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Is a general GRE test required if I have already passed a GRE Subject Test?
Disclaimer: The GRE Program discontinued the Computer Science Test
If I have already passed a GRE Subject Test for Computer Science, do I still need to pass the general GRE test?
Which test should I take first (general GRE or GRE Subject Test) and why?

If I have already appeared for GRE Subject Test for Computer Science, do I still need to take the general GRE test?

Short answer: Likely, yes. If your school asks for the general GRE, then you need to take it. Without the general GRE scores, your application would not be considered complete, and, thus, may never get forwarded to the department's admissions committee. If in doubt, call or email the department(s) you are applying to and ask.

Which test should I take first(general GRE/GRE Subject Test) and why?

It does not matter. Usually the general GRE is offered more frequently than the subject GREs, so many people take it first. There is no reason you have to do it this way. Take them in an order that is convenient for you, but do not wait until just before your application deadlines. Your scores will not get to your schools in time.

The tests are essentially independent, so you can take either one first.
Some schools want the subject test, but others don't care.  This varies from one school to another.  I got a PhD in computer science from a good school, but I never took the computer science GRE subject test.  On the other hand, I did study a bit to improve my scores on the GRE general.  If you want to know which tests to take (and how heavily they'll be weighted in your application), I think your best option is to contact the school directly (or just read the application checklist on its website).

Also, some schools don't require the GRE at all, and others only pay attention to the subject test.


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Research publications in string theory/QFT by undergrads

Possible Duplicate:
Importance of Undergraduate Research

I am a physics undergrad interested in pursuing research in string theory/ Quantum field theory for my PhD. I am feeling pressurized by the notion, that you NEED to publish a paper to get admission to a good grad school. I was wondering how common is it for a undergrad to write a research paper in these areas? Do most of the students selected for PhD admission in these areas at top universities already have research publications? Also how much is an undergrad aspiring to pursue these areas know before entering grad school.

You could look at the web pages for some of the top departments.  They usually list their grad students, and most of the grad students will have web pages including a CV.  By comparing the dates of their publications and their undergrad degree, you can find out whether they published papers as undergrads.

I'm skeptical of the idea that you need to have a publication to get admission to a good grad school. I know some people who are at such grad schools and I don't think they published anything as an undergrad.

See also this recent question: academia.stackexchange.com/questions/6010/importance-of-undergraduate-research/6011#6011

It's certainly overstating the case to infer that you NEED a publication to get into grad school. It HELPS an application get stronger, but there are other things that can do that as well (a clear research statement, good letters, and so on)

I'm not in the same area as you are, so I couldn't speak for students in theoretical physics. However, generally speaking, a publication doesn't make or break a graduate application. They are definitely a plus, but I don't believe any department would simply reject a student because they have no publications.
If you wanted to find out if graduate students in your area had journal articles published during their undergraduate, you can browse the websites for the related departments of schools you are interested in. Almost all of them have lists of their graduate students, some of which may have uploaded their resumes. You can check the dates on their publications.
Although I said publications don't make or break an application, previous work including internships, projects, research with an advisor in a related area is definitely a must. You are required to show that your interests led you to pursue further work in your fields of interest. This doesn't even have to be the same field that you are applying to graduate school for. But you are required to demonstrate that you are willing to put in the time and effort to go above and beyond in what you like to do.

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Applying for PhD admission at more than one department in the same university
I was wondering if it is legal, and also advisable to apply for a PhD position at more than one department in the same university. For e.g. I am interested in representation theory and string theory. So would it be possible to apply to the maths and physics department, or there would be inter-departmental clashes leading to my application being disqualified. I guess the rules would be different. SO what are the rules in US and Europe unis resp.

You have to ask each university.
I don't believe there are any ethical issues with applying to more than one program.  Moreover, I think it's rare for graduate admissions committees in different departments to share information about applicants.  (In the US, that sharing might even run afoul of FERPA, but interpretations of FERPA vary wildly from one university to the next.)
However, at some universities, it is not possible to apply to more than one department.  At my university, for example, all graduate applications go through a central web site that forces each applicant to choose exactly one program.  Yes, I think this is stupid.

There's no way around that? Even by using slightly different name variations or email accounts?

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Master student pursuing PHD: how to spend summer break?
So I'm a master student pursuing a PHD. I'm currently following a research master program of which the natural path is a PHD program, in which I am seriously interested. I already hold a regular master in marketing and a bachelor in business.
My field is business (specifically, quantitative marketing, but I also like some extensions to strategic topics in management).
Now I want to spend the summer (break) doing something fruitful for my skills and/or possibly, carreer. I expect to be done with course obligations around week 19, new semester starts in september which gives me at least (in case of resits) 10 weeks of free time but can easily be around 15 weeks.
I identified some options:

Work in advance for thesis (look for suitable topic, review literature)
Summer school (abroad)
Contact someone from my department to collaborate on research
Contact someone from my department to advise me on extra readings
Find an intership or job (may be difficult when regarding my field, experience, and time available)

Can someone give me some advice or other ideas?

Take a break, see your friends and family, travel, have fun. Because when you do a PhD, you can say Goodbye to most of that. ;-)

I think what you're asking is fairly subjective, might depend somewhat on your field, and also, your options and opportunities can differ greatly according to the country in which you're doing your Masters.
The most I can offer, as somebody who just started a PhD, is to tell you what I did during my Masters (that was outside of regular program) and, more importantly, why and how I think it helped.
I did two research internships abroad, one before my last year of classes, and one during my last semester that played out as co-supervised research for my Master thesis.
What I got from that:

I saw what research entails in other countries where research is important and valued (research in Croatia, where I come from, is at mediocre level at best)

I experienced working in two very different labs, under very different supervision, different lab dynamics and approaches towards research

I discovered which setting works best for me and which setting I work best in
(e.g. I prefer a relaxed, flexible environment and being advised/supervised by somebody openly helpful and talkative (it's just a thing for me) as opposed to strict working hours, getting tasks without understanding the importance and when the feedback (especially the negative aspects) is constrained because of inherit cultural politeness)

I made valuable contacts who are at various levels in the research hierarchies - some of them gave me ideas, others encouragement, and some even gave me recommendation letters

in informal settings, I exchanged concrete ideas as well as general attitudes towards research and science (and life) with people that come from different cultural and academical backgrounds

I found out how (very different) PhD students think of their "jobs" and what they think of their career choices and I was free to make my own assessment about how happy and fulfilled doing the PhD made them and why, so my guess about how happy it would make me was more educated

the proximity to the location where I finally applied for a PhD got me the PhD grant - I would have never gotten that particular one if I wasn't there to have a few informal talks and give my grant presentation

To summarize, what you should be aiming to get from your summer activity is diversity. Diversity in attitudes, approaches, contacts and ideas. You're allowed and encouraged to work and thrive in an environment best for you for anything more permanent (several years long), but you can't really know what you prefer if you never tried anything different.
I'm not going to tell you which activity to choose, but I would go to the one that had the potential to expose me to most new people, ideas and attitudes. You can always sacrifice some sleep to do extra work, but no amount of work in the world can measure up what you get from formal and informal interactions.
In my (a bit Utopian) view of the world, that's how science progresses: scientists travel and during those travels, the best of many worlds collides. By the end of those travels, hopefully, all the worlds are a little bit better off. When you're old, wise and grumpy, you travel to give back to the community and spread the ideas you spend a big part of your life to shape. But, since you expect to be giving back later, that entails you to travel when you're young, curious and perky, and get the most of what the community has to offer - little, baby ideas, and chisels to shape your own ideas.


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Important factors for hiring a young mathematician
Let's list important factors for evaluation of a job candidate (for research post doc, assistant professor, tenure track, etc):

Research experience (research articles, research talks, expository articles, perhaps books).
Teaching experience (tutoring, undergraduate courses, graduate courses, etc).
Academic background (grades, the university of graduation, current affiliation, etc).
Reference (who is writing reference letter and how he is writing it).
Personal (natural) features (nationality, race, language, etc).
Social and family status (connections, marriage, etc).
Other factors (you name it).

I have been in job market for several years. I was always wondering how do the above factors affect my job application in different academic institutions? I would like to know the approximate percentage of importance of these factors in different institutions.
And my second question is How the hiring committees evaluate a candidate? Is it based on reference letters, CV, list of publications, research statement, teaching statement?
My impression is reference letters are very important at least for the first job after PhD. Am I right?

With respect to (6), I am a (young) mathematician who is about to enter the job market and I very consciously placed a picture of me and my son on my website. Mathematicians have a reputation when it comes to people skills, so I believe that telling potential employers that I possess good enough social skills to be married with a child is important (at least for me).

I am not sure being married has anything to do with having good social skills what every that means. I think the phrase "social skills" has very vague meaning.

Perhaps, I don't know. But it does imply I have not spent my entire life in a box.

One thing I like about academia is that we (supposedly) have the freedom to not obey the society in every little detail of out lives. So I try not to judge about people who choose to be single or married or even homosexual.

I don't have anything essentially divergent to say from the other answers, but since you inquired about mathematics specifically and I am a mathematician who has been (and currently am) involved in postdoctoral and tenure track hiring, I thought it might be useful for me to weigh in as well.  Lacking true inspiration, let me just comment on your criteria.
(Let me also assume that we are talking about jobs at a "research university", as it seems you are.)

Research experience (research articles, research talks, expository articles, perhaps books).

Mathematicians are judged on a combination of research promise and research success: as you get older, one looks increasingly for evidence that the former has been converted into the latter.  However, for every kind of research job in mathematics, they are hiring you on the basis of the work they expect you to do in the future.  So, for instance, if you have already solved a major problem, you can coast on that for a time but after a while people want to hear what you are working on now.  Research talks are probably the best way of exploring the dichotomy between past and future research: as such, they are very important whenever they exist, which is almost always on the tenure track job market and in a small (but perhaps increasing?) minority of postdoctoral jobs.
Expository articles generally do not count towards the research component of your application.  (If someone is counting papers, then if you have 8 research papers and 1 expository paper then people will probably say you have 9 papers altogether, so it counts a little bit.  But if pressed, its value could contract considerably: e.g. if there are worries that a candidate has too few papers, than a paper viewed as expository will probably not allay this worry.) Strategically it is probably best to advertise expository articles as having some teaching / mentoring / service component, if at all possible.
With regard to writing books: one of my most distinguished colleagues, Dino Lorenzini, wrote an excellent and rather successful book near the beginning of his career.  He now tells anyone who will listen that junior faculty should not write books.  Of course sometimes the heart wants what it wants, but from a strategic perspective I think this is eminently sound, and I say this as someone who may turn around and write some books now that I am solidly into my mid-career.

Teaching experience (tutoring, undergraduate courses, graduate courses, etc).

Successful teaching experiences are indeed valued for a research job.  At most research universities teaching is still a main component of one's job and, especially, of one's promotion and tenure packages.  Most research departments are looking most of the time for thoroughly solid teachers rather than especially brilliant or innovative ones.  Your teaching dossier should convey most of all that the department who hires you will never have to think about your teaching in a negative way.
Some graduate students do not get to do instruction at all (as opposed to TA work: grading, leading problem sessions, and so forth).  There is a big difference between TA work and instruction, and as a hirer I am very wary of candidates who attempt to convince me that they will be a successful instructor based only on TA experience.  I would strongly advise every math graduate student to be the instructor of record for at least one successful undergraduate course (where "successful" means you can get a strong teaching letter out of the experience).
Teaching experience at the graduate level is almost unheard of for graduate students and is far from guaranteed in postdocs.  Even within my own department, some of my colleagues feel strongly that postdocs should teach topics graduate courses in their areas of interest, whereas other colleagues feel that it is the job of the tenure track faculty to teach these courses.  I lean more towards the latter, and I don't feel that teaching graduate courses is an important part of a tenure track job application: I would be equally impressed or more with other kinds of interactions with the graduate program, e.g. participating in or organizing seminars, reading theses, and so forth.
I'm having a hard time thinking about how tutoring experience could play a significant role.  If you have founded the Khan Academy or the Euclid Lab, you would probably get some attention / consideration for this.  Much less and your employers are unlikely to care.

Academic background (grades, the university of graduation, current affiliation, etc).

No research university that I know of asks for grades or transcripts for candidates for faculty positions.  Of course your pedigree -- i.e., where you did your undergraduate and graduate work, and your current institution -- is of some importance, but not that much importance.  Anyway, what's done is done here: presumably you took what opportunities you could to attend / work at better, rather than worse, institutions!

Reference (who is writing reference letter and how he is writing it).

Or she!  When you are applying for your first postdoc, your adviser's letter may well be the most important part of the application: most graduates, even very strong ones, cannot speak about their research accomplishments and near future goals as convincingly as their advisers can.  Later on your adviser's letter gets less important, but you probably get more letters overall, and they are always a key part of the application.

Personal (natural) features (nationality, race, language, etc).

In the United States it is illegal to discriminate on the basis of race.  Nationality is probably a no-go as well.  Language issues are important: if English is not your native language, employers will (or at any rate, should) look carefully at your skills.

Social and family status (connections, marriage, etc).

Professional connections can be important; e.g. they come out in recommendation letters and in your academic pedigree.  It is illegal for employers to inquire about your marital status, sexual orientation, or whether you have children.  It is not illegal for you to bring these things up, and if you have a "two-body problem" -- i.e., a partner who is also an academic -- than you should do so at some point, and that brings an extra layer of complication to the process.  But if a candidate is not looking for an academic job for her partner, I honestly don't care at all whether she is married, gay, celibate, and so forth.  I can assure you that in most American departments any such talk about these matters in the context of a hiring discussion would be rapidly quelled.

Thank you for your detailed answer. I enjoyed it especially because you presented a mathematician perspective. I have written a relatively long lecture notes on C*-algebras (available at arXiv:1211.3404) which is based on a graduate course I have given. Does it count as an evidence for my teaching skills?

@Vahid: Honestly? Probably not.  It is hard to get credit for expository work.  (But I will download your notes myself, at least.)

One minor quibble: Later on your adviser's letter gets less important — In my experience (in theoretical computer science), with very rare exceptions, once someone has a tenure-track position, letters from their PhD advisor are somewhere between worthless and dangerous.

"No research university that I know of asks for grades or transcripts for candidates for faculty positions." My university needed a transcript as verification that I had a PhD, but this was only after they'd offered me the job (and maybe even after all the signatures were on paper, I don't recall).  The particularly silly thing was that I was being hired by the same department where I had gotten my PhD, and they still needed to get a transcript.

Your question is fairly general, but the title implies that you want to ask about mathematics. I think the more general question makes sense, so I'll answer that one, based on my experience in computer science in the US
Among the criteria you list, (1) and (4) (research and letters) are usually the most important in research-oriented universities. (3) academic background (but not grades) plays a role in initial filtering but usually takes second place to (1)/(4) once people get some familiarity with the candidate.
It is rare that (2) plays a role, unless the job calls for significant teaching, or is in a teaching-oriented university. Since math folks teach a lot more than CS folks, this might be one point of difference.
Many of the factors listed in (5) cannot be considered legally, and rightly so. I seriously doubt that (6) plays a direct role, but personal connections can help open doors, much like (3).

Some of the factors listed in (6) also cannot be considered legally.  At least in the US, it's illegal to discriminate on the basis of marital status.

I disagree about the factors in (5). While "race" is a touchy and usually illegal thing to consider, "language spoken" and "nationality" are often things necessary to be considered for hires. Even for research-oriented jobs, as long as there is a possibility that the job involves teaching, being able to speak the language of the land definitely is a plus. And there can be nationality requirements for hiring purposes (immigration quota allotted to a university, specific grants only payable to nationals, or jobs working with "sensitive" information).

I'll second Suresh’s generic answer (I'm a chemist myself), but I'll add a few points: first, one of the reasons that teaching skills usually play little role in hiring decisions is that they are much harder to evaluate/quantify than research skills. Most people in the hiring committee will be researchers or think they know how research should be evaluated. Most of them don't know how to evaluate teaching skills (and if they did, they hardly have time to do it anyway).
Regarding 5, it probably depends on the country, but some of these can be serious barriers for employment: language is the most important one, especially if teaching is involved. At least in France, most university won't recruit at the junior level someone who doesn't speak French, as that is the language in which undergrad courses are taught. Nationality can also be a stopper in specific circumstances (nuclear research, for one thing).
Finally, I think an important factor you did not list is the performance of the candidate in interviews with the hiring committee: self-assurance, conveying the impression of someone well-prepared, etc.

Thanks for your anuswer. Of course a candidate's performance in interview process is important too.

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Is it ethical to use a data-set made as a research assistant?
Two years ago I was a research assistant during my undergraduate and my sole duty was the aggregation of many economic surveys, a very tedious task. This data-set, to my knowledge is one of a kind.
Now in graduate school, I had come up with a research idea, and this data-set that I made would be perfect for my research. My research idea is not related to my previous professors, though as of yet, he has no present publication for the research he was doing when I was working for him.
My question is, would it be ethical for me to use this data-set for my own research when I had made it while being employed for my previous professor. The obvious response would be to ask him but sadly we had a falling-out just before I graduated.

As with any situation, there are many levels to any answer… Mainly, the question is: was the data-set published? If so, who owns the copyright? Probably not your professor, but the university. If it wasn't published, then it isn't ethical to use the records you kept of it for another purpose, without authorization from your employer.
However, there might be a solution, regardless of your fall-out before graduation. [1] Just get your current advisor to ask him! One staff researcher to another, the situation is not the same as you dealing with your formed professor.

[1] I am amazed at how many times I have read this situation (I cannot speak to my adviser/professor/…) raised in questions on this site! Every time, I think: before or around the time of graduation, aren't you a bit young to make “enemies”? I can sure name many people I thought fools or who annoyed me during my studies and early career, but I always tried as hard as I could to get things done in a manner that no bridge was burnt…

+1 for that last paragraph. A tiny bit of communication now can prevent a lifetime of "hm, I don't like that guy so much" later on.

@F'x: I like your answer. But about your last paragraph, I'd like to say that sometimes it is so much better to separate from people who are so hard to tolerate. We are not living in a perfect world, so sometimes it is better to cut loose and move on.

@Vahid But cutting loose doesn't necessarily mean that things have to end badly… amicable divorce is always a possibility (for academic relationships, at least!)


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why is the impact factor of mathematical journals "often" lower than the impact factor of journals in other disciplines
I was always wondering why is the impact factor of mathematical journals "often" lower than the impact factor of journals in other disciplines?  I come up with some guesses  that I would like to know your opinion about them.

Mathematics papers are so hard to read and follow (or so specialized) that only a few people can read and apply their results.
There are relatively a large number of subfields and branches of mathematics and only a few people are working in each branch.
The number of journals and papers in mathematics (divided by the number of active mathematicians) is relatively higher than other disciplines.
A mixture of these.

Please, share your insights about this issue.

Why isn't the answer obviously "because mathematics papers are cited less often (and less quickly)"?

@JeffE: That just reduces the question to "why are mathematics papers cited less often and less quickly?"  It's clear that they are, and the question seems worthwile (if only to reassure mathematicians that the answer isn't necessarily "because they are less interesting or important").

Mathematics papers are cited less often because the mathematicians are citing less often

Because citations to maths papers can start and continue to accumulate decades after the paper is published, when the real importance of the work is apparent, rather than in the weeks after it appears and others publish papers jumping on the bandwagon, and then basically stop after a few years.

There are a lot of different factors, and I know of no reliable way to determine which is the best explanation.  For example, one theory is that mathematics simply has less impact (in the non-technical sense) than most scientific fields.  I don't believe this, but it's hard to give a principled refutation.  The whole subject strikes me as a little silly, with lots of opinions and numbers with no clear meaning.
One important factor is clearly that mathematicians write fewer, often longer papers than most scientists.  Another is the two-year cycle mentioned by walkmanyi (citations after two years do not count for impact factor, which is incompatible with both the time lag in mathematics publication and the time required to carry out research in mathematics in the first place).
Another factor is the size of the field.  The highest impact factors should occur in an enormous field with some incredibly important research and also a ton of less important papers that cite the great ones.  Mathematics is just not that large a field (compared with biology or medicine, certainly), and it furthermore fragments into a lot of subfields it's difficult to move between.  When someone makes an amazing discovery in algebraic geometry, you aren't going to get a flood of mathematicians from other areas rushing in to take the next steps, because algebraic geometry requires a lot of background.  I don't think that's a bad thing for mathematics as a whole (the things the would-be algebraic geometers are doing instead are probably as valuable as following the latest trends would be), but it cuts down on the opportunities for amassing citations quickly.
Ultimately, I doubt there's any conclusive or satisfying way to determine how much of a role each of these factors plays.
For some published commentary on impact factors in mathematics, see Nefarious Numbers by Arnold and Fowler and Impact Factor and How it Relates to Quality of Journals by Milman.  The first paper focuses on the flaws of impact factors and their abuse/manipulation, while the second explains how impact factor calculations relate to mathematical publication practices (and some of the incentives for journal editors).  Neither directly answers the question here, but they both shed some light on it.

Size of the field: In my original answer I wanted to highlight this, but then decided not to as I cannot argue as IF is a ratio cited vs. published so it shouldn't be influenced by the size of the field. But if you are looking for arguments in this direction, there's quite some support in bibliometric maps of science. See e.g., here which is taken from here. There are more maps like that. Clearly, mathematics is a relatively small field in comparison to other scientific disciplines.

In fact, it seems to me that size of the field should be related to the variability of the number of citations, rather to the the average number of citation by paper (see my answer). However, it makes me wonder whether the feeling that math journals have lesser IF than, say biology journals could be untrue, mostly based on the comparison of the highest IF journals in each field. This would make the size of the field a better explanation for that perception, in my opinion.

I must admit that I tend to disagree with the previous answers: while the description of the specifics of the mathematical community are accurate, I do not see why this should affect the impact factor (except for the time needed before an article is cited, whose influence is clear). In particular, size of the field does not have any impact per itself on the average impact factor of papers. In fact, papers are less cited mainly because papers cite less.
Let me back my point, first assuming we are looking in a field that is closed (only cites itself and is only cited by itself) and stationary (no evolution of the number of papers published or the average number of references per article). Consider the publication graph of a given year : it is a bipartite graph, whose vertices are papers published year 0 (first partition) and years -1 and -2 (second partition) and whose edges are citations from the first ones to the second ones. Then the (article) average of impact factors AIF in this domain is the ratio
AIF = (#citations from year 0 papers to year -1 and -2 ones)/(#year -1 and -2 papers)
which is equal to (#edges)/(#papers published in two years), since the field is assumed to be stationary. This is also twice the average number of references to the two preceding years that a paper in the fields has.
So the article average impact factor of a closed and stationary field is solely governed by the references habits in the field. In particular, this is not affected by the overall size of the field (e.g. math as opposed to biology).
Given the distribution of references, an expending field will tend to have bigger impact factor, as will a field that is often cited by other ones. I do not feel that speed of expansion is an important factor for math compared to other fields, but fondamental mathematics are probably seldom cited outside itself. This has little impact if one consider maths against the rest of the world, though, since math papers seldomly cited outside the field too.
Another factor can be the distribution of papers among journals: for example, if a field has only two journals, one very large and one very small that only gets the very top articles, then the (unweighted) journal average IF will be extremely high. I doubt this explain much of the difference between math and the other fields, since mathematics have a strong hierarchy of journals.
So, what we really have to explain is why math papers cite less papers in the two-years range than papers in (most) other fields. This will explain why they are less cited.
Then the answer seems quite clear: maths papers are often long to read, and take time to be digested. The core of a biology paper is usually easy to understand and such papers are more easy to cite. There is also a small subfield effect: mathematician can work on problems that involve few previous papers. This is different from the size of fields, because it is more about the degree of specialization.

Hmm, interesting.  I agree that math papers cite less within the two-year window for field-specific reasons, but I don't see any evidence they cite less otherwise.  I guess what this suggests is that the distribution of citations per page in mathematics must simply be more uniform if it is less highly peaked?  I agree that the average number of citations per paper can't scale with the size of the field, but I don't think that's what anyone observes.  Instead, it's the number of citations per good paper, and that probably does scale.

(I.e., I doubt the number of breakthroughs scales with the size of a field, thanks to diminishing returns.  It presumably increases too, but a little more slowly, and all the other papers are citing the breakthroughs.)

I fully agree with this answer, and want to add the point that mathematics has few review articles compared to a field like biology, for example. Review articles often contain hundreds of references and thus push impact factors greatly.

why is the impact factor of mathematical journals "often" lower than the impact factor of journals in other disciplines?

Besides your observations 2 and 3, my take on this would stem from the observation that the pace of work in mathematics tends to be a longer shot than in disciplines, such as biology where often there would be several competing groups working on a very close subject. The impact factor is calculated as "recent", but in disciplines with slow pace of development, sooner than a paper gets cited, it already falls of the considered recent period (2, or 5 recent years).

Rather than the "pace of work", I would put this down do the appalling culture, in Mathematics, of taking forever to peer-review journal papers. If it takes more than a year for a paper to get accepted, it takes more than two years for references to said paper to appear.

@Pedro: I don't find it appalling.  Journals simply aren't the primary means of communication in mathematics (preprints are).  Instead, we've got a hybrid system of instantaneous communication of the latest results combined with a slow and careful refereeing process for long-term archiving.  Of course not everyone's as quick or efficient as they could be, and editors are always trying to find ways to speed the process up, but there's nothing wrong with a system where it takes ten times as long to check the proofs in a math paper as to check that a biology paper uses a reasonable methodology.

An interesting perspective here:

Antonia Ferrer-Sapena, Enrique A. Sánchez-Pérez, Fernanda Peset, Luis-Millán González, Rafael Aleixandre-Benavent, The Impact Factor as a measuring tool of the prestige of the journals in research assessment in mathematics, Research Evaluation 25 Issue 3 (2016) pp 306–314,
  https://doi.org/10.1093/reseval/rvv041

Stating the obvious:

A great difference among the journals that publish pure mathematics and the specialized journals in other sciences is that there are very prestigious mathematical journals that publish a little number of papers per year. In other sciences, a typical leading journal publishes hundreds of papers per year.

And

The index of obsolescence of the papers in mathematics is very long, and the articles start their influence in the mathematical research later than in other sciences ( Bensman et al. 2010 ). A 10–20 years old paper may be completely in order for a research that is starting now. On the other hand, the papers ‘start to live’ later than in other sciences. In the first 2 years the articles may have no citations at all.

Mathematicians also don't disdain old sources

Mathematicians do not believe that only recent papers can be useful for their research interest. In fact, old papers and books appear in the bibliography of almost all papers in pure mathematics. Consequently, even the 5-year IF involves a too small evaluation period ( IMU 2008 ). This means that in practice, researchers take into account all the mathematical literature for their research, without considering that new references are in any sense better than old ones. Moreover, sometimes an old paper of a prestigious author is preferred to a new paper with similar results. Classical books in well-established mathematical disciplines are considered as primary sources and appear in the list of references of almost every paper. Also, bibliographic material that is never considered as primary sources in other disciplines—specialized books, doctoral thesis, (even unpublished) lecture notes—are usual references in mathematical papers. These sources of information are not considered for the computation of the IF. Summing up all these aspects, it can be said that mathematics are in a sense more similar to classical humanistic disciplines than to the scientific ones. In any case, the 2-year IF is considered in general as inadequate for researchers in mathematics ( IMU 2008 )

While I am not familiar in detail with mathematical literature, there is a factor I often see when I compare different branches of Chemistry, Physics or Medicine. Depending on the nature of research, it can often be built heavily on other papers and cite them extensively. For example, it is not rare that a short Chemistry letter of 2-3 pages cites other 20 papers, which includes important experimental details, reviews of other experiments etc. Longer paper, of course, can include much more.
What I see often with theoretical papers that they rely much less on others papers, therefore often cite far fewer - in exchange they are also far less cited on average. I can easily imagine that the situation is similar to mathematics, where proofs are not built on extensively on others work.

" proofs are not built on extensively on others work." this is not the case. Proofs in mathematics rely on work dating back hundreds of years, depending on the field. But we don't cite Pythagoras, or Cauchy, or Cantor, or Hausdorff, or Atiyah and Singer, just because we use their techniques, unlike in biology where decades-old techniques that are in textbooks that everybody knows about still need to have their original papers cited (cf https://www.the-scientist.com/research/the-4-most-cited-papers-magic-in-these-methods-62753)

@DavidRoberts "Proofs in mathematics rely on work dating back hundreds of years" and do you cite them? Do you need to cite them? I am talking about information that is not common knowledge yet needed for understanding the paper. This is even truer in interdisciplinary fields - the readership can be very wide. Your examples are more of exceptions than the typical. The vast majority of tenure-track researchers has papers with 50+ citations. Do you think all those papers are written decades ago and textbook knowledge? I think you take this too personal.

I recently started working at the intersection between physics and chemistry. As a physicist, it struck me that the impact factor of chemistry journals of a given quality is always significantly higher than the impact factor of physics journals of similar quality. The explanation is simply down to different citation habits in these fields. Typical chemistry papers will contain about twice as many bibliographic references as typical physics papers of the same length.
In an ideally isolated field where papers only cite other papers within the field, the average number of citations a paper attracts must equal the average number of references that a paper contains. Obviously, this simple models does not take into account interdisciplinary citations, and the fact that IF only considers citations received during the last 2 (or 5) years, but it helps to explain why the IF of chemistry journals is much higher than the IF of physics journals.
In a field like mathematics, where I expect the specific subfields to be fairly isolated in terms of citations, I think that lower IF can be easily explained and understood in terms of short reference lists being the norm.


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Is a good GRE score evidence of merit?
If a student acquires a good score in GRE, does it guarantees that he has a good merit to earn a good grade in a taught graduate program?

No, it does not.

A "taught" graduate program is a course-only MS I presume ?

Not merit.  Just potential.

Short answer: No, not at all.
Long answer:

What I understood from the official GRE manual:

GRE, just like any other multiple choice exam, requires fairly specific preparation. You need to understand how to go about analyzing their standardized types of problems, methods of elimination of the answer choices, and even sometimes think like the person who's writing the question. Getting a good score means that you've acquired these skills and can use them rather efficiently in the 3 hours you took the exam. This is what I understood by reading their official manual.

My personal opinion:

Doing well on GRE does probably also mean that you can, in fact, learn how to do other things, given that they are presented to you in "standard packaging". But so does an undergraduate degree where you get to take classes and prove by taking exams that you can efficiently use what you learned in those classes.
However, none of these (and no other single thing) actually "guarantees" that you will do well in graduate school, regardless of what program you go into. It's just a metric that you should be able to do well, if you are passionate enough to do well in graduate school.

For most people, the hardest part of grad school is research, what you do after you've passed your exams.  Doing well on the GRE shows some aptitude for coursework and exams, but has very little correlation to succeeding in the much more open-ended endeavor that is research.

@DanC but the question specifically focuses on a taught (i.e., no research) program.

@DanielE.Shub Ah! I didn't understand that word in the question, so I ignored it.  Now I see.

My answer would be depending on which GRE are you referring to?
If it is a specialized GRE, like the one of Computer Science, I do agree that it shows some merit, since it test basic knowledge the students should have in order to start doing useful things as soon as they start their PhD.
If you are talking about the general GRE, I think it does not reflect well in some abilities like problem solving and scientific comprehension, since its math part evaluates how fast can you make calculations, not how deep is your knowledge of basic math.
Again, there are a plethora of factors that will affect whether you get in or not in a Grad Course, as far as I remember GPA also affects in some extent, since top universities want people that were at least in the top 1%

The problem I see with the GREs is that the scoring range is highly compressed. The difference between scoring in the bottom quartile and the top quartile tells you a fair amount. The difference between the 90th percentile and the 99th percentile, where the vast majority of graduate students score, tells you very little. It is the difference of a couple of questions.


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Applying to graduate programs unrelated to undergraduate degree
Is it possible to enroll in a graduate program completely unrelated to one's undergraduate degree? Additionally, in my case, my undergraduate degree (computer science) is from outside the USA, and I'm applying to graduate programs (in English Literature) within the USA. Will this be a problem?

I've known teachers at my college that had a BS in Literature, and a PHD in Computer Linguistics, so it is not that farfetched to pursue such tracks. Just know how to "sell" your application and there shouldn't be a reason for them to reject you.

You should definitely apply. I have seen many cases where individuals with degrees in tangentially related fields not only are accepted to, but excel in, graduate programs in different fields.
Do note, though, that if you're applying to be a PhD, it's expected that you'll be doing research in the new field, and you'll have to demonstrate to the application committee that you're up to the task. You may have to be creative about this, given that your background is very different from what they're used to seeing; consider emphasizing any possible applications of computer science to literature (ngrams, maybe?) or anything else which may strengthen your application.


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Are undergraduate reference letters adequate for PhD applications after a masters program?
Currently I am finishing my masters (one year) in economics at a Canadian university and am intending to apply to Canadian universities to do a PhD.
The issue I have is that in the courses I had taken last semester the professors were closed to student contact making it near impossible to build relationships.
For my applications I intended to rely upon professors from my undergraduate university that know me quite well and who I know will write high-quality letters.
A colleague of mine mentioned that when applying for a PhD program, it is expected that my references will come from my masters university and it is generally not acceptable practice to have references from the undergraduate one.
Is this actually the case? If so, what is the best course of action?

"near impossible to build relationships" does not necessarily imply that he would not write recommendation letter for you. Have you asked him yet?

@scaaahu I had already made meetings with several of my professors to talk about references.
Before asking this question I had checked the other questions on this site, and I read a response that a neutral letter may do more harm then good which has me a bit concerned as well.

@D.W. posted an excellent answer; however, if your M.S. studies did not end well due to "circumstances beyond your control," then you have to get creative and find non-M.S. references that can speak to your research capabilities/potential. Getting into a great Ph.D. program without references from your M.S. institution can be done.

A Ph.D. program is about research.  Have you done research?  If not, how do you know you want to study for a Ph.D.?
It is your responsibility to seek out opportunities for research.
Protestations that your professors were not open to communication are not likely to be viewed positively by an admissions committee.
If you've had some research experiences, have you considered asking those you worked with for a recommendation letter?  If you haven't had any research experience, that will make it significantly harder to be admitted into a Ph.D. program, no matter who writes your letters.
And if you haven't been inspired to seek out opportunities to get involved in research, that would make me wonder whether you will truly enjoy a Ph.D. program.  Going to a Ph.D. program "by default" or because "that's what everyone is doing" is a terrible idea; you should only join a Ph.D. program if you are passionate and excited about doing research, because that's what you are going to be spending most of your time doing in a Ph.D. program, and that is what Ph.D. programs are designed to prepare you for.  So, you might also want to do a little bit of soul-searching to figure out whether a Ph.D. program truly is the right direction for you.  If it's not, it's much better to find out now rather than after spending several years in a Ph.D. program.
It is acceptable to have letters of reference from a mixture of your undergraduate and your masters university.  People would probably ask questions if all of your letters were from your undergraduate university and none were from your masters university.  That might make the admissions committee wonder: What were you doing with your time at the M.S. program?  Why didn't you seek out opportunities to get involved in research and other activities beyond coursework?  Is there some hidden story?  (For instance, did you completely alienate all the professors in your M.S. program?  Or, do you have little self-drive to do research?  Or, maybe you have little experience with research, and thus no idea whether you are good at and enjoy research, and thus little basis to judge whether a Ph.D. program is a good fit for you.)
That said, the most important thing is to have letters from people who know you well, and who know well how to evaluate candidates for Ph.D. programs.  So, which professors (or other established researchers) know you well and can best comment on your research ability or research potential?

As you mentioned, though, the instructors who can best comment on research are the ones you want to get letters from. . . .

That makes sense.
I have four previous RAships and a publication I co-authored with a former professor - all from undergraduate. Since the professors I worked with here would better be able to attest to me research capabilities they may be my more appropriate choice.

@Jordan, yup, sounds like asking those professors (who you've done past research with) might make the most sense with.  Certainly do ask the former professor who you co-authored a paper with and who you've done four RAships with -- based upon what you've told us, that sounds like a perfect person to have as one of your letter-writers.

+1 for needing at least one letter from your MS faculty.

Not really. It is assumed that if you are a good student you would be able to get good reference letters from your masters courses. It would have to be from your undergraduate thesis advisor or some sort of exceptional activity you did during undergrad, not just a regular class with a good grade, if at all.


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Is it advisable to mention the dollar amount for grants on a CV?
I'm a soon-to-be post-doc and am currently sending my resumes to people and applying to places. 4 years ago, I applied for a grant and got funding for 3 years for everything — meaning my tuition, pay, research, travel expenses, university overhead and then some more, all of which totals to a large $ amount.
My question is: Is it advisable to put the actual $ amount on the CV (to show I'm capable of getting and handling funds) or would that seem like showing off? I've seen some people (usually folks with more experience) list it, but they're also ones that have won several grants and fundings, so there's stuff to list. In my case, this is the only thing so I'm afraid of it standing out and attracting unwanted attention.

If you mention the details of what the grant covered (like you did for this question), that would imply that the grant wasn't trivial without going into dollar amounts - so, how have you described the grant in your CV?

@TCSGrad Right now, I've just listed it as a "Funding to research X from sponsor Y" without going into any details (I know, it's terrible)

I recommend listing it in the same way as an experienced researcher would, except your list has only one entry and his has many. SO: sponsor organization name, official name of the grant, grant ID number from the sponsor, starting and ending dates, etc. plus a brief abstract of the work, and references to your grant's deliverables.

If you're applying for academic jobs in the US, your ability to acquire funding is one component of your viability as an academic. So definitely add in the information about the amount of money. It will stand out (in a good way)

I would add a caveat to this - "as long as the amounts aren't trivial".


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How to cope with the change from easy undergrad. to difficult masters?
I'm doing a masters course at a different university than I did my undergrad (both in maths). I did well in my undergrad but now I'm finding it very difficult. The shock of the change is hard to cope with.
I'm not just finding it very difficult, but I get zero feedback: we don't have any tests and I was not able to make friends so I don't know how others are finding it. I'm starting to think that I might be an idiot.

How can I build some confidence in my abilities at the same time as I rush and struggle to keep up with the massive rate of new material I need to learn?
How might I get myself some reassurance that I can actually pass, or stop worrying about this so much? (I feel terribly guilty using so much money from my family to be here) It's possible that I don't really have a chance at all but knowing that would be fine.

You are not alone!

Have you tried talking to your teachers?

I don't know what I would talk to them about, and my thoughts are very incoherent so it's hard to have a conversation about things.

Did you try going to forums, QA sites, or just find people doing similar things in the world?

@Leonpalafox, not other than this one. Any suggestions?

Depends on your area, there are many Q&A sites for different areas, Metaoptimize is there for Machine Learning, Biostar for BIoinformatics, Physics and Math stackexchange as well.

Feelings of inadequacy are quite common when starting a new graduate program—you are surrounded by talented people (if they weren't, presumably they wouldn't be graduate students!), and there is often a big leap in expectations between the requirements of a bachelor's program and the corresponding graduate program, particularly if you're at a top program in your field.
As one of the commenters mentioned, talking to your professors or teaching assistants may be one good way to get help, or to get at least some reassurance about how you're doing. Depending on what your university or department provides, they may be able to provide you with resources to help you study or prepare for your exams. This might be as much as arranging a tutor for you, or as simple as providing you with sample exams from previous course offerings. If your department has a "graduate student council" or "society" or something like that designed to help out the students, then a lot of these may have already been collected by students from previous years for use by students in later years.
In general, though, don't get too discouraged. It is recognized by most instructors that graduate school is harder than an undergraduate, and the grading tends to match that view. There are very few graduate school courses that are not graded "on a curve"; otherwise everybody would have bad grades! (When the top score on an exam is 60/100, most schools won't let you fail everybody!)

I guess the level of undergraduate courses  at your new university is higher than the ones at your previous univ. So it is better you audit some of the undergraduate courses or you study them by yourself. For example, if you have taken algebraic topology this semester you might need to audit general topology too or you maybe should study some advanced algebra as well. Ask the professors about the background necessary for master courses and how you can get this background.

I am a big advocate of auditing.  While it may take more time out of your day, it can pay off enormously over time!

My advice is to befriend a second year or older grad student.
I was in the exact same spot as you are now and unfortunately for me, there was nobody there to help me (I am in a foreign non English speaking country, where people were anything but friendly).
I am in my 3rd in grad school and I have learned the following golden rules (the hard way).

If you are not sure what is expected of you - ask as many people as possible. No one will come and tell you what you need to know. If you are not confident doing this in person, an email is also acceptable.
If there is a problem you don't know how to solve, always approach the person you are going to ask, with a possible solution. Nobody is going to do your work for you.
Grad school can be a lonely place. Find some colleagues to share the pain.

My lack of confidence was usually a direct result of the complexity of a certain task. Just because something seems too complex, doesn't mean that there is no solution.
When I find myself in such situation, I like to step back a bit and clear my head. I usually go out with friends or do some sports. This should jump start your motivation.
Next step is to break down a task into smaller junks that are easy to swallow. I use a free web tool called Trello, it also has a smart-phone app and supports collaboration.
Decide on a deadline for the big tasks and try to fit the smaller once into a schedule.
A series of small successes is relatively easy to achieve and can do miracles for your motivation and overall confidence.


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What does "research university" mean?
For example, University of Maryland, Baltimore County is said to be a research university. (Same thing for Rice University, for example.)
Are there "non-research universities" also? What is the difference?

There are research universities and there are teaching universities.

Research universities have graduate programs and their focus is on doing research. This means most professors teach one or two classes (some have 0!) but have other obligations.

Teaching universities on the other hand don't typically have graduate programs (if they do, it is just a Master's program) and the professors have full teaching loads (I think 3-4 courses is the norm) with little expectations to publish.

For example, Austin Peay State University, where I did my undergrad is considered a teaching university. Every professor has a full course load and not a single one of the professors I had has published in the past 5 years.

UPDATE: chronicle.com defines teaching university as one where professors have "a standard teaching load of four courses a semester", from Interviewing at a Teaching University.

Ok. Can you please list one or two Teaching universities?

@BROY Updated my answer!

see this, http://en.wikipedia.org/wiki/Montclair_State_University              it states that Montclair is a Reasearch University.

This is definitely not true for universities outside the USA. E.g., four courses a semester is not a necessary condition for being a teaching university outsides the USA. Edited.

I have again edited this previously erroneous answer who by mistake provided USA norms as universal ones, and added a note that the examples are relevant to the USA.

In the US, the Carnegie classification is used to describe different kinds of academic institutions. The system  changed in 2005, but under the previous incarnation, universities that had significant research components were called "R1" universities. Under the new system, universities with research components are called "RU/H" or "RU/VH" (Research University/(V)ery (H)igh research). It's most likely that the term 'research university' is an indirect reference to this.
Update: The Carnegie classification has many categories of institution: only three of them are predominantly research-focused. So there are many more "non-research" institutions than there are research institutions.

Not sure what the contradiction is. The carnegie classification includes universities of the kind you describe in your answer.

I retract my statement then. However you didn't answer his questions, Are there "non-research universities" also? What is the difference?

Yes. the classification I linked to is very comprehensive, and categorizes all institutions of higher learning in the US. The difference is specified in the category description: for example, Montclair State is categorized as "Master's L: Master's Colleges and Universities (larger programs)"

In the US context (and many other countries) the difference can be somewhat foggy. However, in the past (1900-1930's), US university landscape adopted that invented in Germany (c.f. here, Chap. 2), therefore looking how Germans do it can be indicative.
In Germany, Austria and Switzerland you would see a distinction between a Universität and a Fachhochschule (or sometimes just called Hochschule), also translated as University of Applied Sciences. Citing from:

It (Fachhochschule) differs from the traditional university (Universität) mainly through its more application or practical orientation and less research. ... The Fachhochschule represents a close relationship between higher education and the employment system. ... Nevertheless, in Germany the right to confer doctoral degrees is still reserved to Universitäten.

I guess, the difference applies to different countries as well, though the nomenclature would differ.

However, Eidgenössische Technische Hochschule in Zurich is very much a research university.

@Kostya_I that's true, although ETH Zürich is still a "Universität" not a "Fachhochschule". After the second world war, almost all "Technische Hochschulen" were renamed to "Technische Universität". ETH Zürich (as well as RWTH Aachen) kept the name for tradition. To make things more confusing, recently several Fachhochschulen with focus on engineering renamed themselves into Technische Hochschule. Further, some Fachhochschulen gained the right to confer doctoral degrees. It's complicated ...

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


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How do I get recommendation letters?
I have had a different set of professors every semester and as batch sizes are pretty big ~80, and with every professor dealing with 3-4 separate batches of equivalent size, for barely 3-4 months at a time, it has been hard to develop one to one relationships with professors. In such a scenario,

How do I decide whom to approach for a recommendation?
How should I go about this to get a good recommendation, in this specific scenario?

Related question: Points to remember when having to write recommendation letter yourself

Given the OP’s situation explained in his question and the following comments that he has trouble with getting recommendation letters written by his professors themselves, if I were him I would

Find the professor who would write the recommendation letter himself.
Find the professor who taught the class which I had very good grade.
Find the professor who taught the class in which I was most interested.

Usually, I need three recommendation letters. Now, I have three.
My personal experience is that I tend to have good grades when taking the class I am very interested. If I had good grade in a class I was interested, the chances are the professor would remember me and more willing to write the recommendation letter himself for me.

In addition to scaahu's fine answer, even though I know it is difficult in some places, I would emphasize that students should begin to develop personal relationships with professors long before you need one to write a recommendation letter.
My experience is even with mass lecture classes like you describe (and those aren't even that massive - but 3-4 mass lectures are quite a few per semester) if you take the time to meet with the professor, ask for extra curricular work (e.g. to be involved with projects the professors are conducting), or be very active and engaged within class you can develop that relationship a professors needs to write a quality recommendation letter.

I am always more willing to write a recommendation letter for students who make the effort to come to office hours.  Even if it is just to chat about the subject (vice getting help), it shows an interest in the course.

While both saaahu's answer and Andy W's answer are on target, I will add my thoughts.
Make yourself known to the prof from whom you want the letter. You can do this in many ways. If you sit in the front or are particularly active in that class, the prof will naturally remember you (and naturally feel more comfortable that he/she know enough about you to write a recommendation letter).
If you want a letter from someone whose class you took a while ago and you did not do anything to stand out, then you must take up some extra work now (see if you can help that prof with some projects so he/she can get to know you more).
For me, I don't expect students to develop a relationship with me long before they need a letter but I do expect them to make their abilities known to me. I've had students who are silent in my classes then come to me and ask for a reference. When I tell them 'sorry, I don't know enough about you' they get a little sad but they also understand quite quickly when I explain things to them.
So, if you want a letter, help the prof to help you.


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Undergraduate research field different from PhD field
I am a Physics undergrad who is interested in pursuing a PhD in pure maths in the future (algebraic geometry/topology) but I am a bit unsure. My question is quite general, and I don't wish to provide more background for fear of bias in the answers.
My question: Is it is advisable/possible/unfavorable/favorable to apply for a PhD in a field, different from that in which you have done most of your undergraduate research?
My research (includes just reading and understanding papers, writing summaries until now, I havent published anything) mostly includes Quantum field theory, and gauge theory. Would the selection committee turn down an application to a pure maths field, if I have no research experience whatsoever?
I would also like to ask the question other way round. What if I concentrate my undergraduate research SOLELY on topics in pure maths such as algebraic geometry/topology and take other physics courses, would I be able to apply to a string theory PhD with a high chance of success?
Should I consider spending time on both of these (which is almost an impossible task), to improve my chances in both the areas or would research in one area, and grad level courses in the other suffice?
In brief: Should the PhD field you are applying to be the same as your undergraduate research area?

See this answer for a related discussion.

I thought we had covered this question somewhat in your previous question about recommendation letters. http://academia.stackexchange.com/questions/7870/about-recommendation-letters-for-phd-admissions/7871#7871

@blackace:
I think that question is a bit different, as it asks about recommendation letters from physicists. So it maybe possible, that I get recommendation letters from mathematicians (under whom I have taken courses), but all my undergraduate research is in physics. Would it reduce my chances of getting into a good grad school?

You can definitely apply in a different field than your undergraduate. Some major fields of research don't even exist as undergraduate majors in most colleges (e.g., neuroscience), so it's understood that many students will come from different backgrounds.
The more similar your major is to the new topic, the easier the learning curve. If your major is significantly different you may want to take some post-bachelors undergraduate courses before beginning the PhD program to bring yourself up to speed.

You should do what makes you happy and you find interesting. PhD is a considerable investment and it is worthwhile only if you are highly interested in your research. It is quite common for people to change domain from undergrad to grad studies (between math/CS/physics/Bio-info).

Yes, this is definitely possible.
When I was doing my undergraduate degree, I was pretty sure my interests lied within the area of nonlinear dynamics and systems of ODEs, and I had picked up some research experience in my third year as well as during my MMath dissertation. My third year summer project was on critical factors and tipping points (with application to a prey-predator population model) and my MMath dissertation was on nonlinear laser dynamics. However, I was finding towards the end of my undergraduate degree and the MMath project that I wanted to do something more rigorous, involving pure mathematical analysis and how this applies to partial differential equations (and I had taken some courses in fluid mechanics and PDEs beforehand). My current project is on statistical solutions of Navier-Stokes equations, which is a very different area to what I researched at undergraduate level. My ex-supervisor gave me vanilla advice, saying "your PhD topic should be the same as your MMath project" - in some sense this is true, because one piece of advice I've heard is that one should choose an area to specialise in as soon as possible, even though this may not suit everyone (and when applying for PhDs I was very unsure about the area of research I wanted to pursue, so I had offers to study a wide range of topics with varying mathematical backgrounds). I chose my current project because there would be opportunities to fill in the gaps from my previous university, the area of research is fairly lucrative, it would enable me to see things I had applied before in a new and rigorous light. I explained all this to my supervisor when I had my interview with her and admitted that my background of mathematical analysis wasn't as strong as it could be - but I emphasised that I was willing to learn and that the project in question would be one to help me become a better all-round mathematician. Subsequently I was accepted onto the project and (bar the usual PhD student woes) on the whole I am quite enjoying it as it's a completely different area to the ones my previous university offered. My background would imply that my strengths lied in numerical methods and applied nonlinear dynamics, and even though I would probably have much better luck at PhD programmes along the lines of these, I decided that I didn't want to spend my academic career simply "number-crunching" and doing stuff I found relatively straightforward. Doing more pure stuff is harder, but in my opinion, much more rewarding (as you can actually understand the background theory of why things are the way they are rather than just running a simulation and accepting that it works).
So to answer your question, if you apply to a PhD programme and explain your strengths and limitations of your background (be honest!) and explain why you would benefit from the programme, then that can be equally as important as knowing what the research itself is about I suppose. Some people may not advise making the change of topic, but if your heart is set on it, then grab the opportunity while you can.

When you apply for a PhD, they are not expecting you to already be an excellent researcher in the field you want to go into, most early research is purely for experience and training and seeing whether you like research and they will understand that.
What's more important is that you can explain the choices you've made. They  will look at your research history in context of your PhD choice. You just have to make sure that it shows off the skills they want you to have to do the PhD, those skills are not really subject specific.
I did an undergraduate and masters in Physics and got offers from Oxford, Cambridge and CRUK among other less well known UK institutions to do PhDs in cancer research so it's definitely not essential to have experience before hand, but will also depend on how competitive your chosen field is.


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Advantage of pure maths courses in transcript for physics grad school
Are there an advantages of doing courses in pure maths (master level) courses, if you want to apply to physics grad school for a phd in areas such as string theory, or high energy physics? Apart from the obvious advantage, that you get better at math, which is used a lot in this areas, I am asking about the direct advantage for grad school applications on the transcript? Does the selection committee like to see more grad level physics courses in maybe slightly irrelevant areas, or pure maths courses which have use in these areas?

I am a mathematician, but I suppose having a good knowledge in Riemannian  geometry and/or algebraic topology would be a plus.

I think the real answer is that it depends on what it is that you're planning to do. The more closely your courses align with your proposed field of study, the easier it is for the committee to evaluate. So, taking pure mathematics courses makes more sense if you're going into a theory-based field than if you're doing something more experimental in focus.
However, you should also keep in mind that a strong grade in an upper-level mathematics course will at best be "neutral," and it might be possible to explain away a bad grade; a bad grade in any physics course will not go over so well. So you should factor your interest level and ability to handle the courses in your selection process. You should also consider if the course in physics is considered a "standard" course for undergraduates pursuing graduate admissions. If so, then it makes more sense to take that class than an elective mathematics course. (Otherwise, the question will of course be "Why didn't you take course X?")

Yes. I do planning on pursuing theoretical physics, but a theoretical physicist doesnt need to understand all the maths he is doing in full rigor. Indeed many theoretical physicists consider doing maths like mathematicians do it, a waste of time. So, I was wondering if maths courses would have a negative effect relative to other physics courses (this would not be directly relevant to my area of interest).

It's a matter of "core" versus elective. You could go either way if it's an elective, but I would always opt for the in-discipline core as opposed to an elective, unless you can place out of it, or replace it with a more challenging course in the same area. (For example, if you pass the master's level course in fluid mechanics, it's not as critical to have the introductory course.)


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When changing fields from undergrad to PhD, which department should recommendation letters come from?
I am a physics undergrad who has worked with profs mostly on areas in Quantum field theory, string theory. However, my interests have changed slightly over the areas, and now I want to pursue a PhD in Pure Mathematics, perhaps in algebraic geometry or topology. Is it OK, if I apply for a math grad school with recommendation letters from physics profs, or would this diminish my chances to get selected? Should the recommendation letter be given by a prof working in the same area as that you want to apply to?

I think I need to understand what the possible alternatives are to asking for letters from physicists. Could you get recommendations from people in pure math that you have also worked with? Is your concern that these professors would know you less well and/or write less strong recommendations? Do you have no other choice and just want to know how this will impact your chances?

@BenjaminMakoHill: Yeah, you are correct. My interactions with Math profs have been limited. I have just taken courses in the subject, and have never really studied independently under a prof. So they would know me less well, as there was no 1-1 interaction.

If there's not a lot of other options, than I think it will have to be fine! And I think it will, for all the reasons that others have already given. And if you can get a math professor, that will be better for reasons you seem to already understand.

I agree with blackace that you should probably be OK, but let me sketch what some of the drawbacks are:
Ideally, an application to math grad school will have recommendations from mathematicians.  The further you get away from that, the less meaningful the letters are.  (For example, at least once per year I see a letter from an English professor, which is utterly unhelpful.)  The basic issue is that you need recommenders who really understand what it takes to succeed in math grad school and as a mathematician.  Fortunately, physics is close enough that physicists can do a pretty good job of judging this, so you should be OK.  In my experience, the admissions committee will worry about two things:
One is that physicists may not appreciate certain math-specific issues.  For example, the expected coursework and background.  A physicist may not fully understand the extent to which someone's background is nonstandard or deficient for the math program they are applying to.
A second reason is the belief that most people's standards go down a little when making recommendations for other fields.  If someone is applying to the top schools in your field, you know very well what the standards and competition are like, and you have something invested in the system and your own reputation as a recommender.  In practice, recommenders from other fields seem to be a little more cavalier about making strong recommendations based on a feeling that the applicant is smart, rather than a comparison with the rest of the applicant pool.  This means recommendations with be taken with a grain of salt.
So if you have equally good prospects for letters writers from math and physics, you should choose the mathematicians for math applications.  On the other hand, a physicist who knows you is still a good choice, much better than a mathematician who doesn't know you.  (But a mathematician who doesn't know you is a better choice than an English professor who does.)

OK. I understand. I would probably be able to get a reco from a Maths faculty, but as I say in my comment under the question in reply to Benjamin, but this reco would come from faculty under whom I have taken graduate level classes, they don't know me very well, as there was no long-term 1-1 interaction as such. Thanks for the answer.

@ramanujan_dirac: Taking a graduate level class from someone is totally fine for getting a letter from them.  You can't reasonably expect all of a person's writers to know them well 1-on-1.  It really sounds like you should have at least one math letter to compliment the letters from physicists who know you better.

No I don't think you need to worry about it as long as you have a good track record and evidence for your interest in the other field which is demonstrable. If you get good recommendation letters (not the boilerplate type) from people who know you well and can provide evidence for their recommendation and can talk about your merits objectively you will not be at a major disadvantage. Of course it would be great to have people who can provide recoms in the same area but this is a common thing for people to change their field when they pursue higher level degrees so you will not be the first one having this issue.
It would definitely not diminish your chances if you get strong recommendation putting you in top percentiles of your program and supporting you in your decision. It also comes down to having a very good statement of purpose and explaining in detail why you are interested in changing field and painting a clear picture for your reasons and why you think you will be capable of doing what you want to do it. I have done this personally twice and encourage you to pursue your interest because in graduate school if you want to be successful you really need to be interested and love what you do.
My advise is to talk with your profs and explain your decision for changing your field. They will most likely support you and provide justification on why you can manage (if they think you have the capacity). Good luck!
Edit: I also want to point out that I have had many friends who have jumped from Math to  Physics and vice-versa (and also to CS).

Hey! Thanks a lot for the answer. I am relieved!


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I was rejected from my dream graduate school...what should I do?
I applied to a prestigious university in the States for my PhD but was unfortunately rejected. I had a great undergraduate track record... but still didn't quite make it. The faculty I really, really want to work with are at this University... I really don't know what to do. I spent the whole day refreshing my email, waiting on the off-chance that an acceptance would come... but it didn't. I'm honestly devastated right now. I know I shouldn't feel so strongly about this, but I'm an incredibly competitive person my nature and I've wanted to attend this institution since I was a freshman in high school.
What are my options? I did apply to some backup schools...but I don't know if I should consider going to one of them or just waiting a year and reapplying... Any help would be greatly appreciated.

Anybody remembers or bothers where Einstein did his PdD? No. We only remember him for his contribution to physics. Good institutes are plenty across the world ... try in a better institute and do good research.

I agree with @NilotpalSinha . If one is really interested in physics one should not concentrate on persons. You could get your PhD and go for a post doc to the institute you first wanted.

(also I should say that my comment was only about my own experience. There are pros and cons and it depends a lot on your own personal situation and field of research - @NilotpalSinha's comment is good advice. Also, my PhD was not in physics.)

@user31458
"I'm an incredibly competitive person my nature and I've wanted to attend this institution since I was a freshman in high school."
welcome to real world.

This is definitely for academia and not a physics question - the answer should be completely independent of field. And in any field, putting all your eggs in one basket is just not a viable career move - the "top" US universities get orders of magnitude more applicants than they can admit, and there are far more capable academics in the world than there is economic demand for such people.

@anna v: not to be cynical, but the job market for postdocs can be more competitive than for PhD students. How many particle theory postdocs get a position at Harvard or Princeton each year, for example?

Here are some Terry Tao links http://terrytao.wordpress.com/career-advice/which-universities-should-one-apply-to/  http://terrytao.wordpress.com/career-advice/don%E2%80%99t-base-career-decisions-on-glamour-or-fame/  http://terrytao.wordpress.com/career-advice/study-at-different-places/

I'm an incredibly competitive person — Then you should take this as a good sign.  If you never fail at anything, you're playing it too safe.

One secret of the best schools is that they admit the people who would demand, and get, a high-quality education at a second-tier school. Being a top student one tier down is certainly no worse, and perhaps better, than being a typical student at a top school. Aim high, by all means, but don't let the quest for the perfect keep you from accepting the excellent.

Many wildly successful people have had similar setbacks. Go to a different school.

@Nilotpal Sinha's comment should be taken with a grain of salt. Einstein lived at very different times, where one person could encompass roughly the entire human knowledge on physics in a single lifetime. also, even in his generation, and up until today, he was unique in his fresh approach and sharp mind. so, that's easier said than done!

Disappointment is a real part of life, especially in academia.
My belief is that, in order to succeed in academia, one needs to maintain a concrete yet ultimately attainable set of goals. These goals should be things that have a realistic probability of being achieved, but allows you some room to maneuver around in which to attain them.
Saying "I want to go to graduate school to get a PhD in [insert field of choice here]" is reasonable and gives you several routes to get there. Saying "I want to go to graduate school X to work with professor Y on topic Z" places way too many constraints on yourself: first you need to get into graduate school X, then hope that professor Y is still offering projects in topic Z, and prefers you to other applicants in the program. This is a way of setting yourself up for disappointment.
So, what I would recommend is regrouping. Find an alternate strategy for yourself. What do you want to do in graduate school—beyond working with Prof. X or Y (who by the way, might not be a very good graduate mentor)? Figure out what the goals you have are, both for your graduate degree and beyond, and then figure out what options, among the ones you still have available, will be the ones that best get you there.

Go to grad school at the best place where you were accepted, and work hard to take advantage of whatever opportunities that school has to offer (even if they were not what you first envisioned).  At the same time, keep in mind the possibility of transferring after you finish a masters degree.  This is fairly common in mathematics (my field).  It can be a great way to "move up" to a higher quality school.
If you're considering transferring, you should immediately begin working (at your first school) to network and to develop relationships with professor who can write you letters of recommendation (obviously, you should also publish good papers).  In fact, you should do all of these things regardless, but now you will have more urgency.  One advantage of this approach is that your work will be valuable whether you transfer or stay at the same school.
In short, it sounds like you had your (academic) life planned out, and now you must make a new plan.  One weakness of your first plan is that it was "fragile" in the sense that it depended on many things outside of your control.  You will be happier (and generally more successful) if you focus your plans and energies on things inside your control.

1 upvote is not enough!

OK, I will try to form an answer.
Last week I set through a three hour memorial presentation for the 25 years since the death of Feynman. The person who was presenting the way the Feynman Lectures series ( red books) caught the imagination of physicists made the following comment: ".most of the real students in his audience left physics" . I tried to find a link but did not succeed. But I had some personal experience:
Back in 1964, when I was a graduate student in a nascent school in Athens, Greece, after a semester of field theory from the book by Bogoliubov went to a Cern summer school in Yugoslavia. There Veltman gave three weeks  of lectures where the scales fell from my eyes and I realized in my gut feelings what all the fuss with operators was about: crossections.  Enthused by this I managed to get a place at the Erice meeting of 1964 where Feynman would lecture. I was severely disappointed.
I realize now that I joined at the time the students from his feynman series course :). The reason? At the time we were all excited about the eightfold way and quarks and tantalizing SU(3) . Feynman spent his time in showing us how HE derived the same things in what was for me not a particularly elegant way.
I also followed a series of lectures he gave in 1981 in a Crete workshop when QCD was all the rage, and again , he derived for us QCD in his own unique way. This time I could appreciate it having become sophisticated enough to admire how he could think out of the box still at his age.
My anecdotes are to show that a physics personality may be very attractive to an aspiring physicist but that does not mean that being a student of Feynman would allow one to develop as an independent thinker next to his shade. If you are competitive, you should think of this .
In your place I would choose one of my alternate universities, looking at how the graduate students from there were placed as post docs, and not waste time : most original thoughts come before 30 for physicists.
my two cents.

"Most original thoughts come before 30 for physicists": Citation needed.

{"Brainpower starts to decrease after a certain age, while experience accumulates over years," he said. "Experience is not as important in mathematics as in some other fields, but it is important. So the power of a mathematician often peaks in his/her 30s. Which means that young people do have an advantage. But not people who are 16. Certainly someone who is 32 has a lot of advantage over someone who is 16."} - MIT mathematics professor Pavel Etingof, who also works with a high school research program at MIT., http://news.discovery.com/human/psychology/math-genius-teen-youth-120530.htm

I guess that citation in the first comment mean a reference to a scientific study, not a quotation from any random researcher (even if it is from a famous one).

@NateEldredge for the quote "most original thoughts come before 30 for physicists", Anna v. would like to cite Newton, Maxwell, and Feynman. She is unfortunately not able to comment here, but she has given an additional link that supports what she says in this meta post.

If you really want to study in particular place, you can consider doing PhD another place (where you get admitted) and then apply again. But beware, as aeismail says, putting too many constrains is risky (typically people apply to at least a few different universities).
It may depend on your priorities, but one friend of mine applied to a few PhD programs in US (from EU)

one year he got rejected everywhere,
the next year he got admitted everywhere (and they were only top-tier universities).

So, what was the difference?
In the meantime he has learnt how to apply (e.g. how to write a research statement, how to get an appropriate guy for a recommendation letter) and got external funding (Fulbright fellowship). He spent the extra year doing research in another institute, so it was not wasted in any sense.
(BTW: The story / "how to": http://kni.wikidot.com/gdzie-doktorat (in Polish), and research statements "before vs after" http://kni.wikidot.com/moja-historia (links on the top - at least they are in English :)).)

Voting up for the link shared. I assume your friend got admitted by Berkeley right? One could really see how much your friend has grown in this one year gap. I think this is aspiring for all PhD applicants.

@CherryQu Yes, he is at Berkeley right now.

@CherryQu But, AFAIR, it's not that he has grown much in a year (sure, he did, but I doubt if it was the main point) - rather he have learnt "how to apply to an US university" (there are many non-obvious things, at least from Central-Eastern European perspective) plus he secured a funding.

Yes yes, ref letters, funding, writing research statement are all important. I was basically amazed how much the SOP of your friend has changed in 1 year. In the 2009 version it sounds like the applicant does not really have too much idea about research, while in the 2010 version he speaks like a professor! Maybe your friend was already an expert in research in 2009, but he didn't quite expressed himself on his first try :) So although external things (funding, ref letters) are important, I have this stubborn opinion that it's the inner qualities (research talent) that makes the difference.

I understand that your question has been migrated, and therefore it might not be obvious whether you want to have your career in academia. But if that's the case, not being accepted to your first choice is probably not as bad as it first seems.
First of all, you don't need to be in the same university to collaborate with the faculty you really want to work with. Perhaps it would be easier if you were in the same department, but you're starting a 45+ years career, you will have plenty of opportunities to work with him/her in the future. Getting your PhD is just the first step, not the final one.
As some comments say, in the end, where you did your PhD is not the most important, what you do during it is. If you can find another nice place to work, then consider it as a challenge to work hard enough to get a permanent position in your dream university later.
Finally, just to look at the bright side of things, not getting there might be a chance: a very important aspect to measure the quality of a PhD is to show how you can do independent research, i.e., without your main advisor. Hence, doing your PhD with someone you admire (I'm extrapolating here), although very rewarding on the short term, might tie you to work only with him/her, and thus reduce your visibility as an independent researcher.
To answer shortly your question: since you're competitive (and many people are in academia), go do your PhD where you are accepted, do the best PhD ever witnessed in this university, get the best publications, and then people will look at your work more than the place you did your PhD.

A similar thing happened to me, although I did get the academic position at first, but not the funding a few months later. I was absolutely gutted.
Right now I'm writing from the comfortable position of a PhD student at a place (another place!) which is great in almost any respect I can think of. In retrospect, here is what I learned:

By enrolling in grad studies, you're entering a whole new arena. In good schools, nearly every student who comes in is used to being in the top 10% of his year. Of them, in grad school, only 10% will have this distinction. Sometimes, dealing with this disappointment starts with the admissions process. But wherever you're admitted to, it will continue: a good part of being a scientist is about becoming genuinely interested to hear more whenever you're told you're doing something wrong. This goes against every gut instinct you have, and takes time to internalize.
Universities have rankings, which gives an impression that they're in competition with each other. But great science comes from having many different people poke at a problem from different angles. This means that there is normally good collaboration going on between labs (i.e. universities) working on any given subfield. It is not uncommon for a student to be shared between supervisors from different universities, so you still have the opportunity to collaborate with the lab you were initially interested in even if you go elsewhere.
You can always try again at the original university, either by transferring during your graduate studies, or by applying for a postdoc.
If you have great passion about a particular area of research, it will very likely be ignited once you come in close contact with some other area of research. Mastering new concepts, and pushing the boundaries of your field with exciting new research, is just intrinsically pleasing. So if you like research, you will likely enjoy any lab you get into.
Ultimately, your chances for remaining in academia will mostly depend on your publication record. If you do well in that respect, nobody will take it against you if you didn't go to a particular school. On the other hand, a one-year break in your studies could look bad.

So hang in there: it's not easy being rejected, but not so many options are closed to you as it may seem at this moment. I would just go for another school and work my way from there if I were you.