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How good are Harvard undergrads?
I Studied Computer Science Engineering in India from an average private institute.
I wanted to and I still do want to become a great programmer. I have seen "The Social Network"(facebook) built and come to life right in front of my eyes. He was in his sophomore when he dropped out of college.
I don't know what they teach in Harvard in the very first year but over in India they teach C, C++ in the first two semesters . The curriculum revolved around learning basic syntax, functions, operators, pointers and ends up on files. C++ syllabus has somewhat of object oriented language pedagogy (few extra terms - inheritance, polymorphism etc.) . The problems which we were solving were those of .. writing area of triangle, towers of hanoi. Following these two semesters we studied data structures.
I don't see how a person can go on from his sophomore into building such a vast social network. I understand, he was a Harvard student, that must have meant something.
But exactly how much ahead are they, compared to an "average Indian"?
Is it something to do with the course over there? or the problems they practice or the environment or the individual's efforts ?
And how much time is it going to take for an "Average Indian" to reach that level?

Unfortunately, there is no single "correct" answer to your question.

Keep in mind that Zuckerberg was not an "average" Harvard student -
most do not go on to be self-made billionaires. Beyond that, he didn't even complete half of his cirriculum at Harvard, so why do you think the Harvard education was the seed of his success?

I don't know about Harvard in particular but you have to keep in mind that not everyone from Harvard was so successful, and that not everyone who is successful has been in Harvard. If you are good you will success, and it will be minutely related to the "prestige" of your university

If you're interested in seeing the content of Harvard's introductory CS50 course, the whole thing is online here: https://cs50.harvard.edu/

You seem to be making the assumption that Zuckerberg founded Facebook using only knowledge/skills gained from his Harvard studies.

From the list of social networks, one can see that at the moment when facebook appeared, there were also many additional social networks already created. From there to the domination of facebook over such a vast market is high gap, with possible political interference(and not presented in the movie). Learning a programming language professionally can be made only by working on real life projects, besides school projects which are very simple by comparison.


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Submitting to Call for Submissions After Deadline
I have an unpublished manuscript. A journal I would have liked to submit the manuscript to as a regular submission has a call for submissions for a special issue of the journal on XYZ with a target publication date of next year. My manuscript would be a near perfect fit for that special issue. The problem is that the deadline passed three months ago.
In this scenario, is it fair to email the editor to ask if it is possible to submit your paper first for the special issue, for which it would be a good fit, but several months past the posted deadline?

If it's a week after the deadline you can probably still make it. Three months - probably not. They'd be pretty deep into the review process already, and your paper would hold up the special issue.
Still, no harm asking. It's possible they lack papers and will be happy to consider yours.

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First try vs second try for PhD Qualifying Exam
For universities that give two tries for passing the PhD qualifying exams, are the two tries "equal"? In the sense that does the committee consider more carefully on the second and last try of the applicant before failing him/her?
Just an analogy: for driving tests, examiners are known to be more lenient on the second (and subsequent) attempt, and more strict on the first attempt. Not sure if it is true for PhD exams...
Just to ask any professors/students here who are more experienced in this matter.
Thanks!

To be honest, it seemed to me that who the student has as an advisor seemed to effect their outcome also.  If a student's advisor was leaving the University, they seemed less likely to pass.  Whether there was any causation there, I can't say, I just observed correlation in time as a fellow-grad student.  Over 30 full years have passed, and this was at one department at one University in the U.S.  However, human nature being what it is, I suspect that this may have some (subjective) outcome on what happened.

Yes, certainly, although "fails" are stressful for all parties, if a student has mis-judged the preparation needed, for whatever reason, the first "fail" can send a message that more attention is needed or something needs to be done differently. In contrast, yes, in a system like my university's, where a second fail results in termination from the program, the committee is well aware of this possibility.

My experience as an examiner is that although the committee is very aware that a failing grade will result in a student leaving the program, there's typically no willingness to be more lenient in grading the exam on the second attempt.  Students should expect that they will be held to the same standards on the second try.

What @BrianBorchers says matches how my graduate school operated. However, I remember two cases where a candidate otherwise considered promising was given a third try. In either case, you should not expect special leniency in a second try if you weren't explicitly told that this is the case in your school.

I did not mean to insinuate that standards change, only that people are well aware of the larger ramifications of a second failure. Thus, while the message "go study/work more, then come back" might make sense on the first try, it doesn't on the second.

I saw a case where one student was given a fourth try.

It depends on how common it is for people to fail. In my department, somewhere between a third and one half of people fail on first attempt (but will utimately pass it). They use the first attempt to get a feel for the level of preparedness, and may choose to take it in a semester when they have covered the basic classes, but maybe not the last one in the sequence yet.
If so many people fail, then there is no stigma attached to failing (and we don't consider it negatively either). I would ask how that looks in your department.

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Is tutoring (outside university) while doing PhD a good idea?
Just to ask some advice regarding tutoring students while pursuing a PhD to supplement my income.
Is this a good idea? Tutoring pays well in my country, and I am intending to teach twice a week(2 hours each), which would generate a side income equivalent to 30% of my stipend.
(Side info: I am researching Mathematics)
Thanks for your advice!

A good idea in what sense?  Many people do it.

Of course, whether it is a good idea can only be known in hindsight. But many PhD students work as private tutors, so if it sounds interesting to you, you might as well try it.
Some things to consider:

It will probably take you some time to prepare for each lesson. And unless your students will come to your home or office, also account for travel time and expenses. Four hours of lessons per week may require significantly more than four hours of your time.
What will you do if your students are late to their lesson, or don't show up at all? What if they don't study for their lessons? What if they are late in paying you? What if they (or their parents) demand some different style of tutoring than you had planned? What if they demand that you just do their homework while they Facebook?
Consider the time it will take you to recruit students. Assume that they  will quit unexpectedly, requiring you  to find new students and lose income in the meantime. Do not count on your tutoring fees as steady income.
Ethical issues: if you are working as a teaching assistant or something similar, you cannot be a private tutor to students who are enrolled in your class. Check for other ethics or conflict of interest rules that your university may have. In particular, although your university office may seem like a convenient place to meet your private students, this may not be allowed.

In Germany, most Ph.D. students (with university jobs) do exactly this: they are responsible for tutorials, seminars etc., selecting problems, working with the student TAs that actually hold the tutorials. This is all part of their university job. The workload is probably comparable to 4 hours a week workload. (People on actual stipends are not required to do so; some do, some don't.)
As to whether this is a good idea: we can't answer that question. It will depend on your stipend and your expenses, on how badly you need the money, on whether you could have meaningfully used that time to further your research or not (because you can't do full-power research all day long, and you might just as well include some planned lower-power time in your week), on how much quality of life tutoring gives you (or takes away from you) and so forth.

The question says the tutoring is "outside university", so this answer might not be totally fitting - on the other hand, I do not quite understand what is meant by that remark, either (does it even matter whether the tutoring is inside or outside of the university?), hence I still think this is a good answer.

Mostly you should try in my opinion do proper teaching to a class rather than private sessions, per hour you'll get better pay, and it could be more valuable on your resume eventually.
Unless your PhD contract has some exclusivity clause, making time for teaching should be ok, just clear it with your advisors beforehand (I need money boss !).
Don't undervalue your skills, as PhD student you can already teach up to master level to a class, and should be practicing that skill. Teaching just one or two students is not the best use of your time at this level, imho.

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How do Professors feel about writing recommendation letter?
Just curious about how professors feel about having to write recommendation letters? Is it a chore for them? Or do they actually enjoy writing them? Or is it more of neutral.
I am in a situation of applying to various graduate schools. Last year I only applied to one school and was rejected. This year I am thinking of applying to more schools so as to increase the chance of being accepted. I feel a bit "guilty" about having to ask my supervisor to write 5 separate letter of recommendations. Would it take up too much of their time?
That said, I don't really have any other choice since the recommendation letters are pretty much compulsory.

Possibly useful: http://academia.stackexchange.com/questions/13977/how-to-reduce-the-load-of-professors-writing-recommendation-letters-for-graduate, http://academia.stackexchange.com/questions/12645/how-do-people-manage-recommendation-letters

"his year I am thinking of applying to more schools so as to increase the chance of being accepted. I feel a bit "guilty" about having to ask my supervisor to write 5 separate letter of recommendations." Do you specifically know that your supervisor is writing five separate letters?  In my experience, one letter serves for all graduate applications, perhaps with the most minor adjustments if one is applying for some external fellowship.

Although I'm not a professor, my position has a lot of similarity and I have often been asked to write recommendation letters.  My reaction has been a mixture, depending on who is asking for me to write the letter:

Students who I like and respect: "Sure, I'll be happy to.  What are the aspects of your work that you'd most like to have emphasized?"
Students who I haven't got a strong opinion on: "I'm not sure that I know your work well enough to write a strong letter.  If you really need me to, I can, but I think you'd be better served by getting somebody who knows you better."
Students who I have been disappointed in: "I'm sorry, but I don't think that I would be a good person to write the type of letter that you need."

You only want letters from the first type, who will happily sing your praises.  And for a student like that, it's no burden at all: I'm going to want to push your career forward, because I'm hoping I'll get to see somebody who I like prosper, and maybe even return to work with me as a colleague in the future.
As for the multiple letters question: don't worry about it unless you're applying to like 20 schools.  If the programs you're applying to are similar, they're probably just going to be writing just one template letter about their experiences and filling in a couple of blanks to customize for the institution.  Now certain institutions have terrible forms that will make it a pain to send that letter, but that's hardly your fault, and your recommender will be used to it...

+1 for those three cases of students when writing recommendations.

Writing recommendations is a lot of work, but I take pleasure in doing it.  To control the work, I decline recommendations from students who earned grades of less than B in any of my classes.  When I get a second request from the same student, I tell them my limit is four letters.  I also ask for material from the student that eases the workload a bit.
Here is what I tell my students: https://facultyweb.kennesaw.edu/rbrow211/help/recommendations.php

I do something similar but I find what students come back with (when I have asked them for material to help me write a better letter for them) is often quite weak. Of course, this also impacts the quality of the letter they receive from me (since I realize I might have seen them as brighter than they really are).

Correct.  You learn something about the student when you ask for material to support the recommendation letter.  Often I get nothing, hence I don't have t write a letter.  The best students bring a well-organized packet, then stop by a few days later to ask whether I need anything else.

As a student, I'm interested in knowing what exactly professores might expect as "material". Is it course grades? Bachelor thesis?

@MarkFantini: Have a look at the link in my answer to the question.

I am a professor. It's part of our job. I generally only write one letter per student, and send that letter to all of the programs they have applied to. The exception is if they are applying to different programs (e.g. some neuroscience and some cognitive science) I would tailor the letter for the program. It is work. Just like teaching, reviewing papers, writing grants, mentoring, etc. If I like the student, I will enjoy sharing my enthusiasm for that student.


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Giving talks on ongoing, unpublished research (dangers of getting scooped?)
In my school sometimes the graduate students have to give a talk on what they are up to, i.e. present their ongoing research. Often at this stage the work is not published yet. This is an internal event within the school, within the department. The audience are mainly other graduate students, and professors.
Are there any tips to give such a talk? More specifically, how to reduce the risk (if any) of getting scooped, and ideas stolen? The context is in the subject of mathematics/ mathematical sciences.
Thanks a lot.

Don't worry about people stealing your ideas. If your ideas are any good, you'll have to ram them down people's throats. -- Howard Aiken

Getting ideas stolen is a common fear when starting out (or at least all my Ph.D. students had that worry, and I did too when I was one) but it is much less common that one would think. While the risk does exist, the benefits of opening your research to get feedback from other people greatly outweigh it. Keeping your research secret is just not worth it.
In any case, if you want to reduce the risk, something that you can do is (paradoxically) open up even more! Announce the talk at your website, put your slides online, tweet about it, etc. This means that there will be publicly available evidence that you had ongoing research on topic X by date Y, so prospective scoopers would be easily exposed.


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Should I show mark boundaries on academic CV?
I am writing an academic CV for PhD applications. I have included the marks for each exam I did in my final year.
The marking scheme is slightly unusual: the threshold for the highest mark was 59 (normally around 70). I got (~10 marks) higher than 59 in a few papers and I want it to be clear that I was above the boundary, should I mention in the CV that the boundary was 59?

If you got the highest mark (A?), why can't you just put that down?

@Sverre I thought you were supposed to put the exact marks. Am I right?

I don't know what you mean by "mark", since you seem to be using it for two different things: (1) Grades (e.g. A, B) (2) Scores (points, percentages, etc.). I've never seen a CV that lists scores for exams.

@Sverre apologies. I meant exact score, i.e a percentage. I’ll take it that your advice is just to leave off the scores then.

Most CVs do not contain a list of grades, but sometimes such list are asked for separately. But it is your CV so you can do what you want. There are no rules. If you like to emphasize how good your scores were you can put them in as long as you explain clearly what the scores mean: you correctly identified that others may not understand the scoring system, so if you decide to show your scores you have to make sure they do.

If the exams are listed in your transcript, then you do not need to repeat them in your CV. The reason is that they'll be better (and officially) explained on your transcript.

Some Universities use a "percentile" parameter to show your grade respect to the rest of students. Maybe you can ask for this metric or if possible calculate it by yourself.


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How long should I wait for the receipt acknowledgement?
I submitted my paper by e-mail one week ago. How long is it reasonable to wait for the receipt acknowledgement? What to do if they won't acknowledge receipt of the paper?

Most of the journals handle paper submission through their websites. Are you sure about the quality of the outlet you submitted the paper via e-mail?

Yes, I am sure. This is a respectable old periodical, with the high impact factor.

It's also the holiday season, with many people out of the office between Christmas and New Year's. I'd wait until next week.

@o4tlulz: in mathematics at least, many high-quality journals still use the manual submission method.

Most journals work with electronic submission systems but some still work with manual handling. Regardless, both systems require a person to handle the manuscript once it arrives. Since the past week has been the Christmas holiday for many and persons working with journals such as editors are usually not employed to work with the journal but do it aside their regular job, it is not strange that not much will happen during the holiday season.
I am sure you will receive notice of your submission sometime in the next couple of weeks into the new year, once the persons responsible will have a chance to have a look.
As a side note, as an editor, I can see that the number of submissions is slightly increasing before summer (holidays) and Christmas/New Years (holiday season). Authors, naturally, want to get their works away before taking time off, unfortunately, editors and reviewers, naturally reluctant to take on reviews during the holidays, do the same so the increased flux of manuscripts creates something of a traffic jam at these times. From this perspective, submitting a manuscript away from these times of the year will likely result in, at least slightly, faster response and turn-over times.

You don't mention when the deadline is. If the deadline is a good two months away, waiting a week or so is nothing to be alarmed about.
Moreover, you've asked this question on the week between Christmas and New Year's – a time when many offices resemble ghost towns. Given that New Year's Day falls on a Thursday this year, I'm guessing it's sitting in someone's inbox, and there's a good chance it will remain there, unread, until Monday, January 6th. Even then, there may be a backlog of email and other submissions, so give it another week after that.
If the person responsible for reviewing submitted papers works in academia, there's a chance it might even go longer than that, depending on their institution's academic calender. (In other words, they might not get back into the full swing of things before the semester begins.)


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What should I do if I found too many typos after my Ph.D. thesis being approved but before my oral defense in mathematics?
I am doing my Ph.D. in mathematics and did not have my thesis carefully proofread before submission (which is definitely a mistake that I wish to correct). My thesis was approved after submission and I am now preparing for the oral defense.
Now as I reread my thesis in detail, I found that there are too many typos (probably more than five per page). Some are negligible, but some are essential. For example, I wrote "<" instead of "less than or equal to") in the conclusion of a proposition. Another example is that I quoted a wrong theorem number in a proof. I even wrote a same lemma with the same proof twice. One referee complains about the misprints in his/her report, but s/he still considers the thesis tolerable as a whole. But now I feel all those careless typos very annoying and they make the thesis much less readable.
Now I am seeking suggestions on what I should do. Should I correct all known typos and give each committee member a copy of the revised thesis on my defense? Is there any other thing that I can do right now?

Related: http://academia.stackexchange.com/questions/46938/what-should-i-do-if-i-discover-a-typo-in-the-title-of-my-ms-thesis-after-submiss

Talk to your advisor.
When I defended, my committee came back with a number of such corrections to be made. I made them and they signed off. Then the thesis editing office took the document and came back with even more corrections. I made those, and eventually they signed off. Trust me, you aren't the first to deal with this problem, and likely not the first that your advisor has seen.

Talk to your advisor. — I'm not sure I agree that the advisor is the right person to talk to in this particular case. At my school, we had a dissertation editor who would be the more appropriate person to ask. There are times to ask your advisor some questions, but then there are other times when you should be able to figure out who to talk to without having to get your advisor in the loop.

@MadJack The stated (first) question was: Should I correct all known typos and give each committee member a copy of the revised thesis on my defense? I would think the advisor would be much better equipped to answer that compared to a dissertation editor.

Yes, I see your point, but I'm not sure an advisor would care either way; I know that mine wouldn't have.

@MadJack agreed 100%, I would also guess that the committee won't care. If they've already read it, they won't reread. If they haven't read it and the OP gets them an updated copy, they will probably read that instead.

I agree (+1, by the way).

My institution is clear that they will not make corrections after the final submission :( If it is before your defense, then go ahead and make the corrections and resend to the committee members!


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How to assign authorship when publishing with Bachelor's and Master's students
The usual recommendation I have read here is that when you publish together with a (PhD) student of yours, the student should be first author, and the supervisor will be second author. Although this is not explained explicitly, the context seems to be that the student is the one who does the major part of the analysis and writing up the article. The supervisor might have defined the research design and approach, identified relevant previous literature and might have revised the article.
My situation is a little different:

I occasionally have a small number of Bachelor's and Master's students who have written an excellent Bachelor's/Master's thesis. Because they have worked on topics (which I recommended) that are relevant to research efforts in the field, their results are so interesting that I feel they should be published (and I think there's a good chance they will).
The students rarely have any interest in publishing their results, if it involves any further work. They will most probably not pursue a PhD. Most of them will become teachers, and having published a research article will likely provide zero benefits when trying to find a job, so they don't want to invest time in publishing their results.
Because of this they don't want to invest any (substantial amount of) time in writing up the results in a way that they can be published. I don't think they would mind seeing the results published with their name as a co-author (and then they will have to at least read through the final manuscript), but they might also consent to not being given authorship.
Consequently, if I want to see the results published, I will have to write up the article. I most cases some reanalysis of the data will also be necessary (and sometimes a more substantial effort will be necessary).
The major contribution from the students is that they collected and coded the data (which takes a substantial amount of time), and some of the analyses they did might be usable in a publication.

Does the students' contribution merit first or second authorship even though their contribution doesn't match the ICMJE criteria for authorship? What's the ethical and reasonable thing do do?
Even if it doesn't, should I take into account that hiring/tenure committees might like to see proof that I actively involve students in my research and publish together with them? (I read this in an answer to another question here, but can't find it anymore.)

This will be dependent in large part on norms within your field; I don't think there will be anything universal. For instance, in my field, the student should be first author if, and only if, their last name alphabetically precedes that of the advisor (and other authors).

I'm reminded of a paper on which the first author was noted as being an NSF Fellow, and the second as a Jolly Good Fellow.

There is no universal standard.

I think you misunderstood ICMJE criteria. To quote: "The criteria are not intended for use as a means to disqualify colleagues from authorship who otherwise meet authorship criteria by denying them the opportunity to [write/revise the paper or approve its final version]". You should ask the students to read and approve the paper (which they will very likely agree as it is not much work) thus enabling them to fulfill the criteria.

Mhh, no, I don't think I misunderstood them ;) (1) I wouldn't deny them the opportunity. (2) reading and approving the paper is not the same as "Drafting the work or revising it critically for important intellectual content". If that's the standard, and I'm not saying it necessarily should be, few if any of them are going to meet it.

The students rarely have any interest in publishing their results. Can you elaborate as to why this is? I was absolutely thrilled when I got the chance to publish two papers along with my bachelor thesis studies.

To clarify, they would be quite happy to publish the results. But it means they'd have to invest a lot of additional work that would take time away from other things they need/want to get done. Also, the vast majority are going to be teachers, and for this career having published a paper offers no advantages in terms of how likely they are going to be hired. Of course the situation is different for those who want to pursue a PhD.

...but they might also consent to not being given authorship.

No, no and no. If it is your students' BSc or MSc thesis, they should be co-authors. Period.

...I will have to write up the article.

You are right. That is why in those cases, you may be first author on the paper (according to your discipline's norms).
Also, you should always discuss BEFORE assigning the MSc and BSc theses' topics, that ideally you want to work on the suggested topic so that you will get a publication out of it. Also you should make clear that if a student's thesis results in a paper, then the student gets to be co-author on the resulting paper and additional work might be required from him. Earlier discussion always leads to fewer disputes later-on.

If they don't want to be authors then they are allowed to decline it, they just need to be given the option.

@KraZug Technically yes.  If a student ever declines an authorship in this situation, however, then the advisor has probably done something horribly wrong.

I'd also be careful of how you word things to the students at the outset - you don't want it to seem like you're trying to use students just to make your own publications list longer. I'd put it along the lines of "If you do some really interesting work at the end of this, I'd like to see you publish it, and I'll help with that", not "I'd like to turn your work into a paper, and you can be co-author with me!".

@DTR. Supervising BSc or MSc theses is not paid extra in all countries, I know of. The main incentive for a professor to undertake such theses is to actually "make his publications list longer". There is nothing wrong with that.

@Alexandros You make a fair point - I was more thinking that you don't want the student to think that you're trying to take credit for their work (something that comes up a lot in questions here, so I assume is quite an easy thought for students to arrive at). Of course, sharing credit is why both parties are mentioned on the publication, but I'd personally rather just offhandedly mention the possibility of publishing (something that would excite most undergraduates in my experience) at the outset, and then if the work is good enough at the end explain how the credit will be (fairly) shared.

That is why in those cases, you will get to be first author on the paper. — Unless you work in a field that prefers to give first authorship to the person who did most of the work (and didn't just write about it), or to the youngest author, or to the author whose name comes first in the phone book, or something else.

TLDR: In all cases, the student definitely should be one of the authors. In most cases, I would argue for them to be the first author, but if the work required significant extension prior to publication it becomes a gray area. First authorship also obviously wouldn't apply if there is a field-specific policy on author order (e.g. alphabetically).

You should not deprive people of authorship because they did not write the paper - I think you misunderstood the ICMJE criteria on this point. To quote:

The criteria are not intended for use as a means to disqualify
  colleagues from authorship who otherwise meet authorship criteria by
  denying them the opportunity to [write/revise the paper or approve its
  final version].

You should ask the students to read and approve the paper thus enabling them to fulfill the criteria. I think almost all students will agree to do this as it is not a lot of work.
Personally, I prefer giving students first authorship. The most important argument is that there is a huge power differential in favor of the advisor. The student is usually unsure of the academic conventions and will likely accept whatever the advisor says (if only to make his life easier). Making them the first author ensures, that the student will not feel that someone unjustly benefited from their work - and at least in terms of time spent their contribution is usually several times larger than advisor's.
I actually turned my MSc. thesis into a paper. I had no clue on how authors should be ordered, so in the first draft, I put myself as a third author of the paper (my advisor and my consultant from another department came before me). As no one had any comment, I kept it that way and in retrospect, I feel a little regret about it. From anecdotal evidence (including a few questions here: A, B) I think I am not alone.
I have recently co-authored a paper in computer science (currently under review) with my BSc. student. The student has written the software, designed and performed evaluation of the software with human subjects and performed analysis - all after relatively heavy consultations with me. I have written the text of the paper (reusing literature research from the BSc thesis), extended the evaluation and re-analysed the complete dataset. I gave the student first authorship, although the student was initially reluctant (claiming that I had written the paper and brought in ideas) and I am very happy about the decision, as I think it encouraged the student to think of himself as a scientist, although he does not want to pursue academic career.

Many times the BSc thesis or MSc thesis are supervised by PhD students who do a significant part of the work and also need first author publications to get their PhD. In those cases, giving first authorship to BSc student is unfair.

@Alexandros I am a PhD student and I don't think it would benefit me to be first author of papers where I didn't do the core work. Further I think that who deserves credit is independent on whoever benefits from credit.

Writing a paper and getting it published even from a completed BSc or MSc thesis (who in my country are not even written in English) is the core work of a paper and is usually done by the PhD student in the aforementioned cases.

@Alexandros, why are PhD students doing the core work of paper writing for BS and MS students? I don't get it. MS students should certainly be capable of writing a paper.

need first author publications to get their PhD — [citation needed]!

@Alexandros That might be field dependent. In CS, I find implementing and testing the software to be (usually) much more difficult and time consuming than writing it up - especially for conference paper.

@BillBarth: Because, in some fields and places, a BS/MS thesis is a very different document compared to a paper. A BS/MS thesis is a 60+ (or rather, 80+ for Master theses) pages document that is meant to comprehensively demonstrate a thorough understanding of the topic at hand, and skills to practically solve a task related to the topic and make reasonable decisions. That may or may not also include some conceptually novel aspects that are briefly described in a few paragraphs. A research paper, on the other hand, is a concise document that focuses on one or a small set of conceptually ...

... novel ideas, and may briefly explain some direct context to illustrate the usefulness of the novel approach(es). This difference alone means that the paper needs to be written mostly from scratch rather than copying any sections from the BS/MS thesis, and if the BS/MS thesis is not written in English, writing a completely new text for the paper is unavoidable, anyway. So you wrote "MS students should certainly be capable of writing a paper." - that may be true (even though they have not usually written any papers actually submitted for external review before), but capable and willing ...

... are two very different things. Depending on the field, for the vast majority of BS/MS students, examining and/or developing something and then writing a BS/MS thesis about it is the final requirement to get their degree. They have no interest (and sometimes no time) to invest any time or energy into writing a paper. Writing a paper is the goal of the thesis supervisor, e.g. a PhD candidate, who has usually defined the thesis task in a way to benefit their research, and accordingly was usually a part of the discussions leading up to the novel aspects found in the thesis.

@MartinČerný: That is certainly very subfield-dependent, but I, also in CS, find that while implementing and testing of a software is indeed very difficult and time-consuming, only a tiny fraction of that effort is usually dedicated to the conceptually novel aspects that the paper is about. The bulk of the implementation work is getting things to run (e.g. setting up the databases, loading test data, fixing multi-threading bugs, making the UI look nice enough for user studies, ...). Comparably much work, but nothing that warrants a scientific publication (or primary authorship in one).

@JeffE: Four random examples from different doctorate regulations: Technical University of Chemnitz, humanities department, §9(4): Publication-based dissertations are admissible if they include at least three journal articles, for at least two of which the doctoral candidate must have been the first author. LMU, biology department, (1): At least two manuscripts accepted at peer-reviewed journals are required, for one of which the ...

... doctoral candidate needs to be the first author. ETH Zürich, construction and environment department, amendments 5.2 and 5.4: At least three publications whose first author is the doctoral candidate are required. Justus Liebig University Gießen, joint sciences department (including math and CS), §15(3): Several publications can be joined to a dissertation if the doctoral candidate is the first author. This list could go on.

@O.R.Mapper  Thanks for the examples.  (But: Ugh, really?  How do mathematics students at Gießen whose names start with Z ever graduate?)

Mhh, no, I don't think I misunderstood the ICJM criteria ;) (1) I wouldn't deny them the opportunity. (2) reading and approving the paper is not the same as "Drafting the work or revising it critically for important intellectual content". If that's the standard, and I'm not saying it necessarily should be, few if any of them are going to meet it.

@Robert I understand the distinction you are making but I find it rather technical - (1) To a student who is not familiar with academia "not asking for" and "denying opportunity to" is IMHO almost the same thing, at least in the spirit of the criteria ("to reserve the status of authorship for those who deserve credit and can take responsibility for the work"), (2) if the student reads the paper and checks that it represents an accurate account of what they have done in the thesis, I would say it counts as "revising it critically for important intellectual content".


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How can I proof-read my own work more effectively?
After an article/book has finally reached the pre-publication stage, the authors have to check the proofs for errors (introduced by themselves or during type-setting). I find this one of the least enjoyable aspects of my work and also think I might not be particularly efficient. It varies with the length of the manuscript. A five-page article in conference proceedings is obviously less of a problem than a monograph.

When proof-reading my own contributions, it is the umpteenth time that I am reading the same text. I find it exceedingly boring, which might make me ineffective (taking a long time to read the text, and potentially overlooking errors).
The delay between the actual research and publication of the work can be quite extensive. After such a long time, I am less likely to recall all the details of the analysis, making me more likely to overlook errors in the manuscript.

Asking colleagues to help with this also seems ineffective. They might be less bored while reading the text, but (a) might not be very attentive because they have more pressing issues at hand and (b) can only spot clear inconsistencies, but not other errors you can only notice if you did the research yourself.
How can I make my proof-reading more effective and enjoyable/increase my motivation?

Related: Is there an optimum time to leave between writing and self-proofreading? (which also has a thrice-upvoted comment wondering whether better answers might not be forthcoming at Writers.SE) and What to check when examining paper proofs?

Related at Writers.SE: How can I catch more errors when I proofread?. It doesn't address the specifically academic aspects, though, e.g., that we rarely have to worry about rise/raise typos, and suggestions including text-to-speech features won't be useful in an academic text with non-standard vocabulary - but it may be useful.

Asking a colleague can be very effective if it can be presented in a non-burdensome way.  Just last week, a friend emailed me a single chapter of something he had written and asked me to proofread it with zero context.  I found a few minor grammatical errors--nothing too serious--and one glaring factual error, something I happened to know was incorrect but that my friend had not researched enough to know about, and he was grateful when I pointed it out.  I might not have done it if he'd dropped the entire book on me, but one chapter was something I could do in a half hour of spare time.

From Google:
Proof-read:

from hard-copy
backwards
aloud
a few days after the last revision
after revising the text for clarity and brevity
line by line, covering the remainder
double-checking small words ("if") and proper names
looking for one type of mistake at a time
looking for mistakes and idiosyncrasies to which you are prone (using the search function or even more sophisticated).

Helpful links:

Proofreading and editing tips
Top 10 Proofreading Tips
"Proofreading", from The Writer's Handbook

On motivation:

schedule enough time to divide the task into small chunks and take breaks
reward yourself after completion of each chunk
listen to music
have a nice cup of tea
you have the soon-to-be published result of your hard work in front of you. Indulge in some pride as you go through the paper.

"have a nice cup of tea" - crucial. Completely agree with many other points here too - particularly breaking the task up into sections and not doing the whole thing in order.

Here are some more tips I've used (please feel free to add to your great answer): cut a few word hole in a notecard and read each word individually; read it backwards to focus on each word; and dot each word with a pen or pencil while reading to force myself to read each word.

Double space it and print it. Nothing tops paper.
make a check list of items that you usually forget. You can write macros and codes to check your common mistakes. However, this list should be ongoing and always around your desk. People have blind spots that lives with them. For example lower-case, upper case in the reference list is something I always miss, even though I hoped Mendeley would take care of it (but it is still very unreliable).
Read it from the end to the front, and chapters in random orders depending on the type of paper.
You can use software like Grammarly, but don't expect 100% accuracy.
If you are doing it on computer, change the color of pages and fonts every once in a while.
You can also assign a memory map to each chapter of the book; for example, assign the whole road from DC to SF to the book and create a road trip by reading each chapter in each state. It helps you also memorize where did you say what in your book.

And try changing the margin, so the line breaks occur in different places.

Read it as if you are someone whose opinion on the work matters to you. That will help you read it with their eyes, or as if you are reading it aloud to them.
I find that this, along with the natural anticipation of their (imagined) response gives me the fresh view necessary.

I think this answer begs the question. How can the fresh mindset be achieved? Also, doesn't this advice apply to revising rather than proof-reading?

I find that it answers the question. I am speaking from experience.
I read as if I am someone else that I know - that provides the fresh mindset because I am reading it as I think they would.
You seem to understand this when you ask if it doesn't better apply to revising - and it may well apply to revising, but I find it helps me discover all kinds of errors.
I think my personal success trumps your suspicion that it begs the question; for whether or not it does, it is successful.


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Comprehensive Guide for Ph.D. thesis in Mathematics?
Could any one recommend some comprehensive guide (online version preferred) for writing a Ph.D. thesis in Mathematics?
I did some google search but there are too many results and it is difficult to decide which one to read. Here I am not asking anyone to write such a guide for me (otherwise this question will be too broad and thus not suitable here); instead, I would appreciate if anyone could make some recommendations of those existing references.

Nicholas Higham's "Handbook of writing for the mathematical sciences" has a chapter specifically on theses.

Thanks @DavidKetcheson! By the way, my question was down-voted. Is it not suitable here?

Some users might consider an open-ended request for resources as unsuitable, since there are many possible answers and none are objectively more correct than others (see the [help/dont-ask]). But it's just one down vote and there are currently no votes to close, so it's a little premature to conclude that the community considers the question unsuitable - we just know that one person does.

SIAM's style manual is a very useful source on writing mathematics in general and using LaTeX in particular.  http://www.siam.org/journals/pdf/stylemanual.pdf

It could also be helpful to check this and this short guides and the books by Steven G. Krantz, in particular

A Mathematician's Survival Guide: Graduate School and Early Career Development
A Primer of Mathematical Writing

The first one contains subsection 4.6 which deals specifically with writing a thesis, the second one is on mathematical writing in general but it does not really deal with the theses per se.

This is the best guide I have ever encountered.
It is neither too broad nor too narrow as a guide.
Moreover, it does not contain the policies of a specific university (you should number the figures that way and write equations this way etc.)
The persentation explains how should the overall feeling of a thesis be, and nothing more.
I also find this manuscript very useful. However, some subsections are incomplete and marked as [todo].

Both of your links point to the same file. Is it the way you intended it to be?

@just-learning It is my mistake. Corrected it now. Thanks for your notice.


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References in a PhD thesis in mathematics
I have a few questions about the references in a PhD thesis in mathematics:

What would be a "normal" range of items there? I am not sure if there is only a few items in the reference it may not be suitable. Would 30 be good? 50? Or 100?
Is there any conventional way to order the references?
When I add a paper to the reference, do I really need to read the paper? For example, I may read from some other paper that "the following result was proved in [1]". Then can I also add [1] to my reference by writing "the following result was proved in [1]", without really reading [1]? It is possible that [1] may be too long/tedious/difficult to read, difficult to find, or not in English, etc.

Please ask just one question at a time.

Thanks @EnergyNumbers, I am quite new here and am not aware of the rules.

That's ok, we all have to learn at the beginning. (3) has already been asked. It may be that (1) and (2) have too: it might be worth a quick search. Please do edit the question down to a single question that doesn't appear elsewhere on this site already. You'll see an "edit" link immediately below your question.

@EnergyNumbers, I know the "edit" function, but am not sure how to edit "to a single question that doesn't appear elsewhere on this site already". Could you edit my question?

First, you have to establish if the question is unique. When I search for "read references" - the search box is in the top-right corner of the screen - I quickly find this. So next I'd search for "order references", and see if there's was a question already on that. Then I'd search for "number of references". I'll leave those two to you, so you can get the hang of it. Finding questions already asked is brilliant - it means you get your answer immediately, without even having to work out how to ask the question well.

Thanks @EnergyNumbers for your suggestion. Since all my questions have been asked before, should I delete my question then?

Ask your advisor. That's what s/he is there for. S/he is paid to know the conventions in your field and the requirements of your university.

John Nash's thesis had two citations, to his own article, and to a book by von Neumann.

'Normal' is not really relevant. You must reference your sources. You must not artificially pad your reference section by citing things that aren't relevant. The question left then is how many standard texts etc you reference with regard to things like well-known background. This will probably depend on exactly what you study.
Yes, but it depends on field to some extent. In mathematics, references are almost always ordered alphabetically by first author's surname but check your university rules first, then a standard journal or three if that doesn't pin it down enough.
I'm sure this must have been answered before. If you quote something because someone else did, are you certain they were right? People make mistakes (and maybe occasionally deliberate false claims).

Thank you for your answer! For Question 2, is there any link to instructions you would recommend?

@Zuriel We don't even know what university you're at so we don't know where your university's instructions are on the web.

A supplement to Kimball's answer: In the case of several papers by the same author, the usual ordering is chronological.  In the case of several sets of multiple authors, papers with the same first author are ordered with solo papers first, and the rest ordered according to the second author's surname (and then the third author, if the second is also the same, etc., and finally chronologically when all authors are the same).


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Is it a good idea to combine the glossary and the list of notations in a mathematical PhD thesis?
I am considering including a glossary and a list of notations in my PhD thesis on mathematics. Is it a good idea to write them separately or combine them?
For example, a typical entry of the list of notation is:
[a,b] The commutator of a and b, defined by [a,b]=a^{-1}b^{-1}ab.
An entry of the glossary is:
Commutator The commutator of a and b is defined to be the product a^{-1}b^{-1}ab.
(Note: the definition of commutator is well-known to mathematicians, but since another definition aba^{-1}b^{-1} is also possible, I would like to add the definition to avoid any possible ambiguity.)
I have a strong feeling of combining these two entries together, maybe even combining the glossary and the list of notations together.
Is it a good idea to combine the glossary and the list of notations in a mathematical PhD thesis?

Mathematicians rarely use glossaries, but sometimes include an index and/or index of notation.  On the other hand, there is often a section on notation at the beginning.  Is there a reason you specifically want a glossary?

@Kimball, in this link, the commentator mentions that I can create a "cheat list", which I believe is a very good idea: http://academia.stackexchange.com/questions/32355/using-typographical-variants-of-the-same-letter-as-mathematical-symbols-in-a-pap

@Kimball, basically I want to make my thesis more organized and reader-friendly.

If you mean jakebeal's answer to that question and the comments therein, it seems what they are talking about is what I call an "index of notation," not a glossary.  I currently don't see any reason why an index of notation and/or a preliminary notation section is not sufficient.  BTW, despite the comments saying it doesn't happen in for (shortish) papers in math, I have included an index of notation in this joint paper, and was told it was very helpful.

what does your supervisor say?

Have your definitions in line rather than in a glossary, it improves the readability of the entire manuscript (whether or not those definitions are actually necessary). People rarely go through glossaries anyway, since it would involve spending twice the amount of time just to switch pages back and forth. Inline definitions, instead, help the reader to flow on without dismissing the attention on the context.

How does that improve things? If I encounter something on page 10 and I wonder how it is defined, is it not easier to flip to the Glossary (which is in a fixed place) than having to search through the paper to see where it was defined?

What flipping back and forth? Just tear out the glossary pages. (Or print an extra copy of the glossary. Or open a second window.)

To answer @Jeff: I strongly doubt that tearing out the glossary pages is an intelligent solution to the question. Likewise printing an extra copy does not seem to be much smarter than having to read the above line to find the definitions. Along the same lines also to Tobias: having definitions inline does not mean searching through the entire paper, rather it means providing one more line of explanation whenever suitable for the reader. Even more direct: take any 100 random books in mathematics and count how many of them have inline definitions and how many have glossaries.

I would say keep them separate, because you should:

Inline the bodies of definitions in the ``natural'' narrative progress of your thesis (interspersing them with comments, observations etc.)
Have entries of the list of notations be very short and (always, or almost always) refer to terms in your glossary
Have terms in your glossary either defined very briefly or undefined at all, but always make a reference to the full inline definition.

In my extensive experience reading all sorts of books, "reader friendly" in terms of definitions and notation is to place that into an early chapter, or introduce it as you go. A complete index is very useful, a glossary much less so. A short overview of notation (sometimes found at the back of the title page) can be useful, but no more than one or two pages. Footnotes are a distraction, endnotes just get ignored.

Typically, a glossary defines words while a list of notations defines symbols.  To my mind, at least, these tend to serve fundamentally different purposes in a document:

A glossary is a refresher on standard vocabulary, to support reading by people with a broader set of backgrounds.
A list of notations collects all of your special definitions in one place

To take the example in your question: most mathematicians will know what a commutator is, and thus won't need to re-read its definition, but it's nice to have it in a glossary for anybody who's feeling hazy on it.  There are several conventions for how to notate commutators, though, and lots of meanings for square brackets, though, so pretty much every reader will appreciate a symbol table entry that says:

[a,b] The commutator of a and b

The reason is that words tend to be much more stable from document to document than symbols. Words have some differences in definition (and you should be clear which you're using), but symbols are expected to be variables that often change radically from paper to paper because there are simply too few symbols and symbol-structures relative to the number of distinct objects that need to be labelled by them.
The important thing here is not the names of the sections, or even the distinction between single and multiple-character objects, it is the difference of purposes.  Most readers should use a glossary rarely but a list of notations often: as such, if you create something that mixes the two purposes, then you're making it harder for the reader by swelling a critical section with things they usually won't be looking to read.

Keep them separate, although it won't hurt to incorporate notation into your glossary descriptions. In your example that makes both lemmata virtually identical, but this will not be the case for all items.


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Meaning of "reading law"
In a book recently, I saw a reference to someone "reading law" at such and such a university in England.  But I thought "reading law" was a way to bypass law school and still enter the law profession (after passing the bar I presume).  Is that only in the United States?  Any other countries?
Does England have a similar way to become a lawyer without going to college?  Then what do they call it?
In the US, do persons who read law and then become lawyers get to put anything after their name?  Obviously they would not be permitted to put J.D.

I think there should be existing an exam for the candidates who want to accept professional careers, all over the world.

Some rightpondian can correct me if I'm wrong, but I think "reading" in this context is British for "studying", and it does usually imply university study.  The person in question is most likely attending the equivalent of law school.
In the US, lawyers typically write "Esq." after their name, which doesn't really signify anything specific but is traditional.  This doesn't have anything to do with degrees they may or may not have.  (And even lawyers with a J.D. degree don't usually write J.D. after their names, nor use the title Dr.)

Yes, it almost certainly means 'is studying for an undergraduate degree in law', although possibly without the word 'undergraduate'.

I agree with @JessicaB. Some students would say "I am reading Law" instead of "I am studying Law". From watching University Challenge (quiz show for university students here in the UK), it tends to be people from "posh" universities who say this (Oxford, Cambridge etc.). I went to the University of Reading, and never heard anyone say this there. Edited to add: this isn't just restricted to Law degrees. People will say that for whatever subject they are studying.

It's a traditional way of saying "studying for a degree", and gets used for all subjects, not just law. I don't think its usage is based on the university you study at so much as on context - I'm at Oxford, and hardly anyone would talk about "reading" their subject outside of a prospectus. The contexts in which I'd normally expect to hear it are: (i) on University Challenge (in which collegiate universities tend to be disproportionately represented because there's a team for each college) and (ii) in bios for people in "professional" jobs (because they think it sounds posh).

In the UK, "Esq." is rarely used, but essentially just means "Mr." It's generally only used in official correspondence from places like Buckingham Palace, or by people who either (i) have airs and graces, or (ii) are pretending to have airs and graces for amusement value.

This is a little old now, but I came across it and as a UK law student, I feel obliged to answer. Reading law in this context is exactly the same as studying law, and as someone else already mentioned, it is said by more 'well to do' students, not generally usual day to day conversation.
The letters that would go after a qualified solicitor/ barrister (The two types of legal profession we have here in the UK), could be LLB, which is the degree itself they qualified with before going on to do either of the professional courses, or it could be simply whatever the highest degree level they have achieved so far.

You're right. Reading the law (in the US, at least) is practicing law (as an attorney, etc.) without a law degree. Passing the bar examination is still required; and in lieu of a law degree, some kind of tutelage, or apprenticeship is typically required. I believe it's no longer legal in most states.
Despite this, the general consensus seems to be that the phrase is being used in a different context (in this instance).


text:
Why are [some] professors ambiguous about material that is actually tested on exams?
I've noticed a majority of professors that I have had will tell students something along the lines of, the exam covers Chapters 1, 2, 3, or the exam covers topics X, Y, Z. Sometimes this is ends up being so broad that it is unlikely that students will even see all the material that is fair game on the exam. It also likely ends up with some material being more prominent than other material which means playing the guessing game.
Why are professors hesitant to tell students more precisely what they expect them to know?
I do realize that not all (perhaps even most?) professors have not written the exam at the point of informing students what is covered. However, given that undergraduate course material is fairly static, would not the professor be expecting the students to have the same knowledge as the previous students?

In my institution most (if not all) professors simply put all previous exam tests on their webpage, so students can simply go there and see how exactly the exam will look like (and they can exercise with old ones). In this way they can also see how the program changed during the years.

@user3730788: maybe "chapters 1,2,3" is precisely what they want you to know. Each class of my 5-year undergraduate degree finished with an oral exam in which everything covered in class was fair game. And we survived.

Look at it this way: the extreme end of this is simply telling students what questions are on the exam. Different teachers are willing to make different concessions on the way to that end. The less specific the prof is about what will be on the test, the student will be forced to be more general in their studies, and hopefully they will learn a lot doing that, rather than focusing on solving a particular problem. That said, example questions are also very valuable: I'm not arguing for no sample questions.

I never had problems with the following approach : (1) go to class. (2) take notes. (3) if the teacher seems really enthusiastic about a topic, or mentions it repeatedly, mark it in your notes.  (4) a couple of days before the test, review your notes, focusing on the sections marked.  (5) don't spend more than maybe 1-2 hours studying before a test (it's more important to be well rested).   I only did poorly in 4 classes (2 the teacher didn't let us take notes; 1 had a book written by that same professor; other I transfered in late, and was in a dark room w/ slides and I fell asleep alot)

2 the teacher didn't let us take notes — what is this I don't even

I have to ask why you think a professor would not be ambiguous about the contents of the exam? It's not like I care that you can bone up---anyone who has made it to college can be expected to manage that. Go home and learn it all, already!

Long live Dr. Kong at University of Kansas, many students' favorite.  "When you study for my test you will keep in mind TWO THINGS!  What will be easy to ask!  And what will be easy to graaaaaade!"

There's nothing imprecise about "the exam will cover chapters 1 through 3" if the professor expects you to actually be familiar with all of the material in those chapters, whether or not the test includes questions on every topic in those chapters.

There are at least four worries, in my experience:

The students may be trying not to study any more than they absolutely have to study. So if the professor says something isn't on the exam, they won't study it.
If the professor says what is on the exam, but doesn't explicitly mention something, and then that thing comes up (even as a minor part of another problem), the students may complain that "you said that wasn't on the test!". This can happen even if the professor really made a good faith effort to say what was on the test, and the students simply misunderstood.
The professor may not have written the exam yet, and so she doesn't know the exact topics that will be included.
Someone else may write the exam, if there are many sections of the course taking the same exam. In that case, the professor may not be permitted to say what is on the exam. When I was a postdoc, they didn't even show us the common calculus exam until just before it was administered.

There are various strategies to cope with these worries. A common one, as described in the question, is to just say that the exam can include everything from the class, which is not very informative but is otherwise harmless.
There are other strategies, as well, such as making an exam review packet that includes more than the exam possibly could, and then selecting exam problems based on the review packet. But these don't help with the issue of common exams written by someone else.
By the way, if turnaround is fair play: we professors often ask the dual question: why do students so often ask what will be on the exam, when they have just had a class on the same material that will be on the exam?  As you can imagine, we may feel that we have already told the students what we want them to know, by designing the course to include it!

In response to your last point, I would note that some universities assess points which are not taught on the course and it is expected of students to study them outside of class. It is important in these cases that students know this is so.

"why do students so often ask what will be on the exam, when they have just had a class on the same material that will be on the exam?" -- aside from the work-avoidant ones who'll completely ignore anything not examined, those who are planning to do last-night revision want to plan what to revise, so it's helpful to know whether there's anything to leave out. One could say "ah, well, cramming is pointless, covering the course normally will ensure you retain everything you need to know". But that wouldn't really engage with the fact that students in fact do revise, and believe that it helps :-)

@SteveJessop: I think another important answer to that question is that simply not all content from a course is suitable for exams, and some content is nice to know, but nothing I'd consider remotely relevant enough to include in an exam. Owing to their generally limited overview of the field/topics compared to the lecturers, (some) students tend to be inherently bad at estimating which is which. When I was involved with exams, we usually wanted students to have a fair chance to pass - and that includes pointing out that for the exam, it's more useful to understand (w.l.o.g.) the ...

... conceptual difference between a pre-test loop and a post-test loop in whatever programming language was used during the course than to know the exact names of any runtime library functions that may need to be invoked. Or, as another example: While the class material may mention groundbreaking statements of important people in the field, whether or not exact quotations of those statements, the names of the people that expressed them, or the years, are asked in the exam, is not inherently clear from the class, but requires either old exams for comparison or simply a direct question.

@SteveJessop whether or not it "helps" depends on the goal you want to achieve. It "helps" to get a good grade sure. But you have probably forgotten it by tuesday. Does it help you to actually become proficient in the subject the course has taught you so that you can apply it in the following course or in your professional life? Doubtful. So cramming does not "help" from that perspective, so there is no reason to encourage it if you are trying to achive the second goal. "Any measures cedes to be a good measure once it becomes a goal" - you even seem to forget the goal over the measure

Due to time constraints, most exams directly ask about only a small fraction of the course material. If a professor explicitly tells students exactly what parts of the material are going to be directly tested on the exam, many students would only bother to learn that material.
Therefore, professors often include anything they want students to learn/study in the exam coverage.
(There are obviously tradeoffs involved: include too much and students won't be able to study the really important things at a sufficient level of depth, include too little and the students won't get enough breadth.)

This is particularly because most of the learning benefit of exams comes from the time students spend studying the material.

There are several aspects to this:
First of all: I don't know what questions I will use in the exam before I actually have written it - which may very well not have happened before the actual day of the exam. I have a pool of over 300 questions, categorised by the expected length of the answer (no multiple choice over here in Switzerland - you must word your own answers). The duration of the exam (normally 4x60 mins) determines the number of questions from each category. But the actual questions are chosen randomly, I even wrote a programme to do this part for me, to make sure that it is fair (I have my "favourites", the programme doesn't).
Secondly, I want the students to have a close look at large parts of the most important materials of the field. I don't expect them to know everything and all questions are worded in a way, that you can answer with the knowledge from one area or that of another; e.g. a question on the relevance of Hegel or Nietzsche can be answered from a historical point of view (what lead there and where did it lead afterwards?) or from a philosophical point of view (what did they say and why is that important?). So if you're weak in historical knowledge but strong in philosophical, you can put the stress on the latter and still get full scores - and vice versa, of course.
This way the exams are fair: Everybody knows the area, they can learn what is most interesting to them and still everybody can get good grades, given they really put effort into the preparations.
For oral exams the answer is pretty similar: The examiner and the co-examiner prepare a pool of questions at a meeting normally not much more before the exam than maybe a week. So also here: We simply don't know what questions will be in the exam, we just know which areas we want to cover. Also here we will adjust the questions to the strongest areas of the examinee. They have 5 to 10 minutes at the beginning to show us what they know: They choose a topic and get started. After that we ask questions with stress on that area. You quickly know which students have prepared well and which didn't.
Basically: If we see the effort, the grade will be good.

In addition to the other answers my personal motivation is based upon the fact that any exam is only a sample. To be valid as an assessment of how much the student knows about the subject this can only work if it is a truly random sample. If students know, or can predict due to a bias on topic selection, what topics are actually going to be assessed there is no random sample, and therefore the exam is no longer valid as random sample.
As such I do not give hints on what is covered in the exam. I do make clear which topics will not be covered, or what the structure of the exam will be. I will even help with tips such as including answer plans (such as mindmaps), examples and diagrams.

The question raises a few points that I would like to address separately.

I've noticed a majority of professors that I have had will tell students something along the lines of, the exam covers Chapters 1, 2, 3, or the exam covers topics X, Y, Z. Sometimes this is ends up being so broad that it is unlikely that students will even see all the material that is fair game on the exam.

In your "sometimes" scenario, it sounds like you are saying that the exam covers a chapter or topic that has not been addressed at all in the lectures or in the homework. If so, this sounds like a serious problem that is different than the concern described in the question title.

It also likely ends up with some material being more prominent than other material which means playing the guessing game.

Indeed, not all material from the term can be represented on the exam (because the exam period is so much shorter than the term!) So some material will end up being more prominent than other material (which may even be absent.)  I don't agree that this means "playing the guessing game".  I think it would usually work better to study everything a little bit than to guess a random subset and study that to the exclusion of everything else.

Why are professors hesitant to tell students more precisely what they expect them to know?

There are two senses of "expect [students] to know" here.  In one sense, we expect students to know everything we taught; otherwise we wouldn't have wasted our time and theirs teaching it.  In a more limited sense, for the exam we expect you to know the answers to the exam questions.  Obviously we're not going to tell those.

However, given that undergraduate course material is fairly static, would not the professor be expecting the students to have the same knowledge as the previous students?

In the first sense, yes: for this term's exam, we expect the students to know everything we covered this term, and for last term's exam, we expected the students to know everything we covered last term. So if what we covered is the same, what we expect the students to know is also the same (but this isn't a very useful observation.) In the second sense, no: we ask different question on this term's exam than on last term's exam; otherwise if some students get hold of the last exam, it defeats the purpose of the exam.
Executive summary: We expect you to know everything we taught you—duh :-)

I think your premise is wrong. I've never had a professor not disclose the scope of knowledge and/or skill that I'm expected to know at the end of the course.
I've always been told to expect the exam to cover a subset of that material, sometimes with more explicit relative weighting between areas.

I think the question is why professors don't announce exactly which subset will be covered.

OH... maybe?? But why would that even matter?


text:
When repeating a course, why are the grades averaged for GPA?
When repeating a course, why are the grades averaged for GPA?
For example, a student takes course X and receives a C (2.0) and then retakes the course and receives an A (4.0), my university (and I believe most universities in the US at least) will end up with a "B" (3.0) impact on their GPA.
The student has exhibited an "A" level of "knowledge" so why penalize them. If the student attempted to learn on their own and did not attain "requisite" understanding prior to attending the course but ended doing very well in the course they would not be penalized.
Or perhaps offer two measure's of GPA, one as a summation of everything and one that only includes the students best performance for each course taken?

There are many universities where the second grade replaces the first grade in the GPA computation- even in cases where the second grade is lower than the first grade.  Your assumption that this is a universal practice isn't correct.

Thank you for this information, I was (obviously) unaware of this. Do you have information as to how wide-spread one method of handling this situation is vs. the other?

@BrianBorchers There are also cases where the second grade is ignored in calculating the GPA.

In my experience, policies on this vary.  I don't have any statistics on it though.

As others have said, different universities -- and even different programs within a university -- have different policies about when repeating a course is allowed and if so, how it counts towards the GPA.
Actually, it's even more complicated than this: the same student enrolled in the same program can have multiple GPA's! It is my understanding that at many if not most American universities, there is one GPA that is simply the average of the numerical scores (on a 4 point scale) over all courses one has taken.  With respect to this system, if you take a course once and get an A and then again and get a C, then it does not go into your GPA as a 3.0; it goes in as a 4.0 and a 2.0.  The average is the same, but the weight is twice as much, reflecting the fact that you completed two courses rather than just one.  However, GPA "in your major" may be counted with a different weighting system.
You seem to think that there's something unfair about averaging the grades.  To me, it sounds like a generous system: and in fact, I don't think that it is guaranteed that a student is allowed to repeat a course to improve their grade if the grade they got the first time around is considered "satisfactory".  This practice again depends on the university and the program.
You write:

The student has exhibited an "A" level of "knowledge" so why penalize them.

Sorry, where is the penalty you speak of?  They got a C and they got an A, and both are being recorded.

If the student attempted to learn on their own and did not attain "requisite" understanding prior to attending the course but ended doing very well in the course they would not be penalized.

Again, I don't see how anyone is being penalized.  A low grade is not a penalty.

Or perhaps offer two measures of GPA, one as a summation of everything and one that only includes the students best performance for each course taken?

If you want to present this alternate calculation of your GPA to someone else, you can.  But you also have to record the official GPA.
Finally, I think that the practice of allowing a student to take a course multiple times and only record the best grade is a poor one, for several reasons:
i) It is fundamentally not transparent.  The standard unit of coursework in most American universities is the semester-long course.  You are registered for a certain number of courses each semester, and you get grades for each of them.  If grades get replaced by later grades, this kind of information is lost, and it may be that the student is recorded as taking nothing during that semester!  This leads to:
ii) Because high course grade are very desirable, this practice would encourage students who got good but not optimal grades to repeat the course until they got the highest possible grade.  If you think this through soberly for a while, you'll see it's just a bad idea.  The whole point of a grade like a B is that it's good enough to move on to the next course.  Students who repeat courses until they get A's could take much longer getting through the program.  It will create a culture where most students who are taking the course the first time are taking it "for practice only".  If courses were heavily populated with more advanced students who did well the first time around and are insisting on taking it again to get the highest possible grade, then that could seriously skew where the course is being pitched, which would encourage yet more students to repeat every course they take.  Finally:
(iii) We do not want students to be able to graduate with a perfect GPA if they spend seven years in college instead of four.  Moreover -- sorry to divulge the ugly truth -- we don't want a substantial percentage of college students to have the highest, or essentially the highest, possible GPA.  While the competitive nature of GPAs in the current university environment has many unpleasant aspects, the vast majority of American culture is fully bought into it...especially including the students.  If 50% of every class got a 4.0 GPA then most of the advantages of having such a high GPA would evaporate, and employers / graduate schools would hire you based on other metrics.  (Note that people often talk about grade inflation, but really grade inflation is only a problem to those who are not familiar with the current university system.  For everyone who is sufficiently informed, it doesn't matter whether the average grade in a course is a C or a B+.  Still, after taking about 40 courses, there will be a small tail of students who have gotten almost all A's.  So there is no problem here.)

A related issue to your point ii): it would create yet another major advantage for those students with more money to spend on tuition.

"we don't want a substantial percentage of college students to have the highest, or essentially the highest, possible GPA."
I am looking it from the perspective that a students GPA and grades are a good indicator of how knowledgeable they are in a subject. I assumed the professor or the university would want all their students to know everything perfectly (in an ideal world). Thank you for correcting my erroneous assumptions.

@user3730788: Your comment sounds pretty snarky to me.  Definitely the grades in a course should be a good indicator of student performance in the course.  We don't have direct access to knowledge and can only measure it in certain ways.  "I assumed the professor or the university would want all their students to know everything perfectly (in an ideal world)." I don't know what to say to this.  I would want everyone to live forever and never get sick, but crafting institutions which would work well under this assumption would be silly.

...If in the subjects taught in most university courses a substantial minority of students could learn the material perfectly....it doesn't matter what comes next: this is obviously not the case on a global scale.  It could happen on a local scale: I just taught a course in which the majority of the students were extremely strong...so half of them got the highest possible grade.

You do seem to be missing out on the certification aspect of the university system: we are not just serving the students enrolled; we are serving the rest of the society by assessing the performance of the students and reporting this to the outside.  Given that there is such wide variation in skills, knowledge and performance, we need to report who is better or worse in this regard.

The intent was not to be rude. After re-reading it I understand that it comes across as such. I would like to thank you again for providing a thorough answer. If it is the right thing to do, could you append the comment regarding certification to the main response?
I will leave my original comment for continuity so that those reading this in the future will have context for your response.

An average is used to reduce the impact of grade inflation and encourage people to do well the first time. You always take something more seriously, if it always counts for something.
If not, people could take a hard course once to get all the tests and answers, and then "do it again" to get an A in the class, and have no evidence of the D from the first run.

That sounds like a failing on the professors part for using the exact same material. Why would you penalize students for that?
Furthermore, if a student truly wanted to exploit this they could just sit in on the class or get the work from other students in the class.
I'm assuming the primary purpose of a university to educate it's students and that it's primary (nearly sole) responsibility is to those students. Perhaps that is... erroneous.

@user3730788 This methodology SHOULD penalize people. Universities may choose to weight GPAs using averages to present an accurate portrayal of the student, as opposed to masking the original grade. That is a university policy and the university's choice as to how it displays grades to other institutions.