text:
Referring to a result that comes later
So in writing a math paper, if I am writing a proof of a theorem and I need to refer a lemma that comes later in the same paper. What is the proper way
to say that? For example if I am proving a theorem in page 10 and I need a lemma
in page 15, how should I say that in the proof?

How do other authors do that? Have you had a look at some papers to find out?

Are you structuring the paper correctly?

The proper way here is to rearrange your paper so that this does not happen. It might be possible to put the theorem into the paper twice. Once in the introduction, possibly without some technical details but with more context and intuition around it and once after the required lemmata a proven with all the technical details.
The main reason is that the proofs of your various lemmata and theorems depend on one another but you want the dependence to form a tree and not have any loops. If you have a theorem that depends on a lemma proved later on, it could look like the proof of the lemma also depends on the theorem stated earlier on.

Linear structure for a paper is not the only alternative, and is often not the best. A separate section with the proofs of techical lemmas can be a good idea in many papers, for example. (There should be no logical loops, but this does not imply that the proofs have to be presented in order.)

The logical order is not always the best pedagogical order.  A lemma may be better-motivated if the proof of the theorem comes first, and motivating the reader should be a top priority.  It is not uncommon.  It just requires careful communication of what the logical order is.

if I am writing a proof of a theorem and I need to refer a lemma that comes later in the same later. What is the proper way to say that?

Many approaches are possible, it depends on the precise setting. E.g., when the lemma is relevant to that particular theorem, you could write:
\begin{theorem}\label{mytheorem}
...
\end{theorem}

\begin{proof}

..., by the following lemma:

\begin{lemma}\label{mylemma}
...
\end{lemma}

\begin{proof}[Proof of Lemma~\ref{mylemma}]
\end{proof}

Continuing the proof of Theorem~\ref{mytheorem}, ...

\end{proof}

But what if I am using only one part of the lemma and  also the proof of the  lemma itself is given later?

If you are using only one part of the lemma, then the lemma surely isn't only relevant to the particular theorem, since the other part is relevant elsewhere. (So my example mightn't be relevant.) To get better answers (and to allow me to improve mine), I think you need to provide more context in your question


text:
Is a letter of recommendation from undergraduate professor different from the major I am applying to OK?
I am a recent electrical and electronics engineering graduate. Although an engineering graduate, the major I am applying to is International Studies. Is it okay to get a recommendation letter from your engineering professor as that is my last place of study? I haven't worked anywhere so a recommendation letter from an employee is also out of question.

Have you looked at other questions and answers here on this site using Search that also ask about selecting people to write rec letters? Were those Q&A helpful? If not, why not?

Sometimes when getting a letter of recommendation you have to do what you have to do.  Letters of recommendation are generally supposed to be speaking of you in the best light possible.  Ideally you would want one for the major your are applying to, and, even more ideally, from somebody who has supervised you in a research setting.  BUT, sometimes you would be better off getting a letter from somebody with a lower title if they can speak the world about you in a positive light.  Remember, that the purpose of recommendations is to describe competencies, skills, and other personality traits that will enable you to succeed in graduate school, something that grades can't show.  As such, you will want recommendations to be from the people who know you best, not just people in a specific department.  Personally, even though I had done a small amount of research at my undergraduate institution, I asked for two professors whom I had TA'd under to provide me with recommendations for an REU I participated in that subsequent summer.
You haven't provided too much about your situation, though, so it is kind of unclear what the exact situation is for you, such as why you are going from engineering to international studies or why you don't have any international studies faculty at your current institution to ask for recommendations or why you think the engineering faculty may be better for providing recommendations.

source: Stack Exchange

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

sort: votes


text:
Should I Use the New Term in the Title Which is Introduced in the Paper?
I'm thinking of a title for my conference paper. In the paper, I define a new term, say Hurble Gurble.
In the title shall I use itself or the definition of it, which is 8-9 words?

Very Good Method to Live in Hurble Gurble Streets

or

Very Good Method to Live in in Streets Where Cats Usually Sleep on the
  Containers Rather Than Inside

Which one is more proper?
Edit: The term is planarized, which means points in 3-D are usually grouped on the planes.

If it is not possible to understand what Hurble Gurble means without additional information I would pick the second one. Otherwise, if the reader can get a good idea what you are going to talk about only by Hurble Gurble the first one.

@TheAlmightyBob I have added the term. Is it understandable?

It sounds understandable, but I am not the right person to judge. I would suggest asking someone from your field, maybe a colleague.

This is a judgment call on your part.  Let me say: asking for advice on the title of your paper without including the proposed title of your paper strikes me as unnecessarily inefficient: I don't think "the general principles of paper titling" will be sufficient to guide you to a definitive answer in this case.

At best, your definition will be an overload for planarized. That is, planarize already has several meanings.

Coining a new term in the title of your paper -- while defining it there or not -- is definitely something that you are permitted to do (so it is "proper", as you ask).  I have seen this thing happen: the first example that sprung (!) to my mind was

Duchin, Moon Curvature, stretchiness, and dynamics. In the tradition of Ahlfors-Bers. IV, 19–30,
  Contemp. Math., 432, Amer. Math. Soc., Providence, RI, 2007.
[First sentence of the MathReviews description of the paper:] The author introduces stretchiness, a new and interesting notion describing a kind of curvature of a metric space.

On the other hand, not only is this the first use of "stretchiness" in all of MathReviews, it is also the last.
A recent paper of mine is called "Quadratic reciprocity in abstract number rings", and you have to read the paper (or at least the abstract) to learn what an abstract number ring is.
Whether you should use a new term in the title of the paper is a very subjective and personal choice.  I guess it's no secret that many, many people instinctively roll their eyes a little when they encounter a new word being coined.  (In fact, I this to be an interesting socio-linguistic phenomenon.  But moving on...) Making up your own language can make you look arrogant, overly playful, simply ignorant of existing nomenclature, and so forth.  But the majority of academic terminology was coined by some prior academic within the relatively recent past rather than the mists of prehistory: as new ideas and new objects are created, we need new words for them.
Maybe -- maybe -- a good rule of thumb for this is that if you don't feel acutely that something would be lost upon removing your new term from the title, then it really doesn't need to be there.  If you introduce the terminology within the paper itself, then you give the community a chance to chew on it, and then others can decide whether full promotion of the new term is a good idea.  In fact, if I apply this standard to my own paper above, I am coming around to the idea that the title could be changed.  The concept of an "abstract number ring" is not as important to me now as it was when I first started writing the paper.
Whether it is good or bad in your particular case seems impossible to answer without (i) seeing the title of your paper and (ii) having some real expertise and wisdom in the subject area of your paper.  I would suggest that you find someone who satisfies (ii) -- e.g. a current or former advisor or mentor -- and show them your paper.

BTW: I am now editing the paper I referred to in my answer.  The process of answering this question was helpful in getting me to see that I wanted to change the title.

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


text:
How to respond to a tough referee report?
We received two referee reports from the editor, who made a major revision decision. One referee has a long list of comments, while on the whole it is positive towards our paper. But the other one gave only half-A4-page comment with strong criticism on the paper as well as some other works in the community, as you can see as follows, which is very tough.
Review report:

The manuscript considers proposition. The authors carry out their study in the framework of an approximation. Unfortunately, the approach used in the manuscript
  is totally wrong since reviewer's scientific objection. This issue representing a pitfall for many
  researchers in the past (and unfortunately sometimes in the present)
  is thoroughly described in one reference deleted here, which is an article of another author.
Therefore, I recommend to reject the manuscript. I do not see a
  possibility to repair it and to reduce it so that it will fit for
  publication.

After I read the reference provided, I think that the approach used in our work is correct and the results presented are reasonable, because none of which directly contradict with the reference cited by the referee.
My questions are: what is the best practice to respond the editor and how do I refute the criticisms of the referee?
I apologize if my question is too general for this site. Thanks for your help!

Closely related, possibly duplicate: https://academia.stackexchange.com/questions/167153/i-got-a-very-bad-review-from-one-reviewer-but-the-paper-was-not-rejected

How you reply is going to be largely determined by what's in the paper mentioned in the "described in xxx" reference.  Step one is to read that paper, and understand it.  Then read every paper that cites that paper.  Then, maybe talk to some people in your area about the criticism and see what they offer.  You're trying to refute a referee who flat out says you're wrong.  You absolutely need to do due diligence so you can hold your own.
After doing this work, you might even agree with the reviewer.  If this is the case, you go into salvage mode:

In the original submission, I said A, B, and C.  The review pointed
  out flaw X.  Given this, A no longer holds, but B and C are still
  true.

If, after doing your homework, you still disagree with the second reviewer, the response to that reviewer should take the form of

I don't believe the second reviewer's criticism applies, because....
  In the original paper, this wasn't as clear as it should have been,
  and this is how I've clarified this point in my resubmission.

If the paper is still turned down, if you think the paper is VERY important, and that the literature would truly suffer without publication, sometimes editors can be persuaded to send it out for a third review if there is a major disagreement between reviewers.  This is more likely to happen if the first review is clearly and overwhelmingly positive, and not "on the whole" positive.  Don't go to this well for borderline cases, and certainly don't do it too often-- it's a once or twice in a career thing.

@ Scott Seidman, after carefully read some similar posts on the forum and the others' answers, I realized that U were listening to me and help me from the my perspective and position! Thanks! I voted up your answer and wait for 1-2 days for someone else's good answers like yours. Then accept one.

@ Scott Seidman, just clarify one sentence in your answer. Is it "Then read every paper that cites that paper (the mentioned reference)" or "Then read every paper that cited by that paper (the mentioned reference)"? Which is your meaning? Actually, I am reading the mentioned paper recently :)

@jsxs Nope-- I meant every paper that cites that paper.  You search for the paper in a database like "google scholar" or "web of science", and those tools show you what indexed papers use that paper as a reference.  It's probably the most important bibliographic tool that many don't know about.

@jsxs  The reason why I say go find the papers that cite the critical paper is because of the possibility that the reviewer is simply full of it, and has some agenda.  The reviewer might be pointing you to his or her own paper, and if other published works disagree with that paper, it's important for you to find that out.

+1 for emphasizing to OP to start out from viewpoint that the referee may have valid point and their responsibility to do due diligence to figure that out.  From what was written, the reviewer is stating their serious negative review rather politely and collegially, and it  is 'complete' (they are saying - check this literature for more information). It could be in end simply one important camp fighting over-pedantically about some potential 'sloppyiness' that has crept into field. It behooves someone new in the field to learn about potential issue to either dismiss it intelligently or not.

"If the paper is still turned down, if you think the paper is VERY important, and that the literature would truly suffer without publication" then submit it somewhere else.  After appealing to the editor if desired, but that rarely works.

@PeteL.Clark  -- I tend to agree.  I think it happens every now and again, but not quite by requesting an appeal.  When it happens, it happens because the editor feels compelled by the nature of the existing reviews to solicit more reviews, and not because of a direct request for such action by the author.  That said, there are probably ways to write the letter to put the idea in the editor's head without asking for it directly.

First of all, take this into account that you must provide answers to all concerns of all reviewers so that they become satisfied with your manuscript.
Since you feel that your manuscripts' results are reasonable and do not contradict with references provided by the reviewer, I suggest you to politely describe your results for the reviewer and compare them with that of the references. Tell the reviewer why the results are not in contradiction with previous works.
Moreover, consider that the reviewer has not stated anything about the results. His/her critics are about the methodology.
All in all, be very polite when answering the reviewers.

Politeness may not be helpful, but may come across as an attempt to dodge the criticism.

dan1111's answer is excellent, but I want to add some aspects that have not been mentioned enough.
First, in the second round of revision, the reviewers may see each others report and this may play to your advantage, if the first reviewer disagrees with the second.
Second, it appears that your particular field is characterized by a split between competing theories, with you adhering to one and the reviewer to another. In such cases there is often a almost religious belief in the 'correct' approach and rejection of any alternative (including supporting evidence). If this is the case here, there is very little you can do to change the belief of the second reviewer.
Third, you should not avoid confronting the 2nd reviewer by being just polite. An important argument is as follows. Whether a certain theoretical approach is correct or not should be decided in an open scientific debate and not by peer review. The scientific journals are the platforms for scientific debate, which happens in form of publications. Suppressing publications, not because they are demonstrably wrong but because they follow the 'wrong' theory, is dogmatic and suppresses scientific debate.
Finally, it's not clear from your post whether reviewer 2 is not actually correct and your methodology is out-dated and proven to be unsuitable.
When writing your response, it may be helpful to imagine that the reviewer is the author of the refuting paper XXX.

Walk away. Submit your work to a different journal.
I received all kinds of reports, from detailed and helpful to totally unfair. Don't waste your time to try to argue against someone which cannot be convinced. Try to clarify some points in your paper and try again somewhere else.

Probably depends on the subject: Often one reject is enough to reject the paper.

The good news here is that the editor clearly believes that the paper has merit and could potentially be published with revisions.  If the editor agreed with your tough referee then you would have gotten a reject decision instead of a major revision decision.  In such a case, I would imagine that the referee intends for you to undertake major revisions in accordance with the long list of issues highlighted by the first referee, and to justify your work in regard to the criticism of the tough referee.
Now, you have read the paper this latter referee cited, and you still think your method is still okay.  In view of this, you should add a paragraph to your paper noting the criticism in the cited paper and explaining why your research method is still okay despite this criticism.  That will help to head off criticisms like the one made by your tough referee, and it should therefore improve your paper.  In terms of responding in the response-to-referees document, I would then recommend something like this:

Disagree, but revised anyway: We thank the referee for this general challenge to the approach used in our paper.  We have reviewed Smith and Jones (1994) and we are convinced that our research approach does not contradict this.  In order to address this criticism, we have added an additional paragraph (p. 16) discussing the model criticisms made in Smith and Jones (1994), and explaining why our method survives these criticisms.

The editor will ultimately have to make a decision on whether your method is convincing in light of the referee criticism, and whether or not you have made the other revisions adequately.  Based on the fact that your paper was not rejected outright after the initial review, the editor is obviously open to being convinced on this.

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

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


text:
My math students consider me a harsh grader. Is my teaching attitude wrong?
I am a math major grad student at a big public school, and we need to do TA every semester.
I got assigned to lower level classes last couple semesters, and it's been quite difficult for me.  Even though I am a pretty nice person in general, I have so much trouble tolerating my students' sloppiness, arguing for more points when they don't deserve, and just explaining very simple things to students again and again in general (for example, why log(a + b) is not equal to log(a) + log(b)).
I am sure many will think my attitude is wrong, and probably I need to hear that.  I am also a "harsh grader", as my students would probably call me.  The way I was raised, it's very hard to accept people not working hard, but feeling entitled to good grades.  I have students coming to me asking how they can get extra points without doing any actual work.  I feel offended by that.
Let me know what you think about teaching in general.  I enjoy doing research in mathematics and want to be in academia in the future.  However, I feel this could be a problem for me if I hate teaching so much.  Should I think more positively about this?

I would try to find a way to work through this.  Don't take it personally would be my first suggestion.  You're always going to have to explain things again and again. It's part of the job.  The reward comes the last time the question is asked, not the first.  (Or sometimes even a few semesters later when you get the lovely note that says, "Thanks for all of your encouragement!  I didn't get it then but I get it now!")

Related: What to do about “grade grubbers?”

I suggest this question gets a USA tag or similar, since things are not exactly the same in other countries and systems

Ask them: "Do you want honest evaluation now when it only affects your grades, or do you want to be pampered and learn about your actual skills by being fired later?"

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

I've found this is most difficult among TAs that worked extremely hard to get the opportunity to leave their country of origin in order to study at an American university.
The typical American college student is nowhere near as driven as that sort of grad student -- he probably couldn't give a good reason to why he is in college at all.
I recommend that if you can't find a way to enjoy teaching, you should leave academia after getting your degree.

Due to some negative publicity some years back, most schools require all staff, including tenured professors, to teach some undergraduate classes. (As an example, my daughter's Intro To Physics class last year was taught by Lisa Randall, a well-known theoretical physicist). If you want to be in academia you're going to have to teach, and you're going to have to deal with students who are probably not as capable and motivated as you are in the field of mathematics. Best of luck.

Be transparent, be firm and be strict. Set the grading rules, discuss it with your colleagues and explain it to your students. Then grade all the tests according such rules. If the student complains for extra points they doesn't deserve, prove them wrong. Sometimes you can be really mean and emhasize all the errors the student did while "neglecting" what they did right.

You are not a 10$ note to be liked by everybody. Whatever you do, there will be people who want more.

@TobiasKienzler, you are exactly right.  I would love for that to be an answer so I could vote on it.  ;)

Can you elaborate for the non-USA and non native English speakers? What does "big public school" mean? Is it high school or something else?

How can this question not be entirely option based and that without much data?

Are you the only TA for this course? If not, are the others equally harsh?

You speak of "students" — are they all the same? It's easy to focus on the negative students, the ones who try to game the system (or are rather economical/'grade conscious'). In this process, you might overlook the majority which acts great. So, of all the students in your course, how many actually act this way? You're in math, quantify the problem.

Personally I found that it got better as the years went on. It was irritating when students barely a few years younger than me were complaining and begging for grades, but as you get older the students become so young that they're cute no matter what they do!
Also, you need to assess your situation objectively. If by large public school you mean Berkeley or Michigan or others of that calibre and you're one of the strongest grad students there, teaching might not matter so much in your career (it still matters, but there will be other things that make your job worth it) but if you see yourself as mediocre, teaching matters a lot in tenure-track hiring, so you'd better get used to it. Furthermore, even some top tier schools care very much about your teaching records, even at the postdoc hiring stages, so if you do a bad job you're cutting yourself out of some jobs.
Becoming more approachable and bonding with your students (which is much easier to do as a grad student) will also make it more fun.

Yes, you do seem to have a bad attitude toward it, but I suspect you knew that.  I would suggest trying as hard as you can to put yourself in their shoes:

Not everyone enjoys the same things you do.  What's a subject you had to take in school but didn't enjoy?  Can you imagine not putting as much effort or showing as much respect to it as someone going to grad school for it?
It's totally rational for someone to try to maximize their grades. I think everyone finds it annoying when students push for every last point they can, especially when you don't feel they've earned it.  I like to remind myself that it makes perfect sense to try to get the best grade you can for the least amount of effort.  That doesn't mean you give in to their exhortations, of course, but if you understand where they're coming from then that's not incompatible with both helping them and keeping your sanity.
Everyone is busy.  A lot of undergrads are adjusting to life away from home for the first time, are taking on responsibilities for the first time, and are probably swimming in social and extracurricular activities.  That's what they're supposed to do; just keep in mind your class isn't the only thing on their plate.
The things you find easy, others find hard.  You specifically gave some logarithmic rules as an example.  To you, that's trivial.  You can't understand how it's not trivial to someone else - I mean, you probably even just told them it was trivial!  But I bet you can think of a field where you struggle with things an expert finds trivial.  Foreign languages are a good example for me - I can hear how to say something in a new language repeatedly, and it just goes right out of my head a minute later.

That said, you suggested you "hate" teaching.  If you really do, maybe it's not for you.  On the other hand, you're here asking about it, so maybe you're interested in changing.  To do that, try hard to put yourself in the shoes of your students, and remember that they're just trying to get by.  Some will fail, and that's okay.  But you can help all of them, even those who won't ever get your subject, without resenting them.

@JeffL.Terrific answer, Jeff.  I really like your attention to looking at it from the students' POV.  As an entrepreneur most of my career, I think of my students as my customers.  They pay for me to teach them a subject.  Rather than complaining about them, let me think about their needs so they get what they came for and don't have a reason to complain about me!

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

I don't like this answer.  One can have respect and sympathy for students as busy young adults who don't enjoy the material and want the best possible grade, without yielding an inch on grading standards.  Fighting for points that you do not deserve may be rational, but it is not ethical.

@JeffE I think One can have respect and sympathy for students as busy young adults who don't enjoy the material and want the best possible grade, without yielding an inch on grading standards is pretty much exactly what I said. You're the second one to bring this up though, so either I wasn't clear enough with doesn't mean you give in to their exhortations or this is an issue that teachers have a visceral response to.

This doesn't seem to address one of the main questions in the OP, that of harsh grading, perhaps you could [edit] to clarify this?

I don't think your analogy in the last bullet point is a valid one. In mathematics, one can prove from definitions that $\log(ab) = \log(a) + \log(b)$ and prove from examples that $\log(a + b)\not = \log(a) + \log(b)$ in general. With foreign languages, it's pretty much arbitrary; there's no inherent reason why, say, the past tense of fight should be fought instead of *fighted. I personally have much more sympathy for students who are genuinely bad at math than those who are just sloppy thinkers.

@anomaly Whether something has a logical or mathematical proof behind it has no bearing at all on the fact that some people will find things hard that others find easy - math included.

"You probably even just told them it was trivial" laughed out loud.

Yes, you should think more positive about this, and at least don't take it personal.
The students are sloppy, and you have to repeat stuff. This is how people learn, don't be surprised. If they would understand everything the first time they see it, no teacher would have a job. Don't take it personal. Additional tip: if a student wants to have points for something that's clearly wrong, they can go to your supervisor. Don't draw out the discussion.
The students want to have free points. Of course, everybody wants to have free stuff. Don't feel offended, and just grade the way you think is right. There should be no problem telling adults that they're not getting something.
The idea that this behaviour is unfair, offensive or disrespectful is just in your head. You cannot expect everybody to work as hard / be as smart as you are yourself. Think about how bad you would do in a Chinese language course (and what you would ask the teachers if you really had to pass this course).

I think this response misses, in the other direction, the experience of many good students (esp. in math). We never begged for points in any course of any type (neither myself nor friends; literally unthinkable). We generally always did grok concepts on a single presentation (and the teachers seemed to have secure jobs). It took me several years for it to dawn on me that most of my community college students are in a situation where they simply can't remember things, after showing them once or multiple times. It's still hard to relate to what that must be like.

you don't have to go to your supervisor, though. You are the teacher, you can decide how you grade for yourself. If the student is wrong, you should have the tools to explain why.

I just meant: you can just explain why you're not giving them the points. If they don't agree they can go to your supervisor, and you can say this is not up for discussion.

I agree with most of this answer. The part that bugs me is that I believe arguing for points is completely disrespectful. It's one thing to come to your professor and ask what you did wrong, discuss something you believe to be a mistake, or if there is anything you can do to earn a better grade. It's quite another to try to squeeze out more points than you earned. Even when I wasn't doing well in college, I didn't try to convince a professor to award a better grade than I deserved. And if you insist on trying and the grader says, "No," it is extremely disrespectful to keep badgering them.

Some comments, in no particular order:

I don’t think you have a bad attitude. And, high expectations are a good thing.
It's important to explain domains and codomains. Explain that log : ℝ>0 → ℝ. Make sure the students understand that log(x) doesn’t mean “log times x.”
Not everyone’s brain is wired for mathematics. Some people need to see log₂(1)+log₂(1) = 0, log₂(1+1) = 1 a few times before it sinks in. It's worth spelling out the obvious: we've just seen that log₂(x)+log₂(y) = log₂(x+y) doesn't work for those particular values of x and y. Ergo, it's not a universal law. Okay - it doesn't hold for all possible value of x and y. So it's not a valid rule. So if we've got log₂(x+3) written down somewhere, we can't just replace it with log₂(x)+log₂(3), because we don't have a universal law available guaranteeing that these two expressions are going to be equal. You might find this discussion helpful.
If many students are making the same mistake, your job as a TA is to start the tute by explaining the stuff that people are getting wrong. And, you may have to do this repeatedly, and really spell it out. See (3).
Don’t be too hard on sloppiness. The reality is, it’s not just the students’ mathematics that is sloppy. Your mathematics is sloppy. Mine is, too! Unfortunately, the mathematical language we've inherited isn’t sufficiently excellent to produce non-sloppy mathematics. Maybe in 2066, things might be different. Probably, mathematics will be computer-formalized, and therefore every bit as precise as programming is now. But that’s not currently the case, and if I were sitting in one of your tutes, I could probably point out dozens of ways in which you’re being sloppy. So just go easy, okay? The idea is to teach, not to punish.
Never show any contempt for the student. Ever. Personally, I mainly reserve negativity/contempt for the textbook, the textbook writer(s), the notation, and the general sloppiness of mathematical convention. But I'm never contemptuous of the student. If need be, a firm "no, you need to work harder if you want better grades. I know you can do better" is all that's needed. Mathematics is already frustrating enough, so just be friendly, helpful, approachable, and if necessary, firm.

Apparently there is no TeX support on this subsite :(

@joojaa: Fortunately, there is Unicode support.

@Wrzlprmft that may be but not on my phones keyboard :) Good edit much more readable

Way to give concrete advice on the problems mentioned, and encourage the asker without putting them down.  Have my +1.

every bit as precise as programming is now — Ha! Pull the other one!

@JeffE, I don't quite get it...

@goblin If you think programming is precise, you haven't seen student code.

"It's important to explain domains and codomains." I get the feeling that students that have trouble with log(a) + log(b) != log(a+b) are going to be fully baffled by the term 'co-domain' and may not have even heard or understand 'domain'. And that function notation you used would similarly be completely alien. These are often students that have been taught in their primary and secondary education to equate mathematics with arithmetic and see algebra as just fancy arithmetic.

By all means explain properties of the log function, but you might harm more than help if you try to use the technical terms and they don't know them.

@JeffE, I think you're conflating 'precision' with 'quality.' If a student writes low-quality, inefficient code that nonetheless gets the job done - well, as frustrating as that might be for the person doing the grading, it doesn't change the fact that programming is a precise discipline, much much much more precise than the vast majority of present-day mathematics.

@Shufflepants, completely disagree. It's exactly that attitude that makes mathematics seem so hard! When you try to dumb it down, it actually gets harder, not easier. What we should be doing is trying to help the student's see things from the point of view that we ourselves use, and if that means explaining the concept of 'set' and 'function', then so be it. That's the only teaching strategy that works, imvho.

@goblin I'm just saying if you're going to go into those explanations, you're going to have to ease into it. You can't just immediately start using the technical terms for things with people who haven't learned them yet, and you can only define so many terms in a single lecture or explanation before they can't retain it all in short term memory and your explanation makes no sense because it all sounds like gibberish.

@Shufflepants, oh. Well I agree with that. I should add that imo, the arrow notation is more important than the word "domain" and "codomain". Just using it consistently clarifies mathematics immeasurably.

@JeffE Nor industry code. Nor professor's code. Nor researcher's code.

@goblin, On the subject of computer-formalized non-sloppy mathematics, here on metamath is the top level of a computer-verified proof of the natural logarithm of a product of positive reals being the sum of the logs.

First, as others have pointed out, the students are behaving rationally according to their own preferences, in an "economics" sense. Unless they have sufficient incentives to do otherwise, why should they do otherwise? But this broaches a more genuine problem, namely, that it may seem disproportionate to give them bad-enough grades to communicate effectively... and thereby make them ineligible for their desired major program, students loans, etc.
Second, and relatedly, "teaching" required-course lower-division courses, and even some upper-division "required" courses for math majors and so on, is not really so much about the mathematics (although it is officially so), but about testing/filtering students for somewhat-broader purposes. "In real life", most students have no need of "pre-calculus" or "trig", but their major programs often require that they take such courses (and get a sufficiently good grade) as a filter on prospective majors in not-very-mathematical subjects. Not so that they'll know some odd bits of elementary math, but to see if they can show up on time, follow instructions, do things that are required even if they don't want to, and so on.
So, oddly enough, "mathematics teaching" is mostly testing the general competence (and perhaps willingness to conform to inexplicable rules imposed by authorities) of students.
And, notably, this function is what allows/causes math departments to be so large, and effectively underwrites the research we do. Seriously, the monetization of "research in math" is not so vigorous, but teaching lower-division math as filter is a reliably remunerative job. Supporting our "hobby" of research.

Here's how I've been able to ju-jitsu this situation for myself.
An enormous number of people are in great, desperate need for learning mathematics. It is a great challenge and responsibility and honor to help them, and instruct them in what real college learning is like. It's pretty clear that math is the hardest limiting factor in almost anyone's academic aspirations. I'd argue that almost any other subject can be watered down to meet an institution's desires, but not math. It is essentially a buzz-saw of truth. As JFK said, we do these things "not because they are easy, but because they are hard".
For me, I think of this like being a doctor (or at least a triage medic): Diagnosing what in the world has gone wrong in their heads. You'll learn to spot some common general patterns. But, there will always be rare and unique cases popping up with things you never imagined in your wildest dreams. I'm always learning and getting better at detecting what people don't know, or what incorrect bit in their brain caused a cascade of problems, and helping them fix it. I find it endlessly fascinating.
Personally, I have no problem with your being a "harsh grader" and not tolerating student sloppiness. I think that's well-phrased on your part, and is among the most important things we can help them improve at this level; attention to syntactic detail, and the fact that every symbol counts in our language and grammar (and, truth be told, every other language; perhaps we are the only discipline that assesses the student on structure in this way anymore). To me this sounds like you are maintaining high standards, and we need more people in education committed to that. The real frustration is if you get to an institution where administration doesn't want to allow that.
Now: I'm a dedicated lecturer and I don't have to do any research. I'm pretty happy with that position, and not sure how I would balance adding research on top of that (4 classes per semester). But the teaching alone became really fascinating once I came to view it as diagnosing a spectrum of crazy ailments.

I really don't think maths is uniquely hard or the only subject which can't be 'watered down'. Whatever sense makes this true of maths will make it true of other subject too. I don't see why it is necessary to think that teaching subject X is uniquely difficult or challenging in order to think it is incredibly worthwhile. And, by-the-by, some people have LOTS more trouble learning to read than they do learning all the obvious, simple stuff about numbers!  (By the way, symbolic logic is often taught in other departments. Do you think philosophers who teach logic ignore the syntactic details?)

@cfr: We will have to disagree on that point; our institution has overwhelming, painful statistics that failing math causes most of our students to leave the college, even after years of explicitly trying to make the curriculum easier at the institutional level.

Regarding logic, I'm a huge fan of teaching that, think it should required of all students, and I do think not having that as a prerequisite is a major missing link. A blog I wrote on the subject a few years ago: http://www.madmath.com/2012/07/teach-logic.html

I just think you are over generalising your case quite unnecessarily. I'm not convinced maths is unique in the way you suppose. And I don't deny that more people struggle with maths than reading, for example. But you make it sound not quite universal, but very nearly so. I'm not convinced anything should be a prerequisite in the sense you mean. I'm not convinced that forcing people to study things they don't enjoy does anything more than put people off learning.

[If Comp 101 actually enabled students to read and write fluently, I might be more sympathetic. But that appears to be a pipe dream.]

There's a wide gulf in America between "good" math students like yourself, and "bad" math students (most others) and very little in between. Probably more than in other subjects.
That makes it hard to for the good math students to relate to the bad ones. Even so, having the good ones do "TA" is part of the drill of making sure the bad ones don't get even further behind. Once you realize that it's part of the "social contract" that helps fund your own studies, you will be able to deal with this better.

The most extreme case of arguing for another point on a homework, that I ever experienced, as a TA in a field that involved a lot of math and proofs, was in an upper level graduate course.  I graded homework and exams, and was available for posted office hours.  One day one of the best students in the class came to see me to get his grade changed from 99 to 100.
I have never seen such stubbornness as that student's.
I think it came from anxiety.  He was an international student, from a country where he had had to prove himself to be the crème of the crème many times over in order to get to the U.S. for grad school.  He was used to working very, very hard, and doing very, very well.
Okay, now on to what you can do, to be more effective in your teaching.

When a student comes to office hours unhappy about a grade, put the focus squarely on making sure the material has been well understood.  Show that you are glad the student came to office hours.  Encourage the student to come see you for help with the next assignment, before finalizing it and turning it in.  You will earn students' trust if you show that you are available to help when they are struggling with the material.
You can walk the student through checking whether log(a+b) = log (a) + log (b).  Don't do it on the blackboard in your office -- have the student do it on paper, with you giving suggestions as needed.  You may write things down, but do so on paper, and make sure the student takes these notes home to be able to refer to later.
Elicit more student interaction during class.  A correction made by you (e.g. log(a+b) <> log(a) + log(b)) is so much less effective than a correction made by a fellow student.  (Of course, make sure that students are respectful with each other.)
Set the tone by being respectful yourself.
One way to elicit more student interaction is by having everyone write one of their homework solutions on the board.  This works best if you have several blackboards in the room, and can have everyone write on a section of blackboard at the same time.
You can ask the students to create homework problems, and then assign the student-created problems to the whole class.
Sometimes, make an assignment that must be done in a small group.  Don't wait until the semester is almost over to assign group work.  The main point of this, in my opinion, should be to encourage the formation of study groups.  When students are learning from each other, you won't have to repeat yourself so much.
Ask each student to hand in a short autobiographical sketch, to help you get to know your students.  Ask them to describe their learning style in the sketch, to state what their strengths and weaknesses are, and to tell you about their life goals.
Don't wait until the end of the semester to do a class evaluation.  You can do a short evaluation three times in the semester.
If you have lecturing duties, take the time to prepare well.  (My son's Calculus II teacher would try to make up example problems on the fly.  Sometimes he would have to abandon an example problem after wasting 20 minutes on it.)
Try videotaping yourself while teaching.  When you watch the videotape, check to see if you are audible, if your chalkboard work is clear, if you are being careful not to stand in front of what you just wrote on the board, if your speaking voice is effective.
When you draft an exam, ask a colleague to take the exam to test it out.
Observe other instructors and keep a journal, noting what you see the instructor doing, what you see the students doing, what's working well and what's not working well.
Work very hard to catch any glimmer of a good attitude, good work ethic, or creativity, in a student, and provide positive feedback.  In other words, catch the person acting like a good student, the sort of student you can enjoy working with, and reward that behavior.

Honestly, as a current mathematics student, I really needed the tough graders. When the graders would give me unreasonably high scores on the homework, I thought I was doing okay, but would fail the exam. On the other hand, after receiving several very low homework grades, I'd learn where I can improve and this reflected in high grades in the exams.
In mathematics, it's quite difficult for a first year undergraduate many times to understand where they went wrong and how to write a proof. Therefore, tough grading is a must in my opinion.

(Continuing the thought of @stanri.)
When I was studying, I took lectures and seminars sometimes without getting points, grades, or certificates, just for the purpose of learning something exciting.  Do try to motivate your students similarly. Tell them the following story, for example:

Don't mind the grades too much; they measure your progress with respect to the expectations of a huge machinery called the state.
Do mind what you have learned.
University time is the unique opportunity to study; in general, there will be no second chance. Use this time.

Later, when I was a TA and the students asked me for better grades without doing something, I viewed it as my fault: I have not motivated them enough.  You could think of doing the same.

Respectfully disagree with this advice. You simply cannot spoon-feed motivation into students. That's among the necessities that they bring to the table.

But the external part, provided by the instructor/TA, is... grades.

@Daniel - I agree with this advice, to an extent. You're right, of course: an instructor can only do so much when it comes to student motivation. Still, it can incorporated it into a class every now and then. I work the "Are you here to get a diploma, or are you here to get an education?" conversation into my classes on occasion. The key, I think, is to have this philosophical question at a time when grades is not at the forefront of their minds. In other words, don't try to wax philosophical on the day they get their midterm exams back; that will go over like a lead balloon.

(On phone so there might be some formatting quircks)
Personally I don't have any problem with you maintaining a high standard. "If you don't work for it, you don't deserve a good grade" seems fair and can be a valuable lesson. People have to start working for something at some point in their lives, and if that starts at high school in math class, it seems like the perfect place.
That being said, you indeed sound harsh. The example you gave ( log(x + y) ) can be really hard for some people. Not every person has a brain that works in such a way that they can solve plain, boring stuff like that.
E.g. I was one of those people, I almost dropped out of high school because of mathemathics, even though I worked my back off and took way more math classes than I was supposed to.
Now 5 years later, I'm a junior PHP software engineer (how ironic), make a decent salary and can even start thinking about buying my own home. Just because a student can't solve an assignment, doesn't mean he doesn't work to do it.
I've met a Dutch math teacher who would punish mistakes, but still grade answers alright if the calculation with the errors was correct. For example, you can earn 5 points per assignment and there are 10 assignments. A student accidentally flips an operator ( + -> -), but completes the assignment without further errors. That teacher would then give 3 out of 5 points: minus one for wrong answer and minus one for sloppiness. But since the student has shown he knows how to do the calculation, he still gets more than half the points.
Maybe this could be some solution?

Teaching in general:
I do feel like you need to focus on the students more, - having to explain things "again and again" just means you didn't explain clearly a process -
Complaining about this - is complaining about doing your job (To teach)
You need to make math accessible to them through language and logic in a way THEY understand, giving them the math tools to break problems down.
You haven't achieved this if they don't get it (so stop punishing them for this with your attitude) roll up your sleeves and find a new way to explain
Math can be interesting for everyone when the steps are clear enough and the teaching versatile enough to be able to communicate the same process to appeal in many ways
People love to learn - You have a skill at math.
But the genius of being a teacher its to find many ways to impart the same skill, requiring a great depth of knowledge and versatility in communication skills.
I would suggest to maybe look into Micheal Thomas, a really great teacher - his advice to students, and I believe it to be true -
There are no bad students only bad teachers This is a very important part of the Michel Thomas Method. Full responsibility for learning lies with the teacher, not with the pupil. This helps to ensure they can relax, and feel confident, so allowing them to learn effectively. (His course deals in teaching french) but the same is true for any skill - when something is well explained - then it is learnt. (If a student cant remember it - it wasn't learnt or understood as a concept)
https://www.youtube.com/watch?v=P8jhy7ZQC38
On grading - grade for what they have achieved, it is to show what concepts they are having trouble with and what the need you work on with them)

authors: Bob Jarvis - Слава Україні


text:
On the possible obsolescence of research paper titles starting with "On the ..."
I have observed that most papers with titles starting with "On the ..." are theoretical ones, like pure mathematics, physics, computer science, etc. Most of these papers are relatively old, though I can find a few recent examples as well.

Are such titles becoming obsolete?
If not, when is it appropriate to use it?

I've published a paper starting with "On the" in 2015, maybe it's a sign I'm becoming obsolete too :-)

My most highly cited paper (as co-author) is one from 2012 starting "On the..".  Anyway *everything * is field-specific, and in  "On the use of dated language forms in academic writing" it would be disappointingly modern.

Clearly this requires retitling to: On the Obsolescence of Research Papers starting with "On the".

Isn't there some google tool to determine frequency of usage?

Someone should do a study on this usage of "On the..."  Publish a paper titled, "On the use of 'On The'."

Congratulations @Prometheus: you've clearly captured the enjoyment of the community.

On [the]... is a common translation for the titling style De... used by Roman philosophers (Cicero: De Amicitia, On Friendship; De Re Publica, On the Republic; etc.), which makes this scheme older than feudalism. That it has ups and downs in popularity over the last couple of millenia is no great surprise.

I can't believe someone actually changed the title of my post. Good call though.

Obsolete, no. Unfashionable, perhaps.  One can usually drop the "on the" and still have an acceptable title in current usage, and I expect that is just what many do.
On the other hand, I, like Massimo Ortolano, have also recently published an "On the" paper, so apparently I don't really care about the fashionableness of my titles.  I would suggest that you not worry about it either.

Anyway my secret dream, now no longer secret, is to publish a paper starting "Musings on...".

@MassimoOrtolano I think the "Musings on" part is implied in all academic papers.

@MassimoOrtolano, now I have a new purpose in life: a paper "Random musings on..." ;-)

you could go full Victorian: "Some initial considerations towards a revised perspective on the --- question".

@Andrew - Perhaps "A prolegomena to a proper treatment of ..."

In honor of the direction this discussion is trending, I think this link is quite apropos.

@CharlesStewart If you ever go for it, remember 'prolegomenon' is the singular, so you can leave off 'a' with the plural.

« "On the" other hand », yeah :D

@Andrew "Victorian"? That's a perfectly modern style for postmodernists today.

As I always understood it, a paper called Zero-dimensional vector spaces claims to be an exhaustive overview of the topic, while On zero-dimensional vector spaces would be merely a contribution to the study of those spaces. So it is humility on the part of the authors.

This is how I read it too and have used it in my papers.

As mentioned already, it still happens and is considered acceptable by many, but others feel it is unnecessary, so I would say it's rather subjective like many aspects of grammar and punctuation.  The best thing to do, if you're concerned is read the guidelines for the venue you're submitting to, and look at titles of recent articles in that venue.  I've certainly seen explicit instructions to avoid titles starting "On..." though I don't remember where.  The closest example I could find right now was in the Journal of Clinical Microbiology instructions:

Title, running title, byline, affiliation line, and corresponding author. Each manuscript should present the results of an independent, cohesive study; thus, numbered series titles are not permitted. Exercise care in composing a title. Avoid the main title/subtitle arrangement, complete sentences, and unnecessary articles.


text:
Is repeated citations from the same region a cause for concern?
I have just accepted a paper for reviewing for a journal in neuroscience. While skimming through the paper, it appeared that the authors had heavily cited literature originating from the country where the authors are from. Since then I have carefully read through the Introduction and most of the Discussion section and I am quite convinced that this is so. There also appears to be a tendency of self citation, although it is hard to be certain.
To be clear, the paper has nothing to do with any specific region of the world and there are other papers (from diverse regions) that the authors could have cited but have chosen not to (whenever the authors are throwing in an example citation of the ilk: "...many studies have shown that xyz is quite common (Citation)".
My questions:

Are there tools that can return the affiliation information (specifically the country and additional information like ORCID iD), given a list of references? I would like to see whether my intuition about the possible citation bias is correct (and if so, perhaps mention it to the editor)

Should this be a matter of concern? I am quite new to peer review and I feel that wherever possible, the references should be diverse (once again, to clarify, the paper has nothing to do with a specific region of the world and that there are other studies which the authors could have cited)

Related: https://academia.stackexchange.com/questions/21797/how-to-discourage-irrelevant-self-citation

For some countries this would seem to be the norm, actually. Maybe not for tiny ones with only a few universities, though. Also, the general rule is "cite what you use", not "cite everything that someone, somewhere, might think is relevant".

Is this an observation you would make if the authors and their citations tended to come from your own country?

It's conceivable that this effect could be unintentional, I wouldn't jump to conclusions too quickly on this one.

Actually, I recently just reviewed a paper where the author cited 14 of their own publications, so wouldn't surprise me if people had bias to cite authors in their own region doing research which is much more visible to them then in other countries.

@GregMartin In this particular case, absolutely (given that there are hardly any groups working in the area...therefore, repeated citations from someone local would be sort of a red flag). But I agree with Buffy, for some countries this would be the norm. In the present case, the large number of Asian names in the references caught my attention (again, not that that's wrong in anyway).  Also, as I was not entirely sure whether this was indeed the case (names do not imply affiliation), hence the question on whether there were tools that could help check whether this was indeed even the case).

Well, yes, the citations should cover relevant literature no matter where it originated. I wouldn't worry too much about tracking where the authors are or are from.
Simply note that there are many possible references missing (perhaps provide some), and note which seem excessive. It would be easy to imagine that the authors have been closely following work in their own country and are building on it appropriately.
I would give the authors a round to review their citations before approaching the editor. While I'm sure it's not your intent, it would be easy to come off prejudiced here.

It would be easy to imagine that the authors have been closely following work in their own country and are building on it appropriately. - Yes, e.g., they learn of things from local conferences/seminars.  But it is also true they might feel obligated/pressure to cite certain people they know, depending on culture, etc.

To follow on Kimball's point, there may indeed be pressure from a government perspective - if you're funded by our tax dollars, and you have the ability to cite other work funded by our tax dollars, it only makes sense to increase the return on the government's investment when you can.

As someone who has received similar (valid) criticism literally last week - it's not necessarily malicious, might be just a lack of effort with finding relevant and more globally visible literature on the topic (such as papers with more citations) instead of relying on own or known from local collaborations/conferences work.
Good way to go about it is to cite it as a concern in your review and suggest improving this part.
If a reviewer is familiar enough with the topic and knows most major groups working on it, they might provide an example (e.g. "authors cite a tangentially related work X while a much more well-known work Y deals with the subject directly"). But this is not required, either.
My suggestion is cite this concern of yours in the review as a suggestion for improvement and let the editor handle it from there on.

What language are the cited papers in?  It's possible that some of the authors find it easier to read papers in their native language and that's why they mostly choose those in cases where there are multiple options.  I wouldn't find that concerning, as long as the underlying information is fine.

Citing sources in a language that is not English, excludes many readers, including most of the reviewers. If the source is not super-specific, it might be good to look for English replacements or supplements - depending on the novelty of the aspect the authors are referring to.

In the present case, all papers were in English; you do make a valid point!


text:
Teaching students to complain effectively about behavior of other faculty
I am an adjunct professor. For some reason, I seem to draw out student complaints about full-time faculty from the students.
The  complaints include:

Slapping a student’s hand out of the way when the student wasn’t performing a lab fast enough.
Calling a student “deaf and dumb” in front of the whole class.
Reducing student grades for being “disrespectful”.
Not grading any homework until the last week or so of semester, and then not being available because they have too much marking.

The students tell me that they have complained to the Chair, the Dean, and the President --- to no effect.  I'm not privy to the contents of most of these complaints, but the ones that I have seen are quite thorough and professional.
The complaints I have seen:

Identify specific problematic faculty behaviors.
State specific times and places where the problematic behaviors occurred.
Suggest (partial) remedies for the behaviors.
Request action from the hierarchy.

Is there anything else that the students can do, given that the college management structure seems unable or unwilling to deal with the problems?

The problem here doesn't seem to be that the students aren't complaining properly - from what you've written, they have valid things to complain about (perhaps not including #4), and the complaints they're making are "thorough and professional". So the real problem seems to be that the university isn't doing anything about legitimate complaints. That's not a problem the students can solve by complaining in a different way; the solution is either going to be that the university starts addressing legitimate complaints properly, or the students take their complaints outside of the university.

By "outside of the university" I mean either getting the word out that this is how the university treats its students, or consulting a lawyer to see if there is anything actionable (perhaps on the basis that the university is not following its own published policies, which could be breach of contract, for example). This is assuming there is documentary evidence of what was complained about and what the university's response was.

Ah, yes. The good ol' "We don't want to take any rectifying actions because we don't think your complaints aren't good enough" approach.

First, it isn't your place to get involved directly, especially if the administration isn't dealing effectively with the problems. It jeopardizes your own position.
But, you could mention to the students that joint action is more effective than individual complaints. If half a dozen students go to the dean as a group with a valid complaint, things are more likely to happen than if one does or, possibly, if they went individually.
Some complaints, of course, are nothing more than misunderstandings by students of the proper roles of faculty and students. I'm assuming that you handle those quite differently. Some students have a hard time adjusting to the college environment and its expectations.

Sadly, joint action is also more effective for invalid complaints.

By collective action, do you mean involving a student union? Or something more informal? Student unions vary, but some certainly have good enough political nuance to get changes made.

@Clumsycat, not necessarily unions or formal structures. Among other things they aren't universally available. But just five or six people with the same complaint acting in unison can have an effect.

Sounds like the students have made very sensible attempts to make individual complaints. It's frustrating that has not worked.
Do you have a student union?
Student unions vary a lot. Most of them are run by students and recent graduates who really like advocating and activism. Some of them are well established and have good communication with the university faculty. Some of them are quite minimalist or very disorganised. Provided you have one that is not too disorganised you might recommend that the students raise their complaints with the union.
That they are normally staffed by students/graduates who enjoy advocating makes them likely to try to do something with the complaint (unfortunately enjoying advocating isn't always the same as being good at it). Unions stick around longer than individual students, so they may know of a history of complaints that should be raised. This longevity can also lead to better communication with the university, they might know who would be worth contacting in the central administration.
It's certainly not guaranteed success, but if there is a student union available, it should be tried.

Thanks! I used the phrase “student union” and apparently that came across as the building / facilities. Apparently the term here is “student government” for the same thing I’d call a “student union”.

TIL. That is not a term I had heard before either.

I suspect it's not very common in the US for students to have a union in this sense, i.e. an organization that exists exclusively to advocate on their behalf against the university "management" (faculty, staff, administration). "Union" would typically be reserved for an organization of employees in a workplace. A student government can fill that role to some extent, but it's probably not going to be as effective as an actual union would. From what I've heard, a university ombudsperson (or the office of the ombudsperson), though not a student, might be better placed to serve as an advocate.

@DavidZ Wow, I had no idea. Who takes responsibility for running of student societies in the US?

I'm not even sure if we understand the term "student societies" to mean the same thing! If you're talking about sports teams, performing arts groups, social clubs, and other groups organized around activities, it varies from case to case but they're typically run by elected representatives of the student members, overseen by a faculty advisor (i.e. a professor) and/or an office of the university leadership which might be headed by the "Dean of Campus Life" or "Dean of Student Activities" or some similar role. (If you want, we can discuss this further in chat)

@DavidZ This string of comments has appeared on this site several times before.

@AnonymousPhysicist And what am I supposed to do about that?

@DavidZ Nothing.

Student complaints about faculty behavior are common.  University leadership does not and usually should not address these complaints publicly.
Publicly addressing complaints

invites more complaints
encourages faculty to lower their standards to reduce complaints
is unprofessional

It's not your concern how complaints are addressed privately.
For tenured or unionized faculty, some complaints simply cannot be addressed.
You should use complaints as a learning opportunity.  Students can learn how to use additional resources besides faculty.  Students can learn how they can behave ethically during their careers.  You can teach these things without directly addressing the other faculty member's behavior.
In rare cases of criminal conduct, you may be ethically and/or legally obligated to report the student complaint to an authority.  Check your local "mandatory reporter" laws.  In some cases, you might refer the student to an omsbudsperson or a union that represents student interests.

Where do "mandatory reporter" laws apply to complaints from students who are adults? Are you thinking of the occasional 16- or 17-year-old college student?

@nanoman:  In the US, many employees of colleges & universities are "mandated reporters" for the purposes of the Clery Act. Here's an example policy.  As far as I can tell, though, these policies don't usually include faculty as mandated reporters.


text:
Is it OK to inquire about paper status after 7 months (2nd round) review?
I submitted a paper to an applied-mathematics journal in May 2015, and the first round review took a bit more than seven months. I only received one referee report (there would usually be two), which was generally positive. I submitted the revised draft in mid January 2016, and it is “under review” ever since.
I inquired about the status about four months ago and only got a reply from the journal staff, basically saying that my message has been forwarded to the handling editor (nothing from the handling editor though). I am wondering if it is OK to inquire again? How long should I wait before I make an inquiry on a paper status (without being too pesty).
The journal states that its target processing time from submission to final publication is eight to nine months, and it typically gives reviewers two months.

Possible duplicate of What does the typical workflow of a journal look like?

Some journals take much longer than others. Sometimes this level of delay is considered normal. I don't suppose another formal clarification email would hurt.
For the viewers: downvotes are not that helpful here. The viewer could at least suggest a comment for the OP to understand.

I inquired the status about 4 months ago and only got a reply from the journal staff, basically saying that my message has been forwarded to the handling editor ...

is telling me that the journal has not forgotten about your manuscript. They are still processing it.
As you are well aware of, reputable math/applied math journals turn around time are very long in general. I have read on this site that two years is not unheard of. Please see this answer for example.
If you are anxious to know the status of your manuscript, I think sending another inquiry is okay since last time you inquired about its status is four months ago. I don't think the inquiry is too pesty. They'll understand.

While I agree that math/applied math journal turnaround times are usually long, it seems to me that the editor might need to be nudged from time to time. My experience(although I'm from a different field) is that as long as your email is polite and courteous, there's no harm in sending inquiries to the editor from time to time. This might make the editor sit up and take notice and maybe send reminders to the reviewer. I would suggest sending reminders every two months.  Else, your paper might lie forgotten under piles of new ones.


text:
Using typographical variants of the same letter as mathematical symbols in a paper
Sometimes I struggle in choosing notations for a mathematical paper. There are probably no explicit rules, but unwritten conventions. In a discussion, is it proper to use different typographical variants of the same letter to denote different variables?
For example, is it acceptable to use an italic K (), an upright K (K), a blackletter K () and a calligraphic K () for four different variables in one section?

Follow the style of other papers in your field. Do you mean a paper in the field of mathematics, or a paper in some other field that uses more math than usual?

@OswaldVeblen, I mean a paper in the field of mathematics.

On Mathematics Educators StackExchange, you may be interested in http://matheducators.stackexchange.com/questions/4437/advantages-of-using-script-letters on using script or calligraphic letters in mathematics.

Technically, it's OK, since those K's are four different symbols. Practically, though, you're asking the reader to keep in mind that they're different and to keep in mind what each of them means, which makes it more difficult to pay attention to the information you're trying to convey. I would worry especially about using both the italic and upright versions together. Enough authors accidentally forget to italicize a symbol occasionally, so many of us habitually overlook that distinction.

In typeset maths all maths all variables are in italics and functions are straight, so using both of those will probably confuse people. The blackletter and calligraphic are also easily confused, since we don't regularly write either. On the other hand, you can use lower-case, upper-case, calligraphic and blackboard-bold, and possibly also bold. At some point though it might be better to have some bars, hats, stars, dashes, subscripts, superscripts...

"variables are in italics and functions are straight" nope. I would write a function as $f$ but the cosine as $\cos$ but I also write a real variable as $x$ but ofter Euler's number is $\mathrm{e}$. So "variables are in italics" is generally right. But what is straight certainly depends.

If $F$ is the Fourier transform of $f$, I would confidently write $ F = \mathcal{F}(f)$ (or maybe $F = \hat f$…).

@Dirk You are right, I was thinking of functions like sin when I said functions are straight, and forgetting about ones like f.

Enhancing on some of the other answers: while this is OK, and I have done this and worse in extremis (one of my papers is known as "the one with the four types of arrow"), your paper will be difficult to read.
You need to be aware of the fact that many readers will have a hard time tracking the differences between symbols.  I recommend:

Doing everything in your power notationally to avoid this situation in the first place
If you must, first choose things that are easy to tell apart: e.g. capital vs. lowercase vs. mathcal.  Upright vs. italic or symbol vs. symbol-bar are much harder to tell apart at a glance.
Most important, in any symbol-heavy paper, include a "cheat sheet" table up front that gives the definitions of all important symbols or symbol-classes

I am not sure you work in math. The practice from the question is common in mathematics papers; a "cheat sheet" up front is not. I can't think of any example off the top of my head of a math paper I've read that does have such a table.

@OswaldVeblen While I am not "in math," in the areas in which I do work I often write papers with significant mathematical content.  I will strongly argue that "cheat sheet" tables make a big difference if you want to communicate with people who are not themselves abstract mathematicians.  I also find that building the table is a good means of self-criticism for notational clarity.

@OswaldVeblen: it's true this isn't common, but that doesn't make it a bad idea. In fact when I am reading a paper closely, I often find myself writing up such a table. Why don't we do it more often? (By the way, one example of a paper with such a table is the Feit-Thompson paper, but that is something of a special case!)

@jakebeal: What is an "abstract mathematician"?  Note that the OP indicated that he is working in the field of mathematics, so if your advice is intended to be followed everywhere outside of mathematics, that should be clarified in the answer itself.  On the other hand, I think Artie makes a good point: it is true that we usually do not include symbol lists in math papers unless they are book-length.  But that doesn't imply that it's a good idea.

I wonder if it would be helpful to parenthetically suggest pronunciations for things when introducing them? Some people tend to think of concepts in aural terms, so having "pronounceably" different symbols might help such people maintain the distinctions.

@PeteL.Clark, I thought Artie's point is it's not a bad idea, and you wrote "doesn't imply that it's a good idea". Do you agree with Artie or disagree?

@PeteL.Clark I think that a good table of symbols is always a net gain for readability.  The only disadvantages are 1) it takes space, which can be a problem if your manuscript has a strict page limit, and 2) maybe some scientific communities think less of you or your manuscript for "showing weakness" in this way?  The second point doesn't apply to any community I participate in, but maybe there are math communities that operate that way...

Just an opinion: I think four variants of the same letter in one section is probably too much. In particular, I think (non-bolded) upright letters don’t work well for typesetting mathematics.
Also you say ”for four different variables”; this suggests that maybe you want to denote four of the same kind of thing in four different variants. (If I'm wrong, ignore the rest.) That is definitely to be avoided. As @Wrzlprmft says, the variant should reflect the kind of object you’re talking about, and related objects of different kinds should be denoted by the different variants of the same letter. The first example that comes to mind is a Lie group G and its Lie algebra  (blackletter g).
Here’s an apposite quote from Littlewood’s Miscellany, via Milne:

It is said of Jordan's writings that if he had 4 things on the same footing (as a, b, c, d ) they would appear as a, M3', ε2, ∏"1,2.

Bad Jordan!

Yes, it is acceptable and I have done so in publications myself.
However, you should not use these variants randomly but follow some system, e.g., you could use a calligraphic K do denote the set that contains K₁, K₂, K₃, … and a blackletter K do denote some transformation of that set. You should also check whether there are some generally accepted conventions in your field (and follow them), e.g., in some fields, vectors are indicated by using upright boldface letters while the corresponding normal italic letters are used for their components.
(In general, I prefer to use one typographic variant for symbols representing similar structures, e.g., lowercase italic letters for natural numbers, lowercase greek letters for real numbers, uppercase italic letters for countable sets of natural numbers, calligraphic uppercase letters for uncountable collections of natural numbers, etc.)

So I guess you don't use many calligraphic uppercase letters :)

@TobiasKildetoft: That’s what you get for keeping the examples simple. It’s uncountable collections of natural numbers now.

@TobiasKildetoft, I am not familiar with it; I didn't even quite get your joke (am I right in assuming that it is a joke?). Could you please clarify a bit?

Zuriel: I first wrote “uncountable sets of natural numbers” in the last paragraph. The set of all natural numbers (ℕ) is countable, hence every set of natural numbers is a subset of the set of all natural numbers and thus countable. Thus there exist no uncountable sets of natural numbers. Thus I would have no reason to use calligraphic uppercase letters. There exist uncountable collections of natural numbers though, as they do not exclude repetition.

@Wrzlprmft Of course this is only a tangent to your answer, but whenever I have heard "collection" in mathematics it has been a synonym for "set".  Using it to mean "multiset" strikes me as very non-standard.

@TrevorWilson: I was rather using collection as an umbrella term for all sorts of set-like structures. I wouldn’t mind seeing it replace multiset in usage though, since the latter is such a contra-intuitive name (it implies many sets) and multisets often appear in applications (every data set is not a set but a multiset/collection).

One thing to keep in mind is that readers may want to work through some of your derivations while they read it, using pen and a separate piece of paper. Bold symbols can be handwritten using doublestruck letters, and calligraphic letters are generally fine, but distinguishing between italic and upright Ks in handwritten notes is a killer and it is likely to discourage exactly the sort of attentive reader that you want to really read your paper in depth.
This suggests, then, the rule of thumb that if you can consistently use those symbols in handwritten notes you will generally be fine. What symbols did you use when you developed the material? That is a good starting point, and beware of trying to cram extra concepts onto the same symbols after you've moved off the pen-and-paper and onto the computer screen.

In mathematics, the typeface says what your variable is. It is like writing pCounter in a computer program to make clear that the variable holds a pointer.
For instance, one of the many common notations in linear algebra is that capital letters like $A$ represent matrices, lowercase letters like $a$ represent vectors, Greek letters such as $\alpha$ represent scalars, script letters such as $\mathcal{A}$ represent subspaces.
The actual letter that you use often is a "default letter" for that kind of mathematical object: for instance, $D$ often represents a diagonal matrix, $H$ a Hermitian one, and so on.
Of course, the choice isn't always obvious, and often notations for different fields clash (for instance, you may want to use $\delta_{ij}$ as the Kronecker delta, but $\delta$ as the prototypical calculus "small positive number").
Using the same letter in different typefaces is often reserved for related quantities: for instance, you could call $d$ a vector, $D$ the diagonal matrix with diagonal entries $d$, and $\mathcal{D}$ its spanned subspace (just the first example that crossed my mind). Or vectors and their containing subspaces: $u\in \mathcal{U}$, $v\in\mathcal{V}$.
If you use the same letters for different things, I assume that they are either "default letters" or related quantities. Otherwise, you are just making life harder for your readers.
TL;DR: It depends on what your variables represent.


text:
Is it appropriate to ask for more than one recommendation letter from the same person
I will be applying for Ph.D programs in mathematics and hence I'll be needing letters of recommendation from my professors. There are two or three professors with whom I have a lot of academic interaction and which are also famous in their research areas. As such, having a recommendation letter from them can significantly increase my chances of selection.
Now my question is: Since I’ll be applying to 5–6 universities, is it appropriate to ask for that many recommendation letters from the same person? If not, then how many recommendation letter is considered to be “normal number” to ask for?
I would be very happy if some of the professors here, who themselves write recommendation letters can tell their experience.

Applicants to medical school typically apply to a dozen or more schools and need letters sent to each one. Certainly, you're not asking for the professor to write 6 separate letters, right? Just a single LOR, printed out six times, and mailed to six schools. If you feel it's a hassle, you can provide addressed and stamped envelopes to the professor to assist.

@Compass a single letter of recommendation will not create any problem. But most of the universities send their own recommendation form to the recommenders, that's why I asked that whether it'll be okay if the professor is asked to write 4-5 different recommendation letters (though more or less same in content).

Can you give us an example form? I recall having a few short question sheets asking generic questions in addition to the letter, but nothing that was considered a noticeable amount of work.

@Compass ya, that's true. most of the letters are short, but again i was more worried about the number of such letters.

Well, you should be able to consult with the professor whether they have issue with filling out the six questionnaires then, but the letter-writing itself will take the same whether its one school or one dozen.

@Compass yeah, right. i have seen at another question marked here, that it's common for recommenders to write 6-7 recommendation letters. so i'll politely ask my professors for the same. thank yoy for your response.

Is there some reason to think that the professors will need to write different letters of recommendation for the different universities?  If not, then the additional incremental effort of sending the same letter to several different places is minimal.  Though I am not a professor, my role is similar, and I, at least, do not mind when somebody wants me to send the same letter to a handful of different locations.  If you were applying to 20 places, that might be a different matter...

Somewhere out there, a professor has a Mad Libs Letter of Recommendation. I just know it. That being said, I believe some professors do tailor their message differently. For example, research medical schools and primary care medical schools look for different attributes, so an MD writing a LOR may cover different things.

thanks for the answer. actually most of the universities ask the recommenders directly for letter of recommendation and all them have different forms for it. that's why i was asking that is it ok if a professor has to fill the recommendation letters for 4-5 different universities.


text:
Strategies to remember papers that you read
What strategies do you use to remember papers that you read?
I usually take notes, but when after a while I look at the notes, I don't remember most of the details. So I have to go back to the original paper and read many sections once again.
Are there better strategies for remembering key points from papers you read for a longer time? I am mostly talking about CS and Math papers in which details can be very easily forgotten.

Related questions on MO and MSE: http://mathoverflow.net/q/143309/6518 and http://math.stackexchange.com/q/748197/11323

Related: http://academia.stackexchange.com/questions/30719/how-to-build-a-list-of-seminal-papers-in-a-field/30725#30725

The advice I was given by my supervisor is to write about a paragraph on each of the four following points for each paper you read (note, this is from a very CS perspective):

What's the context for the paper, in other words, what is the issue that the paper's trying to tackle, and what's the prior work in the area, or the work that the paper's trying to build off. For word published as parts of bigger projects, what's the overall aim of the project, and how does the paper fit in.
What's the key contribution of the paper, i.e. what is the central idea, or improvement that the paper presents over the state of the art. I (personally) find this one of the more important sections (especially in terms of remembering papers later), as this is where you need to really hone in on what the code idea behind the paper is, without all the extraneous implementation detail/proofs/arguments.
Criticisms of the work, no research is perfect! I'm personally terrible at looking back at papers I've read with rose tinted glasses, leading to a little bit of imposter syndrome. Having a list of criticisms of the paper can help to dull that, as well as providing a good counterbalance to the "key contribution" section.
Any other thoughts. As the purposes of the four points is to help remember the paper later, it's also important to make a note of what you personally thought while reading the paper. Really liked a sidenote they made? Make a note of it. Found an corner case you don't think they cover properly? Make a note of it - you could turn it into research later!

I usually find that I take about 10 minutes writing notes on each paper, along with about the amount of text that I've written for this answer. Your mileage as to how much you want to say about each paper may vary however.

+1 as I can see the benefit despite suggesting a very different take myself.  There are very few papers in my field that would warrant this much attention (most are short), many make one helpful (to me) point and are more useful for their references.

I try to give a brief summary to every article I read. I highlight and make notes on the paper and transfer this from analogue to digital with Mendeley.
In Mendeley there is a 'notes' section, where I post notes about the article. This includes:

Hypothesis
Interesting methods
Important conclusions
Thoughts for the future

Maybe this is something you can use as well? This is in medicine/biology by the way, more concept based than math based..
EDIT: Here is my full list (which I never manage to fill in completely, but it helps):

Complete citation:
  Key Words:
  General subject:
  Specific subject:
Hypothesis:
Methodology: Result(s):
Summary of key points:
Context (how this article relates to other work in the field; how it
  ties in with key issues and findings by others, including yourself):
Significance (to the field; in relation to your own work):
Important Figures and/or Tables (brief description; page number):
Cited References to follow up on (cite those obviously related to your
  topic AND any papers frequently cited by others because those works
  may well prove to be essential as you develop your own work):
Other Comments:

I get much more from a paper if I do a few things:
First, I try to connect it with the research program it comes from. One of my advisors is really incredible at giving a brief bio of almost any researcher in the field including their PhD advisor, the topics that interest them, where they might have done a postdoc, who their collaborators are, etc. All this stuff can seem kind of tangential until you start to see the connections between researchers and programs. At that point, it becomes an extra associative dimension to help you recall the research itself.
Second, I try to work in a discussion of every important paper I read with an advisor. When I'm approaching a deadline and reading a lot this doesn't work, but in more relaxed periods I try to set a plan in advance (e.g. 'Next week let's talk about these three hippocampal modeling papers') so that I know as I'm reading I am going to need to remember both big ideas and technical details. Talking through the paper lets you relate it to other ideas in the field, compare and contrast, expand upon the ideas, and critique things. All of these are good on their own, but also useful because they offer more associative threads to tie the paper into a web of knowledge.
I'm sure there are other strategies. For really important ideas, Mitchell Carroll's answer probably is best, since you need to work through them on your own to fully understand the subtleties.

Expect to go back to the original for matters of substance, otherwise a 1-bit error in your recollection could make you suffer (e.g. changing the sign in an equation).
Concentrate only on remembering the major author(s) and affiliation (easy way to mention it to someone else), how you would find it again, and the key new stuff (for you) which you should find  in the abstract.  If there's an important equation/algorithm/method etc. then you will want to write it down, but that's not so much remembering a paper as learning something new from the starting point of a paper.
Edit: I should note that I vastly prefer reading papers on paper and can therefore make margin notes and file particularly interesting ones.

Here's some good rules of thumb I saw (or did I hear it? :) ) and remembered (amazingly enough). Can't remember where though...:
What you hear, you forget,
what you see, you remember,
what you do, you understand.

"Jokes" aside, what worked best for me at least while studying and trying to remember things was to try and explain/retell to someone who really is not in your field.
For instance, a sibling or parent etc. The hardest part is to get them to agree to it, but hey no one said education was cheap (sacrifices and returned favors are to be expected in some cases). Perhaps they may put you to the same use for their similar needs :)
It is easier if you can incorporate your theory into what would be a really exciting example for the person in mind. Trying to Re-tell something advanced in an understandable and exciting way to someone who does not know very much about your field does Wonders (at least it did for me).
Because when you have read a paper -> written notes -> finished the exercises -> feeling you "basically understand" what you've studied, the final nail in the memory-coffin is to teach what you think you've learned.
Because once you have managed to successfully explain to someone else (which may take time but is kind of very fun as well and very well spent time!) you will probably have twisted and tried to anser questions, finding alternative ways to explain, simplify, and come up with real-world examples to make the counterpart get some kind of feeling (if not fully understand it, which may not be expected of course), that you quickly realize which parts you had to check up in the book/papers again.
This is no easy task but it is very funny (I think so at least, like to teach and learn) and my heasd usually got really tired afterwards (you know "tired" like when being up late studying and suddenly the brain gets "high" and youtube clips suddenly become very funny and all). This is because it puts your brain to hard work during quite some time, but the key is that it one likes it so it is fine and the brain will remember more than one may imagine.
I shall not share my whole life story, but I can tell you that this was without doubt the most effective (and probably efficient) way for me to not only remember, but more importantly to also understand and get new perspectives on the subject.

As a CS major and programmer who has to look at Java's API for most anything past System.out.println(), I have learned that memorization can almost hurt more than it helps in CS.  That pertaining to programming itself, and not to research and papers, my strategy for remembering information I read is to do an exercise pertaining to the information soon after, if not immediately after or even during, I read it.  For example, if I'm reading about amortized analysis, I always have the associated homework or practice problems next to me, working on them as I read.  I find that memorization is almost a self-defeating goal, as memorization for its own sake almost always fades away quickly for me, where if I apply knowledge or information soon after taking in information, it helps me to more completely digest the information and it begins to become second nature.

The main reason why people forget what they read is the lack of rehearsal.
I used a notebook to keep track of the important notes I've read.
Some apps are also great for that: i.e. Evernote, Readult or any note taker.
While on the road (for example, on my way to the office) - I know always take time to scan through my notes, to keep them in my head.

Take notes. Information passed though brain to hand, especially if you take the time to think about it and rephrase,  ask additional questions, etc., is a bit more likely to be remembered. Reading it aloud, "in character", also sometimes worked for me but requires privacy.

OP stated that he's already taking notes, they're just not helping enough.