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Student wants to show everybody how much he knows
I have read this question, where the OP asked how to handle silly questions. In the excellent answer of Irwin, the 6th point attracted my attention:

If it's a matter of the student talking on and wasting time with questions, then you can ask the student politely to keep questions for after the class. If the student is trolling you with questions and is otherwise being a nuisance this option usually works as well.

I am a TA in mathematics at a university in continental Europe and I organized a weekly question time (one hour) where I answer questions of undergraduate mathematics students. Usually, these hours are very well visited so I struggle a lot to answer all questions in my limited amount of time. However, there is one student who constantly tries to prevent me from answering other student's questions. He first wants his questions answered. But most of the time his questions are not useful at all:

He wants to show the other students how much he knows. He uses a lot of mathematical terminology, sometimes even terminology which was not yet introduced in the lecture (and sometimes will not be introduced in the lecture). For example, if derivatives are the content of the lecture, he asks something about weak derivatives. My advice that he should first understand the special case and not the more general one is ignored. However, he also asks questions about the specific course (which fall into the category of the next two bullet points.)
He has a very tiring way of asking questions. If you answer his question, he often accuses you of "not understanding his question". If you answer his question and politely tell him why his question does not make sense, he usually changes the topic (if the question was about topic A, he says "But I was talking about topic B all the time, you did not understand my question"). Telling him that he has to ask more precisely is ignored, he thinks that the TA is not able to answer his questions, because they are too difficult to answer.
He always wants his questions to be answered first. This is very bad for the other students, because the other students have more or less useful questions which deserve to be answered well. Hence, this student is just wasting time, which could be used in a better way to answer more useful questions. Of course, the other students are annoyed by him, too. I think that it is just a question of time until one of the other students tells him that the question times cannot stay like this.

Now my question is: How do I deal with such a student? The cited advice above does not quite apply here. He does come to my question time and also to the question time of other TAs (who have the same impression of him). If you ask him to keep his questions, he just does not stop asking and disturbs you in the process of answering other questions. For example, if you answer a question, he just interrupts you and says "But isn't it like that? (...)", saying this with a tone which expresses that you are wrong and he is right.
I also offered him to come to my office to discuss his mathematical problems, but he apparently does not want to, because he has never appeared in my office (and I think he won't in the future). My impression (and also the impression of the other TAs plus the professor's) is that he just wants to ask questions publicly to express how much he knows and to demonstrate that he is very intelligent.

Possible duplicate of How should I handle students who ask questions that are "beyond the scope of the course" as a TA

Thank you ff524, I'll have a read. But the difference is that he does not only ask questions which are beyond the scope of the course, also questions about the course. But anyway, I think that this will help me. +1. However, I noticed that this point is not made very clear in my original question, so I'll edit it.

@ff524: Helpful link, but I don't think that's the same problem. OP's situation sounds like they are stuck with one of the infamous "But does this hold w/o assuming the axiom of choice?" types. They tend to be good not great, typically relying on prior knowledge to shine, and end up flaming out. But along the way, they are a major nuisance.

It is indeed very difficult for a professional to satisfy the needs of every customer. Sometimes very specific technical expertise is needed, and I believe for this case the technocrat that could be of help is called, in some corners, "shrink".

Why not refer the student to http://math.stackexchange.com ?

Why not just punch him in the face? Or maybe you are the problem who is a bit insecure at his knowledge?  How bout you simply work with him. Allow him to teach a problem. Force him to stand up and back up his "intellect". Don't put him on the spot, just put him in a position where either he will prove he is an idiot or he will shine and do well. It sounds like you think he is an idiot. If it he, then give him problems with provable truths and ask him to solve them. If he can't then he will look stupid. Show the class how "easy" the problems are but make sure that everyone knows he failed.

When I was studying mathematics, I always felt the majority of the work was too simple so I would study ahead. Maybe that is what he does... and if he does, then that is a good thing. But that also can make class boring, in which he might be so that is how he manages.  You will have to treat him different because it seems he is different. He could be an ego maniac... in which case you can learn to put him in situations that temper the ego. Have him work "special "problems while everyone else does something different. Maybe he just needs a challenge. If he is truly trying to show how smart he

is, then he's a moron, because a truly smart individual knows how stupid they are. In that case, make him look stupid(subtly).  You can't do this by arguing with him, you simply must demonstrate it in front of his peers. If he is just trying to get recognition from them, then it will do more damage to his ego when they realize he is a dumbass and he might learn his lesson(probably not). But to do this it must be decisive without any way form him to wiggle out and justify why he failed. But you know, you shouldn't punish a person if they are simply bored and go above and beyond.

When I took CS in HS, the teacher had me and 2 others to different work because we were above and beyond the others. When I was in college taking a java class the teacher excused me from having to finish the course after 2 weeks and gave me an A. Either this kid is just a moron who cites knowledge but does not understand it or actually is more "intelligent"(harder working). If he's a moron, not much you can do. If he actually is doing well in the class(at the top) and knows the material, it is best to nurture and support that(sounds like he isn't though).

Another way would be to change the format. Don't allow random questions. Give each person equal time to ask questions.  Or come up with some other way to prevent the way he disturbs the class. It's not hard to do, it's part of your job. Just think about it, no one else can really help because only you and the prof know the exact specifics. Is the kid really an ass or you just misinterpreting it? We can't know that. Is he a moron or actually intelligent? (being able to memorize and cite definitions is not intelligence)

If the student is just overexcited and more advanced than others, then the  question linked above by ff524 has an excellent answer. However, that does not seem to be the case. By all appearances, the student talks to talk, and drops references to superior knowledge - real or imagined - to show it off. I've studied with plenty of students whose knowledge exceeded even advanced classes they were forced to take, and - in my experience - the common reaction of a true talent is boredom or eventually failing to show up, not jumping on stage. The closest case similar to yours failed his qualifying.
Hence, I think your problem is one of learning to assert yourself in a challenging situation. Here are some suggestions for what you might want to try:

Be an authority figure, not a friend. When I was a squad leader at the army, I was an unkissed geek-kid; my soldiers included a drug dealer, coal miners, and someone 10 years older, divorced, 2 children. I've found that, absent natural charisma which I don't have, acting somewhat reserved and distant, while always having an open ear for feedback, was the best way to get through this. When later TAing, I resisted the urge to fraternize and acted similarly, which worked very well for me (in both cases, I was top rated among my peers.)
Create a system of taking questions, and stick to it. This might be simple ideas such as one day taking questions front to back, the next left to right, etc. which - as students tend to gravitate towards seats in a particular part of a classroom - means your problem student will only get to lead a discussion every now and then.
Be professional, but honest about your frustration. If the student interrupts others, or you, first follow the advice of the linked question. I expect it to fail though as your student isn't interested in talking after class when no one witnesses their awesomeness. If it fails, tell them "I'm sorry, there are many questions others have, too, and I need to address theirs as well.(meet me after)" If you can't shut them up, keep eye contact, and say, more seriously but calmly, "I really have to move on. Please allow others to talk", etc.
Seek advice from your professor, as needed. If the person becomes disruptive and unresponsive to your hints mentioned in 3., discuss with your professor, and ask if you can kick them out of a TA session when that happens. Express your concern about preparing the other students properly.
Assume good intentions, and talk with your student. This should probably be point 0. Ask the student if you can talk after your session. Be a bit flattering - interested student, knows much - then point out that others don't, and you really need to focus on them, and their more basic questions, while handling his in 1-on-1s, as necessary. This might clarify if they are acting in good faith and just get overexcited, or not.
Mention that TA sessions are optional, and that no one already having the knowledge taught is judged for not showing up. One of my TAs, stuck in a basic linear algebra II class with a 4-time math Olympics participant (b/s/g/g) who had gone through the entire Bourbaki already did this, and it was the last time the student was seen. If it works as in this case, you might also get a chuckle out of the other students who probably understand what you mean.

There is an additional informal way to address this as well. The next time you catch them being wrong in their aggressive ways, talk them into a corner. If they change topic, say so - "That's interesting, but let's not change topic. I'm really curious to understand what you meant when you said (X - the wrong statement)." Be calm, friendly and insistent, and keep this up until an error is admitted, or they shut up. As their interruption is only to show them in a gleaming light, it might help greatly in making it stop. I would only use this as a last resort though.

I'm interested to hear why the last paragraph is reserved for Europe.  I'm not saying you're right or wrong, but why does that seem like something that wouldn't be used in the U.S.?

@JPhi1618: I guess it isn't. You can just get away with more in Europe than in the U.S., where you always face the risk of an overprotective parent filing a complaint over the terrible mis-treatment of their special child. But you're right, if you do this properly (friendly, but insistent), there isn't anything others could reasonably object to. I removed the unnecessary qualification.

Boredom, and following the desire to show off because there is nothing more gratifying to do, go hand in hand :) I would suggest you involve that student in tasks that help the class (e.g. helping other students, preparing parts of a more complex class project that you do not want everyone doing) - gives him/her their stage and helps your teaching.

@rackandboneman: for the first 5 minutes, possibly. Then it's just easier to sit out and read ahead of the textbook :)

Very good answer. I was going to recommend more laconically, "kick his butt."

You, the TA, are currently in a situation where the students are running the Question period.  That's all fine and good, until you get one of "those" students.
What you need to do is turn it around so that YOU are the one "asking the questions."  How?  By establishing a sign-up sheet, and questions should come in on paper.  This is how music open-mic nights are organized.  You don't just show up to an open mic and walk right up on stage, you have to "run the gauntlet" of the moderator.
Then, YOU, the TA, ask the submitted questions, without naming who's question it is.  This strips the questions of any personalization or attribution, and there is only one person in the room that will find this unsufferable, and that's your precious pearl student who will feel himself to be neutered, and will lose interest in the process...because his opportunity to control the dialog has been blocked.
The best thing that can happen from this scheme is that the problem student exercises his "awesome-sauce-ness" by actually answering other's questions correctly and being genuinely helpful, and at worst he loses interest in the process because he has no way to establish himself as center of attention.

This is certainly the right answer. You could have students submit questions after they arrive and then choose from them, or you could have them submit questions before they even arrive. The second option may be even more useful: you can see which questions are most common.

Problem arises in this form: "Yes, this is actually my question, and (...)"

Nice solution +1, this removes the problem and will force the "know it all who is sometimes right" to assist his friends in class on a personal level to achieve the fame he seeks.

One trick I use in situations like this is that sometimes I put questions up for a vote of all the students present. "Let's make sure that we're helping as many people as we can," I'll say, "Raise your hand if you'd like to see this problem worked out?" Generally if I get at least 3 hands up then I'll follow through; but if absolutely no one seconds the strange question, then I'll say, "Maybe you and I can talk about this after class" (and it's probably a minority of the time that the student follows up with it).
This makes it rather explicit when no one else in the room is interested in the oddball question, and effectively creates buy-in from everyone else that skipping it is good. A few times I've escalated this (say, reviewing for a final exam when everyone wants all the exercises covered in one hour) by putting all the proposed questions on the board, recording vote tallies for each, and then using the available time from top-votes to least.

I find your second solution more friendly than the first, which might make students in general afraid of being humiliated by asking a question no one else wants the answer to. They're less likely to withhold potentially "stupid" questions (that might or might not turn out to be shared by others) if the questions can be submitted anonymously. Of course, it's possible that going over the top-voted question might make the next two unnecessary....

@Charles Staats: I don't think that happens in practice because of how very rarely the vote gets triggered. Usually only if one student is asking multiple loopy questions (like, after one student asks 3 screwball questions in a row), or if one student is asking for a whole do-over of basic material that they missed due to being absent. Anonymous (paper) submissions would take too much class time to collate and stymie follow-ups and back-and-forth discussion, in my opinion.

My solution is a partial solution.
This student seems very reluctant to change his behavior. Maybe you could introduce a new procedure for everyone that will block him most of the time.
Since you don't have the time to answer all questions, students interested in asking questions could put their name in a bowl. During the period, you draw name, the student ask the question and you answer (any other method of having a random attribution of who can ask questions could work).
If the disturbing student don't want to respect the procedure and keeps interrupting you, I would suggest asking him to leave:
"Sorry, I will answer your question when your name is draw. If you do not agree with that, I would ask you to leave as you are disturbing the other students."

Why is this a partial solution? Kills the problem while being fair to everyone. Now, I would avoid letting the problem student putting his name several times in the jar.

This is a complete solution, because you can simply lie about the name you draw and call whomever you like.

@vadim123 No, don't be a jerk.  If you say you're going to draw a name out of the bowl, then draw a name out of the bowl.

Why not asking for the doubts beforehand by email, and answering to the more interesting or pertinent to the program in question? That way, the more interesting questions would be selected, the students would benefit more, you would have more time to think beforehand about the validity of the questions, and further valid questions that would not fit on the program or time, could be answered by email or privately.

As a TA, part of your job is managing your time with students to ensure that every student with a class related question is helped.  Part of this is learning how to deal with difficult students like the one you mention.
First, put any student with a question about a homework, quiz or test at the front of the line.  Keep this focused.  If your problem student tries to interrupt, or get off topic, simply say.

I want to make sure everyone understand the material that was covered
  in the assignment.  I'd be happy to discuss this if there is time
  after.

Second, limit the amount of time the student can ask questions.  Next time he takes a long time talking with you, simply say.

I've got several other students, and can only give you X amount of
  time (10, 15 minutes).  Once his time is up, enforce it, and make sure
  all the students have a chance to get a question answered.

Thirdly, if he is good, suggest him for an unpaid undergrad research or TA position if appropriate.  This will give him the respect of the other students, which he wants, and will teach him how annoying he is being to you.


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How to ensure that a reference letter is sent on time if not knowing the reliability of a referee?
It has happened to me the second time that I was turned down by a referee (different one) not taking his responsibility seriously. Of course, I let each of them know about my application and the reference request well ahead of time.
The first time I requested the reference letter I was told that everything would be sent on time, etc. But one week before the application deadline the reference was still not sent (even despite my reminders) and so I quickly found another referee who rescued me. I never told the first referee that I found somebody else and the referee never got back to me over the email again...
The second time I had the "advantage" (or rather a deception) of being able to meet the referee everyday in person and so the day before the deadline I reminded that professor in person concerning the reference, also sent emails, etc. He promised into my eyes he would send it on that very day, but the deadline passed and the reference was never sent... No, the referee did not die, did not have an accident or a bomb in his office. They just could not be bothered.
I think it is very sad to know of the existence of such people and their behaviours, especially considering the fact that they used to be (some of them still are, probably should not be) my close collaborators with whom I spent many hours together.
I believed them. I thought I knew them, but only afterwards I realized that whatever smooth words they may have told me in the past, they did not mean them.
How do I ensure that the reference gets sent on time, how can I determine that I can trust somebody who I test the first time?
Usually more than one reference is required and I know that on some people I can rely 100%. Their yes means yes and their no means no. But what about the new referees? I was thinking of telling them of a deadline that is e.g. 15 days earlier than the actual deadline and in case no reference gets sent by my deadline, then I would contact an emergency referee to send the reference by the actual deadline. But sometimes, an electronic application tells the referees of the actual deadline and therefore I cannot make my own deadline.
Also note that many referees do not want to give you their reference that you may read it, but rather want to send it directly to the application committee. Thus something like having a backup letter, I am afraid, is not an option, especially in cases when the reference needs to be signed electronically by the referee oneself.

This is not really specific to Academia. You may have more success at Workplace, or even Personal Productivity. If you don't get good answers here, you may want to consider flagging your question for a moderator's attention and requesting that it be migrated to one of those sites (possibly after editing it).

@StephanKolassa I would disagree. Academics aren't very like the rest of the world, especially in maths.

One option is to apply to the US, and hence use MathJobs to apply. Then you know when the references are uploaded. A second option is to find out who their secretary is and get them to make sure the reference is done (this won't always work, but I know it does in some cases).

@JessicaB "Then you know when the references are uploaded." In my second case I knew that the reference was not sent yet, so I talked to the referent in person (also send an email), he said he would send it on that day, but he did not... So what should I do in such circumstances if I know that the reference is still not sent in order to make sure it would get sent?

The point I'm making about MathJobs is that you know the reference has been uploaded before you select it as your reference. If one you want to use hasn't been uploaded, you use a different one instead.

If your referee doesn't send a reference when you've reminded them just before the deadline, they don't think it matters enough for their time, and there's little you can do to change that. It's worth noting that many mathematicians assume all deadlines for references are flexible (ie that if the rest of the application is in on time then the reference being a few days late won't matter). I've seen job adverts that are explicit about this not being the case, which suggests that normally it's close enough to true.

@JessicaB In that case MathJobs seems as a good application system to handle references. Thank you. Unfortunately, many applications (not just for jobs, but even for fellowships) go outside of this kind of system.

Whenever possible, I ask more people. If I need 3, I ask 4 professors :)

@FábioDias If they are sincere, they write the reference on time. And I value the time of the good people too much to ask more than necessary. But one never knows...

They didn't miss any letters yet, but one more is not that big of a deal. And sometimes they are on vacation or just overwhelmingly busy... stuff happens

But one week before the application deadline the reference was still not sent (even despite my reminders)

This strikes me as entirely normal.  I try to write most letters a few weeks before they are due, but I end up writing some letters during the last week, and I believe this is pretty typical.  I don't have any statistics handy, but I'd bet that a substantial fraction of all letters of recommendation are written in the last week (or later!).  It may be stressful for applicants, but it's not unusual or particularly worrisome.
It's also worth noting that many deadlines for letters are actually flexible, and experienced faculty often know which ones are.  For example, NSF graduate research fellowship deadlines are absolutely inflexible (if you miss the deadline by one minute then you can't submit at all), while graduate programs in mathematics at U.S. universities are almost always flexible about letters (if you submit a letter a few days past the stated deadline, it won't do any harm).  Someone who doesn't seem to care about a deadline may just know that it doesn't actually matter.  It's not nice to do this without explaining the situation to the student, but it's not necessarily as terrible as it looks to someone who thinks the deadline matters.
Unfortunately, a few people really are irresponsible, and I don't know of any ideal solution to this problem.  One strategy is to propose frequent reminders, along the lines of "I know you are juggling a lot of things this semester, so I wonder whether you'd like increasingly frequent reminders to minimize the chances of a last-minute rush.  I could send you a reminder e-mail once a week for the last four weeks before the deadline, and once a day for the last four days (of course stopping once you tell me it's submitted).  Would that be helpful?  Or what sort of reminders would you prefer?"  I doubt anyone would be offended to be asked, since they could always ask for fewer reminders.  This can't guarantee that someone will make the deadline, but it minimizes the role of forgetfulness or poor planning.

I was thinking of telling them of a deadline that is e.g. 15 days earlier than the actual deadline and in case no reference gets sent by my deadline

I would feel a little offended if an applicant deliberately misstated the deadline in this way.  As an alternative, you could explain that you feel very nervous about deadlines and ask whether your recommender could please submit their letter two weeks before the actual deadline.  They might not agree, but the worst case scenario is that they say that's not convenient.  (I would agree if someone asked me, assuming they gave me plenty of time to write the letter, but not if they asked too close to their proposed deadline.)  I wouldn't generally recommend asking this, since it would come across as eccentric, but eccentricity is better than dishonesty.

As a practical matter, you can't ensure that the person will actually send the letter.
However, there are some things you can do to increase the chances.  First, consider how reliable the person has been in other interactions with you.  If somebody has a history of being unreliable, then either avoid them or make backup plans.  (And if this is somebody you have not had any interactions with before, then why would you be asking them for a letter of recommendation?  Even if they did send one in on time, it would almost certainly be a weak letter -- not out of malice, but out of lack of history from which to build a strong letter.)  Sometimes, if you have reason to believe that the person has written a letter of recommendation for a third party in the past, you can ask that third party what the experience was like.
Second, make it as easy as possible for them to write the letter.  Provide them with at least your CV and an informal reminder list of previous interactions you have had with them and other pertinent details.  Do not just assume that they will remember all the details you hope that they will talk about.
In extreme cases, you can even provide them a draft of the letter you hope they will write.  However, some people may be offended by this, so I wouldn't go this far unless you have okayed it with the person first, and I wouldn't even bring it up unless you have strong reason to believe it would be welcome.

Providing a draft is against my morals. That has already been discussed at http://academia.stackexchange.com/questions/16529/is-it-acceptable-to-write-a-reference-letter-for-yourself

@anonymous_mathematician: Sure. I don't like it either. But in certain groups, it seems to be very common, and in those groups, it could make the difference between getting a letter on time and not.  The tricky part is that some people might be offended at the very idea, so it's hard to know whether it's even safe to ask.

If something is against your principles, then you know that you are not going to do it, and so you do not need to even worry whether to ask that question.

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How to pursue graduate admissions in mathematics seven years after a humanities undergrad degree?
The simple version:
I've been out of college for 7 years and want to pursue graduate studies in a field unrelated to my undergraduate degree but am not sure how.
The detailed version:
My college career began as a Physics major.  I made what I now consider the mistake of changing to a technically driven humanities major (Electronic Media, Arts and Communications) although I completed a great deal of my pure sciences coursework.
Years later I have a very solid job in a field that I hate and want desperately to get back to school to work towards higher degrees in mathematics.  I've spent the last five years as a systems engineer with a focus on network distributed video and have a very solid resume in my field, but my academic credentials are poor.  A 2.8 GPA (albeit from a strong school) and an unrelated B.S.
I've made it a point to keep up studies in math, participing in a great many MOOCs to try to backfill my mathematical education and keep my skills sharp.
What I don't know is how to re-approach academics.  Would I need to earn some additional undergraduate credits before applying for a graduate program?  I expect GREs will be required, but that's not a major issue as I've been scoring quite well on practice exams.
I know that I lack educational recommendations and undergraduate research, and I have absolutely no idea how to supplement this lack...

Given you were pursuing a Physics degree to start with, you most likely have a lot of undergraduate Mathematics coursework behind you, probably enough for a minor. Most graduate programs only require either a minor in the field or a major in a related field. It couldn't hurt to ask a few departments what you'd need to do in order to be a successful candidate for their department.

Is it reasonable to simply reach out to departments directly?  Wasn't really sure of the etiquette there.

I have. I've even made the trip to visit the campus and meet with a professor I liked, just so I could get to know him better and get a feel for what the department was like. That also gives him a face when they are going over which applicants to accept.

My suggestion would be to go for MS Math first. It is far more easy to get into a math MS program than math phd program. After your MS, you can apply for phd at top schools.

Yes, it's very reasonable to email a director of graduate studies (not a general graduate admissions department; they won't be able to tell you anything), lay out your situation and ask if you are a plausible candidate, or what you would have to do to become one.  I'll second @user774025's suggestion that a getting a masters at a localish school, maybe while still working, is probably the way to get into a respectable Ph.D. program.

To get admitted to a graduate program in math, although work experience may suggest greater maturity, etc., the issues will be letters of recommendation and documentable standard-material background (whether in conventional courses or somehow-verifiable self-study...), and possibly a GRE subject test score if only to show that one is aware that the thing exists and is widely believed to be relevant (even while many, including myself, do not consider it a good predictor of anything much beyond multiple-choice-test-taking abilities).
Unless you've self-studied into a quite unusual state of expertise, you'll most likely not have much success in getting an idea of what contemporary research in mathematics is about, and it might be awkward to attempt a conversation with faculty about their current work. Perhaps such a thing would be feasible in other fields (I have no idea...) it is not typical in mathematics. That is, people going to grad school usually have only a general idea of the direction of their interests, even with a solid coursework background. In particular, funding for graduate work is rarely dependent upon connecting with any particular faculty more than tentatively. (Again, this is evidently unlike other fields.)
Helpful letters of recommendations would be from professional mathematicians actively involved in research, acquainted with graduate programs in mathematics, who can speak from direct personal experience both about what such programs will demand of you, and about your qualifications to meet those challenges in terms of prior preparation and in terms of interest.
Probably the way to put yourself in a position to have such letter writers is to take upper-division or beginning-graduate courses at a solid university, as a "non-degree student", do well, and thereby be able to ask the instructor for such letters. It's not the credits themselves, but the information and the certification by faculty (beyond "getting a good grade"). That is, you'll want people to attest to your future potential, beyond accomplishments to date, in the sense that (hopefully) "you've only just begun", rather than having peaked-out.
If you are an outstanding multiple-choice test-taker, getting a stellar score on the math subject test GRE will catch the eye of many! :)
Other routes for certifying that your self-study has made progress are difficult. E.g., certificates from on-line courses are not worth much, and, most often, those courses are too elementary to be relevant to graduate study in mathematics.
If you are not geographically flexible, going to the nearby universities mathematics departments and asking "what it would take" for admission, _with_funding_ (don't go without funding), and try to do it. The whole process might take long enough that it'd be wise to keep the job you have, even if you don't like it, to support yourself (and others?) through the preliminary stages of gaining entry into a graduate mathematics program.

I agree that taking some graduate level courses as a non-degree seeking student would help demonstrate the OP's abilities, in order to get recommendations though he would need to go much further, asking pertinent (but not attention seeking) questions in class. Conversing with the professor, and maybe looking for opportunities outside of the class to engage in research the professor is interested in. In fact the OP may want to talk to the professor first and then decide what class to take based off of that.

@kleineg, yes, indeed, a very dynamic participation in such courses is necessary! However, I fear it is not so plausible that at the level in question a student could meaningfully engage in contemporary mathematics research immediately, especially prior to getting oriented in the milieu.

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Do community college transfer students have a disadvantage when it comes to graduate school admissions?
I spent a year at a community college working in industry straight out of high school. I recently got into a top cs program and will be attending starting spring 2015. However, the school only gave me until spring 2017 to finish my degree, which means I will be at the 4-year university for 5 semesters. Will I be at a disadvantage when applying to top graduate schools in comparison to my peers, who have been at their university for 4 years? I am a CS major who will attend a top cs program.
Also, due to my transfer situation, I feel that I am severely disadvantaged in terms of research opportunities. This is because for most of the labs at my school, professors have formal requirements which often entail good grades in high-level electives specific to the research. Unfortunately, I probably won't have time to complete many of these electives, and even if I do, it will most likely be during my last year. I want to get started in research as soon as possible, but I also know that I don't have much specific experience for my fields of interest (which include AI, NLP, machine learning, and data mining). How should I reconcile these gaps, and what tips do you have for a new student getting engaged in research?

Tip: Ask persistently but politely to participate in research.  I think the overall answer is no.

Simply having attended a community college earlier in your academic career is not going to hurt you if you have a degree, good grades, good letters of recommendation, etc. from a top program as well as all the other stuff that matters like good tests scores and research experience. Having attended a lower status school is not a permanent black mark and simply will not matter if your subsequent work proves that you are top-notch student and researcher.
Having less research experience than your peers who are applying for the same graduate positions will put you at a disadvantage. Ben Bitdiddle's answer on how you might go about getting that given your relatively shorter period of time at a research university is good as are the answers to many other related questions on this site about getting research experience as an undergraduate.

Some things you might consider:
1) Doing a master's degree at a good CS program before applying for a PhD.  This will give you an extra year or two to participate in research.
2) Contacting professors outside your university for research opportunities.
3) Doing unpaid independent studies with professors and later graduating to paid, formal research opportunities.  (Many professors won't have time for this, but it's worth a try I think.)
The usual advice for contacting professors holds (be enthusiastic and demonstrate a sincere interest in their work).


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Why are the acceptance rates of Oxbridge and top US schools not comparable?
I have just had a look at admissions statistics for grad school. Oxford seems to have much higher acceptance rates than, say, Princeton or Stanford. I do not want to conclude that it therefore is easier to get into Oxbridge than Ivy League Schools, lets say (for grad school that is), because I am probably forgetting some crucial factors here.
Or is it just that getting into Oxbridge is easier than Top US unis?
PrincetonAdmissions Data (about 11% acceptance rate)
Oxford Admissions Data (about 24% acceptance rate)
Cambridge Admissions Data (about 39% acceptance rate)

Consider that the acceptance rate mainly depends on the number of applications received compared to the available places rather than the ranking.

Are there higher barriers to applying to Oxford? Is there cultural differences that wouldn't entice less competitive students from applying?

You might want to rephrase this as "Why are the acceptance rates of Oxbridge and top US schools not comparable?" There are a lot of assumptions you're making that are fallacious and the reason why you're getting downvoted.

I am not making any assumptions here, do I? To quote myself: 'I do not want to conclude that it therefore is easier to get into Oxbridge than Ivy League Schools, lets say (for grad school that is), because I am probably forgetting some crucial factors here.'

Raw percentages, or a link to the data, would make this question better.

Higher acceptance rate does not mean "harder to get into Oxford" ... it means "fewer people apply to Oxford".

One immediate consideration that springs to mind is that applicants from the US might be less prone to apply due to the funding situation for non-EU / non-UK people vs. the commonality of full-ride + stipend at top programs in the US.

What is the normal number of schools for British students to apply to?  In the US it used to be just a handful (a long shot, a likely, and a backup) but now it seems students apply to sometimes dozens, either hoping one of their long-shot schools takes them, or one of the likelies gives them a great financial offer.

@BenCrowell Great point. In addition to the travel costs, another difference could be if one of the schools charges an admission fee. I can imagine that simply charging $15 to apply would cut down the applications a lot.

@BenCrowell The undergraduate admissions system at Oxbridge is exceptional in the UK (particularly the interview process), whereas graduate admissions are much the same as the rest of the UK. I don't think there is any requirement for an in-person interview for taught post-graduates, and travel costs would likely be borne by the interviewing department for research post-graduates if they required one.

@FedericoPoloni Oxford and Cambridge charge £60 and £50 for a graduate application respectively, so this is a reasonable hypothesis! I think this is somewhat unusual in the UK, so it possibly is an attempt to reduce the number of applications.

I added overall acceptance rates to the question to make it more "accessible."

@guifa when was 3 schools typical?  By the mid 90s the spam approach to graduate applications was quite common.

Do they limit grad applications like undergrad?  At least in 2010 one could apply to only 5 schools and not both Oxford & Cambridge.

For PhD acceptance rates, many schools/departments essentially require PhD candidates to find a potential supervisor prior to applying. My, non-Oxbridge, department's acceptance rate is something like 90% for students who find a supervisor prior to applying and 0% for those without a supervisor. This "requirement" really changes the dynamics of applying for a PhD.
For Masters programs, I think there are a number of minor factors and one large one that result in UK universities having a higher acceptance rate than US universities. Graduate classes/modules in the UK are only taken by Masters students. PhD students and advance undergraduates do not take graduate level classes. This means departments need to accept enough Masters students to make teaching the classes worthwhile.
Getting enough fee-paying students is hard and the competition between programs is fierce. Departments tend not to pass up on students that they think can pass. While "entry tariff" (basically the GPA of admitted students) is starting to count in league tables, in my experience UK universities are not as adapt at manipulating the league tables. Further, UK universities generally have a hard minimum "GPA" of a 2.1 degree classification in a related field. Since undergraduate education in the UK is more specialized than the US this means that a "related" field is much more narrowly defined. Minimum requirements are strictly enforced in the UK so Brits tend not to apply to positions that they are not qualified for. Overall, this cuts out the bottom of the application pool. That said, something like 80-90% of students get a 2.1, and I do not think thesee factors substantiallychange the acceptance rates.
What I think matters the most is the fact that students only apply to a select few schools. My UK students tend to apply from between 1 and 4 Masters programs. I have less experience with US students, but my intuition is they apply to a lot more schools. I think that the reduced number of UK applicants increases the UK acceptance rates.

The odds of a given individual being accepted (which is how I would interpret the phrase "difficulty") depend on the number of similarly-qualified and better-qualified applicants, as well as on the number of students the school intends to admit.
It is not correct to equate a lower percentage of applicants accepted with lower probability of a given individual being admitted, unless you can verify that the applicants to different schools come from similar distributions.  One school may receive a large number of applications that are very weak, while the other school receives only highly-qualified applications.  The presence of all those weak applications has essentially no effect on the probability of a strong applicant being accepted.
The situation described above often occurs due to differences in awareness among potential applicants of the realistic minimum qualifications for acceptance.  The cost of submitting an application can also influence this, as can the general notoriety of a school.
Finally, a school will try to admit enough students so that the number of acceptances reaches the intended number.  To do so, they will over-admit by a factor equal to the inverse of the yield rate.  The schools may have different yield rates, which will lead to different acceptance rates even if all else is equal.

Acceptance rate is one of the factors used by U.S. News and World Report in their influential "Best Colleges" rankings.  Specifically, it currently counts for 1.25% of the total score.  So universities in the US have a clear incentive to decrease their acceptance rate (by increasing the number of applicants, whether qualified or not).  This may play some role in the difference.

For UK PhD programmes those figures can be highly misleading.
Unlike US PhD programmes, you really need to first get the endorsement of a potential supervisor before making your application if you want to have a chance at admittance. For example, my supervisor was contacted by around 40 people but only endorsed 5. 3 applicants (including me) were made offers. I checked their Linkedin profiles and all had graduated at the top of their department as undergrads and earned distinctions on one or more masters' degrees. From what I hear, this scenario is not uncommon for Oxbridge, and the true acceptance rate must be closer to something like 5-10%. What's more, UK PhD programmes do not provide funding. Because of this, many offer holders have to decline their offers unless they are awarded a scholarship. These are extremely competitive. For example, only 17% of graduate students at Cambridge receive full funding. Prestigious scholarships such as the Gates Cambridge scholarship have success rates of 0.5%. So, as you can see, getting accepted into Oxbridge for graduate study, particularly a fully-funded, is a rare feat and a huge honour.

Not only do you need to find a supervisor, but many PhD positions also require you to write a research proposal, which is not a trivial task. The following interview(s) can also be challenging. Then after, and if, you get a conditional offer, you are still not guaranteed a place (as you need to satisfy the conditions of the offer). And each year there are people who decline their offers just because they were not offered places in their preferred colleges. I am not too familiar with the US system, but from what I do know, the process in the UK seems wildly different.

"is a rare feat and a huge honour" - unless you are from the EU are a woman, of course. It is no secret that those universities heavily endorse affirmative action, and that it is much easier to get a fully funded offer if you are an EU or british national.


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Read both revised and original version to cite paper?
For papers, these questions advise to cite the original peer-reviewed version instead of a revised edition.
Now, does this mean that one should

read the revised edition, and then, if one wants to cite
also read/skim the original paper in order to cite correctly?

Is this the consensus on the correct approach, or did I misunderstand something?
(It seems like an ineffective use of time, thus the question)

I believe that you are somewhat misinterpreting the advice given in the questions that you link: the general consensus seems to be to cite the most recent version (as being the most current state of knowledge), unless you have specific reason to cite an older version.
As such, I do not believe that you generally need to read or cite prior versions.

I am not so sure about this. If a conference paper is published in 2007 and the extended journal version is published on 2010, you should definitely cite the 2007 paper that introduced the method, algorithm etc. I would also cite the journal version as well, but you cannot just ignore the original paper.

@Alexandros Personally, I generally consider the extended version to have superseded the original version.  If the exact chronology is important for some reason, then by all means discuss the original version and its timing (that would count as "specific reason to cite an older version", per my answer).  Rarely, however, is exact chronology actually important to a citation.


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How much time to wait for answer after postdoc negotiations
I was wondering about a case I lived before two weeks. I have applied to a postdoc position even 10 months before getting my PhD degree. After couple of days, a professor from the institution emailed me and showed a lot of interest in my CV. He offered me to go there and write my thesis there. I refused that because of many issues regarding family, supervisor, etc.
I offered him that I can come just after finishing my dissertation writing, and would stay there till the defense day, taking couple of days off for the PhD degree and going back to them.
Anyway, he said they will study my case but they showed potential of acceptance.
They gave me a scientific paper as a task and I did it on time. He finally told me we will keep you updated. So I waited 10 days and never heard back from him. I sent him an email, and did not reply. I resend a new email after another 5 days.
What do you think? Have you been in such case? I am already have the feel they don't want me anymore, but come on where is all their interest in me gone? And why he does not reply to my emails? Never know the answer.
PS. The university is prestigious and worth to think and dream of it.
Thanks for your comments.

Universities can have convulted bureaucracies and slow recruitment processes. It could mean the prof has been busy and can't see any urgency given the 10 month wait anyway. It could mean that he wants to hire you and is waiting for approval from HR or his dean before confirming with you. It could mean that he has lost interest.

So it's been two weeks since you last heard from them? Don't worry, it is fine, they could be busy or traveling or waiting to get some more accurate information about your opportunities. Seems that you still have quite some before you finish your thesis, so also keep looking for other postdoc positions.

Also, we are in the summer in the northern hemisphere, where most people take vacations or go to conferences, so he may just be away and disconnected.

They gave me a scientific paper as a task What does this mean?  No one reasonable expects you to do work for them while you're still applying.

Thank you guys for your replies! I would wait for another two weeks, in the meanwhile i will keep applying.
@Kimball they gave me a task, like to give an opinion in one of their case studies. so, just a review.

It is not clear from your question what you are waiting for. Based on your description of the conversation, you should continue to look for post doc opportunities until you have a firm offer. Do not wait to hear anything more before sending out more applications. It is probably worth noting that 10 months prior to defending seems very early to be actively looking for a post doc.
If you are talking about how long you should wait before giving up hope, then you should wait as long as possible. Right now you do not have another offer, so there is no reason to move on.
If you are talking about how long you should wait until contacting the PI again, I would say generally 1 or 2 weeks between attempts. You might be better off making a phone call next time.

Thank you.. Reasonable answer. But i wont agree you with applying to postdoc in advance worth nothing. I always read and my supervisor asked me to start searching for a postdoc position before 1 year. some positions might not be available but, it could emerge sometime and they dont find a suitable profile.
The second part, in which what am waiting for, i also applied to another postdoc position, and will apply for a fellowship, that's why i was wondering what to do :)


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Which approach to studying is better?
This is not a usual question on this site, but I think it is appropriate nevertheless since I believe that members of this forum have vast experience on studying and all things that affect studying.
I am a student and I have a "problem" that's basically this: when I start studying something I feel unpleasant and restless if I am not completely sure that I understand the content being studied. This sometimes leads me to spend "too much time" on a particular subject and one might argue that it is a waste of time. My personal opinion is that this is the only way to study, I don't go to the next topic unless I have completely understood everything that's presented and unless I've come up at least with one question that I have to resolve in order to proceed. Sometimes the number of questions increases and usually that's what prolongs the studying of that particular subject.
However, many of my fellow students seem to be satisfied with just a basic understanding of the topic, and the questions that are keeping me from continuing, often don't bother them at all.
What is the better approach to studying in your opinion and why would that be? Am I being too perfectionistic or am I just trying to have a complete understanding of the topic?

This is going to be flagged as not the appropriate place for this question, because undergrad questions aren't relevant to this SE. However I'll give what worked for me in a comment.
It depends on your subject, so take this with a grain of salt. My topic was physics. In physics, if you think you understand some topics, chances are you probably don't understand it very well. Having a fundamental understanding of a topic is important, but it's just as important to practice with a variety of problems.

Wanting to spend time to learn a concept is GOOD, because it shows a desire to learn and understand. What I noticed when I was an undergrad was that I could not actually spend all the time I needed to in order to learn a subject, because of time restrictions (coursework AND exams). Myself and most of my cohort were really rushing to be able to answer courseworks and to be able to answer exams. This isn't good, but there wasn't much to work with.
Keep doing what you're doing, BUT schedule your time on each subject with respect to other topics you need to learn and also coursework/exams.

@lafemmecosmique, You are likely correct that it will get flagged as off-topic.  However, this site is very confusing, as the first statement about what is “on-topic” is, “This site is for academics of all levels—from aspiring graduate and professional students to senior researchers—as well as anyone in or interested in research-related or research-adjacent fields.”
Then, further down states “do not ask questions about… undergraduate-specific issues”.  These two statements clearly contradict each other.

Agree it will be flagged but no matter how we can argue about what "academics of all levels" are the answer must necessarily be primarily opinion-based.  Not saying that's right or wrong just saying that's just "Off-Topic 101."

@DaveKaye It seems to me that many questions that are posted on this site are primarily opinion-based since the sole nature of most questions posted here are questions that ask for advice.

@ahra People have called me on making such a comment before.  I pointed out above that I don't necessarily agree or disagree whether or not that should be allowed but that's what it says in the rules.  It's also given as one of the primary reasons to "flag" an entry.  I did not write these rules or guidelines.  My suggestion is that if you wish to change this policy that you raise the issue in Meta.

@MikeP and others There is already a meta discussion on the undergrad problem: http://meta.academia.stackexchange.com/q/3300/20058

It is good if you can understand something completely and thoroughly. However, there comes a point where most of us must leave gaps and accept that the gaps will fill with extended experience and exposure, over time (technical term: "by osmosis"). Failure to accept that gaps need sometimes to be tolerated can lead to collapse of careers.
What you need to judge is how fast you are moving - if you do not trail back too much with respect to what's required in your duties, I would not worry too much. Good understanding is a worthy cause and will pay dividends later on. However, when you fall back or fail to address important aspects of your studies (or repeatedly fail, through perfectionism, to submit reports/works/papers on time), then you should consider ways to get a coarser, higher-level view of what you need to learn and start to leave gaps.
Hopefully these criteria will help you to judge at which level you may want to operate and to switch between levels when required.


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In US universities, how much academic information does a professor have about graduate students enrolled in his classes?
Does he know immediately (from some internet / intranet access) which students in his classes are undergraduates, masters students, PhD students, non-degree students?  Does he typically have access to his students' transcripts, thesis work (dates submitted / approved / topic), and knowledge of his students' academic / research advisors?

"Varies widely" will be the best answer here. At my institution, even individual faculty members have different levels of access.

At my R1 state university in the U.S., I do have info on whether students in my classes are undergrads or grads or non-degree, which are auditing and which taking it for a grade.
I have no information on their transcripts, nor thesis work nor status, nor academic or research advisors.
For students that are my advisees, yes, I have such information. In fact, for PhD students or MS students whose committees I'm or have been on (that are still active...), I do also have such information. But not for any other students.

That said, it would generally be common knowledge among faculty who a graduate student's advisor is; this is basically public information.  And even without reading a transcript, in all but the largest departments, faculty would usually have a general sense of the students' progress through the program, what they are working on, and whether it is proceeding successfully.

@NateEldredge, indeed, who peoples' advisors are is public knowledge, but not trivial to acquire without effort. Also, students might care that, while positive news is often public knowledge, various troubles that students may have tends to be privileged (e.g., FERPA) information, so in principle at least is not everyone's business.

It varies widely.
First of all, federal privacy laws allow information to be shared with "school officials with legitimate educational interest", without needing student consent.  Professors are generally presumed to fall into this category.
Basic information like the student's graduate/undergraduate status are usually listed in the course roster, and the professor very likely has seen that information (which is not to say he remembers it).
Beyond that, there is a range.  Some institutions, based on their own interpretation of the law and risk/benefit analysis, choose as a matter of policy to make full transcript information available to all faculty members.  Others choose to impose various restrictions on who has access to such data; e.g. academic advisors, department heads, administrative personnel, etc.  I don't think they are generally obligated to tell students what those policies are, though if you ask around you can probably find out.  So all you can really say in general is "maybe" and you should be prepared for either extreme.
In particular, as a student, you shouldn't assume this information can be kept secret from a professor.  Even if she doesn't have direct electronic access to transcripts, she can likely get this information easily.  In many cases, it would suffice to write an email to an appropriate person with access, often an administrative staffer, and give some plausible reason: "Dear Joe, could you please get me a copy of so-and-so's transcript?  I need to check on blah blah blah."  She could also just ask around: "Hey Alice, you are so-and-so's advisor, right?  What are you two working on these days?  How is it coming along?"  Faculty usually don't hesitate to share such information with each other.
On the other hand, if there is some academic information about you that you think is important for the professor to know, you shouldn't assume that he will automatically know it.  Even if he has direct access to those records, faculty usually wouldn't bother to read everyone's transcripts without some reason to do so.  If there's some aspect of the course that is particularly relevant to your interests, based on your advisor and research topic, don't assume the professor knows / remembers that information: tell him!

I disagree that a professor could easily get access to student transcripts they do not officially have access to. I am a professor, and if I asked our administrative staff for a student's transcript, I think it would immediately raise red flags, and I certainly wouldn't be given access to it.


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Research topics that gain importance quickly
For instance, there's currently a great deal of attention towards the theory of "spin glasses" in probability theory.  But how does a research direction gain its importance so quickly?  Does it simply start with one researcher who declares that this research direction should be given a lot of attention?

Spin glasses are new??

Extra funny, since I thought of spin glasses as having a huge fad peak in the 1980s or so... but maybe there's a resurgence!

As the OP writes, spin glasses are a relatively recent subject of interest in probability theory, in the sense of "among people who describe themselves as probability theorists, and publish in probability journals".  Physicists started thinking about them much longer ago.

The current answers are both good answers to the general question, but neither really applies in the particular case singled out by the OP or other situations like it.  Spin glasses have been studied by physicists for decades, but until relatively recently the most popular mathematical models of spin glasses appeared to be beyond the reach of rigorous mathematical analysis.  Following some breakthroughs circa 2000 (due particularly to Talagrand), probability theorists now recognize that this is a fruitful area to research, full of problems that are hard enough for progress to be interesting, but possibly within reach of current mathematical techniques.
This kind of thing happens a lot in mathematics.  Many so-called pure mathematicians are much more interested in real-world phenomena than they are made out to be, and are always on the look-out for interesting problems inspired by real-world phenomena.  But most real-world phenomena are simply too complicated to be amenable to proving theorems about them.  So if someone shows that some physical model --- possibly a highly simplified toy model, but complicated enough to reflect something of what might go on in the real world --- is within the reach of rigorous mathematical analysis, then mathematicians often flock to work on it.  If it's just the right level of difficulty, so that new theorems keep getting proved, but it's hard work, then it can hold mathematicians' interest for a long time.

In my (limited) experience in academia, I've noticed that the research topics that gain the most importance & attention tend to be the ones that impact the most people.
Sometimes (often) it takes a while for new research to become important. For example, in my field of computer engineering, machine learning has been researched for decades. But only in the last 5-10 years has it truly caught fire, as computational power, software libraries, etc. finally reached the point where the average researcher could quickly and easily make use of machine learning techniques. Now, you see its use in everything from engineering to the social sciences because of its power in extracting useful information from large datasets.
Sometimes new research topics become important because they disrupt a large amount of research. Einstein's theory of special relativity (eventually) opened up vast new fields of research -- but not before facing criticism from classical physicists who saw their life work as being under attack.

One somewhat counterintuitive thing in mathematics seems to be that a topic A attracts new attention whenever someone finds an application of A to a topic B (this is, of course, understandable), but also whenever someone finds an application of a topic B to A (this is the counterintuitive part). The reason, I guess, is that applications are rarely one-way roads in mathematics, and usually point to deeper connections which can then be walked down both ways (although one of the directions is often easier). The other reason is that people want to be useful and thus like to explore fields where their experience could help, even if they don't care that much about these fields on their own.


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Is any of today's applied mathematics research in academia still done primarily on pencil and paper?
Does there exist applied mathematics research that involves primarily pencil-to-paper work, without the use of computers?  Or, are computers quickly replacing everything that an applied mathematician can once do by hand / traditionally does by hand?
Anything in academia in applied math research that computers can't do?
For instance, do PDE theorists use computers or strictly pencil and paper / chalk and chalkboard -- and leave the numerics of PDEs to numerical analysts instead?  Is there such a distinction, or is there instead always some sort of collaboration between the two types of applied mathematicians?
Another example that I can think of is the work of probability theorists.
Any insight to my very naive question would be greatly appreciated :)
Thanks,

Even in applied math you often need to prove things.

What do you mean by "use computers?" Essentially all papers are written using a computer these days.

There's not really any clear definition of "applied mathematics".  For instance, my own research essentially straddles the fields of PDE and probability theory (coincidentally the two that you named), yet I consider myself a pure mathematician and none of my papers have involved any digital computation.

Today's SMBC: http://www.smbc-comics.com/index.php?id=4130

I'll add a data point which isn't enough for an answer: I have a couple of cosmologists in my group who do theory work, and they use a paper and pencil for everything. They have computers for answering emails, but everything they do is on-paper maths.

I am an applied mathematician and I can't work without paper and pencil and in most cases I can't get things done without a computer.
My computer can't tell me in advance if my algorithm will converge, at what rate and what the error will be. My computer can't figure out how to discretize some new problem (unless I tell him how). My computer (up to now) never had a great idea.
On the other hand, I can't invert matrices with pen and paper and I even can't multiply a large matrix like that. In fact I can't even store most data I use on paper... (and also access rates for data on paper are pretty slow).
tl;dr I basically always use paper, pen and computer.

You could do Gaussian elimination by hand on large matrices, but you're likely to make a mistake.

If they fit on my paper and I have a cubic amount of time and patience...

Newsprint comes on wide rolls of virtually infinite length.

In addition to @Dirk's excellent answer, which I wholeheartedly concur with, I will also note that many types of applied mathematical research are done entirely without aid of a computer.
Consider, for example, this well-cited paper on Brewer's conjecture, which is all mathematical reasoning about the nature of distributed computations.  At the more theoretical side of any applied field, you can find such papers, where the conclusions are in the symbolic mathematics that is still best carried out by hand, most typically on paper, whiteboard, or blackboard in its crucial early stages.
Of course, basically nobody submits physical paper to journals any more, so I guess a computer does get involved eventually...

Thanks so much for your answer and for the link to the paper, @jakebeal :)

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


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Pros and cons of doing PhD research in an applied math topic at a non-math dept,
What are the pros and cons of doing a PhD in an applied math topic from a non-math dept? Let's say I found PhD programs in a research area that are in  aerospace / mechanical engineering departments at some schools and in math departments at other schools.

You can look at the programs of studies and the course descriptions carefully.  Also, look at the faculty bios of the two departments.  You may also check what the university's commitment to interdisciplinary study is like.  For example, can you have a committee member from another department?

Are you planning to go into academia? Might be relevant if you are aiming for a mathematics department in the future.

@AJK, excellent point - I will lean towards applied math departments then ... thanks so much,

Don't let that be decisive, just something to keep in mind - and for other people to think about when writing an answer!


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Having a retired professor write my letter of recommendation,
One of my math professors (in a U.S. university) retired this semester.  He was one person that I had planned on asking to write my letters of recommendation this coming fall semester, when I send out PhD applications in math / applied math.
He is very old and he seems anti-social and seems to not communicate with our math department very much.  I am just basing this on some stuff that he says, which scares me, e.g., "tell them (our math dept.) that I said this..."
So, I wonder whether anyone external to our own math department would even know who he is - or whether admissions committees even value his opinions about grad students, at this point in his career.
Would it be best to find someone else to replace him as one of my letter writers?  Someone who is younger and currently active in research?  I do have replacements in mind, but I am somewhat attached to this particular professor, since I feel that I got my start in rigorous mathematics with him.
Edit:  To add a bit more context, he is a full professor and has served on admissions / doctoral committees at our department numerous times.  So, he's very much qualified, of course.  My main concern is that perhaps he no longer communicates actively with people internal and external to our department, but that is only my best guess.
Thanks,

This question is really impossible to answer from the information you've provided and without information about other possible recommenders that you might have.

So, I wonder whether anyone external to our own math department would even know who he is - or whether admissions committees even value his opinions about grad students, at this point in his career.

First, it's not necessary or even expected that admissions committees will know (of) all or even any of your letter writers.  Second, you will be getting several letters, so they do not all need to come from "research active" professors.  Third, there's no reason to undervalue someone's opinion because they've retired.
Yes, it's a plus if you can get letters from people who are well known, but the most important thing is to get letters from people who know you best, so I don't see a serious concern from what you've told us.  (Though now that he's retired, it's possible he is harder to contact or less inclined to write letters.)

Hi Professor Martin, thanks for your answer.  I struggle with this thought: especially in a math program, those professors that know me best will also know my weaknesses best.  Do professors "calibrate" their opinions, based on the choice of schools that I am applying to?  Thanks, @Kimball.

@User001 Well, the most accurate evaluation of your talents and preparation should get you in the most appropriate school for you.  You don't want to end up in a program you'd sink in.  Anyway, I don't think there is too much "calibration" going on---typically one writes a general letter which goes out to a variety of schools, and committees place this in context.  If you're worried whether your professors approve of your choice of grad schools, you can have a discussion and see if they have any suggestions.

Your letter writer will be judged based on reputation  (Ignoring the unlikely possibility they have a negative reputation).  The faculty with the best reputation will

Travel frequently
Be an active researcher
Be older

The letter content is more important.  A letter from a famous scientist is no good if they do not say anything of substance about the applicant.


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How often do academic researchers use inferior tools for their research, when clearly better tools exist but are too difficult to use?
One example that I recently learned of is the use of ordinary differential equations (ODEs) vs. delay equations in mathematical modeling.  ODEs are apparently "memoryless" - like how Markov chains are in probability theory - though my classmates and I (not surprisingly) have never considered such a question before, concerning ODEs.  However, ODEs are apparently still heavily used because they are so much simpler to deal with.
In general, does this sort of thing happen pretty often in academic research?  Do a lot of researchers choose to use inferior tools that are significantly easier to handle?  This sort of seems to go against the idea of using cutting-edge tools in academia...

Yes - though I'd argue that being easy to handle renders a tool more valuable than a technically superior but difficult to use tool or method. In bioinformatics, for example, BLAST is one of the most frequently used and cited tools, in part due to its ease of use.

The position of a falling object is governed by an ODE, not a DDE.  You want to use the appropriate tool, not necessarily the most "powerful" (aka complex) tool. Simpler models are better, provided they capture the phenomena you are interested in.

@DavidKetcheson Good point - fewer parameters generalise better.

In addition to what @DavidKetcheson said: The point of mathematical modelling and dynamical-systems research is most often to understand why and how certain phenomena occur, not to provide an exact model of reality (which is impossible anyway and would require PSDDEs or similar). If an ODE allows us to model a phenomenon sufficiently accurately to understand what is going, that’s better, because we have indeed a better theoretical understanding of ODEs. And from the theoretical point of view, you do of course begin with understanding ODEs before moving to the more complex DDEs. But I digress …

@user68375: based on your logic, delay equations shouldn't even have to be invented and put into use in current research – How does this follow from my logic? Of course, DDEs are important and necessary to model some systems (at least if you want gain any useful insights), but that does not mean that you should use DDEs for everything. And that’s not even taking into account that there is a huge class of systems where there is no relevant delay or memory whatsoever.

I think my question is a good one and unfairly closed. – 1) Your question is based on an example which (apart from not being wrong, if you ask me) is at best only understandable by a small audience. 2) Without the example, we need some definition as to what an inferior tool is – otherwise the question is way too broad. 3) Even if we have some clear definition, your question is probably not answerable, because gathering general, robust data on this is a gargantuan task (and pretty pointless on top, if you ask me) – all you will get is opinions (which this site is not suited for).

Newton gravitation theory is inferior to Einstein's theory of gravitation, but incredibly more useful for planetary motion, space travel, and most related things unless you go for high precision (GPS), or cosmology etc. Yes, inferior tools are often the right ones to use if they cover many important cases.
Usefulness and simplicity also permit robust use not too dependent on the user's expertise and thus are also often superior from the perspective of error mitigation.
Sometimes even outright wrong theories can be useful, such as Sommerfeld's theory of spectral lines (before it was superseded by Quantum Mechanics, but of course, here the better theory was really preferred). Of course, for atomic physics, as long as no extraordinary accuracy is required, you probably still wouldn't use the full QED.

This doesn't answer the question; it debunks the premise of the question. I think the question should be closed as "based on a false premise."

@DavidKetcheson I am not sure I understand. Could you explain in more detail?


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Do statements giving background about a problem require proper citation?
Say I am starting a paper, with the purpose of showing my work to some professors internally at my department for some high-level feedback - with no plans for it to be published at the moment, but more to be kept as a project and perhaps earn a letter of recommendation for it - and I describe the problem in almost exactly the same way as some earlier papers do; e.g., I want to briefly describe both its theoretical and computability issues, and then give some examples of diverse applications of the problem in the sciences.
Does this introductory page of writing need any citation at all?  Does saying stuff like, "this is a problem that has challenged mathematicians for over half a century" or... "the computability of the matrix, given only partial spectral data quickly becomes intractable in higher dimensions..." need citation?

...not my whole apartment, maybe just for my bathroom.  This way I can multitask in there: brush teeth, reread paper.  take contact lenses off, reread paper.  I also plan to show it to some professors.  I have edited @ff524, thanks :)

I describe the problem in almost exactly the same way as some earlier papers.

If your description of the problem is based on the description in another paper, then you have to cite that paper. If your description is not based on another paper, but is such a standard thing, obvious to any expert in the field, that you have naturally written it in a similar way to other papers, then the following applies:
Statements like

this is a problem that has challenged mathematicians for over half a century

or

the computability of the matrix, given only partial spectral data quickly becomes intractable in higher dimensions

can benefit from citation(s). Not necessarily to avoid plagiarism - if you don't include citations, you're probably not misleading anyone into thinking it's an original contribution - but to support the statements with evidence.
Statements giving background about a problem often benefit from citations  because without evidence, the reader might not be convinced of the truth of the statement. (Or, even if we know our audience will agree with the statement, we sometimes cite evidence to show that we know the evidence.)
To some degree, this depends on conventions in your field, though.

In some fields, statements like the ones above would typically be supported by citations to a handful of papers that either directly support the statement with evidence, or show that other experts in the field agree with this statement and have made similar statements themselves.
In other fields, the standard is to only cite things you really use, and in that case you probably wouldn't cite anything in this situation.

You can look for some high-quality published papers on topics similar to yours to get a sense of what the convention is in your field. If in doubt: cite.


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Does the NSA hire mathematics professors often for projects / contractual work / full-time work?
How often do math professors / math PhDs / postdocs, whose research directions are in abstract algebra and number theory, get hired by the NSA to do some work - either on a short-term contract or longer-term / full-time work?  Or is the NSA highly selective and just because one has a PhD in Algebra and / or Number Theory does not mean that one can just "sign up" to work for the NSA, like signing up to join the military but with math skill sets to contribute.
I've read about some high-profile mathematicians who have done some contractual work for the NSA, while keeping their professorships, so my question is mainly on whether this also happens for lesser-known PhDs / profs / postdocs. I asked my own prof this question and he said that the NSA is highly selective - something that he is not sure he could even get, if he applied.  Yet, another (more senior in rank) professor that I spoke with says the NSA is one of the largest employers of algebraists and number theorists.  So I seem to have two conflicting ideas.

Being selective and and the largest employer of number theorists are not mutually exclusive.

I asked my own prof this question and he said that the NSA is highly selective - something that he is not sure he could even get, if he applied. Yet, another (more senior in rank) professor that I spoke with says the NSA is one of the largest employers of algebraists and number theorists. So I seem to have two conflicting ideas.

Note that these don't necessarily conflict: there aren't many large-scale employers of algebraists and number theorists, so they don't need to have low standards to be the largest.
I have no direct experience with NSA hiring or any classified work, but I'll give an answer since I doubt any NSA employees will volunteer first-hand accounts on this site.  My answer is just based on my observations of people who have applied to or been hired by NSA or contractors.
My impression is that full-time hiring at NSA is fairly selective, but not extraordinarily so.  You have to be a good mathematician, but it doesn't look nearly as difficult as, say, getting a tenure-track job in a top ten department.  You don't have to be particularly well-known in the mathematics community, but you'll need to beat out other good applicants for the job.
It's hard to make precise comparisons between NSA and academic hiring, because of a lack of information.  When a young mathematician is hired by NSA, the outside world typically never finds out how successful they became.  If a promising student is hired, we don't find out whether their promise was fulfilled; if a seemingly less promising student is hired, we never learn whether NSA identified real talents that weren't obvious in academia.  The net result is that I don't believe anyone without a security clearance can do more than roughly approximate how selective NSA is.
There's also a fair amount of part-time and full-time consulting done through private companies.  Some of these organizations are extremely selective, so you should not assume this is an easier way to do classified work.  (In particular, my impression is that the companies that hire mathematicians are among the most selective.)

Or is the NSA highly selective and just because one has a PhD in Algebra and / or Number Theory does not mean that one can just "sign up" to work for the NSA, like signing up to join the military but with math skill sets to contribute.

Definitely not, it's not remotely like that.  Just having a Ph.D. in a relevant field in no way ensures you'll be hired.

A note to the OP of the question: you need to be able to obtain security clearance for NSA to hire you. This ability to get security clearance is actually hard in these days.

Being the "largest employer" is easy, because the vast majority of industry has no need for algebraists (or, at least, they think they have no need). NSA might be a larger employer of pure mathematicians than any individual university, but I'd guess that academia as a whole is much larger than NSA. Everything NSA does is shrouded in secrecy, so I'd be very surprised if you could get much reliable information about what kinds of people they hire, or even how many. Speculations are plentiful, though.


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Asking a professor whether my application has been accepted or not
I applied to a university which has offered acceptance letters to a few students so far. What would be a polite way to ask my professor whether my application has been accepted or not by the review committee.

Is this a school you currently attend?

no.a grad school that i applied to

It's not his decision. Even if he's aware of the outcome you should wait for formal notification.

When a department decides to accept someone, they try to tell them as promptly as they reasonably can (sometimes they need to get administrative approval or the like), so delay indicates that a final decision has not been made.  If you haven't heard anything, you can assume you have not been accepted yet.  It's theoretically possible that the acceptance e-mail got caught in a spam filter, but that's probably not likely enough to be worth worrying about.
If you reach the point where large numbers of people have heard acceptances and rejections, but you have heard nothing, then it's worth asking about your status, just to make sure there wasn't a communication difficulty.  It's also worthwhile if you are facing an upcoming deadline and hope for an answer before that point.
However, if just a few students have received acceptances so far, then your best option is to wait and see what happens.  Asking for a status update will likely just lead to a response along the lines of "Sorry, we haven't made a final decision yet.  We'll let you know when we do."  (And asking more than once is likely to annoy the committee.  It's better to save your request in case it matters more later.)


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Employment in academia for doctorates w/o same field undergrad
I'm an undergraduate in Mechanical Engineering interested in a career in academia, especially Physics. A middle aged person in India (from where I am) I recently met told me he couldn't find employment in academia in India or abroad after completing his doctorate in a Physics field, because he did an undergrad in Mechanical Engineering. Is this situation where there is difficulty finding employment when doctorate and previous education do not match generally true in academia, Physics or otherwise, or probably a very specific problem?

My undergrad was Electrical Engineering, my PhD was in Materials Science, and I'm now building a new pulsed power accelerator. Sounds like a specific problem to me.

People switch fields relatively frequently between the undergraduate studies and the PhD. I rather suspect that he is attributing the failure of finding an employment in academia to this when the issue is actually elsewhere.

@MassimoOrtolano The person told me the catch was that he was expected to teach subjects he wasn't good at, is that situation common ?

Is it that they can't find a job in physics because the physics department sees the undergrad degree and scoffs, or is it that they are short on mech eng instructors and hope someone with a mech eng background and PhD in physics might be able to fill the holes? The latter seems far more plausible to me, or the other alternative that they are completely wrong about why they can't find a job.

@BryanKrause Apparently the former. He says universities denied employment on the basis that he potentially could be incapable of lecturing physics students because he held a Mechanical Engineering degree.

I think it's more likely he's just making up a story and getting it wrong, or someone gave that reason but was lying. Unless his actual physics PhD didn't really involve physics and doesn't demonstrate competency in that field.

@BryanKrause Oh that makes sense. Thanks for the input !

It's certainly true that a faculty member in most disciplines in the US will be expected to be able to teach a variety of courses in that discipline and that not having sufficient background in the discipline (because for example the candidate has made a late switch into the discipline) can be a negative on the job market.

@BrianBorchers From your assessment I'm picking up that having sound knowledge (which is any case needed for a PhD) in some subjects to teach related to ONE particular field, say solid state physics, should be safe. One won't be expected to handle subjects beyond that field?

@Gaurav You'd probably want to be able to convince the department that can teach introductory physics classes too. There's usually a lot more of them than there are courses in, say solid-state physics, thus requiring more instructors. Someone with a ME background likely knows the mechanics parts well, but might not have taken much electromagnetism or optics (or so-called modern physics, if that's included).

@Gaurav  in a large department, you might be able to limit your teaching to say "solid state physics", but in a smaller department (and there are lots of small physics and math departments in the US) you might have to teach a much wider variety of physics courses.  I work in a relatively small mathematics department and have taught undergraduate courses in calculus, linear algebra, differential equations, combinatorics, probability, statistics, numerical analysis, mathematical modeling, and operations research.  That kind of breadth is valued in smaller departments.

@Anyon Got it, thanks. But that doesn't mean I'll be filtered out pre-interview for being assumed to be not suited, right?

@BrianBorchers Understood, thanks for the help and time!

@Gaurav I would expect that, if they're otherwise interested in your profile but not sure if you can teach the required courses, they'll ask you about it at some point (as in stochastic's answer).

@Anyon Understood, thanks!

This is generally not a problem, and many departments may even consider having a more diverse background an advantage.
I have an engineering undergraduate degree and graduate degrees in physics and math, and I was asked (only once) in one of my interviews if I am comfortable teaching undergraduate physics courses given that my undergraduate degree is in another field. If you can confidently say yes to this question and can back it up, there should be no problem.

Thanks a lot for the help !

I have a permanent lectureship in a field that I don't even have a PhD in, let alone an earlier degree...and I lecture in the field too, despite never having even taken a class in it. It makes sense if you follow my research progression, but that's the point, everyone is different. Note this is social sciences/humanities, but nothing is clear cut in academia, and a different undergraduate degree is particularly meaningless post PhD.

All my degrees are in theoretical math. About 90% of my teaching has been computer science (and not as just "misspelled math").

Don't base life decisions on anecdotes. I'm sure such cases exist, and, other cases in almost any combination. But your future as an academic, or even in industry, will depend far more on your later work and far more than that on the potential for success that you can demonstrate to anyone in a position to hire you.
But it would be a mistake to stay in Mechanical Engineering for life just for such a reason. It might be a reason to switch earlier, rather than later, but only so that your path into a physics doctoral program might be eased a bit.
But, a single case is always a poor indicator as there are always, potentially, other, unstated, reasons for the outcome.
Create your own life. But work hard at it.

Thanks, really helped ! The person I'm referring to told me lecturing unrelated subjects was his problem. Is lecturing part necessarily part of the job profile ?

That may vary by country and certainly by field and by institution. Most academics, worldwide, do some teaching. It may be a lot or a little. But to get an academic position you need, also, to be seen as a "good fit" for the current and projected needs of the institution.

Basically, though research might be very specific that eliminates potential lecturing in some subjects, unis might still consider if the candidate's research is aligned with the institute's stated research areas ? Thanks.

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


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I have two last names and want both Arxiv and google scholar to show them both everytime. How can I do this?
So I have two last names: FirstLastname SecondLastname, Nicolás. But both ArXiv and Google Scholar abbreviate this as SecondLastname, Nicolás F.
I have colleagues who have literally given in to the pressure and changed the last name they go by just because of this, but I don't want to do that. How can I ask the platforms to display my name properly?

Since this is common in many places (https://en.wikipedia.org/wiki/Double-barrelled_name), it is a shame that these sites don't have a standardized way to choose the form of the surname.

This is a really common problem for people whose names do not follow the British / American convention of "First name [middle name] last name". There is a lot of variation even within Europe, let alone around the world, yet system developers are often unaware. Unfortunately everybody I know with this problem (some Spanish, some Indian , some from various parts of Africa) have just decided on what their two-name professional name will be and adopted that. With Google Scholar in particular, which has approximately no support, it'd be tough to fight it.

Voting to leave open as this is a common problem with academic systems facing many academics.

Actually, my spouse, American, born to American's has two first names. Correct on birth certificate, passport, ... but a lot of systems can't handle it.

@Buffy two first names as opposed to first and middle names? Isn't a second first name your middle name by definition in the US? It is for me, anyway.

@terdon, nope, two separate words for the first name, plus a middle name. As per the birth certificate, which was created in the pre computerized era. Not a problem then. Something like Bonny Sue (first name), Marie, (middle name), Ogalvie. And Bonnysue or BonnieSue or Bonnie-Sue just don't work and are never used or implied. Note that names are actually fairly arbitrary, though many are traditional. Her mother was just a bit creative and not able to predict what would happen in the computer era. Our COVID boosters were delayed for several minutes while the drugstore puzzled it out.

Naming of some people among the first inhabitants of what is now North America (First Nations) can have many "parts": Henry Cold Moon Rising, for a made-up example.

Because nobody has linked this yet... https://www.kalzumeus.com/2010/06/17/falsehoods-programmers-believe-about-names/

This question is similar to: How do you handle a double barrel name in citations/publishing?. If you believe it’s different, please edit the question, make it clear how it’s different and/or how the answers on that question are not helpful for your problem.

Just put both surnames in the single surname field, as if it were a compound surname. No need for a hyphen. Just treat your two surnames as a single compound block when dealing with systems that suppose a single surname. For Spanish names at least this works just fine.

Early on in my career my PhD advisor suggested I hyphenate my name -- and I did. While there is still some confusion at times, it has minimized the problems, and I am usually alphabetized by L instead of by R, and my lastname is typically recognized as Lozano-Robledo. Both Google scholar and arXiv recognize me as Lozano-Robledo.

Better, though, if you can maintain the traditions of your ethnic/cultural/ancestral background rather than to have to submit to the incompetence of computers. And, not so great if you consider Robledo to be primary, which might be the case in some cultures.

The hyphen is usually unnecessary if you just stick both apellidos in the same field separated by a space (this is almost always accepted, while hyphens often are not).

One option - which is probably not ideal - might be to put a hyphen instead of a space between your two last names. Since hyphenated names are common in white America, web systems are more likely to handle them.

Now I'm wondering if a non-breaking space (or a similar character) would trick at least some of the automated systems.

@JiK: problem is with services that aren't expecting that. I don't think Nicolas FirstLastName SecondLastName (or a ton of other possible rendering errors) looks very nice :)

Or if the non-breaking space is simply dropped. Note that things were fine before computers. This is a relatively easy problem for computers to handle, being only a few options. Why it hasn't been done is lack of attention by those specifying the systems. Computers are good at this stuff. Maybe ridicule of those systems and their creators is the solution.

I'm a developer and although this is an easy problem to solve, the fact it exists also makes sense to me.  It's common to sanitize inputs, and I can easily see either a developer or business analyst saying "let's only allow these characters" - omitting spaces due to not thinking of this "common" use-case.

@aaaaaa, I might describe that "business analyst" as a chauvinistic fool. If they have a world-wide audience, they need a world-wide solution. Why should a computer system be chauvinistic?

I think you're being unnecessarily judgemental.  Not everyone thinks of last names as having spaces.  Not everyone travels or meets people from other cultures, regardless whether they're employed to build a product for them.  I think the fact multiple programs missed this case is proof that this isn't just one or two poeple who should be ridiculed

@aaaaaa IMHO if somebody is employed to build a product for worldwide use, then it's their job to learn about worldwide requirements.

Yup flyto, and the world should be perfect too.  Let's judge everyone who isn't.