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Is it ethical for professors to ask graduate students to teach?
Universities require a doctorate degree to apply for a faculty position which involves both teaching and research. Even if the professor did not receive any formal training in pedagogy, it is expected that they will pick up a few things over time.
If a graduate student who does not have a doctorate degree, nor has any formal training teaches a course, wouldn't it be unfair to the students? In many situations, there are no quality/standard checks in place before a graduate student is allowed/asked to teach a course.

I think this is very dependent and field specific, and can also be advantageous for students in some cases. Take math for example. A first year calculus course is pretty standard in content, and the graduate student could deliver this material very easily and potentially be more social and relatable to current students than the professor. In the latter case, I would argue that you’d get a better education.

I’ve had horrible experiences in classes with professors who could not teach to save a day in their lives, and then gone to YouTube for a non-PhD to explain a concept. What medium then offers the better education in that instance? I think the nuance in your question is important.

Note that in many aspects of life, instructors do not have doctoral degrees. Most yoga teachers, language teachers, painting teachers, high schools teachers have not -- and still can teach valuable courses (in some cases even without  peadagogy courses).

Another side remark: While I find the idea that people teach in high schools without peadagogy or similar education completely bonkers, in this forum I have often read "What can I do after my math study?" --answer: "You can always start teaching in high school after the phd", so apparently in the US one can even teach in high school without peadagogy training. So it is probably not too far off for uni instructors..

It does annoy me when professors fob off work they don't want to do on their students.  For example, I saw a professor buttering a student up to get them to basically read through another PhD student's entire thesis and check it for mistakes, that's not the job of the student.

@user111388: I'd consider "you can go and teach in school" a valid answer for Germany as well: there's a shortage of maths and natural sciences teachers, so most Länder do hire professionals that are not teachers via a university master in education. But: they don't start as full teachers, those professionals go into special pedagogy training programs (you may describe them as apprentice teachers).

@Tom - in my department the ethos amongst the students was that we would be happy to read another students thesis looking for typos and whatnot. Just part of supporting each other. And a very useful exercise as one was getting close to writing your own thesis, just to see what looked like what to please the thesis secretary.

Please say where you believe "Universities require a doctorate degree" to be true. It certainly isn't the case in the UK where many postgraduate students shoulder significant teaching responsibilities while completing their PhDs.

Since cultural differences may be important here: I'm in germany.
As you say, the teaching staff in academia learns teaching mostly in a form of training on the job.  Pedagogy training for university teaching staff is a rather recent advance here, and I'm not sure how widespread that is done (read: likely still rare).
Within that system, you have to start at some point: said professors would lack teaching experience if they had not started accumulating this experience as grad students.
Here, grad or PhD students start their "teachin career" by first teaching "low impact" courses: settings where bad teaching doesn't do too much harm.
E.g. a single experiment in a labwork practicum. Or a seminar that discusses homework (i.e. the excercises that all students should already be able to solve on their own). As they accumulate experience (also experience with oral presentations in general), they advance step by step: teaching internal seminars to the group, at some point teaching a single lecture for a colleague. Someone teaching a whole but still small course (typically on subjects related to their research specialization) is typically advanced postdoc/PI level. All these are still under the official supervision of the professor. Finally, teaching university courses without any supervision (i.e. in their own responsibility) is typically achieved after habilitation.
What about quality checks?
The professor stays responsible for the teaching. So while they can ask a grad student to help with the teaching, they must make sure that this teaching will be at an acceptable quality.

Yes, it is ethical, but it can't be done in a vacuum. You don't just throw an unqualified person at a group of students and expect anything good to come from it. But, where this is done, there are normally some controls in place.
For example, a graduate student given sole responsibility for a course will probably have TA'd in the course previously, working with a regular faculty member. It is also likely that there will be a regular faculty member responsible for some oversight. Most such courses are elementary, where the graduate student can be assumed to be thoroughly familiar with the material, at least, if not with pedagogy.
Also, there is normally a selection process in which some thought is given to who should teach these courses. Again, normally, the students will be somewhat experienced and will have seen a lot of professors and will likely get some sense, imperfect of course, on how to go about it.
But, I think it would be extremely rare for a grad student to be completely responsible for the course design and delivery. Likely the syllabus and learning materials are chosen by others. The exams may be graded collectively if there are a large number of such "sections" of a course. Student complaints would be taken seriously.
And some grad students do get a bit of practice in lecturing, at least when a prof assigns them the task of preparing and delivering a lecture on some topic in a course they are taking. I had this (unsettling) experience as an undergraduate, actually.
In the US, it is rare, in fact, for a new Assistant Professor of mathematics to have any formal training at all in pedagogy. I think this is different in EU, as colleagues there have expressed a bit of horror when they learn of this. New faculty struggle along and hopefully don't do too much damage.

I'm not sure "formal training in pedagogy" is common in the EU. I think by now, one can get some training if one actively looks for that, though.

"a graduate student given sole responsibility for a course" in Germany (and in my field), I know of cases where professors got in trouble for less (having too many individual sessions in a first-year lecture held by his PhD students).

My wife was given sole control of history course, with some oversight, while she was a grad student. Although that involved a slightly unusual situation with the tenured professor that normally taught that course having passed away.

If you ever run a large department or institution or similarly large organization, you will discover that every decision that you make (and you will make lots of decisions, every single day) has many consequences and is strongly interrelated to many other decisions you have to make. Some of those consequences will be good (say, saving money, or allowing an inexperienced employee to gain experience with some essential professional skill), and some will be bad (say, compromising the quality of the work product generated by the employee-in-training).
With each decision you make, imagine someone coming along, pointing out a single bad consequence Y of a single decision X taken in isolation of all the other consequences and interrelated decisions, and asking “is it ethical to do X when it leads to bad consequence Y?”
This is what you are doing. Yes, it’s ethical. In fact ethics has nothing to do with it. You are applying absolutist logic (“professors have PhDs, therefore only people with PhDs can ethically teach undergraduates”) where it doesn’t apply. Allowing graduate students to teach is simply a natural device that can be used to achieve multiple positive goals within an academic institution. It inevitably involves making some compromises about certain things. But that’s true for all decisions made anywhere by anyone.
Look at the big picture, and you’ll see that universities function well overall even though they are regularly engaging in this supposedly ethically problematic practice. And if you think you’ve got a better system figured out, try to found your own university and show everyone how you can produce well-educated undergraduates as well as highly trained graduate students, on a budget that’s competitive with other universities’ budget, without using the problematic practice. Then we can have a discussion about ethics. But remember, to do this you’ll have to take all the details of the entire organization into account, not just a single consequence of a single decision.

I don't think I am being absolutist here. If you see my question, I am qualifying the ethical decision based on placing proper quality checks. If a professor delegates teaching duties to a graduate student because he/she doesn't care about teaching (which is nor rare), I think it is an ethical issue.
You say Universities function well overall. I think this is true when it comes to research. But the average 6 year graduation rate is 60% (https://nces.ed.gov/fastfacts/display.asp?id=40), which is too low in my opinion. I don't think Universities are "functioning well".

@Eracnet sorry, I have no idea what you’re talking about. It sounds like you misunderstand how the system works. The decision to let grad students teach courses is made by the university administration not by individual professors. At least at my institution there are quality checks and a mentoring system. But that’s beside the point, if some other university is poorly managed then that can mean the people running it are incompetent. But incompetence and unethical behavior are two completely different things. And even the conclusion of incompetence is suspect, it’s more likely that ...

... it’s simply not as easy as you imagine to design the utopian university of your dreams.

FWIW -- this question seems to assume that people with PhDs are good at teaching, and people without, are not. Or at least they are correlated. In my experience this is not the case -- in fact, being able to teach something like an Intro Calculus course is more about being willing to emotionally engage with it, and that seems negatively correlated with experience, in my experience. Younger teachers do a better job, because they're not sick of it yet. So in that sense -- it would be unethical to have a full professor teach it.

In the UK, there are teacher training programs and courses for teachers at a school level or university level.
However, one can still teach without those qualifications, if one has relevant experience of the material - more likely at university or college level but not so likely at school level.
To teach in schools, the school is likely to check on your background as any convictions related to minors will mean they will be concerned for the children in their care...
The UK has a government website where those registered are listed with certain details, so that may help schools or universities looking to employ in some cases.


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My teaching evaluations arrived and female students statistically gave me worse scores than male students. Is there any possible explanation?
I'm a new assistant professor and I finished my first semester of teaching. It's my first class, but I think it went good: the students seemed happy and interested, I had many of them (both male and female) doing more than required, and some of them later approached me to tell me they learned a lot.
The scores arrived: numerically they ended up being lower than the average of my school, which was disappointing, especially because in the descriptive part about the strengths there were many positive comments about me and the class, and in the negative part, they were mostly neutral or just slightly negative (and I agree with these, they are about my inexperience and baby steps). There was nothing nasty, ad hominem, or abusive. So based on the descriptive part and the overall experience, I expected the numerical score to be much higher, but it's fine and that's not the main topic of this question. I read a lot about student evaluations here on SE Academia and how pointless they can be, so while I care about feedback as a new lecturer, I had low expectations about them and I was going to take them with a grain of salt.
But the scores are also reported by gender. I am a male lecturer, and female students rated me much lower than male students (who rated me highly). The sample size and the difference are so high that I cannot attribute it to a statistical error and dismiss it.
This left me astonished as it's the last thing I'd expect, and I'm trying to understand why and where is this coming from. I'm very well aware of the gender equality issues in academia, so I am quite conscious about treating everyone equally well, I'm very careful about avoiding everything that might even remotely imply sexism (for example I don't make jokes, and I never even mentioned anything gender related), and I'm careful about never making any physical intrusion (not even a handshake or sitting too close to a student during discussions). I just cannot think of any reason why students of one gender would give a much different score than the other, and what made female students less happy with the course and me.
I know that everyone is biased when talking about themselves, but recently I even had a former female colleague telling me out of the blue I'm the one of the most respectful and pleasant people she worked with.
While you didn't take my class and don't have insights, but is there something in general I might be unaware of, and can improve? Is it possible that there is a teaching style to which different genders are receptive in a different way? Is it just possible that there is simply a discrepancy between how different genders give different scores? It may sound silly, but is it me being too respectful backfiring and seen as condescending by female students? This will obviously be difficult to answer without an insight, so I am at least trying to understand general reasons.
In the comments part of the teaching evaluations there is nothing negative about me or the course that I can interpret being gender related (they are mostly about the organization of the teaching or the course being demanding, and not much about me). The positive comments that are about me say that I am very nice and the course is well organized. This leaves me confused.
I searched online about gender bias in student evaluations, but almost all articles are about the lecturer's gender, with female lecturers on average receiving lower scores than males. I cannot find research on the gender bias of students. I also cannot find anything similar here on SE Academia. I read other question as well (this and this), but didn't get the answer.
In one of the articles I read that some students are so subjective that they evaluate their (especially female) lecturers based on looks. I have experienced this first hand since one of the students wrote that I am the best looking teacher in the school. So even considering that I am always groomed and nicely dressed I am not sure that a group of students would rate me badly based on my appearance.
Some additional notes:

the gender ratio in the class is balanced, about half of the students are female
there was not a single conflict with any student during the semester, which would be amplified among a group of students and reflect badly on the evaluations

For a discussion about the on-topicness of this question, please see this related meta question.

Answers in comments, side discussions, etc. have been moved to chat. Please read this FAQ before posting another comment. Please do not post comments asking for details that may resolve the conundrum (given the broad nature of the questions, these are answers).

I am a female student from Japan and will humbly attempt to answer your question, although I have never attended your lectures if you never taught in my country.
Subjectively, I find that females are on average better at explaining things than males are, but I strongly suspect that males subjectively find that the opposite is true. This has nothing to do with any kind of prejudice: I really better and easier understand explanations by females than by males, on average. Given a choice between a male and female teacher and no further information, I would be strongly tempted by my whole life experience to choose the female.
I guess the root cause of this phenomenon is that the male brain and the female brain are, as research shows, wired differently, and I guess this gives rise to somewhat different thinking patterns or styles of reasoning and learning. So it appears to me that male teachers are better for male students and that female teachers are better for female students, because people of the same sex tend to think in more similar ways.
Such things are difficult to describe, so it is no wonder that you got no hints in the comments of the teaching evaluations, but let me try. I will now try to summarize my own observations about typical shortcomings of male teachers as viewed from my perspective. I emphasize that what I will write is my own observations and impressions based on my own personal experience.
First of all, male teachers tend, in my experience, to explain things by using abstract general ideas and concepts, whilst my thinking processes are mainly driven by analogies to particular instances. Male teachers tend to make very few analogies in their explanations and to operate mainly in terms of purely abstract deductive logic.
Second, the male approach to explain things seems to be turned upside down with respect to what I consider natural. To understand something, I need to be shown a set of simple specific examples that I could use as keys to inferring some general ideas. Contrary to my needs, male teachers start with abstract general principles and methods, build a multi-layered system of definitions and principles, and only then show how that system works in particular instances. In other words, I prefer to go from particular to general, from simple to complex, step by step, and male teachers prefer the other way around.
Third, males tend to have a kind of negative attitude in thinking. Facing a problem to solve, they seem to tend to ask themselves, "What do I have to do to solve the problem? What general principle applies to situations like this one?" I am a much more positive person and tend to ask myself something different, "What steps can I do now to get closer to getting the problem solved?" Males seem to tend to think in terms of necessities, whilst I tend to think in terms of opportunities and making choices. The male approach simply does not resonate with how I am used to think.
Fourth, male teachers tend to be succinct in their explanations, as if they were afraid to overburden students with information. In contrast, I always want more clarifications, more analogies, more examples, more insights from different angles of view, etc. This helps me understand and memorize things.
Fifth, male teachers tend to rarely repeat things or provide alternative explanations, and the result is often disastrous: a failure to understand an idea renders the remainder of the lecture superfluous if the teacher builds on that idea. Apparently, male teachers presume that students will instantly and fully understand everything, every sentence and idea told to them. What makes it worse is that male teachers tend to build their lectures in a highly organized, systematic manner, so it is really critical to understand everything they say. This, in turn, requires utmost concentration and quickly makes me tired. I feel more relaxed when taught by a female.
Sixth, male teachers tend to do their job rather formally, basically repeating what is stated in books, so I often see no point in attending lectures. After all, I can read books myself. What I want from teachers is bright examples, interesting analogies, etc. - everything that can help me interpret and memorize theories written in books.
Seventh, male teachers tend to care little as to why a student is confused and asking a question. Instead of starting a dialogue with a confused student, talking in the student's terms, and building on what the student knows, a typical male teacher blindly imposes his own way of reasoning, essentially repeating what already has been said during the lesson.
Finally, male teachers tend to be simply more boring to me. They talk slower and less expressively, show less emotions, are less empathic, less interact with students, rarely appeal to emotions, and are less involved in general.
The above shortcomings are probably not shortcomings at all from the perspective of male students. As I said, males and females seem to tend to have different thinking patterns or styles of reasoning and learning. So please kindly do not take my post as sexist. I am not saying that any sex is superior. We are just different, as shown by the research mentioned above.
Also, the points made above are tendencies or generalizations rather than strict laws of nature. There are exceptions, and I had a few male teachers whose ways of teaching I really liked. Those teachers were largely devoid of the shortcomings outlined above.
I would like to conclude my post with an illustration of my points. How would a typical male school teacher explain what is the force of elasticity in physics? He would say something like, "The force of elasticity is the force that arises in a body in response to its deformation and acts to return the body to its original shape. An example is the action of a spring." A typical female teacher would rather come up with an explanation of the following kind: "Imagine Tokyo Tower. Have you ever visited it? Great, now suppose King Kong approaches Tokyo Tower, puts his hairy hand on the tip of the tower and pulls it towards himself, thereby bending the tower. To do so, King Kong acts with a force on the tower, and the tower acts with an equal force on King Kong's hand, according to Newton's third law. And that force - exerted by the tower on King Kong - is the force of elasticity. The same name applies to the force exerted by a stretched spring. Or a rubber band. Or just anything that is being deformed in any way and is resisting because of its internal structure. That's what we call the force of elasticity. It's what King Kong has to overcome to bend Tokyo Tower." Learn to explain things in this way, and female students will probably like you more :)
I humbly hope that my post was helpful in shedding some light from the other side of the fence, so to speak.

Comments have been moved to chat. This answer has been controversial due to its generalizations and unsourced/poorly-sourced scientific assertions. While this answer's scientific accuracy may be dubious, I would suggest that its real value is that it illustrates the sort of opinions, impressions, and ideas that students have. Students are, after all, the ones filling out the evaluations, so it's valuable to try to understand the sort of ideas they have, even if we might not agree with all of them.

I would hesitate to draw any conclusions whatsoever from one semester.  File this away, and check whether it becomes a pattern, and if it does then think about it then when you have more information.
Although there's not a single incident that you're aware of, I wouldn't be at all surprised if something being "amplified among a group of students" is exactly what happened.  It's easy to have a miscommunication with a student that leaves them with a negative impression of you, and for that to spread among their friends.  Unless there's a trend in other classes I wouldn't jump to the conclusion that this has anything to do with gender specifically, it may well just be that one group of friends which is mostly or entirely female didn't like you.
Also, I commend you for thinking about this and for seriously considering whether you need to change something in your teaching.  I just think you might be overthinking it at this point.

Darij’s comment about major is similarly plausible to my speculation in the 2nd paragraph.  My main point is that once you’ve taught more than one class you’ll have better tools for figuring out what’s most likely.

I'm not sure friendship groups at university are usually that gender based

Sometimes they are sometimes they aren’t.  I’ve certainly had classes with a close group of mostly women, and classes where that wasn’t true.

The first sentence says you don't answer the question.

@AnonymousPhysicist: My point with the second paragraph wasn't to give an answer, but to illustrate that there's lots of explanations out there which would be consistent with this pattern not being repeated in future classes.  But maybe you're right it'd be better without it.

@RichardTingle - my wife and I have three daughters. I suggest that most males (self included) have NO CLUE about the relationships between women. It's similar to but not nearly as simple as playing three-dimensional chess on a board you can't see with an unknown number of pieces against an opponent who's invisible.

Here are a few possible lines of thought. Of course, we would need much more data and context to know if any were actually the case.

Don't forget the null hypothesis. If you carried out this survey for other lecturers (of each gender) for the same course, other courses, other departments, other universities, would we indeed find that your result is anomalous, and by how much? We may have no reason to think it isn't, but unless we know, we don't really know what phenomenon is under discussion.
How do you know your survey is valid? Which factors in your teaching did you measure? Are they measurable numerically?

As you suggested and Noah responded to, "amplification" is a possibility. Classroom culture is a factor at every level of teaching. I found this especially during practice teaching in a middle school, where the same students and teacher are together all day and it's hard to have multiple atmospheres or moods coexist in the classroom. The verbal and tacit feedback they get from each other promotes uniformity. One class decides they like a teacher, and it's easy to teach the group even if a few students privately feel differently. One class decides they don't, and it becomes very hard to win them back as a group.
Even when the whole class doesn't respond alike, subgroups often respond alike. In the high school classes I'm teaching now, there are friend groups that break along some classic lines, and each group rather than each student tends to have a certain attitude towards the course and the teacher. I could imagine that gender is a possible subgrouping. Such a group was created just recently in my English course on the basis of content when we watched and discussed a movie on how women are depicted in advertising. The overall class cohesion meant it was a temporary divide, but a subtler cause of division could be harder to heal.

Being overly respectful is not likely to be seen as condescending. But standoffishness (even unintentional) is not the same thing as respect. I have an idea of the careful line you're trying to hold by not sitting too close and not shaking hands, and it's a good thought. But consider that a conscious attempt not to overengage can come off as stiff or cold. Some people avoid others because they dislike them or feel disdain for them, which is not the impression you want your students to have.
If you feel more confident that you can comfortably interact with the young men without crossing boundaries than you do with the young women, there might well be a difference in how warm each group perceives you to be. You might even be unconsciously reducing the number of interactions with the girls. Students are highly sensitive to cues about whether their teachers like them.

The same neutral approach could also be an issue in terms of content. Qui tacet consentire videtur. You don't always know what you're saying by not saying anything. I was teaching English in a high school and we were reading essays on gun control. Suddenly, the Stoneman Douglas shooting happened, and the government responded about arming teachers and whatnot. To be silent about it would be to invite the students to construe — on their own, without evidence — what I thought of the issues. So the discussion was opened.
Note that in such a discussion, you don't have to even reveal your own opinions, but give the floor respectfully and affirm what's said and the right to speak of various people, especially those who tend to be intimidated or talked over by the class as a whole. But you can also make direct contributions if you want. It's a great idea to prepare students on these issues that they'll grapple with as adults, bringing insight from whichever field you're working in. Anthropology, biology, history, literature, statistics, business — many fields have inroads if you want to show your hand, rather than hide it, for the positive effect it might have on skeptics.

I think any more requires knowing about your results, your students, and your class.
Here's a suggestion if you want richer, non-useless student feedback from these students, since the people who were there have more insight than you can convey to us here. You could invite a few students who you think were highly engaged and who had good connections with their peers to sit and share more detailed feedback on the class, if they're interested. "After reading through the anonymous surveys, I'm hoping to explore some points further. I think you might have a valuable perspective to offer, based on your participation in class."
You could then ask some open, non-leading questions, not about your results themselves ("Why was there a gender divide?") but about possible factors ("How did you perceive the teacher-student interaction? Did you sense any favouritism?").
You can also ask colleagues, who will sometimes hear from students or even inquire about how the new hire is doing. They may have some things to share through the grapevine. Another answerer's suggestion of inviting a colleague to sit in on a class and take notes on your teaching is also great. I think here too I'd avoid giving them too strong a lead to look for, beyond the premise that you want feedback; whatever they notice will be more significant if it comes up without prompting.
Do keep in mind what you've said — that you don't know what the significance of your results is. (Not that it stops you from making positive moves.)

+1. For instance, it occurred to me that this discrepancy between male and female voting patterns may be present among the other academics (notwithstanding that on average they scored slightly higher than @user117849). It might be simply a case that the female students were more critical. Without further information it's not really possible to make, well, an informed judgement.

I just want to say that i think this is a killer answer and made most of the comments/answers i thought about and more. i need to check if i have some input that is not covered now. @Luke Sawczak

It could be almost any of the suggestions already suggested, but my hunch from the information provided (in particular, that the complaints "are mostly about the organization of the teaching or the course being demanding"), is that it may tend to be one of two things:

Communication style. You may organize and explain ideas in a style that more typical men in your culture use more and follow more easily than typical women in your culture do.
The minor/major point mentioned in the comment by @darijgrinberg . For example, if your male students are mostly majoring in related subjects, but your female students are mainly taking your course to meet some requirement but they're not particularly interested in the subject, or if they have less experience with courses in your field, your course may seem less intelligible to them because you may not be explaining things for people less familiar with the assumptions and language of your subject, making the teaching seem more disorganized and harder from their perspective.

I have posted this as a comment, which has been referenced twice in the discussion; since it now has been moved to chat, I'm reposting it here for better visibility:

Can you check the major/minor composition of your course by gender? If it is significantly skewed, you may have your answer there. I'm pretty sure students will evaluate a (well-taught) class much lower if they view it as a hurdle on their way to something interesting, and that's much more likely if the class is not in their major.

Here is a concrete quasi-example. There are well-documented huge differences in gender composition between majors. If you are teaching (say) a theory-of-probability class that is required for mathematicians (43% female), computer scientists (18% female) and medicine students (84% female), then a woman sitting in your class will be much more likely than a man to view it as a painful hurdle on their way than as an exciting intellectual journey. There is only so much you can help this with good teaching. Students don't like the non-major classes they have to take, and this pulls their ratings of the teacher down. (I don't have any good data for this, but the mechanism is obvious to me and my own experiences confirm this.)
Note that you can probably check whether this applies to you; most universities let you easily see what programs your students are in, what other classes they have taken, etc.

Another possible explanation was mentioned in a deleted answer; I'm going to repeat it here to put it in context. There is a rather significant sex skew in visuo-spatial intelligence with women scoring (on average) the lower (roughly speaking) the more 3-dimensional it gets. This may and may not be contributing to your female students' problems (as well as those of others who have low visuo-spatial abilities). My personal impression is that the significance of visuo-spatial intelligence in learning mathematics is rather minor: With my own lack of it (despite being male), I found a few "topology in pictures" books incomprehensible and am probably getting less mileage out of most graphics than other people; but there is no field of mathematics I found myself blocked from entering. You can easily learn linear algebra without ever seeing a picture. However, you may be significantly exposing yourself to the sex difference if

you are teaching material is inherently 3-dimensional (say, some parts of physics, engineering, etc.), or
you are relying heavily on spatial visualization.

In mathematics, at least, these cases are easily avoided (just give references to more formalized versions of your arguments). I don't know how it is with more applied disciplines.

The visuo-spatial observation is interesting, but it's contentious and unnecessary to tie it to gender. It's just good teaching practice generally to cater to a variety of cognitive styles, regardless of gender valence. There is other research showing that the supposed gender "spatial intelligence" difference is context- and culture-dependent. I understand your point here, but I'm suggesting caution about this because it is often misinterpreted and it is one of the first things bigots reach for when they try to justify the underrepresentation of women in STEM.

@ElizabethHenning: The question is tied to gender already :) I agree that teaching to different styles is best, but it helps to be more concrete (particularly as no one really knows what "learning styles" are, with most specific definitions failing to produce reproducible results). IIRC, visuospatial intelligence is one of the stronger sex differences in intelligence around, and at least in maths it's mostly clear what to do about it (avoid reliance on spatual intuition and 3D animation; if possible, provide alternative "encodings" more convenient to an algebraic/verbal mind; ...

... incidentally, these are also good ideas from an accessibility viewpoint).

If you avoid spatial intuition, then students (such as myself) who rely on it in preference to algorithmic approaches will be shortchanged. I believe that what's true is that there is a (highly variable) gender difference on performance on certain cognitive evaluation subtests, in particular the 3D mental rotation task. It's a significant leap from there to conclude that women are on average worse at 3D mental rotation in the real world, let alone that that difference is "innate."

It's not really supported at all to further conclude that there is a difference in "visuospatial intelligence" generally, whatever is meant by that independent of cognitive test performance. I'm just suggesting that you tread carefully here.

This is getting a bit pedantic, isn't it? Whether the differences are innate or not doesn't matter; they are unlikely to change during a one-semester course. And even if the differences are only pronounced in the environment of a test, then they will still show up in a class environment, since tests are used in classes all the time. Mental rotation only shows the biggest sex difference between the tasks in the study I've referenced; the other tests have smaller differences, but still in the same direction.

And I already carefully worded "avoid reliance" to allow for using visuospatial intuition, just not as a "load-bearing" component that students have to grok in order to succeed in the class. (Though my personal standpoint on this is that my students can watch 3Blue1Brown themselves, and I cannot produce anything remotely as good as this myself, so there would be nothing gained if I tried to turn my class into a movie show.)

Note that there isn't any evidence that catering instruction to different "cognitive styles" gives any benefits. E.g., see Daniel Willingham, Why Don't Students Like School?, Ch. 7

The "sex skew in visio-spatial Intelligence" is a greatly misunderstood and misleading average that males like to believe indicates they understand math better. All it indicates is that more male students understand math in a more concrete, less global way on average than female students do on average. It could reflect a male teaching style that more female students don't benefit from than do benefit from, though. In that way only, it's relevant here.

One possible way to investigate this further is to ask a trusted colleague to observe one of your classes and give feedback on that. This can be done privately, outside of any officially documented peer-review requirement (which may relax you both and give more honest feedback.) Some people also video record a lecture and watch it with a colleague for possible feedback -- this also leverages the fact that sometimes we're our own harshest critic.
Even if the one observation doesn't bring the gender-equity issue into focus, there might be one or more other things that pop up for improvement, so it could be a good use of time either way.

Hmmm. Good advice except that watching yourself lecture is likely to lead to severe depression. Even if you are good at it. ;-)

@Buffy. Why? Students of pedagogy are sent to schools same way as students of chemistry are snet to laboratory. At first they observe the senior teacher and then they teach while the senior one is watching. University teachers does not need that sort of education, though.

@Crowley, in the US, most university teachers never get any training in pedagogy. Mostly they just observe the way they are taught and try to emulate it. But in particular. Watching yourself is often horrifying. You see all your missteps. Your voice sounds weird, etc. A shocking revelation. My EU friends are surprised that this all be so.

A female colleague AND a male colleague.  It maybe that your normal personality results in mannerisms that are benign but don’t resonate with as many females as males.  Stereotypes like Mars vs. Venus are bogus, but the opposite extreme (saying we’re all the same) is equally bogus.

I'm going to do a bit of a frame challenge on this one: before going down this path, you should actually make sure that there's actually meaningfulness to the disparity.

Let me give you an example that happened to me personally.  I just
  started a new job, and within a few months, we had an All-IT meeting.
  The company had conducted a survey of everyone that worked at the
  company, and had found that IT's 'Rate-Your-Happiness' responses were
  lower than the non-IT and were looking at ways of improving IT
  happiness.  But there was a problem.  IT and Non-IT people are
  different.  Ask both to give a "Rate Something X-Out-Of-5", and you're
  going to have different averages between those two groups.  And sure
  enough, it turned out that it wasn't that IT was unhappier than Non-IT
  - it's just that they handed out numbers differently.  If you looked at the non-numerical Yes/No questions ("Would you be likely to
  recommend working here to a friend or family member?" for instance.),
  the two groups had nearly identical responses.

I'm not saying that's necessarily what's happening here.  But right now, for your value difference to be meaningful, you have to first assert:

There are no fundamental differences between men and women that would
result in how they rate things in general.  I have no clue on this
one.  And googling didn't help out, either.  I wouldn't be surprised
if there are differences in the average "Rate something X-out-of-10"
between men and women in general.  And I wouldn't be surprised if
there were no differences at all.
There are no fundamental differences between men and women that would
result in changing how they rate teacher performance between genders.
This is debatable.  Googling was tough (the results were almost
uniform in 'Male versus Female Prof' instead of 'Male versus Female
Student'), but I found Bachen, McLoughlin, and Garcia (1999) as well
as Basow (2000) that indicated female students rated male profs lower
than female profs.  While it's not definitive, it's not a stretch to
believe that it would indicate that a male prof's reviews would be
lower from the female portion of students versus the male portion.
There are no fundamental differences in campus/college experience
between men and women at your university and your degree program.
Just for an extreme, we'll take where I graduated - which was a
college that had twice as many male students as female, and where the
female-to-male ratio in the particular STEM field I was in was a
crazy 1-to-50!  The women in that field had a wildly different
college experience from the men, to the point where I'd hesitate to
even guess the scope of it.  Expecting how they evaluate professors in general
to be identical to the male students is a bit unfair - simply due to
the drastically different environment they were in compared to the
male students.

So what should you do?  Honestly, I wouldn't take the numbers into account at all.  Instead, look for anything like "What would you improve about this class?" or "What things did you not like about how the class was conducted" - items with specific points to address.
Because at the end of the day, even if that numerical difference is meaningful, it doesn't actually help you improve what you're doing.  To improve, you have to find out why you're given a low score.  (Put another way: if you try to solve the problem without actually knowing what's causing the problem, you're just blindly guessing.)

This is a good point. The obvious (arguably, the only) way to eliminate all three (and other similar "is it a wider issue than your class?" issues) is to compare your results with those given to others. Speak to your colleagues.

I feel like if in general, women truly rated things lower on a scale than men (re: point 1) it would be out there, since it would impact a wide range of things. I think your points 2 and 3 are good though, especially #3.

@AzorAhai - oh, don't get me wrong, I have zero clue whether #1 would be true or not.  But... if it were true, it wouldn't surprise me if it wasn't easily google accessible.  If you want to see what I mean, try to replicate what I found in point 2 without googling the specific study authors.  You'll get buried under a sea of 'sexism against female prof' studies/op-eds/articles.  It wouldn't surprise me to find either Yes/No on #1, but after 10-15 minutes of googling, I couldn't find anything remotely telling one way or the other.

I might as well weigh in on this, with all of the caveats mentioned by everyone else.
IMO, the most telling sentence in your question is this:

It may sound silly, but is it me being too respectful backfiring and seen as condescending by female students?

Let me reframe this: it's possible that you're trying too hard to be respectful to your women students and they're picking up on your discomfort with them and it's making them a little uncomfortable too. (Ask a black friend about white people trying too hard to not seem racist.)
Remember that undergrad evals are largely beauty pageants, so you might be coming off as vaguely unlikable to the women and it's skewing your numbers. A colleague probably wouldn't notice this subtle dynamic.
PS I'm guessing you're in a heavily male-dominated field. Your question beautifully illustrates why gender imbalance is a problem.

Can you get the overall statistics? Specifically:

Is there any bias observed assuming all answers asked for all courses (at your deaprtment / faculty / university / field?
Is there any bias observed assuming all answers of your students?

How are you measured? 1-5 stars, 1-10 points? There are zounds of way how to interpret such scales. Can you get histograms how each student evaluated?
I dare to say there are people who never give 10/10 (because there's always something to do better, right). I also dare to say some use only 3-4 values from the 1-10 scale: 10-awesome, 9-acceptable, 8-bad, 7-rubbish; others may use same sorting but with 3 point lower readings...
When I was in highschool the marks were:

Excelent (Výborně)
Remarkable (Chvalitebně)
Good (Dobře)
Acceptable (Dostatečně)
Unacceptable (Nedostatečně)

You can see that mark 4 is acceptable to pass the exam. Still they who had average around 3 were considered underperformers, those with averages around 2 were okayish and those scoring 1.6 and better were considered excelent students...
See? There are way too many factors in the game, the biased performance readings may be caused by the biased audience, by different scale interpretations...
Also remember: Coincidence does not mean Causality.
Were there any strong complaints? Were your lectures hard to follow? Did they consider you xenophobic? If the answers are No, don't bother yourself and focus on improving your feeling of the courses.

This doesn't answer the question.

@AnonymousPhysicist I was questioning there is a real question whatsoever.

Ask others in your department who have taught the same course whether their scores had a gender difference.  If there is an administrator (Vice Chair, say) who keeps records of student ratings, discuss with them.  It may turn out that this is a known phenomenon; if so it is nothing to do with you.
It still may be something of concern, but something for the whole department to do something about, not just you.

Asking people, particularly ones in official roles (as opposed to closely trusted colleagues), has its drawbacks: (1) you are making them aware of weaknesses in your teaching profile that they might otherwise have missed and that can later be used against you; (2) they might infer that you worry too much about your student evaluations, which is bad optics (it reeks of vanity and of trying to optimize your teaching portfolio for a new job).

Obviously I disagree.  A department that has a Vice Chair intent on helping new instructors improve (as opposed to one intent on hurting them later) is my model.

Unless you are an experienced statistician with access to a good amount of studies and/or a good knowledge of the results of meta-analysis in respect to performance evaluations, please refrain from reading anything into this.
By education and cultural background, female students may have a different scale of what the evaluation scale means (when women rate themselves, and men rate themselves the difference is significant, and I assume that some of this may also be the case here). So it's very likely that by your approach and data basis you are even able to validly conclude that you are rated especially badly by females.

The sample is not independent so I think that you cannot say much about statistical significance. One group of friends might be of size 20 and one person complaining about you might change the whole group's perception.
There is the bias of thinking that what is easy or intuitive for you is the same for others. The genders have their differences in learning. Men are generally more visual. Your teaching style may suit men better. Mitsuko gives in her answer examples that I see stemming from the gender differences in learning.
There are also cultural differences. Existing expectations of what a representative of gender should be and how they may behave are still true. You try not to be a sexist might distort how you perceive society. Society feeds some behaviour to the genders. Women are accepted to blame external factors for their failure whereas from men that would be seen as weakness, so men tend to blame internal factors. It is easier to see this from my perspective as the difference is probably more radical. In my nation, there is mandatory military service for men. This changes dramatically what men expect and accept from the professor as they are a year older and have better discipline. More men go through the military probably also in your country. Men are taught to cope and overcome the pressure. If men do not manage they take themselves the responsibility from not being successful. They would not blame you for requiring them to do more work than they expected or are credited for. This would fit your case as you say that you had the students doing more work than required.

A few points. First, ask your department if they can give you the historical average scores for the course (before you taught it) broken down by gender. This will give you a sense as to whether this effect is typical (related to the subject, university, etc) or you personally.
Secondly, as @Elizabeth_Henning mentions, this quote has a few clues

It may sound silly, but is it me being too respectful backfiring and
seen as condescending by female students?

Elizabeth points out that you might be trying too hard and it's making the female students uncomfortable. This is certainly possible. But here is an additional point on this. Make sure you are trying equally hard in the company of the male and female students. I had a professor that was so scared of committing sexual harassment that he always acted super formal around female students. While there is nothing wrong with acting formal around female students, the problem was, he was quite chummy with the male students. He would tell jokes with them, maybe even give them a pat on the back. While probably nothing this extreme is happening here (you say you are very careful about this sort of thing), be sure to treat the genders similarly. If you are formal with the female students and more informal with the male students this will look like you are even favoring the male students. Probably not happening here, but its worth pointing out for others.

Possible paths for investigation that don't seem to have been fully fleshed out:
(1) Correlation is not causation: are there any statistically significant differences between the male and female students taking your classes, such as what prerequisites they have taken, what year and major they are in, what related classes they have taken? For example, it may be that your teaching is more geared to students in a male-dominated major than a female-dominated major, who are both required to take your class, but with different educational backgrounds.
(2) Are you treating male and female students the same way?  Are you sure?  It might be worth having a colleague sit in on a few of your classes and count how many times you call on male and female students, for example, and record (on a simple scale) the tone you take with each of them.
(3) Are your teaching materials gender-neutral? Are you sure? For example, a book I read not all that long ago about a woman's experience at Harvard Business School included an anecdote about lesson module with a business plan that talked about the average single woman's hopes and dreams for marrying a successful man. You don't sound like someone who would be that unaware, but there may be more subtle issues with your teaching materials.

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Am I allowed to use draft chapters of an early version of a book this way?
I am writing a book and am seeking feedback on different chapters before submitting for final publication.  Can I use the draft chapters as conference papers or at visiting lecture seminars?

Which field is this? Do conference papers count as publications in your field?

That is up to the book publisher. Some will be fine with it, others not. Copyright might be one (blocking) issue. If you have given up copyright to some conference, then some publishers will reject your proposal, since they want to hold it and it is no longer yours to give. Lectures and such are no real issue, since you retain copyright.
Another thing that might influence a publisher (around the copyright issue) is how different the book chapters are from the earlier material. But even then, you have to be careful about self-plagiarism since "repeating yourself" in one paper of something in another needs to be handled delicately and with full disclosure.
Just make sure you retain rights (possibly a license) to anything that you publish and want to include in a book later.
You can, of course, publish many things on a topic in conference papers that don't conflict with any rights that you might need in order to publish a book.

There are a few different questions here. Are you "allowed" to talk about the work at conferences? I'd say "of course, it's not a secret". Possibly using your literal book chapter(s) as overheads would be inappropriate.
In any case, the point in the previous paragraph is that you are not prohibited from "ever mentioning again" your own prior work, or to-appear work.
What is possibly problematical is "getting credit twice" for one piece of work. And, relatedly, but differently, copyright violations. The "getting credit twice" prohibition in recent years (decades?) has struck me as strange, but, well, ...
Yes, I understand that there are "popular" algorithms to (supposedly) compute one's "impact" or ... whatever... And writing more than one paper about a given idea is somehow cheating. I have no idea.
So, yes, on one hand, it is certainly reasonable to talk about your own work as much as you want... in my opinion. Perhaps to use any repeated element as a novelty-scoring mechanism is not honest. And publishers will have varying opinions about prior appearances of the literal text (not ideas) of what you give them.

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What are the possible grants/stipends/scholarships that are available in the Republic of Austria?
Yesterday I was offered to join Central European University (now situated in Vienna, Austria). The dream came true, and I was invited to get a MPA degree.
CEU Admissions Committee gave me a very generous tuition discount (more than 70%), but I still cannot afford this. It's too expensive for me and my home country - >3000 euro. I could afford this offer in case of selling all my properties. Obviously, I will not do it.
What are the possible ways to find additional financial support? What scholarships or grants options are available for Austria? What are the most suitable and reliable ways of receiving a funding for the non-EU resident?

Why not to ask CEU?

Alchemista is right - the first point of contact for possible funding possibilities is the university you applied to. This is especially so in this case because that university is a private one, which possibly reduces the number of funding opportunities. They should, at the very least, have an overview of scholarships you can apply for. Sometimes universities have their own scholarship programs as well.

I'll take a stab at an answer later. For the moment, please google "Studienbeihilfe". BTW, what's your nationality? Are you an EU citizen?

@henning--reinstateMonica According to the OP's profile, their location is Moscow, Россия.

@Alchimista it goes without saying that you are right. But today is Saturday which means that admissions office will not respond. I still have a nervous trembling after getting an offer. I want to find all possible opportunities as soon as possible because the offer respond deadline is in a week.

@henning--reinstateMonica okay, thank you! I'll try to check this out.

Major point is the private character of that fundation.

Austria has an official agency for International students, called the OeAD, which, in turn, offers a database of possible funding sources for academic purposes at https://grants.at
Grants.at allows for a granular search. You can select your nationality, state that you are an incoming student, and choose the option of funding of a full study programme.
Here is an example screenshot if you are from Russia:

Good luck (and congratulations on getting accepted at the CEU)!

Thank you, I will contact some of the funding organisations.


text:
Is there a manual of how to write an Introduction?
I was reading a Introduction in a Master's thesis, and this particular example appears to be overly lengthy.

Is there a consensus on how many points can be adequately addressed in an introduction? or a maximum number of pages? or is this question fully subjective?
The goal here is to learn more about best approaches to writing an introduction, regardless of content.

See if improved after edited, would like know about manual of that whats not would should to be done.

This is dependent on the field and the type of publication/work, and more often than not, the journal.

This example is from a Master's thesis, so the total number of pages is expected to be larger than, say, in a paper. Whether or not the length is appropriate depends on the quality of the text but, in general, I'd say it is fairly reasonable to have a 10-page-long thesis introduction (although each field has its own guidelines).

No, there is no "manual" or restrictions on what can and cannot be done in writing the introduction of a paper or thesis. If there are any such restrictions, they are "local"—specific to a particular journal or department (in the case of a thesis or dissertation).
However, that doesn't mean that the example you cited is reasonable: however, without reading the associated content, it's hard to know for sure.

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Is it ok for PhD to come from same school as BA?
If my ultimate goal is to obtain a tenured teaching position, is it more desirable to get a PhD from a different university than the one where I obtained my BA? What are the possible pros and cons?
The original university has a large philosophy department, which is also a factor for me.

I'd say that this fact will be washed away by your much more important graduate and postgraduate performance. They'll look for independent work (don't publish all your work with the same narrow group of people) and it's amount.

When you are nearing the completion of your BA, ask the faculty you know at your institution whether it would be better for you to continue there or to apply elsewhere.   They (and you at that time) should know the answer better than we do here.

The main things that will matter are that the PhD institution is a very good one, and that you do very good work. After that, also having gotten your bachelor's degree from a very good university can make a small positive difference (though it's largely drowned out by the first two things I mentioned), regardless of whether it's the same or a different place. I'd be astonished if anyone thinks there's anything negative about staying at the same school. Lastly, all my degrees (bachelor's, master's and phd) are from the same place, and I'm a tenured professor.

@DanRomik I'd be astonished if anyone thinks there's anything negative about staying at the same school.  I've certainly heard it suggested that this is a bad idea for a student's intellectual development, and I think many US departments incline against taking a lot of their own undergrads, especially in recent years.  But I don't think that this is really the OP's question.

@BenWebster okay, I guess there are all kinds of weird beliefs floating out there that don't make any sense to me, so I'll just have to concede that some people see things that way. On such matters I recommend following Steve Jobs's wise advice: "Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma - which is living with the results of other people's thinking. Don't let the noise of other's opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition."

Many people refer to PhD programs accepting students from their BA programs as "academic incest." (The same term is used for hiring PhD students from the same program into the tenure track).  The reasons why doctoral programs generally don't want to commit academic incest are:

As with physical inbreeding, academic incest reduces the intellectual gene pool. You've already studied under a singular group of faculty for your BA, go to another program for your PhD to widen your intellectual horizons.
As with physical inbreeding, if your program is known for academic incest, it dissuades possible future candidates from applying -- or at minimum, feeling that you prioritize your 'own' over others.

There are clear reasons why a program might not want to be known for incestuous tendencies. However, the question is whether this hurts a candidate. Here, the risk/benefit analysis is a bit more murky.
Pros: If your program is indeed the best in X-Studies, why not remain at the best?
Cons: There is a risk that you might be seen as parochial -- that you only really know the intellectual currents at your single alma mater. To be honest, I'm not sure how significant a risk this is in terms of jobs although I would for the reasons of scholarly diversity above, still suggest that students not apply to their own PhD programs.

Fine print: Note that claims of the negative aspects of academic incest are much more pronounced (and pernicious) in the humanities and social sciences; and are much less common in the lab sciences. If there's only one university lab in the USA that does the type of gene splicing you want to do and you're continuing a project that you've done as an undergraduate, it'd be silly to think of going elsewhere.

My BS and PhD universities are the same, and I have a good life. Although, I've never applied for a tenure track position.

My situation is much the same. I did apply to tenure track jobs, but my failure to get offers had nothing to do with my undergrad institution and everything to do with my state of preparation at the time.

My BS and PhD are from the same institution and I've had a reasonably successful career despite being told that I was making a mistake by getting my PhD from the same institution where I got my BS degree.  I think it would have been better for my career if I'd gone elsewhere for the PhD, but as it happened, the best program I got into was at the institution where I got my BS degree.

I had already line up research work with my eventual PhD supervisor, so I just kept going. I didn't apply to TT positions because my (more or less) current job fell in my lap with 6 months to go on my PhD.

My BS and MD will be coming from different organizations. I know tenured professors who have all their degrees from one school and other professors that went all over the place. The advice that I have been given over time is to focus on ideas that interest you, people who inspire you and institutions that provide enough resources for you to pursue your intellectual curiosity. In the end, academia is about publishing work that interests you and pushes science forward. If you are good enough to do that than you will find tenure somewhere.

"If you are good enough to do that than you will find tenure somewhere" -- is way too optimistic a statement given the current job market.

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Peer-review in ‘fully peer-review journals’
If, after 28 months of waiting and the third request, I within a few hours receive “Reviewer # 1: Sorry that this review took so long. However, this paper does not contain any results of value”, I know that the referee read only the author's name and, possibly, the title of the article.
If I get the message "How about you try to establish a reputation for yourself on several less serious questions before claiming to solve * both * the Goldbach and Twin Prime problems?", Then I begin to think that the solution of these problems is reserved for the author of this message And he was promised to show “the Book". Is it ethical to give such advice?
If they write to me “Yes, I will not accept this work. ... From very general considerations, I believe that you have a mistake in your work. Formally, of course, I have to specify it, but I do not want to do it because of saving my own time”, I understand that they read the work, they did not find any mistakes and  refuse, just in case.
Of course, the referee can save two hours of his time, and as a result, the author loses months, years, and sometimes, and all his life.
Obviously, in order to recognize the results of my work, courage is needed.
But, if “Reviewers' comments: ... I suggest rejecting it on grounds that it does not meet the standards of mathematical correctedness practiced by our journal”, I do not understand what is more important, form or content. I’ve always believed that the result is more important.
Sometimes they refer to feelings (“the referees felt given the methods you are using, it is hard to imagine that the results you claim are valid”), or belief (“I'm sure that your "elementary evidence" of Goldbach and the twins have mistakes, many years of experience does not allow me to believe in them, but I also can not spend time searching for them”).
But I'm not interested in the feelings of referees who did not even get acquainted with the proposed method and, I did not ask anyone to take my word for it. I offer the proof.
This is only part of the disclaimer, but there is not a single review or indication of an error.
Is it ethical for judges to make a conclusion about a job without reading it, but only on the basis of their feelings and assumptions about what is written in the article?
Is every referee a priori smarter than any author to such an extent that in several phrases pulled out of context, can determine where the author's thought can turn?
Should not the referee read the article at least until the first error and point to it? And if the error is not found, recognize the work as correct. Otherwise, he should declare himself incompetent and ask the editor to transfer the article to another referee
Really all mathematicians not only do not see, but also do not want to see beyond their nose?
How can the author get an honest, unbiased assessment of his work in this situation?

Comments are not for extended discussion; this conversation has been moved to chat.

I think most of this question should be closed as a duplicate, and I would strongly recommend the OP read all of the highly upvoted answers here before commenting further:
I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank?
However perhaps the last part of the question can still be answered:

How can the author get an honest, unbiased assessment of his work in this situation?

Have your work reviewed by a close colleague who knows you better than the strangers your work goes to through peer review. Ideally, this is what an academic advisor is for, but other people can act as surrogates in some situations. The person should be someone close to you, who is willing to spend some time reviewing your work because of that relationship, but who has the academic abilities, rigor, and qualifications to review your work.
Impress upon this person that you fear your work has some error, because otherwise it is a very important finding, and ask for their assistance in finding the error. Make it clear that you are not looking for praise or affirmation, but want to find the error. Don't tell them how long you have worked on it or say anything else that makes it seem like you have some personal need to feel good about this work: you only want to find the error.
If together you actually find no errors, and given you have followed my advice about finding someone qualified, then, given the importance of your finding, I would expect this person to make every effort to help you with explaining the work to others.

I hase appealed in the Department of Number Theory of Mathematical Institute. Professor rolled up his sleeves, brewed some coffee, and tells his graduate student to read the paper and report back to him. It was absolutely pointless. With the same success, I could turn to anyone on the street.

Are you close to that professor? Does he have any stake in your success, trust or knowledge in your abilities, or owe you a favor? If no, then you didn't read my answer thoroughly. He has no obligation or reason to give you time beyond his own interest and curiosity.

No conjectures and assumptions are a criterion for the correctness of the work. There is only one criterion - there is an error in the work or not

"No conjectures and assumptions are a criterion for the correctness of the work" Huh? What is that in response to? (also, have you already read the linked question and all of the answers?)

That's what I wrote about - mathematicians not only do not see, but do not want to see beyond their nose. How does science develop?

"How does science develop?" - By, as Newton referred to, "standing on the shoulders of giants." Did you come here looking for an answer to your question, or did you come here looking to rant and complain about people not taking you seriously? (note: you said before in a comment you needed truth rather than politeness)  The rest of your comment: "That's what I wrote about" I still don't understand what you are referring to. There is a lot of back-and-forth here so it would be helpful to be explicit.

Everyone is working on his theme and sees nothing except her, and does not want to see

It is easy to make a claim. Making a claim in itself does not incur debts on the part of others, experts or not. I'd recommend that an author think in terms of persuasion of expert readers, in particular, to be transparent enough, and write in a style palatable to them, so that those secondary issues are not the problem. And, especially, when one claims extraordinary results/progress, such persuasion is all the more critical. To complain that expert readers are not persuaded is function-less, if your goal is to persuade expert readers.

If I understand you correctly, then I do not agree. The very logic of constructing the proof, which the author owns, sets the tone and style of the article. The author can not think from a point of view that does not fit this logic. Of course, the author should try to be as transparent as possible. And, is there a style acceptable at the same time for all expert readers?

@AndreiAllakhverdov If you want to reply to particular people and get them to read your comments here, you need to flag them with @ (theirname) like I just did here with you. I got notified for this comment only because it's on my answer. I don't think paul is saying anything about a particular style being acceptable for all expert readers, he is saying that it is the author's responsibility to persuade readers. You can ignore that advice, but don't be surprised later that they aren't persuaded. You don't need to take all the advice offered here, but remember you are asking for advice.


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What is the prestige/status/merit-value of a Graduate degree in Pure Math/Philosophy(of math, or logic) in industry (particularly programming jobs)?
I tried asking this same question here previously but worded it poorly. Please let me know if my muddled style is unclear to anyone alongside myself.
What I'm essentially asking is: all else being equal, does an advanced degree (MS or PhD) in Math and/or Philosophy (phil of math, or logic) provide one with any "smart points" such that it translates to a merit in itself on the job market, particularly in the context of programming jobs, which would be, as of now, the type of non-academic job I'm most interested in? So, e.g., if there were two self-taught coders with identical coding skills, one of whom has no Uni education while the other has a PhD in Math, would the latter be more attractive to potential employers, all else about them being equal? What if each of them had Bachelor's degrees in CS, while only one had the advanced Math degree, would the additional "smart points" of the Math degree then be irrelevant? How much do "smart points" or reasoning ability and critical thinking skills, as conveyed by such a degree, mean to employers in industry?
As you might have guessed, I'm a Math and Phil undergrad. I genuinely enjoy both subjects and would like to study them at an advanced level for their own sake. Yet, I do think about having to buy food and shelter one day. So, is such a degree worth anything on the job market, simply due to being one in a highly abstract and logically rigorous subject, or would the two hypothetical job-seekers described above be considered to have equal merit due to their perfectly equal domain-specific knowledge?
(And I guess that on that note I'll just add: assuming I go on to get a PhD in one of those subjects, should I just bite the bullet and get a Bachelor's in CS as well? How meriting would that be as compared to self-taught programming skills?)
PS
I understand that this is Stack Academia and not Stack Career Experts, and that answering my question scientifically would require empirical data from the world of industry. But I'd be happy to receive intelligent guesses from intelligent people. I think it'd be interesting to explore the collective beliefs of employers a little.

You’ll want to consider the kinds of people you’ll be competing against. They probably have a capacity for abstract musing too. Start by exploring summer internships to see first hand.

Perhaps you gain the most "smart points" by never going to grad school. Take a look at this.

Mathematics provides a way of thinking about things that is valuable in a lot of things. However, the "prestige" of a doctorate is mostly valuable with your mom. Likewise, philosophy, gives you a certain valuable insight and a way of thinking about things that is valuable in itself.
An advanced degree may enable you to do some things that are harder to do without it, but you won't get hired based on any "wow" factor. Suitability for the position is what is looked for. Some masters degrees are industry focused, of course, and applied math is useful but not for prestige.
In fact, it is a feature/bug of industry that if you seem over qualified for a job ("Wow, a doctorate") you will be less desirable as an employee in the vast majority of positions. People will assume that you can't possibly be satisfied with doing the mundane things required. The exceptions exist, but are relatively few (Google, IBM, Oracle, ...). In most industrial positions you will be valuable only in as much as what you can do for their "bottom line". They don't make money by listing the degrees of their employees.
I finished my doctorate in an impossible academic marketplace so looked around initially for other jobs (caveat: long ago). I was told by an employment counsellor to only list my masters on any application as a doctorate would be disqualifying. Most jobs don't really do serious (non product related) research, which is what a doctorate in math is all about. Too many places don't want you "thinking deep thoughts" but making the next widget run faster.
You mention programming. It is a valuable skill, but an advanced degree isn't needed to write interesting and useful programs. Again, a CS degree isn't focused on programming and certainly advanced degrees are not.
If you want to go to graduate school, do it for what it is; a chance to go deeper into the underlying nature of things and increase your knowledge. Doing it for the "wow" factor is not going to add enough to make up for the time and effort spent.
I'll note, also, that there is an old saying (true in my case) that "You don't choose mathematics. Mathematics chooses you." Lots of people went into math and would accept no compromise because they (we) were driven to it. I caught the bug at the age of about 16 in a not-very-good high school geometry class. It was actually the first positive educational experience I had after kindergarten.
But, yes, a degree (masters, at least) can be valuable, but only for what it enables you to contribute, not for the status. The same is true for a doctorate in academia, of course.

"They don't make money by listing the degrees of their employees." While the spirit of this statement is correct, it is contra-factual! At one point, various investment banking firms were advertising that PhD's in mathematics and physics from the best graduate schools were writing the programs that drove their investments. Of course, some of those firms have since folded up! :-)

@Kapil, I didn't say they don't do it on occasion. Lots of things go in to advertising.

Thank you! "If you want to go to graduate school, do it for what it is; a chance to go deeper into the underlying nature of things and increase your knowledge." That's the thing... What I didn't mention is that I already did CS for a year, dropped out, and began this other programme. I did it because my current subjects interest me infinitely more. And while I'd like to think that as long as one pursues their passion this pursuit will end up paying the bills, it's beginning to dawn on me that this is false -- which is why I ask. Now, on the topic of programming being a valuable skill ....

..., would a Bachelor's in CS on the side be significant for job security as compared to just learning how to code in my free time? As you said, a CS degree isn't programming-focused, but it still seems to be the most common degree among programmers (the ones who have degrees in the first place). I could see myself persevering through a Bachelor's in CS, but likely nothing beyond that. Math and Phil are what interest me, is what I've learned. And, lastly, you did say that my favourite subjects do in fact provide ways of thinking that are valuable in themselves; so I wonder, for what? Coding?

@ksmks3n1 it's complicated because none of us know what the future holds. Right now, most countries are experiencing a shortage of programmers, and folks are being hired with no college degree, but maybe a stint in a coding academy, or simply a portfolio of projects on GitHub. You have to have something to show that you'll be able to do the work. Right now many employers are fairly flexible. The danger is that the market will eventually shift, and employers will retreat to requiring a CS degree before they will even look at your resume. It's happened before.

@CharlesE.Grant This is what I'm thinking about preparing for. I've also thought that an Econ Bachelor's would be an added layer of security. I guess I'll have to think about this more. There's time left for an additional degree, afterall. As of now I don't want to compromise on my Math and Phil focus.

Just be aware that in the current market most employers will favor a coding academy graduate with a portfolio of completed programming projects over someone with a high honors math degree and no verifiable coding projects.

@CharlesE.Grant Yes. I'll have to learn how to code one way or another, no matter what (if I want to make money from it). I was basically just wondering if the high honors math degree and/or CS degree would mean anything assuming that one actually knows how to code, in the context of landing jobs.

There are varying sorts of PhD's in math. One stereotype involves huge specialization, to some obscure technical issue of interest to only a few people in the world, ... and broader mathematical competence or scholarship seems not to play a role.
Also, one can take a broader approach to mathematics, while, yes, doing a research project to add some "focus" to the whole enterprise. Oddly (to me), some people (both faculty and students) object to requiring or encouraging breadth, since this is perceived as "obstructing the research program".
But, as a relevant skill-set "out in the world", mathematical breadth would surely serve a person better than narrow specialization (regardless of status-points). It is obviously important to not portray one's mathematical work as ostentatiously disconnected from anything real. :)

disconnected from anything real -- Definitely not a problem with this paper, since it appeared in the Real Analysis Exchange!

@DaveLRenfro, sigh... ha... :)

Thank you! I have no clue what kind of Math I would want to specialize in yet, if any at all. Now, when you say that mathematical breadth is a relevant skill-set, do you mean for programming in particular? I mean, it would seem as if the logical ability gained from mathematical training would boost one's coding skills, sure, but then one has to let potential employers know about it; which is why I asked about "smart points".

Yes, you absolutely get smart points ... scored in awarding an interview.
But that has no value if you can't answer the interview questions.


text:
Is having my essays proofread inappropriate?
English is not my first language. My pronunciation and grammar are not perfect. I tried to write an essay in my own words. After that I asked for help from my friend to proofread the essay.
She told me I’m cheating to have someone help in this way, because when I submit the essay, the words and grammar will be different than what I wrote (the first version of the essay has too much incorrect grammar). That’s why she will report me.
I don’t think I am wrong because the tutorials in every school are still using proofreaders to help students.
The instructor just said that we should be using sources from class to do the essay, and to cite any other sources. The policies don’t say that I can’t use proofreading.
So what do I have to do? Will the report affect me in the future?

Much depends on the topic. If it is English language/literature/translation, the skill of perfecting a language is what is being co-assessed. In Natural Sciences, probably less so. Ask your instructor if proofreading is ok and to which extent, and remove all doubts.

The only correct answer is to ask your instructor.
As a general rule though, proofreading is encouraged. In the professional world, proofreading (or copy editing) is a normal part of scholarship because the goal is to make the final paper as neat and polished as possible.
Sometimes it is appropriate to cite help you have had with a paper. If there is legitimate contribution and collaboration, this is often done with giving co-authorship. If a specific idea is used, this is often in the form of a footnote. For proofreading, this is sometimes in the form of an acknowledgement; sometimes proofreaders are not recognized at all.
Unless your instructor specifically prohibited proofreading, this is not cheating/plagiarism.

I assume in ELL courses it's your job to proofread, re-edit and re-edit more until it's polished. So put in more work to fine-tune your essays yourself. Even native English speakers need to do this. Edit your essay over and over again until you think it's the best you can do (or the best with the time available).
For the specific situation, perhaps ask the instructor yourself (hopefully before your "friend" reports you). If you were in the wrong, perhaps suggest an additional assignment to replace or at least slightly improve your standing in the class.

Well in my case in the past that's not a problem because I will always have my classmates, friends, relative or parents and sometimes my teachers proof read my essays.
Maybe now some teachers would punish there student but in the past your teacher would praise you for it.
Or as an alternative ask first if its okay or not to ask somebody else proof read your essays .


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How and why are PhD programs free in Europe?
In some European countries, PhD programs are free. As I understand, PhD opening depends on the research funds of the supervisor. In other words, PhD research is funded by a national agency or EU.
Some countries offer the programs for free and an international student in the UK should pay about $20,000 per annum?
In addition to the research cost (which is funded through the same routes), a PhD student has other expenses for the university, which is provided by the tuition fee in the UK, while in countries with free PhD programs, the governments provides the supports (correct me if I am wrong).
My question is: Why/how such governments support PhD education of international students? And if it is reasonable, why isn't it the case in the UK?

I'm having a little bit of trouble with your phrasing. Do you mean "an international student in the UK must pay about ..." (probably pounds, not dollars, right)? And by "expenses for the university" do you mean fees due to the university from the PhD student?

@AzorAhai I cannot speak for the OP, but a PhD student needs physical space and uses the university resources.

@Googlebot I know, but I'm confused as to what they mean.

It is difficult to answer if you do not explain which expenses you mean. A PhD student in, say, mathematics, can work at home with their own computer. The supervisor's time is valuable, but, well, supervising is part of the academic work so it is somehow included in the salary.

If you're a fully funded PhD student in the UK, your tuition fees will be paid for you (essentially the same as a fee waiver). You will also be paid a stipend to cover living costs. Hence, the PhD is free. If you're not funded, you will have to pay tuition (undoubtedly more expensive for non-UK students, which is why it may be harder to get funding) and be able to support yourself.

PhD research is funded by a national agency or EU - Or from the regular university budget.

@Miguel The way advising is included in the salary of a professor is (usually) by charging tuition to the student. Even when a PhD is 'free' that tuition is being paid by someone.

@BryanKrause Do you mean that tuition fees result in a direct salary increase for the professor? This is certainly not the case in Spain. Then, I repeat my question: which direct expenses does the OP mean?

@Miguel I don't think the OP asked about any 'direct' expenses. I was referring to your statement: "supervising is part of the academic work so it is somehow included in the salary" in saying that yes, it's included in the salary because graduate students pay tuition (often that tuition is paid via other sources within the university, such as monies paid out for the student's work on grants). There isn't a magic pool of money that pays for "academic work." That isn't the same as saying that taking a student on gives a salary increase.

I believe what you're talking about is the issue of tuition waivers: that is, are students obligated to pay fees for the tuition, or are those handled by the university.
In many countries in central Europe (including Scandinavia, Benelux, Germany, Switzerland, and Austria) PhD studies are actually paid employee positions, so what tuition charges exist are small, since students normally don't have to take many courses as part of the PhD program (international students may need to register for a few classes to satisfy qualification requirements, but it's not a coursework requirement per se). In other locales, such as as some programs in the US, grants cover tuition charges as well as stipends, preventing students from having to pay those charges. And in many of those countries, the tuition fees amount only to a few hundred euros, not tens of thousands.
It's only where students are expected to do large amounts of coursework and where no arrangements to remit or waive tuition are made that students are responsible for paying large amounts of tuition.

Generally speaking, the chance of an international student is much higher to get admission to a PhD programme, say in Sweden, than winning a scholarship in the UK. The latter is highly competitive and only a fraction of PhD students (both home and international students) receive full scholarships. Of course, after enrollment, there are various ways for compensation.

@NajibIdrissi Technically, I believe most PhD students in Europe do have to pay some sort of registration fee—but the cost is on the order of hundreds of dollars per year, not tens of thousands, and there is some benefit received in exchange (for instance, students at my university in Northrhein-Westphalen got access to all public transportation in the state as part of it.)

Europe is large and varied... even without the UK :) For instance in Spain PhD students are not employees per se (although many paid teaching/research assistants are expected to complete a PhD). In contrast, fees are negligible, say 60 euros per year.

"In most of continental Europe, PhD studies are actually paid employee positions" aeismail understanding of continental Europe and practices are different from mine, this is not first time we have disagreement, I dont know how or where he/she found these info, but it is not correct.

@SSimon Whether or not their paid positions, the important issue is that the tuition charges are not in the tens 9f thousands of Euros, and I don’t believe that is a controversial statement.

I’ve done that now. Hopefully the new answer is clearer.

@Miguel Tuition fees in Spain used to be about 60 €/year. Nowadays they are about 500 €/year.

@NajibIdrissi for a short time, German universities in seven conservative federal states charged a tuition fee (Studiengebühr) for all students (not only on the PhD level), but currently the first degree is free in all federal states. A few states have permitted universities to charge a small fee for the second degree, for "excessively long" studies, and for non-EU foreigners. In sum, the situation in Germany is quite heterogeneous over time, across states, and even across universities. https://de.wikipedia.org/wiki/Studiengeb%C3%BChren_in_Deutschland#Urteil_des_Bundesverfassungsgerichts_2005

@NajibIdrissi but overall, the situation in Germany seems not too different from the one in France, as you describe it, i.e. the amounts are rather small and don't always have to be paid.

Actually™, the situation is more complex is Germany, too. While being a payed employee (typically: wissenschaftlicher Mitarbeiter, "a scientific employee") is one side to a PhD studies, being the actual PhD candidate (Doktorand, the doctorate candidate) is the other. You can finance your PhD studies from some other source than being an employee. Being an employee does not guarantee in any way that you get your PhD. Depending on the money source, you might be required to do teaching as an employee. But typically your PhD supervisor and your work supervisor is the same person.

@Pere Maybe in some parts of Spain, in others it is 60,30 up to the current year http://www.juntadeandalucia.es/boja/2017/134/1

At least in Austria you can be a PhD student without being employed by the university (though it's rare to choose that path). However, simply being a PhD student puts a negligible strain on university resources - you don't get any working space, you don't have a right to a set amount of a professor's time (and the professor can decide whether or not to supervise you), ...

So the main reason that a PhD student needs to pay a large amount of money for tuition is the university expense derived from their course work? Then in UK, where PhD programs are divided into research type and course & research type, would people admitted into PhD programs of research type not be charged a big amount of tuition whether they are offered scholarships or not?

Many people believe that education is not a commodity. They think that tuition fees are wrong and cannot be justified. While this belief may not be as widespread as it used to be, it is one of the most important reasons why many European countries charge low tuition fees or no fees at all.
There are also practical aspects. Many European countries are small, with often only one or two universities offering any particular subfield. Without sufficient international mobility, those subfields can easily become inbred. Governments often encourage universities to hire more foreign PhD students, researchers, and professors. Many politicians who otherwise support high tuition fees for foreign students prefer to keep PhD education free.
Let's assume that the typical cost of undergraduate education is €10,000/year to the university. PhD studies are more expensive, maybe €15,000/year, because the students need more one-to-one time with their supervisors. International PhD students are typically employed, which may cost €40,000 to €50,000/year. Then there are reseach expenses, which vary greatly depending on the field. Most of these expenses are ultimately paid by the government. If the university tries to pass a large fraction of tuition costs to the student, it becomes less attractive to foreign students, without reducing the overall cost to the public significantly.

"Many European countries are small, with often only one or two universities offering any particular subfield"... Really? Can you cite some examples of countries that small to support your claim that there are "many"?

@Miguel In my subfield of computer science: every European country except Germany, France, and the UK. Or at least that was the situation when I was looking for a place to do a postdoc. If a country has only 10-20 research universities, the chances are most PhDs in a particular research area come from the same departments.

Maybe we have different definitions of subfield. In Spain there are 52 public Universities, all of them are research institutions, and almost all of them have Computer Science departments. So, unless you demand excellence or have already focused on a very specialized topic, you have a wide choice. Anyway, the generic assertion "Many European countries are small" seems a bit US-biased.