would be they recognized the writing, esp. if you became noticeable during the course (class size doesn’t matter then). But identifying students is even possible if there is only numeric information, and if student votes are aggregated. However, just because it’s (easily) possible to identify students, it doesn’t mean it should be done. If anonymity was promised it would be highly unethical if they would identify you by the evaluation itself. There are two conditions in that sentence. First, was anonymity actually promised («allegedly anonymous»)? If you only assumed it would be anonymous, because you don’t sign it, you have no right to be surprised. Second, unless they explicitly make the connection between you and the evaluation, it’s an assumption that they have identified you. Other explanation: You criticized the course, they might have gotten a bad evaluation and want to find out how to improve. But if both hold true — anonymity was assured and they do identify you as the author, then it would raise a huge red flag about the people involved.
(It's a bad idea to give a «scaredundergraduate» a virtual gun, but if the highly unlikely case happens and the conversation turns actually hostile, and you are in a one-party consent state (look it up!), it might be an option to secretly record the conversation. This is a «last measure» option. Personally, I think recording without the other person knowing is a major breach of trust — reserved for criminal acts, no matter the law. Any relationship and any trust is irrevocably broken if you do it — and I strongly advise against it. The idea of a meeting is to resolve an issue without anyone losing face. A recording blows that option out of the water. The conversation would really have to go downhill to think about using, e.g., the laptop you took out to read what you have written and record the conversation.)
Also, I wouldn’t expect hostility here. It’s much, much more likely that they want to resolve a very unhappy situation for all involved.
Style
As others have written in comments, it is better to stick to the facts and take emotion out of it. After all, it’s about the issue and anonymous comments don’t hurt less than comments made in person. Even worse, it raises questions about the person who makes anonymous comments («coward» comes to mind). Frankly, after some ‹learning experiences›, I go with «If you wouldn’t say it in their face, don’t say it at all.», combined with «If you snicker while writing, it’s time to pause and reflect.» However, you’re not the first person to whom this has happened and while you can’t change what you have written, you can still control how you deal with it. It’s painful learning, but given you ask the question here, you’re on the right track.
From their side, it depends on how they deal with these type of comments. Some instructors take it personally, others chalk it up to inexperience. You are a student after all. If they are professional, they might talk about they style and that it’s not conductive to improving the situation. Imagine you’d gotten this evaluation, would you have changed your behavior? Seriously? There might also be misconceptions about the course involved, and there is also the responsibility to avoid having students leaving one’s university/course and thinking this style is good practice.
Issue #1: Class Content
When it comes to the issues you’ve mentioned, I think it pays to go into the conversation with an open mind and listen to their point of view. I once had a student who wrote a scathing paper about a course, seeing everything in the worst possible light. There were a lot of misconceptions about the academic world in that paper (e.g., thinking my colleague and I were like full-time teachers and we were only giving two courses and had the rest of the week off). Once she did understand what we did the whole week, she saw things a bit differently. My guess is that «took a long time to grade our assignments» might fall in that category, but I might be wrong.
Other issues like «too easy» and «standards were too low» might be individual problems (you might just be in the wrong class). However, you also write that the class is a prerequisite and if you are not learning what you need to succeed in another class, then this is an issue to talk about (and focus on).
Issue #2: Interaction with Instructor
I would differentiate the issues with the content from the issues with the instructor. Again, his perspective might be interesting to know. You interpret his comments («I have to do this the hard way now since [me] will see the handwaving.») negatively as «you’re a spoilsport/know-it-all». However, even if you cannot phantom it otherwise, the intention might have been different. Social interaction is messy.
And yeah, perhaps this person is not competent to teach the course, but perhaps he adapted the content to the average student. Perhaps he will take the anonymous criticism very negatively, perhaps he understands your point of view. And perhaps a skillful mediator can make both sides to see the issue from the other perspective. In general, you don’t have to like the guy, but you have to work together professionally. And at least on the learning side, this seems to have worked out well. Some improvements are necessary on the «you can say anything, as long as you do it respectfully» side.
Recommendation
In situations like these, you can’t undo what has happened, so it matters how you deal with them. So, first, chill. Yup. Chill. You’re in a situation which nobody wanted, and that is something nobody can change. Pretty much the worst that can happen has happened, so chill. And yes, you did act badly, but you can still act with integrity in how you deal with it.
A way that might work (social situation, depends on all involved) would be to focus on the actual teaching issue — the content of the course and the interaction with the instructor.
What you have going for you is that you are passionate about learning (even if it’s only for the next course) and that you have mastered the content. That this passion leads to frustration if you don’t think you can learn what you need is understandable, as well as the style. If I were you I’d go this route. You wanted to learn and be challenged — and the course was very frustrating to you.
On the negative side, I think your interpretation of Dr. Smith’s behavior as hostile (and unfair) has strongly influenced your evaluation. When it comes to him, focus on the actual observable behavior, not the person. You don’t know him and it would be arrogant to assume you can characterize him as a person based on your limited interaction in one setting. Plus you can change behavior, personality not so much.
In general I’d go with assuming the best case, both sides want to find a good solution to the unhappy situation. Take a deep breath, go into the situation, let them start the conversation, focus on the issues, listen, state how you see the situation as your perspective (not as «fact»), and on the emotional side that you were frustrated with the course because you want to learn and be prepared for the next courses. As for the style, an apology might be in order if you actually feel this way — because you were frustrated with the course and wrote unprofessionally, not because the anonymity was lifted. It wasn't constructive, and yeah, it was wrong. It feels good emotionally in the moment, but it further complicates the issue and is likely unfair to the instructor involved.
Best outcome, you might end up understanding Dr. Smith’s behavior (perhaps it’s not hostile/unfair), and they might get some constructive feedback on how to improve the course.
BTW, an update would be appreciated how the conversation actually went.
Edit: Some pre-coffee spelling/wording mistakes.

In addition to the other advice here, I would recommend thinking about what you're hoping to achieve.
You mentioned that you made by far the highest grade in the class. Probably that means that the difficulty level was appropriate for the majority of students. So I would not try to convince the department chair otherwise.
You might have erred by enrolling in this class, and there may have been another one more suited to your background level. (This is true even if the course is "required"; such requirements can often be waived.) I would seek advice from your chair about how to plan your course of study, so that are challenged to the extent you can handle. Ask if there are opportunities to take more rigorous coursework in the subject, or on other topics that you are interested in.
I'd recommend this Paul Graham essay to you. One memorable quote: "Rebellion is almost as stupid as obedience. In either case you let yourself be defined by what they tell you to do." If you are stuck taking an easy class that you don't like, then invest only as much time into it as needed, giving you more time and energy for something more productive and enjoyable.
And remember that a good department chair will try to keep his/her strongest students happy. I'd recommend going into the meeting with the idea that you would like to seek out a sterner challenge, and that you'd appreciate the chair's advice for how to do so.

"I had actually complained about Dr. Smith in the middle of the semester to the chair."  It seems quite plausible that this is a big factor in the request for a meeting.
First, relax.  You can go to the meeting and listen, and then decide whether you want to say anything.  You can decide you don't want to say anything.  You can tell the chair that, calmly and politely, and then leave if you want to.  You don't even have to acknowledge that you wrote the scathing critique, or that you even filled out a course evaluation form.
I think the mostly likely explanation of the invite you got is that the chair wants to get ammunition to try to make things better.  I certainly hope so!
This isn't about you.  "Ask not what your department can do for you, ask what you can do for your department."  Think about it that way.
Oh, one more idea.  If you like, you can invite a friend or colleague or ombudsman to go with you.

I would seriously try to determine the cause of this request for a meeting. If it's because they want to follow up on your first complaint it's ok, but if they clearly state that they have traced back an anonymous evaluation to you than I would take this to the dean of the school as a clear misconduct on their part. If it's anonymous is should stay as such and they should not guess or investigate who wrote it.

If this about your anonymous evaluation I’d refuse to discuss it  with the chair.  The only issue at that point is that someone is admiting to have broken their commitment to anonymity.

Perhaps a bit more than a "comment": why do you care whether the course was easier than you thought it should have been? That is not an obstacle to your learning whatever you wanted. That is, it is not necessary (in my opinion) for anyone to have to suffer for others to succeed... in scholarship, etc.
Yes, over the years, I've had several "colleagues" declare that, at both undergrad and graduate levels, it's necessary for someone to get a bad grade so that the good grades are meaningful. Yikes! Of course, this does become more bizarre when talking about graduate-level courses where all the people have already passed a quite-high bar just to be admitted to our program in the first place!
Nevertheless, I vividly remember (because I was so non-plussed) a couple decades ago when "a colleague" expressed violent doubt about the legitimacy of my grading in a graduate-level course (of students who'd already been admitted, etc.) because no one got a grade worse than a "B". I was a little slow to object, in that full faculty meeting, because I was so surprised, ... but I did manage to finally say that... "well, they all learned the stuff...?"
I understand that there is the competition element of higher ed, but I do want to resist having that contaminate the "education and scholarship" aspect... Sigh.
Oh, forgot to answer the question: do nothing.

Even the very experienced don't always notice the date on the post ;-)

@ScottSeidman... ha! :)

Do nothing? As in, don't go to the meeting with the department chair?

@Allure, well, to my mind, depending on the wording of the request to talk to the chair, one might decline! But, sure, why not go? If the "complaints" were/are factually correct, no reason to apologize or rationalize or...? Maybe the chair will apologize to the student?!? :)

@allure-  oddly, when I saw the question come up because of a new answer, I asked myself what this student would get out of this meeting, and I didn't really have an answer.

Aaaaand, someone down-voted! :)  I am somewhat interested in trying to imagine the mindset and motivations of people who downvote (without comment), especially on somewhat-technical issues. One over-riding conclusion I reach is that any attempted reframing, that makes endless border skirmishes meaningless and pointless, is construed as insulting by those whose lives consist of exactly that (and do not want to be dissuaded...).

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text:
What degree of borrowing from a Stack Exchange answer and submitting to a peer reviewed journal, without citation, is ethical?
I posted a highly-upvoted answer on Skeptics Stack Exchange based upon numerous Chronicling America database newspaper quotations, and chatted in comments about this with a psychology professor.
The professor, listing himself as sole author, then submitted an article with highly overlapping content to a peer reviewed journal, without any citation to my Stack Exchange answer.
(More specifically, in Stack Exchange comments, I criticized a specific 2012 paper of the professor, which was primarily based upon google book ngrams, and showed in my answer numerous quotations from the Chronicling America database that result in a different conclusion. The professor then submitted an update of his 2012 paper to the same journal adding numerous quotations from the Chronicling America database.)
Is this ethical? I've only published in chemistry/biochemistry journals and don't have any idea what is typical for psychology journals.

Comments are not for extended discussion; this conversation has been moved to chat. Note that comments cannot be migrated twice, so any additional comments not directly related to the question will simply be deleted.

General Case
Ideally the author should acknowledge you in an acknowledgements section if you contribute assistance in some way. Unless you wrote part of the article, authorship is not warranted.
This Case
The post your wrote was quite good and provides a lot of good material, but other than saving a researcher time, it doesn't appear to do any original research. That's in line with the policies of Skeptics.SE as well. Likewise, while the person asking the question has reasonable grounds to be skeptical of the claims, the thesis is not novel.
I will also note that it the edit history shows that you started working on the answer in June 2017. The letter to the editor that you linked to says that it is in press as of the same month. I'm not sure what the lead time is like on that journal, but I wouldn't be surprised if the author has been working on the paper for significantly longer than you were working the Stack Exchange post. This is somewhat borne out by the author's publication history - they previously wrote on the same topic.
In short, it appears that you were both working on the same material independently before encountering each other.

In the article the professor says he conducted his database searches on 7 June, which is 2 days (US time) after I posted my initial answer.

@DavePhD Yeah, I noticed that as well. I'm assuming good faith in that the author had an interest in the subject before seeing your post given their publication history. I think the SE post might have given them some more ideas for places to search (I would acknowledge someone for that), but the SE post is very bibliographic which makes it tough to argue for authorship.

Yes, he definitely had an interest in the subject earlier.  I was criticizing his 2012 article on the subject in comments, and now he is submitting the new article to the same journal  based, apparently, on my comments and answer.

@DavePhD, I replied to your comments in the previous discussion. Please let me know what original text, data, or ideas you think I used without acknowledging it. As I noted above: I've been one of the few people working on this topic since 2012. I was notified of the StackExchange discussion on June 6 and that prompted me to write an update, based on material I've bee collecting since 2012 and a new search that took me a couple of hours on June 7.

Your apparent charge of plagiarism seems to be based on the fact that (among other things in the letter) I searched the same database you searched. Those are publicly available data, and using them in no way qualifies as plagiarism. Again--and I'm serious--if there's anything original you wrote that I used in the letter without acknowledging it, let me know and I will be happy to make a correction.

@MDG I never said "plagiarism". I didn't know if acknowledgement or citation was appropriate, that's why I am asking here. If I had a definitive opinion, I wouldn't have asked here. I never published anything that didn't involve physical experimentation, so I just don't know what is appropriate. It seems you got the idea of searching the Chronicling America database from my answer, and maybe the analysis of duplicate newspaper articles versus unique ones, and thereby used many of the same quotes.  But I don't know if citation or acknowledgement is appropriate or not in such a case.

@DavePhD: I will be happy to acknowledge that I got the idea of searching Chronicling America from the discussion. Just contact me by email if you want me to use your real name. On a final note (I know it's tiresome, but given the context I'll be extra precise): I didn't even copy the quotes from the discussion--I didn't know what search criteria you had used, and I wanted to see how many standard/reversed quotes I would get within the same search.

Also, you wrote "The professor, listing himself as sole author, then submitted an article with highly overlapping content to a peer reviewed journal, without any citation": that definitely reads like a charge of plagiarism, which is no small stuff.

@MDG I deliberately avoided using the "plagiarism" tag, which is one of the tags here, when I asked the question.  Anyway, thanks for offering the acknowledgement.  I'll pass just to stay anonymous. I was originally thinking you could cite to the Stack Exchange question website as a reference, but I'll leave it up to you to decide if that's appropriate.

I have no problem adding a link to the discussion to the manuscript.

FYI - I updated the online preprint with a link to the StackExchange discussion

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