text:
How to come up with research ideas?
As a very new researcher who is exploring the best way to generate ideas, some guidance on this question would be very helpful. I have found that this is NOT easy. Ideas seem to pop out of my Professor every day and I wonder how he does it. This question is broad;

How do you tend to come up with initial/seed ideas? What is your search method (if you have one)?
What proportion of your ideas for past papers come from; (i) colleagues, (ii) intentionally browsing the literature for ideas, (iii) on the spot inspiration, (iv) conferences, (v) other?
How do you prioritize research ideas?
Is there any special, generalizable method that you've discovered to sift out those ideas that are likely to be unrealistic early on in the process of idea generation?

Based on small amounts of anecdotal evidence I have reason to believe that there is vast heterogeneity among professors regarding the above questions. For example, economist Steven Levitt says he works on 22 papers at once. A professor I know will have maybe 25% of this at any one time.
Related but not duplicate: Is there any software or tools for managing developing research ideas?

Anecdotally - for me it just happens (and I have much more ideas than time to develop them), while either reading or (much more) solving other problems. Just sparks of "what if?" or "can I generalized it?". For me it rarely happens on purpose - it it not hard, but impossible to force myself to be creative (on research or anything else). Related - Paul Graham, "How to get startup ideas".

Okay, as you say, this is very broad, and possibly argumentative. So, I'll try to section off my answer for your various sub-questions, and talk not so much about how I do come up (and organize) research ideas, but how I see it done by everyone (including me).

Coming up with ideas

The most exciting phrase to hear in science, the one that heralds new discoveries, is not “Eureka!” but rather, “hmm... that's funny...” — Isaac Asimov

It's probably very akin to asking a large number of artists “how do you come up with inspiration?”, i.e. you can probably get one thousand different answers, and yet not useful answer at the same time. However, there are some elements that I think are common to all. You can't “trigger” new ideas to come into your mind, but you can put your mind into the right disposition to host these new ideas: recognize them and welcome them. Below is a list, certainly partial and limited, trying to detail my perspective in this matter:

Be challenged! Nothing sparks ideas more than being confronted with contradiction, healthy criticism, a spirited debate, maybe a bit of competition. Some people manage to do that by themselves, arguing against their ideas and improving them. I myself (and most of the colleagues and students I have seen) need an echo chamber, someone to discuss things with. If they're not exactly from your field, all the better, as they may have unusual/naïve/silly questions or expectations.
To give an example, some of the most “successful” ideas I have had came while answering questions, for example from a PhD student or colleague, and replying by “no, it doesn't work like that… in fact, it's probably always guaranteed to be false, because… see, it's linked to X… or maybe it's not? hum…”

Be curious! Ideas come from problems. Identifying worthy problems in your field of research, and dissecting larger issues into of specific problems of manageable scope, is at least as hard as coming up with new ideas. In the end my feeling is that, especially for a researcher, all ideas are the result of one’s curiosity.

Manage to get some free time for thinking (and not: teaching, supervising, tutoring, reviewing, writing, sleeping, …). Body and mind. Sure, an idea can pop into your head any time, but it's probably less likely to happen when you teach basic calculus all day that when you get some time to really think.

Know your field, know where a new development need to occur, what is currently missing. Read review papers, search for such ideas through people's articles or blog posts, discuss with senior colleagues who have a comprehensive view of the field, …
One of the ways you can come with ideas is by analyzing how different groups work in your fields, seeing what has been addressed and avoided, what big questions are still open, and how you can link between different works to build a coherent global picture… This is not always successful, but it usually generates some good ideas along the way!

Explore more or less closely related fields, and see if there is something from your background that you could apply to their problems, or ways you could build something together. Such ideas tend to be very strong, because you can oftentimes apply an entire branch of knowledge (ideas, methods, algorithms, etc.) to a very different problem. In that case, the added value comes from your different perspective, as you might try things that others would not think of.

Ways have been devised to come up with new ideas on a given topic, either alone or in group sessions. Brainstorming is probably the best know such method (and might be the most popular, in one form or another), but a really large number of creativity techniques have been developed. They can be applied both to enhance creativity or to boost problem solving efficiency.

Organizing ideas
A quote often attributed to Kant: “someone’s intelligence can be measured by the quantity of uncertainties that he can bear”. If that true, that has serious consequences for research. Accepting that your mind can only efficiently support a finite number of ongoing research ideas, you have to come up with ways to write them down, organize them, prioritize them, come back to them later, etc. Just as you cannot juggle with as many balls as you'd like, such “external” tools will help your brain focus on the ones that you assign high priority (or the ones to which it gives high priority; the brain works in funny ways).
Most people use very low-tech tools for that:

Notebooks, either sorted chronologically or thematically; in the later case, open a series of blanks pages for each new project/idea, and flip through the book whenever you want to check on them. I use a Moleskine (WP) for that purpose; having a nice, leather-bound notebook somehow helps me “value” it more and treat it with care (always have it with me, actually use it).

Post-it’s scattered through one’s (real or virtual) desktop. Downsides are obvious.

More people than I thought actually don't use any tools, and just keep all in their mind. Apparently it can be done, but I don't advise it.

But more complicated methodologies have been devised, that are supposed to help you with it:

Mind mapping, either on paper or software-based.
Using todo-list flat or two-dimensional todo-list software, or more complex task-tracking software (see, e.g. Trello).
The software side of this question is already covered (though possibly not extensively) here on this very Q&A site.

Finally, don't underestimate the possibilities opened by delegating: people in charge of a specific project or sub-project (PhD students or post-docs) can be tasked with maintaining a list of ideas by all contributors of the project, to come to later on.

Answers to your miscellaneous smaller questions:

What proportion of your ideas for past papers come from; (i) colleagues, (ii) intentionally browsing the literature for ideas, (iii) on the spot inspiration, (iv) conferences, (v) other?

Most ideas are hardly “traceable” to one source or another. A given idea might have formed in my head during a conference, seeing how people were failing to address a certain issue, then crystallized during a discussion with colleagues, but would never have occurred to me if not for a literature review I had performed a few months before.

I'll come back a bit later and continue working on this answer :)

+1 for the Asimov quotation. I had this as an epigram in my PhD thesis.

Agreed! +1 for Asimov!

What do you think of using something like OneNote as a surrogate to the physical notebooks you were recommending? Latex equation typesetting websites can effortlessly generate .gif pictures of your equations that you can copy into OneNote. Wouldn't this do the same thing with the same level of efficiency (or even more because you won't have any clutter) as a physical notebook?

I've only been using it for a few days, but TiddlyWiki seems promising as a non-linear notebook for ideas.

I'll address two points in your question (the overall question is quite broad):

Ideas seem to pop out of my Professor every day: If you've worked on enough problems, you amass a collection of tools and mental shorthands that you can apply to a new problem. It's a matter of experience. You also might see someone else's paper and realize that they are doing something in a clumsy way and you have learnt a better way to do it, and so on.
I wouldn't worry too much about this: it's a matter of time and experience, and will happen on its own. You're not evaluated on the number of ideas you have in any case. You might want to check how many of these ideas are actually good ones :).

How do you tend to come up with initial/seed ideas?: When you're first staring at a problem, it can be intimidating and difficult. While there's no single strategy for getting a "leg up", some useful techniques (and these might be very math/CS specific) are:

simplify the problem: can you solve a simpler version ? if not, can you simplify even further ? Often, finding the largest solvable element starts to get your mind rolling
pattern match: does this problem look like something related that has been solved ? can you borrow a method from there ? if not, why not ? again, the goal is to get your mind off the "ZOMG THIS PROBLEM IS TEH HARD" and onto "Here's a tiny piece that I can chew on".

I'm sure others will have useful ideas as well. Ultimately, you'll find that getting ideas isn't the problem: it's getting GOOD ideas that is hard.

+1 for pattern match; found it very effective specially among different graph-like representations.

+100 because I expect that your simplify the problem and pattern match advice will be very helpful.

Check out e.g. Pólya's "How to solve it" for related suggestions

Here is some things I found useful:

Attending public seminars at the department could spark nice
ideas (even if it seems not related to your research).
Chatting with other graduate students.
Reading deeply with why? in mind. This means reading a lot and also means stopping more than usual in the assumptions hypothesis and results for different papers.
Read future work and conclusions of the papers. Some papers have a real list of future research ideas.
Capture the Big Picture. This usually will result in many whys for what you encountered.
Ask Questions.. Even what seems as silly and fundamental questions for some can be the key for good ideas.

Do you, when presented with anything related to your research, routinely ask, "Why is that?  How can I tell if that is the case?"
If not, try doing so.
If so, you probably won't be short on ideas.  Your problem will be sorting the good ones from the bad ones.
Then start asking "Is this important?  How can I explain why it is important?"

Be open/curious to what related disciplines are doing. In some you'll see that the way they solve their problems could also applied to your field but hasn't been tried yet.

I am also a green researcher, and similarly to you, I find coming up with ideas a daunting task. I have tried to approach this task in a bit more systematic way, than to just be waiting for Godot. Feel free to draw inspiration!

Finding a problem to work on

I keep a list of interesting problems. This could be something a hear about at a seminar, read about in an article, or just something I think about. I write it down - usually half a page, only few references - and forget about it. I can then pull out my list, and find something. Some of the problems quickly turn out to be too small to be interesting, others not.

Starting out

When one of my problems are deemed interesting enough, I turn to lit. study. This goes on until I find someone with an interesting treatise. Then I read it, and try to reproduce the result as they do it. (I should here mention that my field is theoretical)

Reproducing - talk about it

I can use quite some time reproducing previous authors' work. But it is very fruitful, and you tend to learn something. I try to give a local seminar about the work at this point, the junior people in my department does bi-weekly blackboard seminars, where presentations like this are encouraged for exactly this reason.

New work!

At this point it is hopefully possible where I can go in and improve state of matter. So I start. This can sometimes require correspondence with the author of aforementioned work.

Talk about it - again!

For me, discussing my work with peers is essential. At this point I would try to sneak in two slides about 'ongoing work' in a conference presentation in order to get feedback from peers and seniors from the field.
From this point on it is not so much getting the idea anymore, as following through on it. I will leave that to another day.

The most practical way is to go to the Library and look through journals for articles that interest you.
When you have found a selection, then sort them by
a) Is this a current concern in your field?
b) Is the prevailing methodology/technique practical - have you the resources?
c) Will your supervisor(s) find this project interesting?
When you can answer all three questions as Yes, then do a deeper literature research and assess again whether the project is doable in the time available and publishable (sound and interesting to people in your field).

I think it would be much more efficient to do it over the internet where every single journal article can be accessed instantly (which is not the case in the library where some references are inaccessible or take 5 minutes of wasted time to find).

Maybe you could try approaching the problem from another direction,
"What is it that you would like to achieve? what is the purpose of your research?"
There are millions of problems in life at the moment, and finding things to research is not the problem at all, even though it may seem that way.
 Inspiration is not purely found in a textbook, but are a function of the mind and soul and body.
Experience is what probably allows your professor to come up with constant questions. He probably practices free thinking, whereby he doesn't feel constrained in any way by other people and current belief systems.
 Maybe a lot of the problems that actually need to be understood, such as mental health and problems that people and our planet, experience everyday, just aren't being taken into your current world-view.
Science in itself is not an end. Science is a state of being, including understanding; and is a way that you as an intelligent, caring and investigative person (I presume) approach problems.
 A classic example of a problem is, that we don't understand. However, simply not understanding something is not a problem. A problem is something that has effects in the real world, such as, how can we help infertile couples reproduce and have children? Although it appears that now that we have resolved this in some detail, that it was the problem of not understanding DNA and the details of reproduction that probably is what resulted, with in vitro fertilisation, and even in vivo transplants etc. If one were to take the time to step out of this 'curiosity breeds progress' mindset, it would appear that these problems weren't purely driven by a quest for knowledge, but from real world problems, that have fortunately been solved.
I'd be  interested in further discussion, as I have only this evening come up with an idea myself!
There's always a thirst for improvement, and this won't cease until people realize that happiness doesn't come from materials. Happiness is within all of us, all we have to do is tap into it. Being only 24 I have seen some truly eye-opening things and I am very humble to each of our personal strengths, but I do feel its a shame that research has become so fascinated with one-upmanship, and away from the real potential and benefit of being so intelligent.

I would recommend Pragmatic Thinking and Learning: Refactor Your Wetware by Andy Hunt.  This book has some very good tips for coming up with ideas, research or otherwise.

I don't think this is very useful without giving some indication of what is actually in the book.


text:
Does being a top-tier university always imply unhealthy graduate student environments?
Main Question: To what degree is a competitive (as opposed to collaborative or mutually-supportive) academic environment endemic of famous/top-tier/high-powered institutions?

This question developed out of my recent experience doing a masters program at one of the top universities in the world. Perhaps in part due to my cozy experience at a small liberal arts college for my undergraduate degree, I was caught off-guard by the competitiveness — and what felt to me like toxicity — of the graduate school environment. I had a sense that unless I had already done amazing work, it was very difficult to feel respected by my peers or get the attention of the excellent academics lecturing my classes. And in classes there was so much discussion of who wrote the best paper, or who got the highest score.
This culture created a lot of anxiety for me and led me to a number of unhealthy and counterproductive behaviors. I wasted significant amounts of time seeking acceptance in a culture which, by its very nature, is not exactly accepting.
Research holds a lot of meaning for me, so I would like to return to school for a PhD. But I just need to make sure I can find an environment that feels successful and healthy but also challenges me as a thinker and a researcher. As such, I have a number of questions:

Is this culture inevitable in top-tier institutions? I wonder whether this pattern will always emerge due to graduate students' competition over the limited resource of these famous professors' time. That being said, alternative explanations of the above exist, including a) that my experience at a small liberal arts college was abnormally sheltering, and that my masters program was actually normal; and b) that masters programs are not good predictors of the PhD experience: a masters student occupies an awkward, liminal position in a department and likely must do more grasping for recognition than a PhD student.
If this culture is inevitable, what are some suggestions for combating the insecurities and inefficiencies that result from it? How can I maintain my health within these communities? I believe that some of the best research, some of the most creative ideas, requires relief (at least temporarily) from the pressure of constant judgement. I want to be able to find or create that shelter for myself.
One alternative to dealing with these communities is to attend a mid-tier program. Would I able to receive the same level of academic excellence, be challenged and enriched as deeply, at an institution which is not publicly understood to be top-tier? Are there examples of top-tier academics whose pedigree (in advisers and institutions) is relatively humble?

Further specifics:

The degree was a taught masters in mathematics.
Interactions with peers:

Attempts to do homework with others from my course were unsuccessful. I realized that compared to the students I attempted to collaborate with, I prefer to take a long time on homework, connecting the problems to other areas I know about, thinking about extensions, generating questions, and interrogating my understanding. When I tried to do homework with others in the course, I would frequently be seen as slow. It was the student who completed his assignment in 30 minutes who was lauded by other students. (And my attitude toward homework is not entirely by choice; I am not at the moment capable of that speed).
Discussions of ideas with peers outside of the classroom was also difficult. I learned that unless I had already done the work of formalizing, carefully defining my thoughts, I would be met with criticism. Sentences starting with "what about something like ..." were met with "I can't see how that would work" or "that doesn't make sense," rather than, "tell me more," or "hmm, what if we added this...". The whole point of discussions for me is to explore hazy ideas collaboratively, but it felt like the culture of discussion was more like a performance.

Interactions with professors: I was lucky to receive support and attention from certain professors, but both my degree adviser and my thesis adviser appeared less-than-interested in me, sometimes missing scheduled meetings without notice. I got a sense that if my existing work were more interesting or important, this might have not been the case.

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

I don't like closing this question because clearly it resonates with a number of people.  But I think that for this question to be useful, the word "unhealthy" in the title needs to be replaced with something less subjective, and this needs to be elaborated more precisely in the body of the question.

Also, it seems there may be multiple questions here; one that isn't elucidated much is "why might vaguely-defined questions tend to be disregarded in mathematics?".  I think that's an interesting question and quite separate from the main thrust of this one.  It's also one that should probably be asked on mathoverflow instead of here.

Thank you @DavidKetcheson, I largely agree with your reasoning, in particular I do see that I have conflated "unhealthy" with the unqualified property of competitiveness. At the same time, I believe the main question has been answered in a meaningful way in the answers: that no, top-tier programs are not necessarily noncollaborative, competitive, or otherwise perceived as unhealthy.

@DavidKetcheson  Perhaps a better question would have been: "what factors determine the degree of competitiveness in graduate communities?" I am happy to edit the question title and body, but it may be at the risk of rendering certain answers below confusing or less-relevant. How much of a concern should that be?

No, not all graduate programs at top tier universities are unhealthy. I can't say how many are, and it could be the majority in some fields, but it is definitely not all. I have personally been in several departments (One US ivy league, two UK golden triangle, genomics/systems biology) where the grad program was incredibly collegiate and friendly, but I know plenty of people that were places where this wasn't the case, even at the same institutions.
I think the best thing you can do is go to the open days/recruitment weekends and really make sure you question the current students there with this particular question in mind. And I wouldn't worry about seeming naive, or that such questioning might jeopardize your chances - it they think that, then you probably don't want to go there anyway.

It's perhaps worth noting that the PhD environment may sometimes be less competitive than a (taught) masters one because people are working on different things - so there's no direct comparison of "who wrote the best paper for this assignment". Doesn't mean that some departments aren't still toxic for PhD researchers, of course.

@Flyto I'm no graduate student, but I thought it was exactly the opposite, that masters students don't compete with other students as much as PHDs because the scopes of their works were smaller, and because the students are not necessarily aiming towards a career in research.

@user4052054 - several 'top' programs I knew of back in the 1980's had a horrible reputation for masters students - they would admit a large class, and only offer admissions to the PhD program to fewer than half. The rest got the masters and were asked to leave. I avoided them, even though I was brash and arrogant enough to be sure I'd be in the top half. The reputation was of a very cut-throat anti-teamwork environment through the masters portion. After that it didn't matter.

This question developed out of my recent experience doing a masters program at one of the top universities in the world. [...] The degree was a taught masters in mathematics.

I'm going to add yet another answer to this question, because I'm in the unusual position of doing two taught master's programs, and from the hints in your question I strongly suspect one of them is the one you went to.
The fact is that academia is a small place. Your experience is largely going to be determined by one advisor and a handful of colleagues. If you just go with the flow, you can have a great time or a terrible time just due to chance. A liberal arts college is probably more likely to have a good environment by default, but if you work proactively, you can create a good environment from scratch anywhere. All it takes is a few likeminded peers.

Attempts to do homework with others from my course were unsuccessful. [...] I prefer to take a long time on homework, connecting the problems to other areas I know about, thinking about extensions, generating questions, and interrogating my understanding. When I tried to do homework with others in the course, I would frequently be seen as slow.

Doing homework "with" a group, especially a large group of at least five people, usually leads to this. People get tunnel vision and just want to complete the work as soon as possible, without reflecting on it. This isn't really a property of top tier institutions; it happens whenever you get sufficiently many sufficiently busy people together.
These dynamics can be avoided, but you need to take initiative. Find one or two likeminded friends, who work at the same pace, and form a small group that encourages discussion. Or, do the homework on your own and organize separate meetings solely for deeper discussion. You don't need to get many to show up; I find the best discussion happens in groups of four or less. You can also have discussion groups meet immediately after lectures, for convenience.

Sentences starting with "what about something like ..." were met with "I can't see how that would work" or "that doesn't make sense," [...] The whole point of discussions for me is to explore hazy ideas collaboratively, but it felt like the culture of discussion was more like a performance.

The same point applies here. In small communities (and all Master's programs are small, even Cambridge's Part III) the "culture" is not fixed, but rather something that emerges anew every year. As an individual in a small cohort, you have the power to change it, or at the very least the power to find a circle of likeminded peers. Your complaints are not new; I guarantee you at least a quarter of your cohort was feeling the exact same way.

If this culture is inevitable, what are some suggestions for combating the insecurities and inefficiencies that result from it? How can I maintain my health within these communities?

This has already been well addressed by other answers, but academically, again, you can have a great time if you find even one or two likeminded friends. You may have the sneaking suspicion that somebody in the cohort might be judging you, but that's a fact of all human interaction, and you're best off ignoring it.

One alternative to dealing with these communities is to attend a mid-tier program. Would I able to receive the same level of academic excellence, be challenged and enriched as deeply, at an institutions which is not publicly understood to be top-tier?

In 2018, absolutely. For any topic you might want to learn, there are over ten sets of lecture notes available online at any level you could want. And don't forget that half of these lecture notes are cribbed from books! If you work through a graduate level book, you'll end up with a deeper understanding of a topic than you would from following any one lecture course in the world.
It's a little trickier for a research degree, but at least 80% of your interactions will be within your own research group. If you find one good group, it's not really important how the whole university is ranked. And there are many top groups outside of top-tier institutions.

Are there examples of top-tier academics whose pedigree (in advisers and institutions) is relatively humble?

Yes, there are many examples. If you don't believe me, go through your department's website and browse through the CVs of your professors.

I was lucky to receive support and attention from certain professors, but both my degree adviser and my thesis adviser appeared less-than-interested in me, sometimes missing scheduled meetings without notice. I got a sense that if my existing work were more interesting or important, this might have not been the case.

Sorry, but professors are simply busy and forgetful people, and some really don't care about advising. This has nothing to do with you; just about nobody at the taught master's level is doing anything remotely interesting to a professor. Students who are trying to impress these professors with big words are probably coming off like a 15 year old would to you.
It's a well-kept secret that all professors at these institutions are great, but at least half are bad advisors. I've heard lots of tales of woe about how a bad advisor ruined a PhD, but it's really not up to chance. It's your responsibility to look them up, ask around, and find the best advisor for you in advance. It may be true that some top tier institutions have a larger share of bad advisors, but you only need to find one good one.

Main Question: To what degree is a competitive (as opposed to collaborative or mutually-supportive) academic environment endemic of famous/top-tier/high-powered institutions?

There are a few top-tier institutions I could name that are markedly more competitive on average, and a few that are markedly less. In the course of visiting graduate schools, I found many good, supportive groups within the competitive institutions and many toxic, competitive groups within the collaborative institutions. The variation is huge, and it's your job to figure it out, before you commit.

I think there are several excellent and constructive points here. +1

"Professors are simply busy and forgetful people" This doesn't excuse missing scheduled meetings without notice. Being a professor is no excuse to be unprofessional. Now, to be fair, scheduling miscommunications or last-minute changes are not impossible (I've had them happen before, both on my part and on that of the other party/parties), but in general that sort of thing reflects more poorly on the professor than on the student, in my opinion.

@JAB I’m not excusing them, just explaining why such things might happen. I make about 8 separate points in this post and all of them could have been rephrased in terms of blaming somebody else, but I feel this is not useful.

My impression, as a mathematician, is that "unhealthy" is subjective. For almost any graduate program, you are likely to find people who thrived in it. For example, you experienced the competitiveness at your masters program as "toxicity"; I imagine there are others who found it a positive motivator.
Ph.D. programs vary highly in mood and culture. Although you will probably find some of what you described at any Ph.D. program, whether top-tier or not, it will probably be less pronounced at some places rather than others. With hard work and good luck, hopefully you will be able to find Ph.D. programs that fit your personality.
I suggest that you pose your questions to professors at your undergraduate institution. (And, alumni who went on to Ph.D.s, if you can get in touch with any of them.) They have firsthand experience with the environment in which you thrived, and perhaps know where else you can find similar environments.
Another thing you might do: look at the websites of academic departments in your field at a variety of small liberal arts colleges, and see where recently hired faculty members have earned their Ph.D.s. Are there any institutions that show up often? Those might be good programs to pay particular attention to.
Good luck!

Is this culture inevitable in top-tier institutions?

Definitely not. Frequent? Maybe (though hopefully not). Inevitable? No.

I wonder whether this pattern will always emerge due to graduate students' competition over the limited resource of these famous professors' time.

I’ve never heard of “competition over professors’ time” being an important factor in competitive environments: Either a PI will take time for their students, or they won’t. Competition occurs over other things (mainly research topics and publications) but, in my experience, rarely between PhD students and more readily between postdocs.

what are some suggestions for combating the insecurities and inefficiencies that result from it?

I think this is a bad idea: you’re attempting to fight the symptoms rather than the root cause. Practically, the best solution is to not let it come to this: if you interview for a PhD position at an institute that gives off a toxic vibe, avoid that place. You’ll find other places with a supportive, friendly environment.
Next step, foster such an environment. You don’t have to forego healthy competition but it has to happen within reasonable limits. Beyond that you will spend an inordinate amount of time surrounded by other grad students so it’s imperative to at least get along with them. I did my PhD (at a top institute and top-tier University) surrounded by an immensely supportive community, and I credit my graduate student friends with my success during that time — literally. In fact, my fellow graduate students weren’t the cause of my insecurities and inefficiencies, they were the cure.

How can I maintain my health within these [toxic] communities?

You can’t. See above: avoid them at all cost. Such environments may be more frequent in academia than we’d like to admit but they are definitely not the norm, and not unavoidable. If you find yourself in such an environment and cannot leave, then my best advice is to find good friends, and support each other.

I think you've touched on an important truth: The degree of cut-throat competiveness one might encounter probably varies from university to university, from department to department, from research group to research group, and from cohort to cohort. In many ways, it's a crapshoot, although, as you say, we can control our own actions and attitudes, thereby increasing our chances of finding ourselves in a supportive, "we're-all-in-this-together" environment.

Short answer, no, it isn't an essential element of high level education at a top-tier university or anywhere else. But there are jerks everywhere who refuse to work cooperatively and some who aren't jerks, but just don't play well with others.
Top tier institutions are very competitive for admissions of course, but not necessarily thereafter. But the pace is fast, and eventually the research needed raises the pressure, since it is less deterministic. There is never a guarantee that a research project will actually produce anything. It is in the nature of the beast. People get focused - too focused in many cases. It isn't healthy.
Some top universities actually rely on student working/reading groups to enable students to keep up with the pace.
But the more serious issue is what does a student do who finds him/herself in a high pressure situation. It doesn't matter to that person whether the situation is common or not if it is their situation.
If you are in a high stress situation, I recommend that you find ways to specifically reduce the stress. For some, moving out of the environment may be required, but for most you can find ways to reduce it, not just "live with it."
Before you consider leaving for a lower stress environment, try to find ways to reduce the stress itself. That is the problem, not the environment, per se.
The key to reducing stress is to find some activity that will give your mind a rest from the normal activities of your work. You have to make a break, if even for a few minutes. You have to find ways to calm yourself both in body and mind. There are many ways to do this. Even reading a chapter of a book not related to your work (sci-fi, mystery, ...) may be enough for some. Meditation, yoga, taichi, riding a bike, racket ball...
There is evidence that pushing your brain constantly to try to force it to think-dammit is counterproductive and will both make it stall and raise your stress. The key is to let your brain muscle relax.
There is further evidence, noted by most scholars, that when you do take a break, the "answer" to your current work dilemma will pop into your head unbidden. This is because the brain itself is an active organ that will work, making connections, even when you aren't actively trying to make those connections.
My personal stress reducer is taichi and it works since it is a mind-body exercise. Even fifteen minutes makes a difference. I used to use bike riding and was part of a student-faculty riding club. For this, you need an hour or two several times a week.
You might be able to find some local resources on stress reduction. The counseling center at your university likely understand the problem and can give suggestions. You can form a club of some sort, like my old bike club to make it a community thing.
There is an advantage, actually, you can do stress reduction in a group of peers. It might, in fact, make them more willing/able to cooperate with you on the educational task you all face.

Thank you @Buffy for your answer. Your description of the "think-dammit" pattern resonated a lot with me. I think that if I had felt less immediate pressure from my surroundings to "perform", I would have, paradoxically, performed better. It sounds like the only antidote is to have enough faith in oneself to relax.
I had a hard time committing to stress reducing behaviors like the ones you mention because they felt, at that time, like escapes from the real problems--engendering more stress because they weren't productive. Perhaps I simply need more life experience to recognize their value.

I'm mostly answering this from my own experience (grad student at MIT in maths, 2011-2016):
I found the community of graduate students at MIT highly collaborative. It was easy to meet others interested in my subject (my thesis advisor even organized weekly unstructured meetings for everyone interested in combinatorics), and easy to discuss homework with other students (office hours are a good occasion to get to know your colleagues). Notes were also freely shared (or even posted online). Maybe this is specific to MIT or even to its maths department, but I have never felt any destructive competition or politics happening between the grad students (or between faculty either -- unlike other places I've seen).
Now there are caveats, of course:

At least to me, collaboration isn't "working together for hours", but rather "working alone for hours, and talking to each other from time to time to catch up". If you are looking for the former, you'll have a much harder job finding someone interested.
I was in the PhD program (and so was pretty much everyone else, even though some got masters in passing); it's possible that those are much more collaborative. If there is a choice between PhD and master's, probably the research nerds will filter into the PhD track while the master's students will be more focused on outside careers. This is likely to affect the communities. If you care about the subject, you probably want to be among the nerds.
MIT is famous for a different source of stress: the "drinking from the fire hose" problem. No one will ever tell you to stop. If you ask a professor whether you should read any given book or not, they will always tell you that you should. Likewise for attending any given class, going to any given talk... basically, no one will ever assume you're a mere human; no one will prevent you from overworking; no one will draw you any boundaries. You need to find your limits yourself. I enjoyed this system much more than I'd have the opposite, but you seriously need to get used to it, particularly if you are more used to rigid environments (I was fortunate in that I was not). Do not expect your fellow students to help you with this -- many will be equally helpless about it!
My impression with mid-tier places is that they burden their grad students with teaching much more than MIT does. Even if you like teaching, this will still drain you of time and energy. So be careful what you're getting into -- less competition doesn't mean better work-life balance. Ideally, visit the places and talk to grad students there (and not just 1st/2nd years, who usually don't get the full teaching burden).

Is this culture inevitable in top-tier institutions?

No. While anecdotes aren't always useful, here they work as a proof-by-counter example. The institution where I got my PhD is, depending on who you ask, either the 2nd or 3rd best in the field, and at the level where the differences between those is pretty safely hand-waved.
Some of the schools in our tier are indeed vicious and cutthroat. Mine was not. The students supported each other. Funding was, while always tricky to get, not intended for there to be someone left at the end without the means to support themselves and subsequently leave. No one was intended to have their aspirations dashed upon the rocks.

I wonder whether this pattern will always emerge due to graduate
  students' competition over the limited resource of these famous
  professors' time.

Not necessarily. There may be some competition for a particular professor, but if graduate students are having trouble finding advisors due to the advisors not having time, then the program is admitting too many students and has created an artificial scarcity problem.

masters programs are not good predictors of the PhD experience: a
  masters student occupies an awkward, liminal position in a department
  and likely must do more grasping for recognition than a PhD student.

This is somewhat true - Masters students are weird, and can vary wildly based on department and field.

If this culture is inevitable, what are some suggestions for combating
  the insecurities and inefficiencies that result from it? How can I
  maintain my health within these communities? I believe that some of
  the best research, some of the most creative ideas, requires relief
  (at least temporarily) from the pressure of constant judgement. I want
  to be able to find or create that shelter for myself.

It's not inevitable, but the answer is the same. Find people. Don't pick an advisor based on fame - do your homework. Are their students supported and happy? Does their preferred working style match your own? The same thing is true with your peers - build a cohort for yourself.

Would I able to receive the same level of academic excellence, be
  challenged and enriched as deeply, at an institution which is not
  publicly understood to be top-tier? Are there examples of top-tier
  academics whose pedigree (in advisers and institutions) is relatively
  humble?

If you go to the right program, it's possible. One of my mentors, for example, has had an amazing career, and his PhD is not from anything close to a top tier school. It's a harder road, but it's possible.

I am from Europe, but I stayed a quarter year at a top-tier university. I felt somewhat left alone; everyone was focusing on their work / thesis / research. There did not feel a team spirit among the PhD students. When I returned, a guy who stayed at another top-tier university asked me, whether I had this experience, because he had the same feeling back then.
All my colleagues from universities a little further from Ivy League, a little bit more cozy, but still with an international reputation, did not report this.
I think only the best are accepted to top-tier universities. They have to work hard and focus on becoming and staying so good. You have to decide whether you want the reputation of such an university or whether you want to remember your time as a PhD student as one of the greatest of your life.

“I think only the best are accepted to top-tier universities” — no. “They have to work hard” — yes, but so do PhD students at other Universities. “You have to decide whether you want the reputation of such an university or whether you want to remember your time as a PhD student as one of the greatest of your life.” — These are not mutually exclusive. Proof: I did my PhD at a top tier Uni. I’m far from the best. I worked hard, got my PhD, and had the best time of my life, hands down.

What do you by "There did not feel a team spirit"?

@PeterMortensen PhD students telling each other their problem and helping each other. This costs time which could be invested in own problems.

@KonradRudolph Your experience is for UK, mine is for US.

@usr1234567 That's not the reason.

As often happens here, the question in the title and the amplified form in the body of the question are significantly different... They would be the same only under several substantial further hypotheses, with which I'd mostly disagree.
First, yes, in my observation of hundreds (actually, a few thousand) of math grad students, many small liberal arts colleges apparently do deliberately cultivate a certain atmosphere... which, whatever else one might say, is different from upper-tier graduate programs. In particular, and I think this is reasonable, there is a professional standard of quality for PhD's, especially, so that "trying hard" (while having some virtues) does not guarantee reaching a professional, externally prescribed plateau.
Second, yes, in many scenarios Master's degree students are second-class citizens in some ways... In a PhD-oriented graduate program, the coursework that M.S. students do is of very secondary interest, akin to the "required" first-year courses for PhD students that appear in many U.S. programs. Yes, worse, some programs in the U.S. (and elsewhere, but I'm not as well acquainted...) treat M.S. admissions as provisional, and they're not well funded.
Third, indeed, especially in top-tier places (I went to such a place), coursework may often play no role whatsoever. My own alma mater may have been an extreme in that regard... Also, "worse", when current research of faculty and visitors was described, there was no "accommodation" for people who didn't know much yet. Real things were happening. The train was leaving. Yes, this is a little harsh... but it was, in fact, not malicious, I think. For me, the huge point that it was "not about me", but was about the math, and that things were happening whether or not I understood them, was very, very helpful.
At least in those days, people did solo PhD thesis projects, and it was unreasonable to imagine that other grad students would really understand each others' projects, if I recall correctly. So "cooperation" did not make sense. At the same time, of course, 20-somethings are inevitably pretty mean to each other about random, meaningless things, yes.
It is important, also, to appreciate that "being challenged" may occur in a way that one is not able to prescribe or require, but is set by the faculty. E.g., I myself thought that the challenges of grad school would be particular things... but they weren't those things at all, etc. Understanding what more-genuine challenges were was part of the benefit of a top-tier place.
Yes, once one sees what top-end activity and standards are, it is hard to "go back" to a sort of happy complacency... Seeing top-end stuff is undeniably psychologically stressful. No, in that context, no one is going to tell you that "whatever you choose to do is fine, because it's your own choice"...

I did a taught masters course in mathematics at what is, at the very least, one of the top two or three schools in the world, and I do not remember the kind of environment you're describing.  Attitudes such as

It was the student who completed his assignment in 30 minutes who was
  lauded by other students.

really have no place in a taught masters course, where the point is to teach you the mathematics you need to know in order to do well as a graduate student.  Whizzkid Genius #5876 may find the homework so easy that (s)he can do it in 30 minutes, but there comes a point for everyone where it stops being so easy.  If you find that you need more time to do the work, then you're getting a head start on learning what it's really like to do research.
Do try and use the competition as motivation to work as hard as you can, and don't try and do the impossible and catch up with the top of the class.  If you're at a top-tier university, these will likely be some of the cleverest people in the world, but even they will need to do considerably more than 30 minutes of work if they want an academic career.
Don't worry about not having done any amazing work already - that's not what a taught masters course is for, and this attitude is not widespread among top tier universities.
I'm doing a PhD now in a computer science department in another top university (not quite as prestigious as where I did my masters/undergrad, but the research department is world class).  The atmosphere is relaxed and not at all like what you've described.

Anecdote as counterpoint: I did what I am guessing is the same taught masters course in mathematics that you took, and I must say that sadly some of the environment mentioned by the OP did sound rather familiar. Intellectual machismo, and all that. However, I think it's reasonable that you shared your more positive experience here, to encourage the OP

(Top two or three in the world is, though, really debatable if not downright false, if one is talking about training for a PhD)

@YemonChoi I'm sorry to hear about your experience, and I'll be the first to admit that my own time there will never be representative of everyone's.

Please be encouraged.  You can do this in a way that benefits you and the world that you will contribute to, after finishing your studies.  I find the timeline to be the most important element in the course of study.  I took the maximum time allowed and did a grad certificate, not Master's, at a top-tier university.  Some peers had two full-time jobs on top of a Master's program or doubled up on classes.  I did half the work in double the time, but I have much outside responsibility that I could not delegate.  I wasn't always eligible for financial aid because I wasn't taking enough classes to be considered part-time all semesters.  It was expensive, which is again a reason why I went slowly.  However, it was a positive experience.  Homework took longer for me and I needed to acclimate to other's expectations, even if I couldn't change the speed.  One-on-one's worked best and a lot of work was done solo.
 I absorbed more and adapted well.  Because I am a business owner, I had freedom in my daily schedule and studied in the morning.  In your situation, look for a combination of educational financing/employer tuition reimbursement/free-lance or a flexible work in an area that you already know so that the only new element is doing the PhD.  The fit with the University and the scheduling has to be something that keeps you on an even keel.  Your being O.K. is important.  You did graduate, you can do the work, you get to pick what's next.  Be a spy at the campus cafeteria and measure your comfort level - when fellow students are not on task, do they do things like you would?  Some part of the future experience needs to give you energy, so you can be a place of rest.  Keep looking - even look at a higher level.  The surprise for me was that it was at top-tier university.  Absolutely you can do it.

source: Stack Exchange

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

sort: votes


text:
Assistant Professor at my state university, Research Scientist at my Ivy League, or both?
I am a Research Scientist at an Ivy League. I have been offered an Assistant Professorship at the state school. The Ivy League has suggested that if I take the professorship, I could stay on in a 20% role and continue my present research. The state school seems amenable to this arrangement, and would credit my past time here toward tenure, and the ongoing 20% as a tenure-admissible external collaboration.
Within my network, I cannot find a single person with this kind of arrangement. Are joint appointments an uncommon thing? Pointed questions:

What might be the unanticipated issues of joint appointment at different ranks (asst. prof. and research scientist)?
How can I frame this relationship such that my tenure committee is positive about the arrangement? Any other political considerations?
Is it generally permissible to write for money from two institutions, in effect to be your own subcontractor?
The department at the Ivy is much more highly ranked than that at the state school (top 10 vs 80-90s, engineering). When I move to my next position, how will the time at each institution likely be viewed? Will the Research Scientist role even be considered? Worse, will it be fairly necessary for such a move, such that I dare not let it end?

Relevant additional thoughts:
My other offers are not superior.
I have good relationships on both sides. Both work environments are dynamic, interesting to me, and provide freedom.
These schools are in the only two locations I can live (family reasons).
These offers are financially similar. Combining them won't cost too much.
State school offers more access to space, a good start up package, and far cheaper resources.
The Ivy League school has name recognition, better network of partners, etc.
Having access to both MIGHT offset  difficulties (travel, politics) of doing both?

You may get better answers if you outline more about the difficulties you anticipate (travel - how often would it be feasible to go to each location? and politics - the state school would accelerate your tenure; do you think there are colleagues who would be against your tenure case?) and your preferences (do you want to teach at all? are you trying to maximize your income? your number of publications? status?). Would you feel bad about leaving your alma mater for a fancier job in a few years? Are you worried about getting trapped there with few resources if the Ivy League arrangement ends?

why not both? we do all the time this in europe

This question seems to be borderline off-topic due to being framed as one, focusing on author's individual circumstances. However, I will not vote to close at this time, since, I believe, the question could be re-framed as a general one. For example, you can take a look at how I approached a similar situation here - note the bullet points with generalized questions.

Excellent points, and reflected in my newly framed question. Thank you for the advice.

@Industrademic you are owerthing it, I know examples where the professor had 15 positions, which make angry education minister. If it is not against the law in USA to have two possition, I would advise to take it. You are lucky!!!!

@Industrademic I assume your prior comment was directed at me. You're welcome. You definitely improved your question, however, I believe that you can do even better (some of your bullet point questions contain too many Is, which make them non-generic). I suggest you to work on those, rewording them in a neutral manner (e.g., try replacing I with one).

Perhaps an additional useful edit would be to the title, e.g.: "Considerations on joint appointment at separate U.S. institutions." (Though I don't seem to be in your field) I have to admit some envy from reading your title. ;) But actually the title change would signal the substantial change in the framing of your question.

There is nothing against having a joint appointment. I would take both! At 20%, you gain from networking at the Ivy, and show up once a week...or even half day to attend faculty meetings or seminars. However, focus your research at the State school. In return for 20% support, you must co-list the Ivy in pubs and seminars you give. I’ve done this before, and it’s not hard. Good luck!

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:
Life cycle for Physical Review Letters
What is the average time does it take from the time you submit your paper to the time is it published in Physical Review Letters?

Unless they publish the information, or someone has done some research on this (relatively minor) problem it is hard to know. But I'll point out, in case you are interested in what is happening with your paper, that the average is essentially meaningless in interpreting any particular paper.

It strongly depends on the paper that you submitted to Physical Review Letters or any other journal. I mean there is no strict time frame...

Mathematically speaking, the average is infinite, as many submissions get declined and thus never published. But anecdotally they pride themselves on being really fast and only give reviewers a single week, so I would expect the average of accepted papers to be in the order of a few weeks as well.

There are some old slides from a colloquium given by a Physical Review editor containing some relevant statistics for the year 2008. I assume it's trustworthy data, but it might be a bit outdated. The most relevant slide is:

Hence, in 2008, the average time from submission to acceptance in PRL was 138.52 days, or just over four and a half months. The median was just under four months. Since then they have talked repeatedly about a) reducing handling times, and b) being more selective, so handling times might well have changed. I don't know if there's any more recent statistics publicly available, but this data should at least give a reasonable first approximation. For time from submission until publication, I would anecdotally say that you can add another 2-4 weeks for production.


text:
Chicago Manual of Style chapter and section title capitalization
Ploughing through Chicago Manual of Style Online, I can't seem to find any concrete reference to whether chapter and section/subsection titles are capitalized in headline style or sentence style.
It seems, given some examples that claim to follow CMoS that at least Chapter and first level Section headings are headline style, however, I'd love to find an authoritative statement from the Manual itself, but I can't find it (I'm referring to the actual manuscript, not to citations of book chapters, which should definitely be headline style).

If your publisher has its own guidelines, follow them. Otherwise this is described rather clearly in the "Manuscript preparation, editing, and proofreading" chapter of the Chicago Manual of Style. Their definition of 'manuscript' includes both books and journal articles; and 'subhead' means title or heading of any subdivision of the text below the chapter level.
CMoS 16th ed., sec. 2.55 on Editing part titles and chapter or article titles.:

Chicago recommends that all titles be in headline style unless a work is part of a series or journal that follows some other capitalization style (see 8.157).

CMoS 16th ed., sec. 2.56 on Editing subheads:

Chicago recommends that all subheads be in headline style unless a work is part of a series or journal that follows some other capitalization style (see 8.157). But if an author has consistently used sentence style for subheads (see 8.156), that style should not be altered without consultation with the author and publisher, since it may be more appropriate in a particular work. Where subheads consist of full sentences, sentence-style capitalization is preferable.


text:
How many reference letters are too many?
A friend is applying for a junior faculty position which asks for "at least 3 reference letters from professors". He was lucky enough to have worked with big names in our field, so he was thinking of getting 5 reference letters. Is it too much?
Keep in mind that these are well known professors in top/good universities, not friends and family type of references.

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


text:
Is there an archive like arxiv.org for agricultural papers?
Is there any internet archive like arxiv.org intended for publication of agriculture-related conference papers or similar?

I assume you know about biorxiv.org, right?

No, I didn't know about it. It is a first proposal, good for some plant biology related aspects. However, with the lack of a section dedicated to agriculture it cannot be considered a good answer. Thank you!

Posting on biorxiv.org should be an acceptable practice. Did you try and they removed it?

I didn't tried, for sure it is good for some less applied subjects, but where I can post here papers about irrigation, soil tillage, phytochemicals, precision agriculture (remote and proximal sensing...), or some food production related arguments, such as enology (excluding nutraceutic, and chemical aspects), and so on?


text:
What are some good ways to keep students coming to lectures?
Having taught calculus for several semesters, I've noticed that the number of students attending lectures are gradually declining (especially for the 9am session). I would not be worried if they have learned the material by themselves so don't see the need of coming; However looking at their exam scores I concluded that a lot of them are not doing so well in the class when they miss lectures.
So what are some good ways to keep students coming to lectures?

Free coffee might work for the 9am session. Few college students can refuse free food/drink. (You may find this cost-prohibitive, however.)

Crossposted over at matheducators: http://matheducators.stackexchange.com/questions/9932/what-are-some-good-ways-to-keep-students-coming-to-lectures

I think you're asking the wrong question.  The right question is "How do I help struggling students better learn the material?"  The answer might involve increasing attendance, but it might not.

In line with what @JeffE is saying, increase attendance by making the lectures worth attending, and appearing so (Caesar's wife).

Maybe to add "real life" examples if you can.

If your lectures are interesting, they will come.

Don't schedule 8am to 10am.

It might be better for you to expand on your answer with some examples of your own.

@CaptainGiraffe Beat me to it. Stop scheduling early lectures. Calculus, physics, and 8-9 am do not mix well. Otherwise, politely remind the students that they're adults, that your lectures are available to help them learn the material, that you will not repeat your lectures in office hours because they skipped class, and that both the decision and the consequences of whether they avail themselves of your lectures or not are theirs.

There will always be students who are convinced that their time is better invested somewhere else and that they'll be able to master everything by binge-learning 3 days before the exam. The consistency with which this strategy leads to mediocre results at best and often failure seems not to influence said students much. I doubt that there is much you can do against that. I know, for a time I was one of them.

Please don't cross-post. See Is cross-posting a question on multiple Stack Exchange sites permitted if the question is on-topic for each site?

I had to deal with the same problem, and I took a lot of inspiration from this talk by Kathy Sierra. Find a way to make the students feel like they've really learned something at the end of the lecture.

@CaptainGiraffe I don't think anybody takes the 8am slot voluntarily. But if there's a room shortage at your university, you take what you're given and you do what you can with it.

Of these three, suppose you can choose only two.  Which will you choose? (1) party last night (2) Calculus class this morning (3) sleep.

As a student: if your lecture is interesting, I will be there. If it isn't, I'll probably just Google for materials instead before the exam. This doesn't necessarily mean that you should change anything in the material that you cover, possibly simply that you need to convey your material in a manner that adds extra value. Think of it this way: why would you attend a lecture if you can just read some slides ten times faster?

If you aren't an interesting speaker, then you've got that going against you and will generally always have that going against you.  You have the same problem that non-profit organizations like churches have and the same solution applies here as it does there:  Involvement, ownership, and overworked/underpaid/tired/hungry attendees.  I don't know how you can fix the first two issues (it's a lecture format), but if you bring coffee and a snack for your class, people will show up simply because they know there is free food and drink to kickstart their morning.

Here are my suggestions:

Make sure your lectures actually add something to their learning experience. Ask one of your coworkers or someone from the teaching support center (if you have one of those) to come watch a class every now and then and give you feedback on how to improve. (Even if you are a teaching super star, there is always something you can improve.)
Take 5 minutes to ask the students to fill in anonymous "exit tickets" with three questions: Something you should keep doing, something you should stop doing and something you should start doing. This should be done in class after a few weeks, but before the attendance starts dropping. Actually follow any reasonable suggestions.
Over the long term, create a scatter plot of number of lectures attended versus final grade. If your lectures are useful, then there will be a strong positive correlation between the two. Show students the plot during the first class every semester and tell them to make their own decision about attending or not.
If you really want to make them attend class, schedule daily quizzes that account for some not insignificant percentage of the grade. If they don't attend class, they receive a zero.
Remember that your students are adults. They are responsible for their own learning, and if they decide to sleep in rather than come to class no matter what you do, that's still their choice and their responsibility. You can't force them to attend. If your lectures add value, and they still choose not to attend, that's ultimately their problem.

+1, especially for #3 (and #5, although it technically doesn't answer the question). Let's call #3 "evidence-driven encouragement of attendance", or EDEA ;-)

I have some qualms about 3; the sorts of students who are more likely to skip class are also more likely to do worse in general, to the point that the correlation between attendance and class performance isn't a convincing showing of correlation.  Of course, people often see it as one, but as teachers, I don't think we should further that confusion.

@Henry I agree with you. Furthermore, Generally people who skipped class have below average scores. However last year among the 10 highest exam scores in class, two of them never attended lecture.

ad #3: Proof or it didn't happen.

@Henry I must not understand you correctly.  "The correlation between attendance and class performance is so strong that the correlation between attendance and class performance isn't convincing evidence of a correlation between attendance and class performance"???

@JeffE: That's an awful mistyping on my part.  I meant to say that it isn't convincing evidence of causation.

Ya please remove #3, since it's encouraging mathematically erroneous reasoning. =)

Please don't do number 4. If missing your lectures means students don't learn the material, they'll fail the exams anyway. If missing your lectures does not mean that students don't learn the material, then what's the problem? Maybe the student just learns better from reading on their own (or maybe there's a problem with the lecture... or the time at which the lecture is scheduled.)

@user21820, or rather, scientifically erroneous. But yep, I agree. Its amazing how often this mistake is made by the educational establishment and its employees.

#4 could easily be against the university rules if the lectures are explicitly stated as optional. That was the case during my studies, attendance was always checked during tutorials, labs and demonstrations only.

#4 seems like a rather passive aggressive way to mark attendance.  I would certainly make sure that if you do #4 it is in the syllabus.  I didn't really attend my undergrad classes and I had teachers try to sneak this (they couldn't stand the fact that someone who didn't show up would get an A while the kids who were "trying" got Cs).  I know I had to go to the head of the department to get these things taken off a couple times.

This answer is spot on.

An alternative to daily quizzes (which cut into class time) is simply assigning homework that gets turned in at the beginning of class. (I've noticed: one my students this term always shows up when an assignment is due, and never shows up when nothing needs to be handed in.) Of course, this should only be done if the HW assignments are truly meaningful and helpful, not just an underhanded way to increase attendance – along with animosity.

Academic literature
A study found that "motivation, prior GPA, self-financing by students, hours worked on jobs, quality of teaching, and nature of class lectures" to be significant factors influencing attendance. Let's focus on the latter two.
Quality of Teaching
It sounds like you are a new educator at the university level. In my opinion, the think the single biggest thing you can do to improve your lectures is to prepare them well. Most of us could teach, say, factoring quadratics, in our sleep. That easily leads to little to no preparation, especially when there's other work we feel we must do. Unfortunately, just because we're clever enough to lecture extemporaneously, doesn't mean we do it well. I have found the quality of my preparation has the greatest effect on the quality of my lectures.
As you prepare on lectures, try to develop empathy. Ask yourself: where will students struggle? How can I can help them understand the difficult parts? Your ability to prepare lectures well will improve with practice, so work hard at it.
Try to bring your passion into the lecture. Some teachers yell and jump around, others are quiet and careful, but every great teacher I've ever seen brings their passion for the material into the lecture. Work to give your students a taste of the power and beauty of mathematics.
Type of lecture
How can you design your lecture to increase attendance? Engage the students in work of learning actively. A few things I have seen used with success:

Give students a problem and few minutes to work it out. Ask students to share and discuss their solutions.
Put students in groups, and have each group work on a challenging problem together. This works best if the problems are on the board so that each group is standing and working a section of the board.
Begin each class with a short quiz. Make it easy problems related to the previous day's lecture, but award no partial credit so you can grade them in a minute.
If the lecture is large, consider using clickers for quick quizzes during your lecture.
Use the Socratic Method.
While difficult to get right, you might consider using a flipped classroom, where students watch recorded lectures outside of class and work problems in class.

If you design your lectures to include learning activities, you can grade students based on their participation and performance, and this encourages them to attend. Allow some grace: students may sometimes be preventing from attending by illness, work, childcare, etc.
Work to create a social fabric that enmeshes the students. Learn their names. Ask and answer questions. If they know that they will be missed (by their peers and by you), they will be far more likely to attend.
Why bother working on attendance? The above-mentioned study found "strong empirical evidence of the positive influence of class attendance on student performance."

I'm a bit suprised that no-one else seems to have said: make sure the lectures are different to the online/handout material.
If you put up slides that the students can read online not at the lecture, and work off them, you are just inviting them to do this "more efficiently" themselves.
Make the lecture an interesting and valuable exposition on the material in the handouts/online material.  Add value to those materials.   "Here's something I think you might struggle with in the material" and explain it in a different way.
Then your students have twice the opportunity to learn: the way it is in the online/handouts and the way it is in the lecture.    Those who want to learn will soon find that your lectures are a worthwhile and irreplaceable addition to to what they can do themselves without attending.
The only lectures I ever skipped in my time at Uni were the ones read off the slides.

Let's assume that your lectures are as polished as you can make them, that you teach passionately and in an engaging fashion, that you have active-learning in-class exercises (which is, thankfully, trivially easy in a math class), etc. Then I'll be somewhat contrarian and say that it might be best to not worry about student attendance; they have to meet you at least halfway and that's the part that's their responsibility.
I teach at a large open-admissions urban community college, and many of our students are poorly prepared for college work. I could and have in the past made attendance mandatory, assessed points for it, ejected students with over-absences, etc. But what I found was that I then had numerous surly, combative, argumentative students in the room just barely complying with that requirement, and more-or-less sabotaging the learning process of the other students (talking, playing music, laughing at students asking questions, egging other students into fights with me, etc.).
By lifting those requirements, I have lower day-to-day attendance numbers, but what I find is that the quality of the learning has gone up. The students in the room are highly motivated, they are engaged, and the level of our discussions is much higher. I have more time to spend on individual inquiries and work. I don't spend time on attendance or tardiness arguments (in-class or after-the-fact). I don't have any saboteur students. I am personally much happier specifically due to the higher level of mathematics conversation. If a student really doesn't want to be there, then it's a good thing for them to not be there.
I actually say on the first day that statistics show that regular attendance is the #1 best practice and predictor of success in a college math class. And then I let them take responsibility for how they act on that information. Give regular assessments (for me: weekly online quizzes and monthly tests) so that students can check and re-align how their study habits are working for them. Be clear and transparent about grading protocols, and don't scale any tests just due to low class performance. Around the midterm (2nd test), I have a number of heartfelt conversations with individual students about why they're not succeeding on tests, and what in their life needs to be re-prioritized to reverse that. But having a small, focused, motivated number of college students in the room is no bad thing.
(P.S.: I have had a small number of winter-session trigonometry classes at 8 AM in which I started lecturing to an empty room, and when students started showing up they could catch up based on what was on the board.)

Your first sentence is a very big assumption. I agree with what follows from that assumption, but I question the assumption.

@petehern - especially the part that asserts: active-learning in-class exercises are "trivially easy in a math class."

@J.R.: I'm currently facilitating a faculty group on STEM strategies, and it's made me appreciate how much harder other sciences have it: they need to arrange equipment, materials, space, etc. for in-class experimentation. In contrast to that we have it relatively very easy in a math class, as we deal with pure thought-stuff.

Meaningful grading is inherently subjective, so there’s a rather restrictive limit on just how clear and transparent one can be in describing it ahead of time.

@Daniel - But when it comes to "active learning in-class exercises," that's a two-edged sword – isn't it? I mean, when students are using Bunsen burners or dissecting animals or wiring circuits, the kinetic activities are almost inherently "active" and "engaging." When dealing with "pure thought-stuff," however, it can be a challenge to keep the activities interesting. (At least, I wouldn't say that it's "trivial.")

The "obvious" solution is to find a way to incorporate attendance into grades.  This has some disadvantages (it takes time and effort and is paternalistic), but for some classes it's the right solution.
There are a number of ways to do this which may be appropriate for different situations:

Literally write down who's there, of course
Have an in class quiz.  (In a class where the pre-class reading was particularly important, I found this useful---it not only automatically took attendance, but it also gave quick feedback to me and them on how well they'd understood the pre-class work, and served as a transition from the pre-class work to what we were doing in class.)
If quizzes every day take up too much time, a few unannounced random quizzes have the same incentive.
If technological solutions are an option, using "clickers" to have students answer questions during class can be incidentally used to take attendance.  (You could treat participation in the question as showing attendance, and not grade based on whether they get it right, which is often appropriate for such questions.)

That's not a solution. It's a punitive measure. If students don't want to come to class, then there is something wrong with the class. Forcing them to sit through it solves nothing.

@Mohair: In many cases I agree with you.  These aren't things I do in most of my classes.  But students, like all humans, aren't perfectly rational decision makers, and the choice to hit the snooze button at 8am isn't necessarily the decision they'll be glad they made a month later when they're studying for the exam.  Some of our students really do benefit from having a small but direct incentive to do the thing that they know is in their best interest.

From my experience as a student, I can suggest you:

Don't be just the lecturer. Make the lectures interactive and fun, not only about the material you teach. Add something to the lecture that is interesting and cannot be found in the lecture notes (for example, if you teach something abstract, try to make people understand where is that useful).
Make jokes. They are a nice way to make people relax and wake up if they are asleep.
Make them curious in a similar way the movie series make us want to see the next episode. If your lectures are recorded, try watching them and asking yourself if you have the same curiosity you get at the end of an episode of a movie series to see the next one.
Don't try to teach them everything. One of my best lecturers has very short lectures. And he is doing a good job since he has our full attention for 20 minutes or so, time when he presents the core ideas and says a few words about how it can be extending, letting us study the details on our own. And, in my opinion, this is a way better approach than lecturing for 60 minutes and nobody paying attention.
Don't make the lectures compulsory. They will come and sleep.
Be friendly. If you are lucky enough, you could get to know few good students better and be able to ask them in an informal environment for some advice about the lecture. Personally, I would be more open for a discussion like this if the lecturer manages to make me feel comfortable than to some piece of paper that ensures my anonymity.

+1 for point #3.   Definitely worth putting it out there what will be interesting about next lecture.

I am a visual learner - I learn by reading and doing, and not by listening. The first thing I do on a new purchase is read the manual; then play with the controls; then read the manual again while playing with the controls. Take no offence, but recognize that most lectures are consequently a complete waste of my time, for most of their length. Only the most spectacular lecturers will say anything of true value to my learning process more than a few times a semester.
I also have dysgraphia, making it extremely difficult to take legible notes. Not only is my writing painfully hard to read, I can write (cursive) only as fast as most people print. In 4 years of undergrad and 3.5 years of post-grad studies, plus four years of part-time study to get my CPA CGA designation, I took meaningful notes for only 4 half courses given by truly superb lecturers who kept their notes concise; wrote them on the board clearly; and spoke to them after presenting them. Those notes I still have nearly 4 decades later.
So, if you want the attendance of someone with my learning disability you must not only add true value beyond what is available in the text books, you must write it clearly on the blackboard; before you speak to it. If you merely state your contribution to my learning I might as well be in Timbuktu. If you speak and then write I again might as well be in Timbuktu. For me to learn I absolutely must be able to read the material before it is spoken to. Any lecturer who insists on revealing his slides bullet-point at a time, after speaking to them, is not only wasting my time, he is deliberately wasting my time. I am likely to be spotted throwing paper airplanes at this lecturer.
I actually attended most lectures while at university, but was much more likely to be reading the text or looking at the pretty girls than actually paying attention. I am too much of a control freak to risk missing an announcement regarding exam contents or assignment due dates, but don't mistake my casual attendance with actually paying attention to a mediocre lecture.

Nowadays, at least in the U.S., with dysgraphia you can get a 504 plan that calls for notes provided.  (Bravo for you for understanding how you learn best.)

I answer this from the point of view of a student. One approach that is NOT a good way to accomplish this goal is to make attendance mandatory. Courses with such policies have a very strong correlation to problems in all the other areas mentioned in other answers to thie question.

Pop quizzes! Make participation a part of the grade. And tell students that the tests will include material taught in class, not just in the book.
The classes I was most motivated to attend in college were ones in which the professor performed example problems that closely resembled the problems to appear on midterms. After the first midterm, pretty much the whole class realized the easiest way to do well on tests was to attend and take good notes. If any of us missed class, we would collaborate (i.e. scramble) to get notes from one another on the missed lecture. The students ended up bonding and cooperating to study together too, which was crucial in an engineering major!

As a student at university I took a module on proposition logic which looked into Calculus. Our class behaved in a similar manner as yours. I would suggest using real life example of use of Calculus which can relate to students. Also I ask myself why am I studying this? as student can't see the relations to computer science so making the relations more clear would keep them interested. I learned using YouTube and a few books as the formal notation which is show in class puts me off, maybe just teaching the method first then introducing notation will make it more fun. These are my personal thought which I can relate to hope this helps.

Just wanted to add my 2 cents:
I had a professor who played one of his and ours (the students) choice of music 15 minutes before the lecture started. I liked that a lot.
I find the best lectures are the ones where the professor tells small anecdotes that may or may not be related to the curriculum. It may just be a few minutes or so, but I find it to be a nice break and you get the feeling that it's really just another human being standing there instead of some robot going through a book. Bonus if it's a funny story.

On the other hand, I had a lecturer who gave us a coughing break (it was winter) and a story in the middle of each lecture. We still found those the worst lectures of the year.

Here are my answers (mostly from my experience), and by the way, the other answers above and below too are gems of knowledge worth any teacher's time (I have already made a note of all of them :)) -
1) Make sure you are teaching what students will find useful, and show them how / why this will be useful. Show them its relevance.
(If you feel it is not, you need to ask yourself why you are teaching it in the first place. And yes - it can come in the exam is as excellent a reason as "you will end up using this in your first year at work when xxxx happens")
2) Use Von Restroff effect to your advantage.
Every 10-15 minutes, add / change something to break the monotony. Students like that. Say something funny, ask them questions
3) I tend to use the white board a lot, and many of my students like this as it gives them time to write. I also use cartoons as it helps them remember things better and makes them smile and thus remember by association. (Confession: I am a bad artist, which makes this even more effective!)
4) Reconsider if you really wish to upload ppts before the class - Students have told me that when all the ppts are uploaded in advance, they sometimes feel there is sometimes no good reason to come to class. They after all do not know that you have planned somethign additional
5) Related to 4 above - write your ppts such that they can only be understood if a person sat through your class. I tend to write questions in my ppts which are only answered in class (often through discussion)
6) Involve your students in activities. And do something (related to the subject!) that they will talk about later. This makes students who were absent curious, and they turn up next time sheerly for the entertainment value. It is left upto you next to merge this entertainment with teh topic at hand
7) Use good and creative videos - I used a vlog by Superwoman (!) to make my students understand how not to do their assignments. They loved it. And for the first time, there was not a single late submission.
8) Use Activities as far as possible ( My kpi is one activity per class - even if it is a short 5 minute discussion with their seat mate. I know I am saying this twice) -
Similarly, to teach the various downstream and upstream legs in supply chain management, I used DHL's short advert on hot pepper sauce from West Indies to China. This was followed by a team exercise where the students had to figure out each leg, and how this could be further optimized keeping in mind the restrictions of each country involved. The all discovered new hub ports in Miami, and our Jamaican and Chinese students were in much demand as students wanted to learn about transport systems and issues there.
9) Dont shout at students / Dont scold them unnecessarily
This may not suit everyone, but I dont like to scold students in class, as it insults them in the peer group / in front of other boys and girls and embarrasses them. Some of them show their resentment by not coming for future classes. If you need to tell them something, as far as possible say it in private, or if telling in public, put it in a jocular fashion.
10) One of my lecturer friends always invested in a small bowl of candy that he would keep out 30 minutes before his class was going to get over. It became a ritual and the candy always changed each time. There were always a few special ones that he knew his students liked (he actually asked them!) - and those students came initially (a) for the candy (!) and (b) because they felt that the teacher cared enough for him / her to do this extra action
11) Related to 10 above - do something different from other lecturers. This is actually easily - just do what comes naturally to you, and most of the time it will be different from others.
12) Always focus on students assignment topics / their future career aspirations and relate what you teach in class to these. It is best to do the former right at the beginning - it is interesting how those magic words "this forms part of the answer to your assignment essay blah blah" miraculously result in pens and notebooks coming out.
13) Lastly - don't take anything, including their absence personally (I know that is difficult, especially if you are a dedicated teacher). Remember, sometimes students do sleep late and wake up late, they sometimes miss buses and trains, and sometimes, they may just want to not come. At the end of the day, your are answerable to yourself and if you did your best, that is it.

You're asking the wrong question. It's not about getting students to come to lectures but getting them to understand calculus.
If you need them to show up for some reason, irrespective of their learning, just mandate a 10% grade attendance policy. If you'd like ideas to help them learn calculus, edit your question accordingly.

I make attendance 10% of the grade and I still don't get great attendance in lecture.

Normal human intuition about normal human psychology suggests that attending more lectures will cause improved understanding. In other words, without further elaboration and conceptualization, I think this answer is pretty silly.

authors: Vladimir F Героям слава

authors: 十大最受欢迎道术小说_八十一道送命题凤凰小说网

authors: 系统逼我做娇妻笔趣阁围魏救赵_快穿之夫贵妻娇叱咤风云


text:
What questions should I ask as a candidate during an interview for a tenure-track assistant professor position?
I will soon be at an on-campus interview
for a tenure-track assistant professor position.
I expect that in the course of the day,
I will be asked the question,
"Do you have any questions for us?"
What are good questions for me to ask
to show that I am interested in the department
and would very much like to join?

Related: What should I ask deans during my interview?

Do you have any questions?. You may like to ask yourself if you do?. Dont you have any questions?. Are you willing to accept anything that is offered?

I don't think that most candidates are very good at faking interest. So, ask the questions you are genuinely interested in, and your interest will show through. It is true that you have to give the best impression you can during an interview, but you don't want to come across as fake or scripted.
I would start by reading the university, college, and department websites. That may give you some questions.
If you run out of questions, you can always ask other faculty in the department about themselves. It is rumored that academics love to talk about themselves.  You can also talk about your research, which is an easy way to make small talk and show off your communication skills.
Given that general advice, here are some questions that I think are common and "safe":

Ask about the tenure process. How long is the probationary period? What is the general process? Is there any form of mid-tenure review?
Ask about teaching. What courses do new faculty typically teach?  How tightly controlled are they? Will you have a lot of new preparations? Do faculty often teach over the summer? What process is used to make teaching assignments (seniority, rotation, etc.)?
Ask about benefits. They can tell you about the insurance and retirement benefits, which vary significantly from school to school.
Ask about housing. Where do most of the faculty live? How far from campus do they live? How expensive is it to live in the area? Are there any particularly nice locations to live near the college?
Ask about living in the area. Is it a lively place? A quiet place that's "good for raising a family"? Is there much nightlife? Is there convenient local shopping?  Is it good for biking?

Here are some questions that you have to think about carefully before you ask them:

Salary. Some prefer to talk about this during the interview; some prefer to wait until an offer is made.
Two-body problems (if your spouse is also looking for a job at the university or in the area). Again, some prefer to wait until an offer is made, others mention it early. See these questions: Should one disclose his/her family information in an academic job interview? and When during the application process should a candidate mention that their spouse is also looking for a job?
Unusual goals. For example, if you are being interviewed by department X, but you want to work mostly with people in department Y. In some cases, this sort of thing is a mark in your favor - in others it will doom your chances of getting hired.


text:
What does one do if one receives a less prestigious offer while waiting for a decision on a more prestigious one?
Alice (for argument's sake) is a postdoc in maths in an Australian University, but did her PhD in Europe. She is making two applications for funding. The first is to funding scheme A in her home country, the second is to funding scheme B in Australia. Scheme A is less prestigious and is worth less money than Scheme B. Alice's preferences are obvious: she prefers B to A, and A to whatever her next best option is.
Applications for Scheme A are due in November, the outcome is declared in April, the position begins in October. Applications for Scheme B are due in March, and the outcome is declared in November, the position begins in January. The application to Scheme A must be declared in the application to Scheme B. And, should Alice be accepted by Scheme A, she would have to notify Scheme B before they have made a decision on her application.
Question: Suppose Alice is offered Scheme A, how does she indicate this to Scheme B without prejudicing the outcome? Assume that Alice is willing to resign from Scheme A, say after six months or a year. Assume further that Alice stands a reasonable chance in both schemes. There is no guidance online about how this situation is resolved by the funding body for Scheme B.
TL;DR: What does one do if one receives a less prestigious offer while waiting for a decision on a more prestigious one?

I put some effort into making the question precise and (to my mind) clear. Do you have a specific problem with what I've written?  People who feel it is too long or too confusing are under no obligation to offer an answer. (And such answers would be of questionable value anyway.)

Alice should tell scheme B something like "I have won competition A, which shows that I am very well qualified for B."
I do not see how winning A can be all that bad for Alice unless A requires her to commit to stay for some period.  In any case, I think she should remember how fortunate she is to have A.

I do agree with you. Scheme A will require a commitment of two years, and leaving would be breach of contract. But such decisions are sometimes necessary. The concern is that Scheme B would be biased against Alice's application on the grounds that she might require some delay in commencing, or might be considered less likely to take up the funding for whatever reason.

Alice might consider using a "decision tree" to help her resolve the best route to take.
The following resources will aide Alice in making informed decision based on her odds of being accepted (within reason) to B, the risk of rejecting A and not being accepted to B, how much she values the prestige (and pay) of B, and any other relevant factors Alice considers important.
http://vserver1.cscs.lsa.umich.edu/~spage/ONLINECOURSE/R4Decision.pdf
http://www.mindtools.com/dectree.html
http://en.wikipedia.org/wiki/Decision_tree#Advantages_and_disadvantages


text:
What kind of administrative duties might a postdoctoral associate be expected to take on?
Applying for a postdoctoral research role in the UK, the application says I should demonstrate willingness to take on administrative tasks. Can anyone tell me about what kind of administrative tasks a postdoctoral research associate might be expected to take on? Does anyone have any experience? I'm trying to tailor my application, but I don't want to go into depth on administrative experience that might not be relevant to the role.

I think you need to find out exactly what they are expecting from you.  I would normally associate postdoc positions with research duties rather than administrative duties.  Some exceptions that I have known involve postdocs who are expected to act as the supervisor for a number of graduate or undergraduate researchers, but these are unusual cases.  Contact the people offering the position, and find out what exactly the administrative duties mean: otherwise, you won't know how to tailor your application, and (more importantly) you might end up in a position you really didn't want!

I agree.  Also I want to say: asking intelligent questions about a position shows interest rather than ignorance.  Potential candidates should not hesitate to ask.