text:
How to build a better positive image of yourself to your Ph.D. advisor
I am currently a first-year Ph.D. student taking a course sequence with my Ph.D. advisor. The first class of the sequence went really well, however, the second class is not going as well.  The most notable instance is I copied down a problem incorrectly from the homework prompt.  This is the first time in my life I have ever done so, and I was extremely embarrassed about it.  An embarrassing instance outside of the class was during a one-on-one discussion.  He asked me a question, and I froze and could not think correctly, and said a factually incorrect thing.  With the combination of these things, I am beginning to worry my advisor thinks I am stupid, and thus not cut out for a Ph.D.  I think one aspect of why I am so nervous around him is he's extremely famous and I think that gets to me.
Anyway, I was curious if anyone had suggestions on how to proceed with any of the two instances I mentioned to help me improve my situation.

Everyone makes mistakes. You are fine, and probably overthinking this.

Does this answer your question? How to effectively deal with Imposter Syndrome and feelings of inadequacy: "I've somehow convinced everyone that I'm actually good at this"

Yes, as @Roland says, even if your advisor is extremely expert, competent, quick, etc., hopefully they are not aiming to kill-and-eat you... but maybe help.

Don't try to build an "image" that is different from how you actually are, especially with your supervisor
I would counsel against the idea that you should be trying to build a positive image with this person at all.  In particular, you should not be trying to build an image that presents you as more competent at your work than you actually are.  The purpose of a PhD supervisor is to train you and assist you to improve, so if he has an image of your competence that is more favourable than your actual competence then it will harm his ability to assist your learning.
You are only in the first-year of your PhD.  Accept that you are a novice and that you are in training to attain basic competence in research.  Don't be embarrassed about making mistakes in front of your supervisor and don't worry about the "image" your supervisor has of you (see related question and advice here).  Let me put you at ease --- your supervisor almost certainly views you and all your peers as incompetent, which is how almost all PhD students start out.  Focus on learning and practicing your research area, making mistakes, learning from those mistakes, and improving your work.  As you go through your PhD program you will get more competent and your supervisor will keep track of your progress.  Focus on substantive learning and improvement and don't concern yourself with your image.  You will have an entire career to build up a positive good image through good quality work.

While I agree fully with this answer, especially the first paragraph, I have a small quibble with the notion that "your supervisor almost certainly views you and all your peers as incompetent," since if this were the case it's unlikely any of you would be in the program at all. I haven't yet advised students so I could certainly be wrong, but my sense is that while advisers may (and should!) view students as inexperienced and in need of training, it doesn't seem plausible that an admissions committee would admit a group of students whom the committee members judged to be incompetent...

I think we're just using a different bar.  Since the purpose of the PhD program is to train the student to be able to conduct independent research, presumptively, the student would not be competent to do this prior to the training program; hence the diagnosis of incompetence (in the skills that the academic already has).

Ah, yes. I was originally reading incompetence as general ineptitude or incapacity rather than lack of competence in a particular skill.

Take responsibility and move on.
You cannot do anything to change what has happened in the past, but you can learn from what has happened. If your advisor chooses to dwell on what has already happened rather than evaluate you based on your current progress, you might consider giving less weight to your advisor’s opinion since they are not assessing you with relevant and current data.
If you feel is is helpful, you could offer an explanation or apology for your errors. And if your advisor asks about the situation, you should talk about it. But unless this awkwardness is impeding your work with your advisor, I doubt it is necessary.

Embarrassing things happen all the time. I’ve blanked on factual questions in areas that I know really well, and I personally have evaluated it as being nervous on my part. Since then, I’ve tried different strategies to prepare better for meetings so I’m not caught off guard. Was it embarrassing? Absolutely. I’m sure my advisor found it odd and supplied his own narrative for why it happened. Take responsibility and move on.
I’ve also made mistakes in copying information and have had a misunderstanding based on my lack of proofreading. This is usually solved with a remark to the effect of “Looks like I copied that wrong, I’ll make a note to fix it on my own time.” Take responsibility and move on.
Both of these situations were embarrassing, but I hope they demonstrate that 1) you are not alone in not being a perfect person and 2) they are not career-devastating mistakes that color your advisor’s opinion of you as a good student.

If that's the first time you've copied a problem down incorrectly, I'd bet you're the type of student whose conscientious work is obvious to your advisor and other professors in your department (whom you should also be developing relationships with, even at this early stage, btw). Also, keep in mind that admissions committees (especially in departments that can attract "famous" professors) don't casually accept students; if you weren't cut out for it, you probably wouldn't be there to begin with.
In any case, no reasonable advisor would expect a first-year student to get every fact right or never make mistakes. In the unlikely case your advisor does happen to have those expectations and/or does think, based on two inconsequential mistakes, that you're not cut out for the program, you have plenty of time to find a new advisor, which is not at all unusual. More importantly, it sounds like you may be assuming the advisor thinks these things, since you don't mention any specific reaction he had that indicates as much. But even if he did give some feedback or correction, keep in mind that giving feedback and critique is what they're there for, and receiving that critique and advice is what you're there for. It's crucial for survival in grad school that students not take criticism personally—after all, if you're planning to be an academic at least, proposing some idea and having other people critique it is pretty much what you'll be doing for the rest of your career. If your advisor did give some clear indication he's displeased with your progress, you might consider explaining the circumstances or somehow remediating the situation—but if there wasn't an explicit indication (and even if there was) he's probably forgotten about the whole thing by now. You're likely better off just keeping on with the hard work and reminding yourself as often as you can that you belong there and that all grad students who aren't egomaniacs are constantly wracked with self-doubt and that you're probably doing just fine.
But here's the most important thing, which I don't think most grad students (of which I am one) realize soon enough*: the professors are there because they want to teach students! If you showed up and knew every single thing perfectly before your first year was over, their lives would be pointless (slight exaggeration, but still). Being a professor is about teaching people things they didn't know before and guiding students in their acquisition of knowledge, so don't feel bad when that occasionally happens. A good advisor will genuinely enjoy feeling like they're actually contributing to your development from student to colleague, and your making mistakes early on is part of that process.

*I didn't figure it out on my own; I was lucky that someone very wise told me this when I was distraught after my first teaching evaluation (which in retrospect was actually full of constructive feedback, which I took as harsh criticism simply because it included room to improve).

I'm also a first year PhD student so I get the pressure to feel impressive to your advisor. That having been said, I think the best advice is to try not to take your small mistakes too seriously. Everybody freezes and everybody misses homework questions. As long as you're putting in the effort (and if these mistakes are bothering you enough to ask about them on stack exchange, I bet you're the hard working type) you're advisor is going to see it after a little while.
In short - try not to be too critical of yourself, I really doubt your advisor thinks you're a bad student because of them. If not already, in time your advisor will recognize your strengths and see you're a valuable student. Just be patient and keep the faith.


text:
How to write papers fast and efficiently?
First, my question is not about how to write a good a paper, since there are already many guidelines on the internet, e.g. this one.
What often happens to me is: I designed algorithm, did all the experiments, and got good results. Now, I only need to write up the results to submit. But I just feel I can't do it, or at least not efficiently.
Although I have everything in my mind, I just stare at the screen and can't write anything. I just can't do it. And this leads to procrastination, which I hate so much.
Sometime, when I was doing the experiment, I thought I should write this way in the paper, and it should be very awesome. But when I actually wrote the first few sentences, they were just crap.
I thought I would start by describing the core algorithm first. But I didn't know how to present the idea, so I ended up polishing the introduction first, etc.
I'm not a new researcher; I'm already nearly one year into my post-doc, and have 6 papers published. It never took me less than a month to write just a 10-page paper, after several iterations, while some of my collaborators can write a paper in just a couple of days.
I thought it would be better with experience, but it didn't and I'm really frustrated with myself.

UPDATE
I think I'm suffering from the so-called ''blank page syndrome'' (or white page syndrome), but I'm not sure.

in addition to the "how to write a good paper" advice you mention, there is also a lot of "writer's block" advice.

I think you should be more concerned with writing a paper well than with writing it efficiently.  Lots of "fast" papers aren't well written.  That said, have you tried outlining?  And maybe writing the introduction last?

It seems like you are overthinking it and also thinks it is easy to churn out good papers quickly.   This is only true if you have a standard template you have developed over the years, the ideas are crystal clear in your head, and no problem with the English language.  Otherwise, I would do a brain dump, throw it away if you have to, but continue to iteratively churn out better versions.

One month is a reasonable time to write well a paper.

I would suggest reading the book Publish and Flourish.

Somebody emailed me and asked about the book Publish and Flourish. Here's the link to the publisher's page: https://teaching.nmsu.edu/academy-bookstore/

A more general term for "blank/white page syndrome" is writer's block. Having said that, if you have that issue, it's mild. Producing quality work requires spending enough time. I would be happy to churn out quality papers at the one per month pace. As for staring at blank screen (which is a sign of the writer's block), I recommend a simple, but quite effective, strategy, which I call the extended plan approach: start by writing down a plan of what you're supposed to write and then gradually expand it with details of increasing level.

(Obviously this one won't apply to papers already in the pipeline) Keep detailrf research notes as you do work. Write a barebones introduction with your key ideas for why you are starting the project when you start the project. Write little summaries of key results as they come in. Keep the note up to date, and in a state that you could show it to a colleague to get them up to speed if needed. This note will note be a paper, but by the time you get to writing it up for real you won't be starting with a blank page and you already will have had to explain some of the most technical parts.

Don’t give in to the temptation to write a ‘paper for the ages,’ that’ll get you stuck overthinking and premature polishing. Pick an initial audience, say your advisor or a classmate or the department chair,  for example, and write to that audience. Once you’ve explored your content, circle back and rewrite and tailor for the audiences of the journals you have in mind. Fast and efficiently come with experience and practice.

I'm not sure if it helps, but here are two ideas that work for me (sometimes).

Don't try to write the paper in its order. Instead, start from the technical parts. This is simple - it is just writing your algorithm. Now, once you try to write the algorithm (and abstract it from code into pseudo-code), you will get stuck because something is missing (notations? a neat observation? a cool idea that makes things clearer?); note these down. Then, expand on the things you wrote down. Another way to begin is with the "cold" facts: the numbers, the experiments - just write the details down in the most dry way...  (After the technical parts are written, move to writing the introduction and conclusion; by that time, you will have already broken your "writer's block", and the writing will flow much easier).
tl;dr start with the most simple (and technical) parts just to make the writing start.
Writing a paper is telling a story. You can't write it down? Try this - tell "the story of you paper" to someone else, say, a colleague or a family member. Do this twice or thrice, until you have a complete "story" in your head, and you gained some practice in telling it. Now, writing it down (just following the conversation you had with real people) may be way more simple.

Addendum: This is not a competition. Writing a paper well, takes about a month. Writing a good draft takes at least 2 weeks (of intense work!). Of course, some people can pull an all-nighter and come up with a paper. Don't pay attention to those, they are at the tail of the distribution.

Ran, thank you for the information. I end up writing most of my papers (4-6 pages usually) within a day or two, and I come out of it frazzled and really frustrated. The paper is good, but man do I feel it. Could it be, that I'm slave-driving myself to write something too quickly, causing the frustration? I absolutely hate writing due to this.

@DanChase As different people behave differently, I can only share with you my experience. My usual writing throughput is 1-2 pages in a day of intense work, after which I'm quite exhausted and ineffective. Note that I'm not a native English speaker so obviously my pace might be on the slow side. Such a day of writing consists of a lot of revising, editing, and pondering on each written sentence. Maybe just try to slow things down and see if this works for you?

I got around a similar problem by using a top-down approach:

Leave your desk, go outside, and take a walk. Return when you have decided on the overall story the paper is going to tell.
Write down placeholders for section headings. You can change them later. They just describe the high-level structure of the paper for you.
Write down subsection headings. You're probably not going to use subsections in the final paper, but the headings help laying down the second-level structure of the paper.
Describe the contents of each subsection with a few bullet points.
Write a little bit every day. Finish one subsection in the morning and another in the afternoon. Spend the rest of the day doing something else. Remember that the other subsections don't exist, and writing them up is not your problem.
After a couple of weeks, you have the first draft of the paper. You probably didn't spend more than a couple of days on it.

The natural order of writing a paper is often different from the natural order of reading it. My typical writing order is something like definitions and notation -> technical background -> results -> experiments -> conclusions -> introduction -> abstract.

I had the same problem. My solution is ridiculously simple: just write every day.
Recipe: You write every working day a specific number of words. Start with a small amount, say 150-200, and it can be any part of the paper you are writing. When you start, most of it will be garbage, but that is fine. You can re-write it the next day and that will likely go faster and smoother. As your "writing muscles" develop, the quality will become better. When I had this problem, I had to start my day with this writing task, which is what I would recommend for you as well. Also, very important: no vacations from writing days until you have mastered the skill.
I hope this helps.

Based on my experience it helps to have the introduction and prior works at least somewhat taken care of. Then you can focus on writing up your algorithm. I do this by:

Reading at least one article every 2 days and write about its strengths and weaknesses. Save this abstract somewhere - like Zotero or Mendeley notes.
When you start to write your paper, chose the most relevant from the prior works that you have already read.
Get the abstracts you wrote, paste in, edit.

If you use this method you will know the relevant prior works, and have a lot of the introduction already written. After that you can focus on the fun main contents. The only hard part is writing the abstract every two days.

BibTeX Anote/Annotation fields are good too, for storing notes on papers.  (If you are a pure BibTeX user, or using something that directly maps to BibTeX like JabRef)

The "ridiculously simple" solution offered by @Aolon is, I think, borne out not only by the experience of many authors from all kinds of backgrounds and with all kinds of material (novels, short stories, poetry, etc.), it is also one of the lynch-pins in the approach described by Wendy Belcher in her book Writing Your Journal Article in 12 Weeks: A Guide to Academic Publishing Success. If you aren't familiar with the book, I suggest that you get a copy. If you know of it, but believe that it could only be relevant to inexperienced writers, then I would like to disabuse you. Moreover, you should not be put off the idea of working steadily through the book while you write at least one paper, even though you want "efficiency" as your primary outcome. As Belcher remarks in the book, she's had many academics say to her, "I haven't got 12 weeks; I have to write my paper in a week". The fact is, that the tools in the book will help you to write any paper more efficiently that you are likely to be doing currently. I commend it to you.
There is one other point that I'd make which links @Aolon's remarks to your own. You remark that you "designed algorithm, did all the experiments, and got good results. Now, [you] only need to write up the results to submit". I would suggest that if you wrote every single day, no matter whether you think you have much to write about or not, then you would already have a considerable amount of written material about your algorithm, your experiments, and the results that you would be revising and amalgamating to turn the pieces into a thesis, journal paper, or whatever. This is not intended as a criticism; rather, I'm pressing a point made by Wendy Laura Belcher. Namely, that it is a mistake to believe that writing, thinking and doing experiments, are separate activities. For many people, writing is thinking. We discover what we think by writing. And if you're working every single day on writing something, whether it's directly connected with your thesis or not, you will become more efficient. Sure, work on the easier (non-argument) parts first, but write something every day. You don't become an efficient craftsman by slogging away with blunt tools; it is by sharpening the axe of writing that you will be able to cut through your task more efficiently.

Nice, I did not know this (I learned this from my music teacher studying composition). I will look up the book you mentioned, it looks very interesting.

Adding on to what other answers have already said:
The 'trick' to writing your paper (or any other 'end product') is to let go of the idea of the end product when you are stuck. Write ANYTHING when you start out. Even if it is "I need a paragraph where I am going to discuss the idea behind the algorithm".
Anything goes to get text on the page to get over that white page bump. There are all sorts of things that can help here (like the writing x words a day, just let go of the thought that those words need to be perfect or final), including recording yourself to tell the story and then transcribing that into written text. Anything that works for you - and this is wholly personal. Some people like an outline and depart from there. Others like to dump any random thought on the page and then structure those as they go (I'm in that category).
A good first draft is a bunch of text that you can then start editing and shaving. Style, perfection, etc. - all of that comes later. You mould that mishmash of words into the final product and that takes time and effort - even people who seem like natural writers will spend time polishing and polishing and polishing. It's after the first full draft that the real work starts, so just try to get to that stage in any which way you can.

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text:
How to stop spam from ConfDriver of TU Wien?
This year I submitted a paper to a conference that used ConfDriver of TU Wien. From the time of submission, I started receiving a lot of CFPs from conferences that also use ConfDriver.
All the conferences seem solid, and the emails are from researchers of well-known institutions. However, I find it really annoying, because they are completely unrelated to my research area, and sometime unrelated to Computer Science.
There is no option to "unsubscribe" to these kinds of CFPs, and there is nothing in common to make a filter in email client.
By the way, I find ConfDriver much worse than EasyChair, and it even doesn't notify the co-authors when making (or updating) a submission.

UPDATE
I understand that some people from TU Wien may be upset with this question. But what this ConfDriver is doing is really spam, and it is really annoying. Unlike spams from junk conferences, this kind of spam is much more difficult to block, since the emails are from well-known institutions, e.g. MIT etc.

I'm voting to close this question as off-topic because it is about how to use spam filtering in an unnamed email client

@EnergyNumbers: I do know how to use spam filtering, but in this case it is impossible to use it.

There is no option to "unsubscribe" to these kinds of CFPs is unclear to me. Most of the CFPs I received has the option to "unsubscribe" either at the beginning or at the end of the e-mail. Did you check? Or there are too many those e-mails you didn't bother to look at?

@scaaahu: I check both in the CFPs and in my ConfDriver account. I can't delete this account, because there are solid conferences in my field which are using this system.

The "Dexa Conference" was set up at the TU Wien using ConfDriver. The website notes that "In case of difficulties please contact confdriver@ifs.tuwien.ac.at". Maybe you should give that a try.
BTW, ironically one of the workshops was about "Defence against Spam in Electronic Communication".

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text:
Should I put two loosely related results into one paper?
I'm working on a problem A, and recently have two small results:

The first result is using technique X for A1, which is a particular instance of A. A1 is a long-term problem, but nobody has used X for it before, and I achieve slightly better performance with it. In other words, it is only an incremental result.
The second one is solving A2 using technique Y. A2 is totally new problem that nobody has touched before. However, the method is extremely expensive, and only works on toy programs.

Since both two results have clear weaknesses, and we don't know how to improve them, my advisor is suggesting me to put the two results in one paper to submit to a major conference, since each of them is not enough contribution.
It is only a suggestion and I can decide whether to do it, there is no problem with the advisor. I'm only confused if it is a good idea to do so. My concerns are:

A1 and A2 are just loosely related. It is difficult to tell a story that connects these two problems.
The first method is only applicable for A1, the second method is only applicable for A2, while they are different instances of the problem A. Putting them together poses another weakness: the usability of each method.

The other option is of course: submitting them separately to lesser conferences. We only want to do this if the first option is not promising.
Some context: my advisor is a leading expert on X and Y, but knows very little about A (but wants to explore). On the other hand, I did my PhD on A, and only have some minimal background on X and Y. I'm a new postdoc, hired to work on A using the tools for X and Y that my advisor had developed. Therefore, none of us are 100% sure about what to do in this situation.

http://www.phdcomics.com/comics.php?f=1678

Could you say what field you're working in?  In my field (mathematics), this strategy would be a poor one: if you have two results that individually could not be published in a certain venue, then unless they fit together synergistically to make a stronger result there is no way that a paper which contains the two results together could be published in that venue.  Also I'm confused as to why two small results would be suitable for publication in a major conference.  Finally, you have a PhD and an advisor?  I'm a bit confused about that.  Is your advisor a coauthor?

Let me follow up by saying that there is no inherent problem in publishing a paper containing loosely related results: that happens commonly enough; one just does not (in my experience, in my field) gain any advantage from doing so.  In my experience, papers are evaluated primarily by the strength of the best result in the paper and secondarily by how much space they spend establishing that result.

So if you have two minor results of about the same strength and length, you might as well try to publish them together: it's less fuss for you.  The other alternative is to tuck a minor result into a paper which has other, better results.  As long as this doesn't take up an inordinate amount of space, referees are unlikely to object to the inclusion of the result, even if they don't care about it at all.  This is a good way to make sure that all of one's work gets published; certainly it's not as good if you want separate credit.  But if it's truly minor, how much credit do you want?

@PeteL.Clark I'm in Software Engineering, which is easier and less rigorous than maths. I'm a new postdoc, and my advisor is my boss. Maybe I used incorrect words due to my poor English.

@qsp "easier and less rigorous": setting aside whether or not this is true, it doesn't mean we're interested in publishing papers containing unrelated, unexciting results.

Just reading and trying to understand your question made my head spin, most likely due to use of generalization (X, Y, A1, A2), but not only that. Therefore, IMHO, the safest approach to solving this dilemma is to separate results into two papers. The rationale for this approach is the following.

Each paper would have a clear and, thus, easily understandable scope, goals, methodology, results and their interpretation. That would significantly improve readability and overall quality of each paper and chances to form a positive impression.
Since the problems A1 and A2 are "loosely related", shoving them into a single research study simply doesn't make sense from an architectural / logistical / layout perspective. It would be very difficult to present two sub-studies in a synergistic manner ("tell a story", as you put it).
Based on the above-mentioned points, I don't see how combining the studies would make the resulting "study" of higher quality, thus, warranting a publication in a more major conference. Quite the opposite most likely would be true (due to coherence and, thus, readability issues).
Your advisor's recommendation in regard to improving your work is quite strange, to say the least. It is based on the assumption that combining two studies of different scope/topic with weaknesses would make the resulting "study" less weak. If anything, it would make it even weaker, since weakness is one of multitude of characteristics, exhibiting additive properties.


text:
Did the Emperor of Japan really write a paper?
I just ask this question out of curiosity.
I would like to hear opinions from researchers in Japan about this paper:
Speciation of two gobioid species, Pterogobius elapoides and Pterogobius zonoleucus revealed by multi-locus nuclear and mitochondrial DNA analyses
The first author is Akihito, unless there is another person with that single unique name at that unique address.
Did he really contribute anything to that paper? Note that he doesn't have any degree, and he was 82 years old when that paper was published.

Updated:
I'm asking this question because the author is an emperor, i.e. somebody with immense power.
An author with similar level of power was Elena Ceausescu. She only finished primary school. However, during the communist period, thanks to her dictator husband, she had a PhD, countless of papers and awards etc etc.
That's why I'm asking people in Japan. I do know how to use Google.

Did you Google it? https://en.wikipedia.org/wiki/Akihito#Ichthyological_research

@AzorAhai my question is: did he really contribute anything to that paper?

This is probably better at Skeptics.SE, though the answer seems readily obtainable. Besides being listed as first author, though, it is likely to be difficult to know objectively his specific contribution to that one individual paper (as is true for any author, even when contributions are listed in the publication); however, it is consistent with his prior publishing history so I see no immediate reason to doubt it.

He has a whole bunch of papers, so he probably did have something to contribute to that specific paper, but only its authors will know the full story on that.

This reminds me of the question about Obama's paper.

Re: "immense power", it's worth nothing that modern-day Japanese emperors are essentially symbolic figureheads with very limited political power.

I knew that his father published papers in marine biology; news to me that the son does too.

The members of the Imperial family do make an effort to educate themselves and they generally do research (often in biology) as tradition. Off course, generally in private settings, but they actually do the legwork. I know a European zoologist who hosted one of them for a week or so on a research visit.

I suggest you discuss specific papers on Pubpeer.com instead of SE communities.

According to the Indian embassy of Japan he did author a similarily titled paper in 2008: link (titled Evolution of Pacific Ocean and the Sea of Japan populations of the
gobiid species, Pterogobius elapoides
and Pterogobius zonoleucus, based on
molecular and morphological analysis), so it is a safe bet that the paper you are asking about is authored by His Majesty as well.
The Internet also confirms he specializes in ichtyological research.

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text:
Pros and cons to submit a poster?
Our paper is rejected, but we are invited to submit a poster. We are given two options:

Poster with 2 pages proceeding.
Poster without a proceeding.

Another option is, of course, not submitting at all.
We still want to submit the full paper. What is potential risk of submitting a poster, with or without proceeding? All the conferences we want to target adopts double-blinded review.
I'm in software engineering.

It depends on what you want, and can, get out of that conference. I am from sociology, and in sociology proceedings do not count as publications. So I do not care whether I were in one or not. I heard that in other disciplines this is very different.
I attend conferences to network, to get inspired by others, and to get feedback from others on my own work. Networking happens at the breaks, and to get inspired I go to other talks and posters. So for those it does not matter whether I present a talk or a poster. For getting feedback I found that posters allows for a much more direct interaction with the audience. So even though they have lower "status", I found presenting posters often more fruitful then giving talks.


text:
From whom do prospective grad students get recommendation letters?
Most top graduate programs require at least 3 recommendation letters. Do students who apply to such programs (and have a reasonable chance to get in) typically have such extensive research experience that they know three professors who can write in detail about their research? Or is it more common for such students to have some recommendation letters from faculty who can confirm that the applicant is competent (for example because they did very well in their class, won an award, ...) but with whom they have not worked much personally?
I understand it would be ideal to get all letters from faculty with whom you have worked closely on a research problem. But I wonder how commonly this actually happens, especially considering the fact that the final undergraduate year typically cannot be taken into account for applications in fall.
If it depends much on the discipline, I'm in physics.

It's totally fine to have mediocre letters (e.g. from relevant professors whose classes you enjoyed and did well in). Just make sure there's at least one stellar one in there about your research.

I had two from professors I did research with and one from my internship boss.

In general, I don't think all that many students have three unique reference letters, all of whom can vouch for research ability. Two is quite common, as most undergraduates who pursue graduate degrees (at least in the sciences) do have some research experience at their home universities. Many of them also pursue a summer research project separate from their main undergraduate research project (or projects), providing another reference.
But I do agree that the third letter usually comes from a non-research source. I wouldn't even necessarily expect a third research letter.

I have reviewed PhD applications in Communication, Computer Science, HCI, and Informatics. I'll answer questions first:

It is not typical, in my experience, for students who apply to programs to have three faculty write letters that speak directly about extensive first-hand experience working on research with the candidate.
It is most common, in my experience, to have one or two letters from faculty with extensive first hand experience overseeing research (often a coauthor on a paper) and one or two letters from people who know the candidate somewhat less well.

You don't need every letter to give a first hand description of your research experience. If you don't have anybody who talks about it, it will be a problem.
You want letters from people that:

Describe your ability to do excellent research in the area or field you are applying.
Explain how you are very smart, skilled, hardworking, generous, easy to work with, etc.
Demonstrates enough history and experience with you that we can trust the opinions expressed in the letters to be informed and accurate.
Are from colleagues whose opinions the letter recipient will know and respect.

Not every letter needs to do every one of these things. The  important that the entire package convinces the reader that they're not taking a risk by accepting the student. Do what you can. If no one person can say everything, it's totally OK to the fact that you're turning in multiple letters to give a more full picture.

Nobody expects every letter to do all of these things. — Maybe not in your department/field.

This is a useful answer on its own, but does not really answer the question.

@JeffE Could you please add an answer corresponding to CS then?

I reworked that sentence. I suppose somebody might expect that, even if I think it's silly for them to want that. I changed it to say "Not every letter needs to do every one of these things."

@Onsager I've added text to more directly answer the question.

Which field are you in? In the humanities and social sciences, we expect letters from faculty you've taken seminars in, not just your thesis advisor.


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How far will my Masters counterbalance low undergrad GPA in PhD applications?
I'm currently pursuing a Masters degree in Philosophy at a top UK university, and as my grades currently stand, I'm looking to graduate with a Distinction.
During my second and third years of undergraduate study, I was struggling with diagnosing and dealing with a medical issue. Unfortunately, this affected my grades in several modules throughout those two years. My undergraduate degree transcript features a patchwork mixture of Firsts, 2.1s and then a couple of those 2.2 grades. As a result, I graduated with a low 2.1 overall. Of course, this is all documented, supported by my physicians, and my supervisors were aware of my situation.
My issue is that I am now in the process of preparing to apply to PhD programs in Philosophy. I am hoping to apply to several Canadian institutions to be closer to family, but I will likely apply to some UK institutions too. I can see that GPA is an important factor in the admissions process.
My questions are:
How far will my undergraduate underperformance be likely to affect my chances of admission, and what can I do to strengthen my application to these programs in light of this?
Will my strong Masters GPA be enough to counterbalance my undergraduate transcripts?

@Science12345 No, it doesn’t mean that. 2.1 and 2.2 are upper and lower second-degree honors levels.

Welcome to Academia.SE. This is a question tha is very similar to existing questions on the site, so please have a look at the indicated link above for answers that can help you.

@Science12345 It’s a duplicate for SE purposes. If there is a vastly different answer for a specific field, it could be mentioned in the linked question above. It’s better to have one main question with inbound links from duplicates rather than separate questions everywhere.


text:
How do top graduate school in Mathematics view BS (Mathematics) from a top engineering school?
One of top engineering institution in my country offer Bachelor of Sciences in Mathematics. They start actual mathematics (Real analysis, Abstract Algebra etc) from sophomore year. By the senior they offer graduate level classes and I am sure I won't run out of it. However this school is primarily known for CS undergraduate program. Every year one or two graduating CS majors go to the best graduate programs (CMU, MIT, Stanford etc). As I want to major in pure mathematics I am pretty skeptical how top graduate programs (Princeton, MIT, Harvard) will view my application as they will be unsure of the rigor of Math degree at my institution?

Math is math. The admissions committee will have a way to view your background. This depends on the school.

Well, it really matters much more how YOU did. But then AFAIK good CS schools with math departments are almost always decent math schools too (can't think of a counterexample off the top of my head), given the history of CS...

If you're doing proof-based real analysis and algebra by your sophomore year, you're doing superbly. Many well-regarded schools don't introduce such coursework until the third year, opting to spend four full semesters on calculus. Sometimes the ultimate or penultimate semester is replaced by an intro to proofs, discrete mathematics, or linear algebra course, but the effect is the same. One of the major draws for me going to my undergraduate institution was that the norm was for mathematics majors to do real analysis their second year, with exceptional students starting little Rudin on day 1.
The extra year of advanced mathematics courses will be a huge boost to your application. You can increase this effect by demonstrating breadth and depth that other students won't be able to match. If you spend your first three years accomplishing the theoretical coursework that most students do, and then spend your fourth year taking, e.g., the graduate sequence in algebra, graduate courses in discrete mathematics and algorithms, and advanced undergraduate courses in functional analysis and algebraic topology then you've effectively demonstrated your ability to succeed in graduate level coursework. You'll also have a far deeper understanding of algebra and it's applications to computer science than the vast majority of applicants, and taking more advanced courses in analysis and topology lets you show that your advanced status isn't shallow or restricted to one area. And just in terms of a numbers game, you'll have ~12 advanced mathematics courses to other people's six (please correct these numbers if they don't make sense; I've only attended quarter systems schools and am not 100% on what numbers are normal).
Breadth and depth of coursework is a commonly used proxy for future mathematics success, and if you're able to take these fourth year graduate courses with professors you had already, then in their letters of recommendation they'll be able to talk about how you excelled in their previous courses and that they're excited to have you doing graduate work and that they expect you to succeed. Comments like that can go a long ways.
I don't think that you should be too caught up about the reputation of your university. In my experience talking to people who have served on admissions committees (note: I have never done so personally) is that, if they explicitly think about the reputation of a university at all, it is in very broad strokes that encompass dozens if not more universities per tier.
If this is an issue that concerns you particularly, you might find better success asking people at your institution who are more familiar with where you go to school than I am. One thing you should definitely ask is about what graduate schools other students like you have attended recently. This last bit is very important as, especially at a larger school, your outcomes and those of the average student are likely to be far apart.
In addition to talking to members of the mathematics faculty, you should also consider talking to any CS Theory faculty that you have. If you suppositions are correct, they're probably as likely or more likely to have written letters of recommendation for students who went on to top mathematics PhD programs. A sizable chunk, if not most, CS Theory people have mathematics PhDs rather than CS PhDs.

This seems like excellent advice. You should be fine. In fact, if applied math concerns seeped into your pure math experience you might be able to leverage that as an advantage. If your school is well regarded generally it should matter not at all that it's focus is more applied.

I'll note, however, that CS folks nowadays tend to have CS degrees more than in the past. But their teachers were likely mathematicians. Generational shift. I'm one of those old mathematicians who taught CS primarily.


text:
How can one overcome the disadvantage of studying in less prestigious international school for admission in top 10 Math PhD programs?
I am a international applicant. I study in fairly less prestigious undergraduate school. I am aware that this will have a affect on my Grad School Applications. Since I am freshman I was wondering of how I can minimize the disadvantage. I do think of four possible ways:

Taking toughest courses possible:
My school is kind of a unique model. It has very less permanent faculties. It usually borrows Math professors from other institutions in my country which sort of have a international reputation. They usually offer grad level courses known as electives. I do have the option of taking as many of them. I won't run out of these courses. However the undergrad transcript will not show the name of professor under which the class was taken. I am kind of skeptical how admission committee will judge these courses just by looking at name of undergraduate institution.
Amazing letters of recommendation :
Since good and internationally known faculty take courses at my school I do hope to get recommendations from them. This should
help but I am not sure how much.?
Budapest semester in mathematics and IMC :
I am sure BSM will help however will doing really good in IMC make my application better ?
Good honors thesis:
I do have the option of completing my honors thesis abroad at a different institution. Usually honors thesis don't contain publishable material however that's a matter of hard work. It won't be published before the application deadline but will a letter from advisor highlighting the work and results of my thesis do any good ?

Even if I check each one of the above box's how worthy and comparable my application will be to those from the very best undergrad schools ?

Looks like a good roadmap. But note that it is easy to make big plans and difficult to carry out all of them: BSM for instance is challenging and it would be hard to get good grades in it...

In previous questions and answers, people have mentioned (math) graduate programs asking applicants to list the textbooks they used in their classes rather than who the professor was.


text:
Do superficially encouraging statements within rejection letters for faculty job applications mean anything?
Over the past few years, I have written a lot of job applications for permanent academic positions. None of these have been successful. I have been interviewed a few times, but mostly I have received either no reply or a very standard rejection letter.
A handful of the rejection letters contain some kind of statement seeming to imply that although they don't want to interview me, the committee did like my application to some extent. For example, here's a sentence from one such letter I recently received (emphasis mine):

We received many excellent applications and although the search committee was impressed with your credentials, we have decided your application will not be advanced for further consideration at this time.

My question is: does this statement, and other ones like it, mean anything or is it just a bit of fluff inserted for politeness?
To put it in another way: should I infer from this that the committee actually was impressed with my credentials and that they sent this reply to only a subset of candidates they rejected? Or is this likely to just be part of a totally generic rejection letter and I should therefore infer nothing?

https://academia.stackexchange.com/questions/1303/how-should-one-turn-down-academic-job-applicants

It could be both an honest statement or generic fluff. Unfortunately, there's no way for you to distinguish both, and to derive useful information here. (Maybe unless they comment on specific things they found impressive, but that doesn't seem to be the case.)
The more informative fact are the rejections themselves. A single rejection means hardly anything, but if you only received rejections, there would be some problem that you need to fix. The fact that you got some invitations is indeed a good sign.

Of course we can never know for sure (+1). But in my experience these evaluations are usually honest - they would not want to give you false hope, or keep getting applications from unqualified candidates.

It is almost certainly an automated form letter.  It was very probably sent to every applicant to who reached the same stage in the application process.

This is obviously the right answer, and it doesn't take anything more than a cursory understanding of human behavior to grasp this. I'm surprised by the suggestion in the accepted answer that we "can't know" for sure whether it's fluff or not. Of course we "can't know" for sure whether the sun will rise tomorrow, but a betting man would be wise to put all his chips on it rising. The case is of course different if you were interviewed, but if not you can be as assured as you can about anything that it was a generic letter.

Of course I understand that the letter wasn't uniquely personalised. The question was whether the presence of positive statement confers no information or only a very small amount. I could imagine, for example, a situation where there is an intermediate shortlisting stage, and only candidates that reach the shortlisting stage get "the committee was impressed..." in their rejection letter. Or I could also imagine just sending everyone the same one, regardless of actual impressiveness. Hence the question.

IMHO, they all mean one and only one thing: you've been rejected and they would rather tell you something nice than to explain why exactly that decision was made or where you stood compared to other candidates. Note that they are not obliged to disclose their decision process, nor should you suspect any foul play in such cases. However, I would really appreciate some plain informative letter like "you were our #3 candidate out of 10 interviewed and #2 accepted the offer" much more. As to the phrase "impressed with your credentials", it could mean absolutely anything from admiration to shock.
Whether they wrote this nice thing to everybody or just to you cannot be determined with any degree of certainty unless you have a friend who applied to the same place and has been rejected too, but the point is that the only part that matters is "we have decided your application will not be advanced for further consideration", which more often than not (in my experience on the both sides of the hiring process) means that you were sorted out at step one of a multi-step process.


text:
Collaborator has shared a draft paper with a significant amount of self-plagiarism. Should I say something?
I am a theoretical physics postdoc. A while ago I began collaborating with a certain group of experimentalists on a joint project. This group has a good reputation in the field and I regarded the collaboration as a good opportunity. They work at a different institution from me and I am the only person from my institution involved in the project. My boss knows about the project but was happy to let me pursue it without being involved.
I sent my collaborators some calculations a while ago, which I believed should more or less wrap up the project and bring us to a point where we could write it up. They were a long time getting back to me - so long in fact that I began to assume they had lost interest in the project - but then out of the blue they sent me a draft paper and asked for my comments.
On first reading the draft seemed good. It gives an accurate description of both the experimental and theoretical results from the project. But then I went back and read another recent paper from the same group (which I was not involved with). I then realised that several paragraphs from the draft paper were copied verbatim from this other recent paper.
The paragraphs in question are from the introduction and methods sections of the paper. The draft paper and the recently published one are closely related in subject matter and the experimental part of the work uses a lot of the same methods, so to some extent I can understand why they may have regarded it as efficient to simply copy certain parts of the text over. On the other hand, I feel uncomfortable about this degree of self-plagiarism.
Is it worth making a fuss about this? I am very much the junior partner in this collaboration and getting this paper in collaboration with this group would be helpful on my CV, at a time when I really need to find a job. So I have incentives not to rock the boat too much. On the other hand, I know some people regard self-plagiarism very badly and if my name is on the paper I will be as much to blame for it as anyone else.

Not everyone knows that self plagiarism is an issue, so for many it is very natural to just copy from previous work. However, you should certainly mention the issue to them and recommend that everything be properly cited. Publishing the paper as is could bring comments, even condemnation, from readers and reviewers.

If the review is double blind (some are in my field) it might simply come across as straight plagiarism.

Journals nowadays run automated checking so they can be the ones to deal with it. Also, if it's an expanded version of a prior paper, and their subsequent paper will have a note of this, what they are doing is perfectly acceptable. So you don't know enough to decide yet.

@ASimpleAlgorithm Huh? What information do you imagine the asker here is missing, as a collaborator on the second paper who has access to its full (draft) text? I presume that if it were indeed an expanded version of the group's prior paper and explicitly framed itself in those terms, the OP wouldn't've asked this question in the first place, or at least would've mentioned those facts.

You do not need to make a fuss, or mention "plagiarism". All you need to do is to recommend adding a reference to the copied paper for each paragraph in question. That is a legitimate review comment, proposing an improvement in the draft paper.
Andreas Blass, in a valuable comment, suggests something along the lines of "The following description of our methodology is taken from [17]" or "Our methodology is the same as in [17], described there as follows" is adequate, without needing to also put quotation marks around the quoted description.

Actually, not mentioning plagiarism is a failure to educate. People who haven't even heard of it (a lot, possibly, especially older researchers, as it is a fairly new concept of interest) need to know. If you give them a solution without the reason behind the solution they have no way to know what is expected these days. Make a bit of a fuss, at least.

I don’t think this is sufficient. A copied paragraph should be enclosed in quotes, As a citation implies you used the ideas, not the exact words.

@Dawn It depends at least somewhat on the sections in question. Especially methods paragraphs, there is little to no reason to change a perfectly cromulent statement just to be different from previous papers. There may only be one way to state what you did.

@AzorAhai, It isn't a question changing the wording, but one of citing the previous work correctly and quoting it.

@Buffy Right, but there are "boilerplate" phrases that my group will use from paper to paper because they are the best way to describe that section of the methodology. They aren't usually cited (because there's no need to cite them, you're describing the methods independently) or quoted. This is typical in my field, although "several paragraphs" sounds like a large amount. But, I'm not in physics.

Does a relatively junior co-author have authority and responsibility to educate more senior co-authors? All co-authors have responsibility for ensuring any source papers are cited correctly.

@AzorAhai In theoretical physics, there's always a bunch of non-novel information in terminology and definitions that needs to be (mathematically) precise and consistent. Modifying the text to gratify some aversion to "self-plagiarism" risks introducing errors for no real benefit. Omitting things with reference to a previous work is sometimes done but risks alienating readers; who wants to cross-reference definitions between papers? What if the reader doesn't even have access to that previous paper?

As far as I can see, you and your co-authors just need to make it clear that the material in question is copied from their earlier work. I think  something along the lines of "The following description of our methodology is taken from [17]" or "Our methodology is the same as in [17], described there as follows" is adequate, without needing to also put quotation marks around the quoted description.

@Andreas Blass I agree that this would be a suitable way to handle the methods section. I still think the intro should be reworked.

@AndreasBlass I think your comment is too use useful to leave as a comment,  you should either turn it into an answer, or edit it into this one

I agree with @AndreasBlass's comment, and have edited it into my answer with acknowledgement so that it will not get lost.

I would say something like, “I’ve noticed some reviewers/journals reacting negatively to using text from previous work verbatim. Here, I have suggested a rewrite and citation to address that potential issue.” Then actually rewrite the paragraphs in question. If the original author was copying text, they were likely trying to write the paper quickly and would appreciate that you took the time.

As @Xerxes points out in a comment to Patricia Shanahan's answer, this would actually be a disservice to readers. They might be familiar with the 'plagiarised' paper, and start to wonder why the description has changed. Better simply to make it clear that the previous paper is being quoted verbatim.

@TonyK I can see how verbatim repetition may be useful at times in a methods section, however, I don’t see how the argument would possibly apply to an introduction. Furthermore, If I were going to replicate work, I would certainly look at the original method paper regardless of what I saw in the second work. Verbatim would not save someone extending the paper any time, so I really don’t see any downsides to AyalewA’s answer here.

If the draft paper is addressing a new (though related to the previous work) research question, the background/introduction should be tailored to the new research question/objective, and as such needs to be original based on citation of a set of related previous works. However, the methodology may, for the most part, be the same as the methodology of the previously published work. In that case, it is worth stating that the details of the methodology have been published previously and to cite reference to the previous work and provide in the present paper a brief and pertinent summary of the methods. As per this editorial,
"simply referencing the earlier paper" regarding the methodology may suffice, yet providing the pertinent aspects of the methods with referencing to the earlier paper may be more useful.
By and large, as per this article, if a new academic work involves some form of "text recycling" from a previous work, there is a need to clearly acknowledge that through reference citation. Besides, "...being somewhat lazy not to have attempted to rephrase/rethink previously written passages," seems worth avoiding (ibid).
However, when communicating with your collaborators about the need to avoid "self-plagiarism", you need to be wary (as pointed out by @Patricia Shanahan) not to tend to tell them that they have committed plagiarism but provide your inputs and forward your suggestions on how you feel the draft work can be improved.

A suggestion is to simply comment on it as if you already assumed they would (of course!) be fixing up those sections because they were at present verbatim copied from a prior paper. Under assumption that for a draft, they had put them there as placeholders for what type of information needed to go in those sections.

Great advice, especially on how to deal with the methods piece.

It's common to reuse text in a draft, especially when after all it will likely be similar whether it is rewritten from scratch or copied. I don't think it's a good approach because it affects the flow of the text, but I wouldn't mention it to the collaborator, I would just try to edit it into the same style.


text:
How do graduate schools in Mathematics view advanced graduate courses taken at a less prestigious undergraduate institution?
I am a junior undergraduate at a less prestigious school. I have the option of taking graduate courses. I am sure I won't run out of them. However I am skeptical of how committee especially top graduate schools in Mathematics view the courses taken at an unknown school. In my view these courses are as rigorous as a good school. I do hope to get few letters from instructors of these courses. Are graduate classes viewed equally irrespective of the institution or they won't do any good for my application as I am coming from a unknown school.?

graduate courses are not just about learning. They're also about forging relationships with possible mentors. Knowing something about a course before you take it isn't a bad thing.

For context: I am a relatively senior faculty member in a math dept at a fairly well-ranked state university in the U.S., ... and have been involved in graduate admissions, advising, etc., for 35+ years.
First, at nearly every (but not every...) U.S. university, the purely undergrad curriculum is a bit lightweight for people wanting to go to a serious graduate program. Thus, to have a more serious-looking undergrad transcript, it is highly desirable to have some "graduate-level courses".
Second, the content and demands of "graduate courses" vary widely. There is no enforcing authority, etc. But, at least, such things explicitly aim to address mathematics for future mathematicians, as opposed to just having some course-of-study for U.S. bachelor's-degree requirements. (Whose breadth is generally a good thing, but whose "major area" requirements are very thin by world-wide standards.)
So, no, taking grad courses at X versus Y are not automatically equivalent. But nevermind about that. Take as many, and as advanced, courses as you have available to you. And reading courses with faculty.


text:
Is there a difference between Top Tier and Second Tier graduate programs in Mathematics regarding tenure track?
I am unaware if this question has been asked anywhere on StackExchange before. However, I would like to know what is the major difference between a top 6 and a top 10 graduate school in Mathematics. Forex: Top 6 would include Princeton, Harvard etc. Top 10 would have a few more like Michigan or Columbia etc.
I know that it depends a lot upon quality of theses and advisor. But can a graduate from Michigan be better than someone from Princeton? Looking at the faculty of top schools this rarely happens. Usually, everyone at Princeton received their doctorates from Princeton itself or maybe Harvard. Harvard/MIT also have the same situation. So is it really difficult for a Michigan(or any top 10 school) graduate to get a tenure-track job at a very prestigious school like Princeton ?.

"But can a graduate from Michigan be better than someone from Princeton?": Indeed they can ;-)

What you could consider is that most of the teachers who do a good job in teaching many thousands of students don't have a PhD, and have not attended Ivy League institutions. What they do have is a passion about what they do and an attitude that the students respect. Many teachers find that students surpass them and are pleased for them.

@SolarMike, +1 for the last comment. If students didn't surpass their professors pretty often we would be on a downward slope to extinction. It is the most joyous moment of all, just as it is for a parent.

I don't think you have gone very deep into rankings. Certainly not deep enough to suggest any relationship meaningful for individuals. I've never heard anyone scoff at a PhD from University of Michigan. You are suggesting that the top graduate from some place is invariably less skilled than the worst graduate from some other essentially similar place. That doesn't happen in the real world.
But if your life goal is to be a tenured professor at one of the top six schools in the US, prepare for disappointment, no matter where you study or how good you are. The problem is that the total number of open positions at such schools in any given year is minuscule and the competition for those few positions is huge.
But you should also think about the following in choosing a graduate school, if that is why you ask. Many top (and other) schools don't like to hire their own graduates. It certainly isn't that they doubt the quality, of course. But they like to bring in people who may have fresh ideas, not having studied with the current faculty and been exposed for many years with their ideas primarily. This has less effect now than it once did as it is easier to collaborate across distance and even internationally because of the internet and cheaper travel.
But some schools do permit hiring their own, and many students prefer to stay around a place where they are comfortable, so such places can collect a faculty made up of their own graduates. But, even in these, I'll guess that a lot of those "from here" people went out into the bigger world and made their reputation there before returning "home."
On the other hand, there are some incredibly fine mathematicians at quite small and out of the rankings places who simply want to live and work in a "home" environment of a different kind. Princeton isn't, actually, the finest place in the US to actually live. Too many cars, too many deer ticks.
But there is more to life than the quality of the institution you attend or the institution you work for. Lots more.

This is quite a good answer (+1).  However, a comment: "Many top (and other) schools don't like to hire their own graduates."  I've heard this for more than 20 years (going back to my undergraduate days).  But after a similarly long period of observing who hires whom at college and university math departments: I am not aware of a school that hires its own graduates at less than the statistically expected rate, and I am aware of many schools that hire their own graduates at more than the expected rate.  I think the OP is correct that Princeton is such a school.

@PeteL.Clark, I don't know of any research on the topic for math. My "observing" is just personal, not statistical. But the statistics, if available would show a pretty small number, I think. Most institutions in the US operate under rules that require a national search for listed positions and make it difficult to advantage one person over another. Back when, I knew a post-doc who the university really wanted to hire so wrote a job description with just about every detail matching his CV except his name. They got one or two applications better than he was on paper.

Amendment to my statement: "I am not aware of a school" |-> "I am not aware of an elite school."  With regard to your comment about national searches: suffice it to say that I am well aware of that and do not regard it as working against my assertion in practice.  The search committee and/or the department faculty get to decide what it means to be best, and institutions can and do make reasonable choices that result in hiring more of their own graduates.

@PeteL.Clark It appears that there is only one full professor at the University of Chicago who received their PhD from UChicago (Kenig). There are 31 full professors of mathematics (32 if you count the president of the University) which is plausibly below statistical expectation: http://math.uchicago.edu/people/faculty/

But can a graduate from Michigan be better than someone from Princeton?

Yes, of course.  Consider how implausible the alternative is - that the sorting process as people applying to grad schools could actually succeed at sorting grad students so perfectly that the top 6 schools catch every top tier student and exactly those students.

Looking at the faculty of top schools this rarely happens. Usually, everyone at Princeton received their doctorates from Princeton itself or maybe Harvard. Harvard/MIT also have the same situation.

This addresses a very different question.  Only a small fraction of Princeton/Harvard/etc math PhDs go on to become professors at Princeton/Harvard/etc.
It's quite possible that the best students from Princeton/Harvard/etc are slightly better than the best students from Michigan/etc, and that the faculty at Princeton/Harvard/etc are selected mostly from that very top group.
But the range of students at the very top schools certainly has a lot of overlap with the range from the schools a small step down.
Also, even the most cursory investigation of the actual faculty lists at Princeton, Harvard, and MIT, would reveal that the premise is false - all three schools do, in fact, have faculty whose PhDs come from other schools, both schools that might be in your "top 10 but not top 6" and schools that aren't in the top 10.

So is it really difficult for a Michigan(or any top 10 school) graduate to get a tenure-track job at a very prestigious school like Princeton ?.

Yes, it is really difficult for a Michigan graduate to get a tenure-track job at a school like Princeton.  It is also really difficult for a Princeton graduate to get a tenure-track job at a school like Princeton


text:
Does high school success in Math have a correlation with Undergrad success in Mathematics?
I will start in freshman in a fairly good undergrad institution in August 2018. I am planning to major in Mathematics. However this school attracts the most brilliant high schoolers in Math. This includes IMO gold and silver medalists. Participation in IMO guarantees admission to this school. I have already planned to go to graduate school. However seeing the enormous competition I am pretty skeptical of my chances. Usually the best student of our school in a given year has a fair shot at Princeton. Looking at my result I might have barely crept in their freshman batch. I do have 1 month left, shall I start on standard Math textbooks like Rudin, Munkres, Dummit and Foote or are the IMO medalists way ahead of me?

There may be some correlation, but less causation than you seem to think...

Most likely, you will never in your entire college career be tested on your ability to do well on IMO problems. IMO success is mostly unrelated to one's ability to do meaningful mathematics research.

You are who you are. Don't be overly concerned about others. You will need to work very hard, of course, but the fact that others may be able to pick things up more quickly than you doesn't mean that you can't excel.
The fact that you were admitted suggests that others have faith in you. Have faith in yourself.
You can also try to find a study group with others at the new place so that you get additional exposure. Use good study techniques and never - never fall behind. Start early on assignments. Ask a lot of questions. I was once thought to be very smart because I asked a lot of questions in class. But in reality I just wanted answers that weren't apparent to me.
You might also try as much as possible to limit outside interests until you find your way in a new environment. However, agreeing with a comment by user aeismail, that doesn't mean to give up everything for academics. Spend several hours each week on something that contributes to your health, reduces stress, and engages your mind in a different way. I now use Taichi which does all of these things. As an undergraduate I practiced Judo several hours a week. I didn't get very good at it, but it was a great complement to studying. As a grad student I rode a bicycle with a local club - fast but not competitive. That was physically satisfying, but didn't have a mental element like Taichi does. But don't occupy yourself with trivia.
But yes, studying great books in advance ain't gonna hurt you any. I studied out of Rudin over 50 years ago and still have the book(s).
You might also find that some courses are more challenging than others Analysis v Algebra for example. That is natural as the core thinking processes and insights are just different enough that you can groove on some things and find others a bit more work. Put your best efforts where they do the most good.
Talk to your professors. Ask questions. Listen. Ask more questions. Correlation only matters for groups. You are who you are.

Why you ask questions:
Here is a story (real occurrence) from the University of Kansas about 50 or so years ago. A prof, quite well known and respected, was lecturing in Topology. This meant writing proofs on the board. Occasionally a step wouldn't be filled in with the statement "Of course it follows, trivially, that ...". On one such statement, a student didn't see the obvious connection and so asked. The prof looked at the board and the developing proof for a few minutes. Then walked over to the corner of the (chalk) board and started making notes to himself in a tiny script. He went into totally abstract thinking mode, ignoring the class. After a bit of writing and erasing, etc, he wandered out of the room toward his office. The students followed along, gathering outside the office. The prof started pulling books off of his shelf and consulting them - several books - several more minutes.
Then he seemed to find enlightenment and returned to the classroom. When everyone was again seated he announced. "Yes, of course. It's trivial."

I agree with everything except the outside interests suggestion, as it implies too heavily focusing on nothing but academics. This can have horrendous consequences in terms of long-term stress and even performance. I would say that some form of regularly used “outlet valve”—even if only a few minutes a day or a few hours a week—is absolutely essential, especially for new students, and should even be written into their schedule, just like a class or job.

@aeismail, Actually, I was referring to such things as social media and  such that are mere distractions. I agree with you and use Tai Chi myself as an activity that is (a) active and (b) engages the brain in a different way. I'll consider a rephrasing. Thanks.

Glad to know we’re in agreement. My outlets were usually musical, so it’s just whatever works. (My PhD advisor’s drug of choice was ballroom dancing!)

@aeismail, Your reputation here is well earned. I find I'm in agreement with nearly everything I've found of yours here. (Not thinking of any exceptions, actually). Thanks for your care in moderation and improvement here.

Thanks. I care a lot because it's my chosen profession and one I think scares a lot of people unnecessarily. But I think we can do better: it's largely about remembering that we're all human beings, with all of our inherent strengths and flaws. Most of the advice has come from experience and observation of what's worked and what hasn't (including my own many mistakes!)—and remembering the Golden Rule (and not its academic inversion—"Do unto others as you had done unto you"!).

Are you personally sure that this happened at Kansas? This story is hardcore mathematics folklore and I've heard it told about at least 10 different places (and sometimes conference venues!)

@StellaBiderman, Thats my story and I'm stickin' with it. Actually, blush, that's where I heard it and it was presented as a local story just before my tenure there. I knew the prof about whom it was said and it therefore seemed perfectly reasonable. Maybe apocryphal, but keep the secret if so. shhhhhh....

In my own experience, I found that being successful at high school mathematics was detrimental to me. I went to a small rural school where math was a breeze and got to a large state school where I was placed right into advanced an mathematics course after doing well in a combination of the SAT Math and the University's placement test. I failed this course as I was unprepared for the necessary work and discipline needed to succeed. This was a wake up call that got me into gear, thankfully.
What I have found though, as I went through my graduate studies was that often, everyone in the program is good at math and is smart. Some are a bit quicker than others, but everyone is generally pretty bright. For the most part, the successful graduate students are the ones with the work effort and the grit.
If your read any of Julian Stanley's (and now Lubinski's and Benbow's) work out of Johns Hopkins on mathematical precociousness you will see that even the most brilliant mathematical minds can fail. Talent gives you a leg up on your competition, but being willing to work hard gets you across the finish line. And then being dedicated to your craft gets you ahead of your peers.
My point is, if you are willing to work, and put in the effort to maximize your abilities, you are already on the right track to being a successful graduate student and scholar in mathematics.
Also, one last bit of advice: If in class, you are not able to follow at first, you are unlikely the only one. Math is hard and complex and requires work to get good at. One of my favorite quotes is "...in mathematics you don't understand things. You just get used to them." ~Von Neumann (i.e., math is hard and requires work).

Yes, high school success in math correlates with undergraduate success in math.
That said, relax. The admission committee isn't a charity organization. Unless (even if) you are from a minority/child of a rich alumni/famous etc, you wouldn't have gotten accepted if they didn't think you were capable of passing their curriculum.

That correlation is just about very orthodox curriculum, and even then just "first-year", which does not mean challenging/honors courses in R1 or elite places in the U.S. It appears that the questioner will not take lower-division math courses at all...

@paulgarrett I don’t know of any US school that would guarantee admission to an IMO participant, so I suspect this is an international student (probably Southern Asia, based on the term “batch” to refer to the year).