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How do I know if I am truly prepared for graduate school in mathematics?
Tl;dr: Having taken lots of math classes, I've managed to forget a lot of information. Also, since I'm at a small university, most of my peers are not interested in pure mathematics graduate school, so I am not sure whether I am truly prepared for graduate school. I also feel that my GPA indicates my ability to work hard as opposed to any real ability. How do I know if I am actually ready for graduate school, as opposed to being a big hardworking fish in a small pond?

I am currently in my fourth year of undergraduate school at a small public liberal arts university (I transferred in during my sophomore year from    community college). I plan on spending another year here in order to graduate with the degrees I want. I came in as a biology major, taking mathematics courses for fun. I ended up getting As in each math course and was hooked. I am now a math major, with minors in biology and chemistry.
I've taken several classes (including Proof/discrete math, Linear Algebra, Real Analysis, ODE, Advanced ODE, Abstract Algebra, Number Theory, Math Methods Operation Research) and some independent learning studies (fractals, Cantor set, some real analysis, measure theory, etc). I'm currently in Complex Variables, Real Analysis - 2, and Mathematical Modeling. In the future I am planning to take  Abstract Algebra - 2, partial DEs, and an independent learning study on primality. So far I have a 4.0 GPA in math (3.92 overall).
I am not required to take many of these courses to graduate, but I have taken them because I enjoy math and to broaden what I know. I have pass failed only 2 classes (mathematical modeling and operations research) because I did not have enough time to devote to get the grade I wanted, due to pledging into a fraternity and being ill. I attained a pass of course in these two classes. Plus, these are more applied courses which I did not care as much as the purer courses.
My ultimate goal is to go to graduate school in number theory, mainly focusing on pure mathematics and primality.
My main problem is that over the years, I have taken more math courses than the average undergraduate would at my university and plan to do more. Although I've maintained an A average in all my math courses, I have managed to forget a lot of information I have learned. This mainly has occurred due to the fact that I've focused so hard to maintain this GPA that I often work very hard to get that A and then the knowledge is never used again for the most part. I am very, very afraid that when I attend graduate school, I will not know as much as I should, that I will be subpar, much far behind other applicants who have more mathematics memorized. Granted I have decent grades, it almost feels as if I don't deserve it since I can not recall a lot of the information I knew so well at one point or the other. I want to pursue a career in mathematics as I love it. I am just worried.
Also, aside from one very gifted student, I do not know of any other students in the small math department with grades like mine. Many are pursuing teaching masters and not as interested in pure math. Many of my classmates believe I am intelligent or gifted of some sort, but I do not feel like it. I feel like I should know everything if I attained an A in every course. The problem this is late in the game and I'm not sure what to do. Having a course load so difficult and challenging for the past few years, with taking organic chemistry/biology lectures and labs, with 2-3 math courses each semester, I barely have time to sit there and recall information from earlier courses to jog my memory.
I also don't believe I have the mind like some select few who just know how to do things or apply things. Sure I can work on something for a few hours and eventually get it but it does not just spark into my head to do certain things.
Overall, I honestly do not believe that my GPA is a good representation of what I know, but more how hard I can work. I know the simple answer is to just take the time and review things, learn it again, and use it so it isn't forgotten; but surely I can not do this for all the courses I've taken.

I think this question is too vague, but you might want to look at this question.

You might consider the possibility that the students in the teaching masters program are less interested in pure mathematics because they are in the teaching masters program, as opposed to because they are 'females'.

@AruRay I do not believe it is because they are females, but because I know from personal experience in classes with them and their words that they do not particularly care; they rather just pass and all assume they'll never use it again. I mean no sexism.

@Frumpy The wording was 'Most are females (no offense) who are pursuing teaching masters' as opposed to 'Most are pursuing teaching masters'. It's not unreasonable to interpret that as your saying that their being 'females' is relevant. In any case, from your comment above, I'm happy to give you the benefit of the doubt.

"Indicates my ability to work hard as opposed to any real ability..." Classic presentation of imposter syndrome - don't think that way.

You ability to work hard is real ability.

One of the reasons I vote to close is because I think this question is better suited on Math SE. If you agree, please flag the mod to migrate. Please do not ask the same question there. Thanks.

I wanted to comment on "other applicants who have more mathematics memorized" This could just be true of the small bubble I am in, but conceptualizing and understanding rather than memorizing is the way to go with mathematics. A great thing for a mathematician to do is ask "why does this work like this" until they get to the very base of the system, and understand it from the ground up(from the axioms and definitions, not authority or intuition.) If you haven't been doing that, don't worry. pre-candidacy work for a PhD is all about realizing this kind of understanding in a host of subjects.

@scaaahu This question would not be well suited for Math SE and would be closed quickly on there. Math SE is for asking and answering mathematical questions. This is not a mathematical question, this is a question about going to graduate school(albeit in math)

In case you are worried about not knowing by heart that many theorems, korte at my undergrad alma mater (fairly big name in discrete math) proudly claimed in a seminar a friend took that he only knew 3 by heart (one of which was the normal distribution). I'm sure this was exaggerated and he knew more, but not every mathematician has photographic memory (even though the number of those with it seems high and it helps greatly). I like your humbleness, but don't let it get in the way of your dreams.

@SE318: correct. As it happens, their biggest opinion maker just posted a request to make this type of question (disregarding the condescending tone) explicitly off-topic; and the top-rated comment suggests to send them here.

@SE318 It was a mistake on my phrasing; it was late for myself.

@JeffE I never really thought of it like that. Thank you.

@gnometorule I do have one goal; and it is to hopefully one day prove something great, and contribute to math at a higher level.

@Frumpy, That is fine. If you are seeing the deeper truths of mathematics, and understand the underlying structure of the objects you are studying, then in my opinion you are probably fine to enter a graduate program in mathematics, as many people are not able to do this type of thinking when they first enter graduate level mathematics. Having a large number of facts and theorems memorized can definitely be helpful, but getting a glimpse of the bigger picture is more so(in my opinion.)

@SE318 My goal is to understand how things work and why. Not to memorize things as I have done in a lot of my other courses such as organic chemistry and biology. That's why I enjoy math. My goal, in these last few semesters is try to have a deeper understanding.

I think the courses you listed would have prepared you quite well for grad school, unless they were all inordinately easy versions of what's usually taught under those titles.  (Except for "partial ODEs" which looks like an oxymoron.)

@AndreasBlass I meant partial DE.

It was a bit surreal reading your question, because my own thoughts back when I was an undergraduate were eerily similar. Are you me?
Anyway, first and foremost, as JeffE would say, do not listen to the imposter syndrome! Here's some information on that in case you are unfamiliar with the term; it's worth keeping in mind - imposter syndrome is far too prevalent in academia.
Secondly, I don't know which university you are in, but unless you have massive grade inflation where everyone gets an A all the time (which you have indicated later in your question is not the case), if you're consistently getting great grades, you're doing something right. The underlying thread in your question seems to be the notion that the ability to do math (research) well is some sort of innate spark that some people have and some people don't. Nope, doesn't work that way. Math, even advanced math research, much like research anywhere else, is mostly about hard work. Some people do math more quickly than others, which must be nice for them and is an advantage sure; but the rest of us can do math just as well.
The point I'm trying to make is that you shouldn't knock hard work, it's at least 95% of any PhD.
Your (sub)question about remembering every single thing you have learned in college reminded me of this question on quora, which is about physics, but is pretty relevant to math as well. To summarize the many good answers there, no, you're not supposed to remember every single detail of everything you learned in college (ok, I guess there are people with eidetic memories, but not every person with an eidetic memory is in research, and not every successful person in research has an eidetic memory). If you learned something well, as in understood it and didn't just memorize it, it will come back to you when you need it (and it will take less time to understand it the next time).
A couple things about this: firstly, preparing for the math subject GRE, which you should take if you are planning on graduate school in mathematics in the US, was really helpful for me to recall a lot of the information I had managed to forget as an undergraduate. It also made a lot of connections between fields clear to me. (Of course I have now forgotten it all again!) Secondly, and very importantly, your statements about memorizing mathematics are odd. Maybe this was just an odd choice of phrasing, but you're not supposed to memorize mathematics, beyond say differentiation/integration formulas in calculus (although even those are better remembered by understanding where they come from). Memorizing proofs is different from understanding proofs; I hope this is clear to you.
I was also in a small department where not too many of us were interested in graduate school (we also had a large math education program, so again, are you me?). But, remember that you do have access to lots of people interested in mathematics, namely the faculty in your department! It sounds like you've taken several independent learning courses with some of them, why don't you ask them if they think you are prepared for graduate school? Back in the day, I got a lot of useful advice, ended up taking a reading course in graduate-level math which was lot of fun, which was a large part of how I decided that why yes, I am prepared for this.
Lastly, math is not just for a select cadre of geniuses. In order to succeed in graduate school (and probably beyond, but I am still working on that myself), you should have the ability to work really hard, feel really dumb most of the time, and yet still keep going. Being a genius is helpful, but neither necessary nor sufficient.

I have talked to the head of the math department here and he believes I am capable and that I should just spend some time relearning things.

Ultimately I think I do suffer partly from the imposter syndrome; not some crippling problem but something to get over.

Imposter syndrome isn't always crippling. For me, for example, it's usually more of a 'sneaking suspicion'.

This is a great answer!

My wife suffers from Imposter Syndrome.  I will tell you what I tell her:
Rationally:

As @Aru-ray suggests, take the GRE.  It will be a requirement for admission to graduate school anyway.  Even if it isn't necessary, take the math subject matter portion of the test too.  This will give you an idea of how you compare in knowledge and ability to apply that knowledge against all undergraduate students who intend to continue with graduate studies as well as undergraduates who intend to study Mathematics.
Your grades give you a comparison of your ability to complete the assigned work at your school.  See if you can find the distribution curve of grades vs. number of students for your major.  Also see how your school compares to other schools in Mathematics.

Doing just these two things, and applying a little of your mathematics skills, should give you a very good idea of how you compare to other students who intend to pursue graduate studies in Mathematics.
If you still feel uncomfortable, talk to guidance counselors at the school you wish to perform graduate studies for their opinion.
Emotionally:
My wife informs me that Imposter Syndrome often does not succumb to rational arguments.  If this applies to you, use the following argument:
If post-graduate work in math is what you want to do, you are enjoying it, and you qualify to do it; why do you care how you rank among other students?  Just do it!

+1, in particular for 'why do you care how you rank among other students?'

The part where you said "why do you care?" hit me pretty hard. Thank you. I want to have a career in mathematics and accomplish something; so I shouldn't let rankings get in my way

Very good points from @Aru Ray. I'll throw one more disclaimer out there, in reference to the last line of your summary:

"How do I know if I am actually ready for graduate school, as opposed
  to being a big hardworking fish in a small pond?"

In truth, many mathematics graduate programs at well known and respected universities are pretty small ponds. I got my degrees from Vanderbilt, and their graduate mathematics class size averages no more than a dozen (there were 7 of us in my year). So if you were thinking you'll be adrift in a vast sea of geniuses, it's not really like that. Instead, if you choose well, you can become one of a very tight-knit group of people working together and supporting each other through the difficult, but very do-able task of getting your graduate degrees. There are small ponds everywhere, sometimes where you least expect them.
While I'm at it, I'll throw another tidbit out there. How and when you enter the PhD program, the requirements for the Master's and the PhD, and the choices you need/get to make along the way can vary wildly from program to program. Some schools reward you with a Master's after passing 2 years of their regular graduate level program. No Master's thesis required. Some don't even allow you to petition for the PhD program until after you've got your Master's, while others tend to weed out Master's candidates right from the start based on their likelihood to continue to their PhD.
I knew several folks in graduate school who were unsure, but applied, got accepted, worked until they got their Masters degrees, and then decided whether to continue. And even if you stop there, there are a lot of advantages to a Master's degree. For instance, you can teach at most community colleges across the US with just a Master's, and no education courses or certificates are required.

I think the only thing I would add is in your last year try to do some research with a faculty member(or REU). For any area of grad school actually doing research as an undergraduate can help give you a good idea if you will enjoy doing that for the next few years. I've been told that doing research can be quite different then course work. If you are able to present your work at a conference(poster board) or maybe even publish then I think that would be a big indicator that you would be ready.(not required at all).

You are drawn to the tough stuff.  You deal with it.  You master it.
You are afraid you don't remember enough of it.
You sound like a sword master who had won a fight against one of the great after preparing for a year.  Now he's afraid that he might not remember all the winning moves in case this great sword master met him in an underground station and ambushed him.
And since he cannot remember the moves in detail, he considers himself unfit for a fight.
That's not how it works.  Of course, sitting back and sipping wine is also not how it works.  But it does not sound like that's what you are doing.
You'll meet more great challenges.  But you are not expected to walk into them unprepared.

I think the OP is looking for something more specific than platitudes.

"You sound like a sword master who had won a fight against one of the great after preparing for a year. " While this is a colorful simile (maybe work in Braavos and/or Arya Stark to really sell it?) it does not in truth sound very much like the OP's situation.  You seem to be telling the OP that their lack of complete memory of all the courses they've taken is not a cause for concern.  Sounds fine to me, but could you do so less broadly and also explain why you feel that way in the context of a student considering a graduate program?


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Have I dug myself a hole that I can not get out of?
I graduated from my undergrad with a B.S. in math and cellular/molecular biology in 2017. Shortly after, I started a fully funded Ph.D. program in Computational Biology and Bioinformatics. I spent a year there and did very well. However, I felt as if something was missing. At the time, I thought it was the fact that I wanted to have more math in my studies. One thing led to another, and I was able to get funding and a transfer into the math Ph.D. program within the same college of science. I thought this was the right decision at the time but I feel as if I rushed into it too quickly.
This upcoming May, I will have spent a year in the math program, as a fully funded student. I did okay my first semester, and I chalked up not doing as well as I am used to due to it being a while since I had done this upper level math. However, now I am realizing it’s mainly because I don’t actually enjoy this anymore. I thought I would enjoy upper level math but I don’t seem to have the passion I used to. At times I feel absolutely miserable. I have no motivation because I don’t enjoy any of this anymore. I can’t see myself doing this for another year let alone 4 to finish my phd. My grades have fallen drastically. I’m not doing well.
I’ve thought about this a lot, and I believe I made a mistake. I want to go back to more biologically based research mainly and apply some mathematics to it when able. Not the other way around. So I’ve applied to transfer to a biological sciences Ph.D. in the same college that will be able to take some of my credits. I’ve looked deeply into it and I believe that is where I would be most happy. I truly believe it. It took me 2 years, but I think this is the right choice.
However, the transfer has been difficult. I need to get my departments approval to transfer to the other department. I thought my transfer would be guaranteed according to the new department’s head, but after some emails back and forth she has to “consider my application” and so now I’m not sure if I’ll definitely get in. The issue is I need this paperwork done before she can consider it. If I get it done, I’m out of my math program. And if she doesn’t allow me in to her program, I’ll be stuck not enrolled in anything. This is a major issue as most of the jobs and internships I’ve been applying to require me to be an enrolled student. I’ll lose these possibilities (I’ve applied to 18 positions all requiring student status).
To top it off, I feel so disheartened by all of this. I feel like I’ve set myself so behind, and that I’ve really screwed myself. I feel like I can’t climb out of this. Funding is near a 0 chance in this new program and I’m even willing to take that chance because of how miserable I am in my current program. I’d rather go unfunded than stay here. But it feels so hopeless. Can I recover from this? Is it even worth the risk of losing it all? My grades have gone from perfect to below average and I’m worried this will also be a huge stain in my records putting people off. I don’t even know how I’ll tell my current advisor who helped me transfer in that I’m leaving. It feels as if I’m letting her down after she helped me so much to get in. This past year my mental health has deteriorated exponentially. I have 0 motivation. I’m barely able to get the minimum done. I used to be a near perfect student. But I’m so unhappy with what I’m doing that I’m suffering. I’m trying to make a change and do something I’d enjoy but I’m not sure if I can make it happen.
My main questions -

Is it worth giving up most of my credits to transfer to a program to be happier even though I would be setting myself behind and losing funding most likely?
How do I attempt to explain to my current advisor that has done a lot for me to get into my current program that I’ll be leaving?
I’m not sure what I can do if somehow I leave and my transfer isn’t accepted and I’m stuck without being enrolled in anything, losing the possibility of a lot of paid internships I’ve applied to.
Is this situation salvageable? I’ve done poorly these past two semesters and I feel like it will be a major stain on my records.

My biggest concern right now is the fact that I'm doing horribly right now. I have fallen very behind. I do not think I can pass my courses this semester at this rate and I will most likely fail out. The first year in my biology based program I got a 4.0. This year, I will most likely do very, very badly. I'm hoping that when I apply to the new biology based program they consider how well I did in that field, and not how badly I did in the math field.

What's the actual question here?

@Olorun I will edit it to be more clear

Does the program you are in actually affect the lab you can participate in? My husband was in a computational lab with applied mathematicians, physicists, biologists, and engineers.

@dawn Yes. I was under the impression I’d be more in an applied math program but it doesn’t seem to be so. I want to do actual lab work and write a biologically based research thesis eventually that has mathematics in it. On my current path, my thesis would need to be a math based thesis, which I could apply to some biological system but I wouldn’t be doing that sort of lab work. It is not as interdisciplinary as I thought. I used to think I wanted to do math modeling of infectious disease but I want to study the disease more in depth than the math component if that makes sense.

I think the most important think is to finish something. Sometimes you get stuck, because you think you know what you want, but than you realize you don't. Sometimes a sense of responsibilty or usefullnes can help - do what you find usefull and later you can get another chance to do what you enjoy. Sometimes you cannot have both.

What is your long-term goal? I think that's the question you really need to try to work out. That could point you to either of these programs or a third path entirely.

Realism is important -- becoming a professor might be a nice "dream job", but there are so many applicants and so few jobs that you might want to reconsider if this is the only acceptable outcome.
Also consider the job market as a whole. PhDs in math (particularly those with good technical and soft skills, such as coding and presenting) can find lots of good jobs in the US right now, for example.

Anyway....

Is it worth giving up most of my credits to transfer to a program to be happier even though I would be setting myself behind and losing funding most likely?

From what you describe, you will not be able to slog through another ~5 years to finish your PhD in your current department. So, you should transfer at any cost. (But, consider what I wrote above -- there are options besides "PhD A" and "PhD B". With a solid goal in mind, you could also recommit to your current program.)

How do I attempt to explain to my current advisor that has done a lot for me to get into my current program that I’ll be leaving?

He'll get over it. It's annoying when we put time into training a subordinate who leaves right as he's becoming useful. But that sort of thing happens. Further, if he has been tracking your difficulties, he may be glad you've identified and fixed the problem early before he had to get involved. Changing the course of your life for this guy is not a good idea.

I’m not sure what I can do if somehow I leave and my transfer isn’t accepted and I’m stuck without being enrolled in anything, losing the possibility of a lot of paid internships I’ve applied to.

Again, this is not something that should change the direction of your life. I realize this is a serious short-term practical problem for you, but it's a second-order problem; the first-order problem is figuring out what the goal is and how you're going to achieve it.

Is this situation salvageable? I’ve done poorly these past two semesters and I feel like it will be a major stain on my records.

After the PhD, the only thing people care about is: (a) did you get a PhD, and (b) what was your research about? Maybe also: (c) what skills did you acquire? [for jobs] or (d) what do your letters of rec say [for post-docs]. Absolutely no one cares about grades or whether you transferred schools. In that sense, it's much better to have problems like this as a grad student than an undergrad.
Now this stain will be a larger problem in the short term: once you decide what the goal is, you may have difficulty with admission to a new grad program (indeed, you indicated that this may already be a problem). But you'll find something. Further, there's a very nice "story" here that is easy to tell: I was great at subject A, thought I might prefer subject B, but I was wrong and I'm now 100% committed to subject A. That's a straightforward enough story that it should be easy to tell, if that's the direction you decide to go.

I believe that that is the direction I want to go. However, this semester has been very bad. I’m not sure if I’ll even be able to pass all my classes this semester. I’ve fallen behind, and I’m struggling. I’m afraid that my new program will be turned off by this. However, it can easily be seen that I got a 4.0 in my biology based program initially, and then when I moved to this math based program, I did very poorly. And so going to another biology based program, I hope that my math grades won’t affect me too much in the new biology program admittance. I worry a lot about this aspect.

Without analyzing your post deeply or even in detail, the answer should really be obvious if you step back. Life is short and you don't get a do-over. There is little worse than continuing on a path that you think is wrong for you no matter how much you already have invested in it.
Hopefully you will live long enough to enjoy retirement (as I have). You want to be able to look back on what you have done with pride and satisfaction, not with regret.
It is good, actually, that you explored something that you thought might be good. You did so with imperfect information, as we all do. It hasn't worked out.
People in general understand these kind of things and that people's goals change. The hole is only filled by time and effort. Digging deeper won't improve your life. Do watcha gotta do. ("Do what you've got to do" in case you aren't from NYC).

This is the main factor pushing me towards all of this. I don’t particularly like uncertainty as many don’t, but normally I’d err on the side of certainty. However this feeling, that you’ve summed up in your post, is the main driving force pushing those thoughts aside and moving me forward.

My own experience:  I got a Ph.D. in EE {Electrical Engineering} US.  It was mostly applied math backed by computer simulations (MATLAB).  For several years I worked in digital audio firmware, then I became a software engineer which suits me much better.  So you will probably find something, but if you gear toward your strengths now, you will wind up on a better path more quickly.

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Ethicality of continuing my Ph.D. with intentions of leaving
I am currently in my first year at a funded Ph.D. program. I have a graduate teaching assistantship in the form of teaching three introductory biology labs (1 credit per) plus the other responsibilities of being an instructor. I also have a six credit (tuition waiver) course load and a stipend.
Prior to coming to this program, I declined an offer from another funded program. It was due to financial reasons such as making a big move to the city and whatnot. I was a fresh undergraduate out of college and I was not ready for that move. I am in the position to make this move now and the offer is much better than my current program.
I have many different quarrels with this current program. There is a lack of structure and much of what I expected at a Ph.D. level course/program was not met.  I dislike the current field I am in and I don’t believe I would be happy doing this for the next 4 years. I did not have intentions of leaving prior to starting here, but as I mentioned things here are not as what I expected. Through discussion with the head of the department I declined, I was able to get my declined admission deferred to next fall. In February, I will hear if I receive funding again.
Now my issue is that I am currently in a lab rotation with my prospective advisor and I have not told anyone that I will be leaving. I am afraid that if I tell anyone that I plan to leave after the year, I will be looked down upon and it would affect my courses for the year. I want to withdraw from the lab rotation because the program I will be going to does not have any use for such a course. However, I am worried that if I tell my advisor why I am withdrawing, it will impact me negatively. In the off chance I do not receive funding, I will most likely be staying in this program and if they know I wanted to leave and didn’t because of funding, I fear I will be looked down upon.

How unethical is it to continue this year and finish up without mentioning any of my intentions to leave the program for another?
If I do withdraw from the lab rotation, should I mention why I am doing so or just mention that I was not expecting the course work to be so intense (which is true due to my teaching taking up so much time, I am behind).
How unethical is it to use my 6 credit tuition waiver to take courses in the spring that would hopefully transfer to my other program?

My contract runs 9 months so I can’t just leave.

Do you actually have a valid offer for next year? Having been offered (and declined) does not mean that is still an option. If you have a valid offer in hand for next year, certainly you can tell people. But, getting experience in various lab settings is not a bad thing at all. As for transferring coursework, that would be a question for your new program.

I declined my offer of admittance and funding but I managed to get the offer deferred for next year. The funding will be discussed in February but I am hopeful about the funding. I have the offer of deferred admittance coming in the mail.

@JonCuster I don't think OP wants to know if they CAN tell people, I think they want to know if it is okay NOT to tell people until they hear about funding.

@Dawn - as in moving jobs (lots of similar Q on Workplace SE), until a real offer is in hand, don't say anything at all. So, yes, it is OK to NOT tell anybody.

How unethical is it to continue this year and finish up without
  mentioning any of my intentions to leave the program for another?

It is not at all unethical to continue until you know for certain. I see this as a situation where you are considering your options. You would LIKE to leave, but you are also considering staying if you have no funding at the second program. I certainly don't think you have any obligation to mention your decision until you hear about funding. In February, your current program will still have the opportunity to give away your funding to a new student/another student, so you are not harming anyone by waiting to speak up.

If I do withdraw from the lab rotation, should I mention why I am
  doing so or just mention that I was not expecting the course work to
  be so intense (which is true due to my teaching taking up so much
  time, I am behind).

I don't think you should withdraw. If you stay, this would be your advisor. And if you don't get funding, you may stay. So you should make sure you have a good backup plan with this advisor at your current school.

How unethical is it to use my 6 credit tuition waiver to take courses
  in the spring that would hopefully transfer to my other program?

You will likely need to decide on spring courses before you decide if you should stay. If possible, choose courses that would prepare you for either path. If not possible, I don't see a problem with using the waiver you have earned through your teaching in a way that would be of most use to you.

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How would you give your students a tournament as assessment?
I am currently teaching calculus and I thought it would be a good idea to do some kind of limit (and later derivative/integral) calculation tournament. The thing is... The students only seem to give their best if the activity is an actual assessment so I was wondering how can I prepare a tournament as a fair assessment.
The main issue is that as an assessment I want every student to be able to get the maximum score (otherwise it wouldn’t be fair), however since it is a tournament only one student can get the first place...
So I was wondering how one can organize a tournament in a way that is fair for all students? There are some remarks to take in consideration:

There should be a prize/incentive for attaining a better place in the tournament compared to the other students.
Everybody should be able to get the maximum score.
There should be some kind of rule which determines whether a student is out the tournament or not.
Every student needs to participate.
The whole tournament shouldn’t take longer than two hours; I can’t spend too much class time on that.

So with those remarks in mind how would you guys organize a tournament? I'd like to compile some suggestions before planning it.

I've had good success with doing exercises in a game show format, with the emphasis on having fun.  We invited family members and served refreshments afterwards.

Why isn't a regular quiz / in-class test fine? Do you have in mind some other requirements that would make it not suitable?

I think technically speaking "give them a mandatory exam/quiz like usual, and grade it like usual" satisfies all of these.

While you and many others just see a tournament as a frame for an exercise or display of skill, it’s a format that has a huge tendency (and arguably was designed) to appeal to sensationalist, martial, and other primitive instincts – which should have no place in academia. Quite a few of my fellow students had abhorred such events in school for this reason and would have been hugely demotivated by such an event – not only for the exercise itself, but also for studying in general. You cannot control such associations and the possibility that it brings out the socially worst in your students.

I think the techniques in this article on competitive, team-based learning by Kristine M. Trego could be adapted to your purposes. Trego is a Latin professor, but I think elements like the discussion of separating the incentive of low-stakes competition from the grade earned for participation, balancing such incentives against "the pressure of performance and responsibility for work outcome", and how to allocate time to the competition would be useful to you.

@Wrzlprmft other primitive instincts – which should have no place in academia The worst primitive instinct in academia, IMHO, is the "ownership one" (It was I who...). There is a whole culture and legal structure about it and nobody seems to do anything to discourage that. Pure competition for symbolic rewards (rather than for better positions, salary raises, promotions, etc.) just to measure your strength against others is actually very healthy. If one cannot stand losing occasionally, it is he who should work on his character, not the others who should pamper him.

Eager et al. describe how they use flipped classrooms to teach a mathematical biology course. As part of their course, they use "competitions" to motivate students. They discuss some of your concerns in a method paper:

One of the difficulties in teaching a class via the flipped classroom is how to properly assess and examine student learning [3]. Because the class is very modeling focused, and modeling is a time-consuming process, traditional exams are very difficult to administer in a course like MTH 265. The authors’ solution to this problem is to do away with traditional
  exams in favor of both individual quizzes and group mathematical modeling competitions.
  The individual quizzes involve the students choosing two small modeling questions from a
  group of three questions and solving them with help from their class notes, homeworks,
  past computer programs and video lectures. These quizzes are given over a 55-minute time
  period. The questions in these quizzes are structured in such a way so that, after the student
  chooses which two problems to work on, he or she can solve both questions in a combined
  40 minutes—meaning that some (but not all) of the modeling process is given to them. These
  exams provide the students with an incentive to learn the material on their own (which is
  nontrivial in a flipped course with a large group component), as well as the motivation
  to become proficient in using some of the elementary skills a mathematical or quantitative
  biologists would need to possess (e.g. diagram building, script writing/amending, elementary
  algebra and calculus, scientific writing).
The mathematical modeling competitions stemmed from the successful 24-hour Wisconsin
  Mathematical Modeling Challenge at UW-L, as well as the success of similar activities in
  other mathematical biology courses [8]. These competitions complement the individual, inclass
  quizzes by providing students with more open-ended modeling problems and a longer
  timespan to produce their solutions. These modeling problems can ofen be introduced with
  only a few paragraphs of text—with few or no equations. The students, in groups, then
  have 24 hours to come up with an appropriate model for this system, as well as answer
  the biological question posed. The group of students with the best solution is rewarded
  with perfect homework scores until the next modeling competition. The class has either
  an individual quiz or a modeling competition at the end of every other week for a total of three individual quizzes and three modeling competitions during the semester worth roughly
  30 percent of each student’s final grade.

Full citation (in case link breaks):  Eric Alan Eager, James Peirce & Patrick Barlow (2014) Math Bio or Biomath? Flipping the mathematical biology classroom, Letters in Biomathematics, 1:2, 139-155, DOI:
10.1080/23737867.2014.11414476
As a disclosure, I have collaborated with Eager and gave guest lectures in his Bio Math course about my own research.

Here is a suggestion. It has its advantages and disadvantages and I haven't tried to implement it myself, but you asked, so here are my 2 cents.
There should be a prize/incentive for attaining a better place in the tournament compared to the other students.
Apparently you are not willing to give out extra points or anything
else that might influence the grade. Then just make a few nice drawings,
write "The first (second, etc.) place in the calculus tournament" with
the date and your signature over them, laminate, and attach some silly
little prizes (a box of pencils, a figurine, a notebook, etc.) to each.
It'll cost you 40-60 bucks and a few hours of drawing, but it'll work.
Everybody should be able to get the maximum score.
If you have 10 students, prepare 30 tasks and hand them out one by one. For every task the first one to complete it gets 10 points for the task (counted towards the grading score) and 31 minus the number of the task (from 30 to 1) to determine his rank (the first problem is worth 30, the second 29, etc.; the rank is the sum of values of solved problems). Once a student solves three problems, he is not participating any more. You run the tournament until either everyone is out, or nobody can solve the current problem, or the time is out.
There should be some kind of rule which determines whether a student is out the tournament or not.
Addressed above.
Every student needs to participate.
Well, with this scheme at some point he'll be the only eligible competitor if everybody else is done, but if he just cannot do the task anyway, it is his problem. I think it is fair enough.
The whole tournament shouldn’t take longer than two hours; I can’t spend too much class time on that.
That depends on how many and how good the students are and on the difficulty of the problems assigned. Also, do you want just answers or explanations? You can replace the factor 3 by 2 in this scheme, but with more than 20 students it becomes somewhat problematic to implement in under 2 hours. What I expect is a fierce competition with quick answers in the beginning, followed by a slower run once the top students are out, followed by a bunch of dropouts staring mindlessly at the problem (or at the ceiling) forever (unless you impose a time limit on each problem). One partial remedy for this unevenness would be to present hard problems first and to decrease the difficulty along the way.

Can you please state more explicitly whether you suggest that tasks are handed out one after the other?

A big problem I see with this scheme is that you rank all students, so you do not explicitly state who is the best, but also who is the worst, second worst, etc. Ending with such a position would be very demotivating for some students.

@Wrzlprmft Really? If they are so sensitive, they have nothing to do in the university (or in any professional setting). I know the feeling of being the last. It makes you clench your teeth, set the engines to full steam, and go ahead as fast as you can at the expense of "social life" and other nonsense. But, of course, you can just decrease the problem value only to 15 and then keep it level, so all students at the low levels are formally tied.

@Wrzlprmft Yes, one after another. The first one to solve gets the credit and then the next one is given. You can try 2-3 at a time too but then it becomes a bit of a lottery.

I agree with you that one has to learn how to deal with failure and certainly with not being the best. But being the last has quite another flavour. I cannot remember any situation in academia where somebody was officially declared the last. I also cannot think of any situation in professional life where this would happen, other when a public shaming component is intended. — [Being last] makes you clench your teeth, set the engines to full steam, […] – This does not apply for the vast majority of struggling students I know.

@fedja social life and other nonsense? Academia thrives on social life and cooperation at least as much as on competition.

@Wrzlprmft, allow me to introduce you to the wooden spoon.

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Would it be possible to publish a journal paper about data-visualization website?
I am graduated with a bachelor’s degree in computer science. I want to know whether is that possible to publish a paper about my final-year project? The final-year project was about a website which contains data visualization of one company’s data. This works had done by help of my supervisor during my bachelor time. Does anyone know about it?

Does it solve a problem or shed new light? This is with respect to existing body of knowledge.  If it's just a paper that says "i've done this", then it's no different to a brochure.

How did your supervisor answer this question?  (You did ask your supervisor this question, didn't you?)

@JeffE he said it could be a kind of revision of work paper,no problem to publish it

@Prof.SantaClaus your perspective is logical to me  and i respect it but is it all the publication in the world adding knowledge all the time? in my case lets say i m new to web analytics and i want to review an existing web analytic system to learn, could not be possible for me to study review papers?

@moh89 You can publish anything as long it is written down.  The only issue is 'where' it is published. For reputable researchers, they only publish when they have something new to say.  Otherwise, it's a waste of time.

This would entirely depend on the contribution your website and techniques involved add to the state of the art. Is any element of it new and novel? I.e. something done nowhere else. It may be worthy of a conference paper for example, if he contribution is weaker.
What is your supervisors opinion? Have they hinted at this possibility?
Edit: The company's data may also feature as an issue during publication. Would they be happy for it to be used and if not can you describe your work well enough without it? i.e. if you use a figure in your paper that shows their data, such as a screenshot.

my supervisor was satisfied to participate in the publication, and he said : there should be no problem for publishing such a paper, but i wondered for continuing my masters degree,could be a case to mark down my resume for such a review work paper?

I don't think it would harm your resume. The explanation of what you was doing is clear, so there would be no gap in your CV. If you to go into academia publications will help.

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


text:
Why does the Nobel committee not award prize to collaborations?
The 2013 Physics Nobel prize went to François Englert and Peter Higgs, for their discovery of the Higgs boson. I was wondering why the CERN, as an institution, or the ATLAS collaboration, are not co-awarded the prize with Englert and Higgs. Apparently, “collaborations” cannot be awarded the Nobel prize. Is it a tradition, or something written in the rules of the Nobel foundation? Has there ever been an exception?

Why should they? I mean almost any scientist works in some company and why should this company also get co-awarded? It is true, that without the LHC, they would not have been able to discover the Higgs boson, but it is still an achievement of only a little team out of the more than 3.000 employees of CERN.

CERN was mentioned as the firs possible collaboration to get a prize. "First" in this sense excludes the Peace prize which has been given to "groups" since quite a while. There are no formalities that would prevent such group-awards.

Because when Alfred Nobel wrote his will to setup the prizes most science was done by individuals or very small groups where only recognizing the leaders was reasonable; not massive teams of hundreds or thousands.  Despite there being an institution or organization clause that would be reasonable for a lot of recent work it's never been used because:  TRADITION!

Isn't the IPCC (2007 winner) a collaboration?

@mankoff Yes and awarded the Peace prize

In paragraph 4 of the statutes, it restricts the price to be only awarded to two works and to a maximum of 3 individuals.
But it also says, that it can be awarded to an institution or organization. Which has been done with the Nobel Peace Prizes to the EU.

A prize amount may be equally divided between two works, each of which is considered to merit a prize. If a work that is being rewarded has been produced by two or three persons, the prize shall be awarded to them jointly. In no case may a prize amount be divided between more than three persons.
[…]
Each prize-awarding body shall be competent to decide whether the prize it is entitled to award may be conferred upon an institution or association.

More precisely, it is up to each prize committee to decide if organizations can receive prizes. So a collaboration needs to be a self-standing organization to be eligible, it would seem.

So, if it's up to each committee, has the physics committee ever taken an “official” position on the matter? Have collaborations/institutions ever been awarded the prize?

As far as I can see, only the Nobel Peace Prizes has been awarded multiple times to an organization, but none of the other Nobel Prizes.


text:
How do I invite an expert to contribute to a review article I'm writing?
I am in the process of writing my PhD thesis, and I would like to extend the state-of-the-art part into a review article. Although I am confident that I have investigated and understood the existing literature thoroughly, I think the overall quality and visibility of the review article would increase if I find an expert to collaborate with on the paper. My PhD supervisor is not an expert in the field and I expect his willingness to actively contribute to be near zero.
I have already identified a rising expert (junior PI) that I would like to contact. A strong plus is also that he seems to be an expert on the area of the article where I have no published results, whereas I have some published research in the other of the two subareas of the review article. However, I am not sure how and when to contact this person (I have not met him in person).
One approach would be to (nearly) finish the paper and then send him a direct email, asking whether he would like to contribute, and send him the paper after he agreed to handle the draft confidentially so he can decide if he wants to contribute. I would also mention that I am willing to do the ground work but expect him to comment on the draft and help improving the overall quality of the paper.
Another approach would be to upload a finished (to the best of my abilities) paper on arXiv and than send him the mail asking for his willingness to contribute.
Is there a better approach?

By passing. .. It is unlikely you will change him. The idea of contacting a young researcher sounds ok as, if there will be any benefit, you will likely share it. Most important point is IF there is need for a new review. Reviews can (should) be original, too. In the sense that they resume new results, critically discuss the current state and pose a minimal base for future development.

@Alchimista There does not exist a review on this specific topic and the existing literature is very scattered. The publications use very different figures-of-merit and are targeted at different applications. I plan to "norm" the experimental results of existing publications, combine them with (simple) calculations and classify different types of experimental realizations for specific applications. So I argue that such a review would enable other groups to build the best device for their specific application.

@Alchimista The majority of publications regarding this topic were published after 2011.

Do you have a comparable track record?  Do you have high quality papers?  It is harder to form any collaboration if your professional standing is different.

I suggest that you contact the other person and ask for their advice on your ideas, but not for collaboration, initially. See where that goes. It allows the person to make a small commitment without feeling any pressure for a larger one.
Your idea for a review or summary article might be a bit unusual, but in many fields these are occasionally needed as the field splits but the different pursuits have some common but unnoticed features. Partly for this reason, I don't think that the other party would think about going into competition with you on the idea, and might want to participate. The advice would be valuable in any case.
If the collaboration starts naturally then you can write a joint paper, perhaps after you complete your degree so that your advisor has less sway. Write and explain your ideas, expanded from what you write here, send a draft, and ask for any feedback that he/she might give.
The other person might also be able to suggest others with whom you might profitably share your ideas.

I mention the competition issue only because you don't really know the person. Most everyone behaves ethically, but not all do. So in some situations it is necessary to be a bit cagey when you are a newcomer to academia. I don't really see it as an issue in this case, however, as mentioned above.

I find the best way to go about these situations is to meet in person and talk. It is much easier to share ideas than to try to guess what will work best.

Over the last ten years, personal communications have shifted more towards
  asynchronous methods that can be polished and perfected. People feel nervous and unsure if they cannot proofread their ideas before releasing them to the world.
But ... it is important to meet and talk. Being spontaneous and responding in real time to eye contact and body language are important parts of communication. It
  may seem much easier and safer to send emails and post online, and it
  is, but relationships are built on interaction in real time. There is much more to it than the words on the screen can convey.

Professional collaborations are built on clear vision, managed expectations, and reasonable timelines. You have several valuable opportunities here:

Show Respect for Advisor: Meet (coffee? lunch?) and talk to your advisor and get feedback there. Even if you learn nothing tangible, you keep him in the loop and this shows respect for the person who is officially your 'advisor.' Technically, an 'advisor' is there for this very reason even if it doesn't always work that way. This is an appropriate opportunity to build on your relationship with your advisor.
A Bit of Networking: Find people to brainstorm with. Consider whether you really need this collaboration. Is it necessary to accomplish your goals? I think you lay out a good case that it is, but make sure you are doing this for a valuable reason. It will be something that takes time from both of your schedules. This is what you are doing by posting here, but if you have people you can talk to in person, it is a great time to further professional relationships with them.
Specific Networking: Meet with your prospective collaborator and discuss the proposal. See if there is interest. If you feel that this person is reluctant, it will likely cause friction and limit the value of the contribution. If this "rising star' is actually a friend of yours, then focus on how you can help each other. Ask if they need anything in the way of help (expert advice? typing? research? chart creation?). This is always appreciated!
Team Building: If the collaboration sounds feasible, discuss and decide who is doing what and set some deadlines. Be friendly, but you need a timeline that works for both of you. You are busy. They are busy. We are all busy. Be realistic and ask what they think a reasonable timeline is. Ask what reasonable goals and outcomes are. Agree on these things before you leave. If you can offer them something valuable (publishing without doing much + helping you) with clear expectations and minimal investment of effort, you will be well received.
Leadership: Follow this up with an email setting out the agreed upon details in writing. This sort of clarification tends to reduce misunderstandings and CC it to your advisor. Thank them both for their specific contributions. Ask for further feedback or ideas. People love to give advice. This sort of clarification tends to reduce misunderstandings by managing expectations. It is also a good way to reiterate that they are doing you a favor and that you appreciate it. It may seem counterintuitive, but you can show great leadership even when asking more expert people for help.

This is just my 2 cents, but I think this situation is much more about the personal opportunities than the actual collaboration. You can keep up communications online, but an in person discussion once in a while is important. The thesis will get done either way. You will be rich and successful. Life will go on.
... but the relationships you form as you go through life is what will matter the most.


text:
Who should I ask for reference letters for academic positions?
I am planning to apply for tenure track academic positions, and I already got 3 letters from people who I have worked with during my PhD, including my advisor.
Do you think I should seek out letters from my former supervisor (masters) and a few that I have published paper with during my master's program? Does it add value to the application?
Also, I have worked with a few fellow students who are now assistant professors in other institutions. Does it make sense to ask for letters from them?

I think you should also ask your post-doc advisor.

@JessicaB If you have one. Maybe NeoN applies directly after his PhD, or he did his postdoc in the same group he did his PhD studies in.

Imagine you are applying right after your PhD. No Post doc.

Short answer: Extra letters do not improve an application, but could undermine it.
Elaboration: One advice often given in career center presentations or online articles about post-doc/TT applications is that the application packet should only contain the documents (and the number of documents) requested. If the announcement asks for 3 letter of reference, it means the hiring committee expects 3 letters, not 2 or 4. This is a simple yet often overlooked fundamental criterion of a successful application.
Assuming you are planning to supply only the requested number of letters and the issue is which letters to include, I recommend sticking with the traditional approach of letters from the individuals who you have worked with in subordinate capacity with during your PhD studies. This typically includes your dissertation advisor/committee chair, perhaps another committee member, or (if different) a PI on a grant you worked on, whether in or outside of your department (e.g. an affiliated research center).
I would advise against letters from very junior faculty at other institutions (e.g. your recent peers) as they carry relatively little clout and the hiring committee might get the wrong idea if they suspect your choice of using them as reference may have been forced, to some extent, by circumstances that prevent letters from more reputable/senior colleagues (in other words they may come across as less convincing and perhaps even suspicion-provoking reference choices - and you don't need that).
Generally, I would advice including letters from the individuals (faculty) you have worked with most recently. The dissertation advisor is an unavoidable choice and a must. Beyond that, if you worked with other faculty who were PIs or partners you have collaborated/co-authored with, choose the individuals you have worked with on most recent projects/publications as consistent with the chronology of your academic appointments/experience in the CV.
It is also a well known and accepted (if not publicly advertised) practice to pre-write letters of recommendation to save your references' time. Whether you have done this already or not, good to keep in mind. Just ask your reference in a matter-of-fact way if they prefer to author the letter or could use a summary draft (or at the very least, a current copy of your CV).
Good luck with your apps! Let us know how it goes!

Start by looking at the type of academic position. What skills does the position demand? Who can best speak to those areas of strength? Do you know anyone outside of your academic department who will write a positive letter for you? For some additional guidance, consider this document.http://careers.washington.edu/sites/default/files/all/editors/docs/gradstudents/Academic_Jobs_-_Letters_of_Recommendation.pdf


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Are MOOCs a good way to show grad schools that I've gained proficiency in a field which is not my major?
I'm an undergraduate computer science major with a specialization in networks and communication looking at a masters in molecular genetics. In addition to a GRE biochemistry and molecular biology subject test score, I'm interested in MOOCs to enhance my resume.

There are several issues with MOOCs, all of which make them a poor substitute for actual classes for admissions.

Poor penetration. There is more widespread knowledge of them than a couple years ago, but they are still fairly unknown. Chances are high at at least someone reading your application won't know about or understand them.
No grades. Few MOOCs offer anything more than a certificate of completion, and many don't even offer that. Even if they offered grades, verification of identity is a problem.
Wildly varying quality. College classes are generally of a certain quality/difficulty, and knowledge of the quality/difficulty levels for certain field-specific classes across schools is something that application committees will use to judge candidates against each other. MOOCs are much more of an unknown.

It is difficult to say as it differs from university to university. But an MOOC course cannot act as a substitute to an actual course in a college because the depth of the subject is simply not enough in an MOOC. Hope this helps.

No, because many people still do not know what MOOCs are (though they have been in the press a lot).  Those who know what they are may not be sure if they are effective.


text:
What should I do if a professor says she doesn't understand my questions in office hours?
I am having difficulties in math, and every time I try to go to my math professor's office hours she always seems annoyed. When I ask her a question she always says something to the effect "I don't understand what you are asking," I understand being precise with math but it's as if she purposely feigns confusion. I can ask a professor a math question in another one of my classes who barely speaks English and he seems to understand what I mean just fine. In short, this prof always talks down to me and is rude, I am struggling with the math, and am just trying my best to understand it. What should I do in this situation?

Try bilding up the question step by step. "I know x=y and z=q. You said we could use that to derive the value of k, via Gibble's theorem. I'm stuck on that step." In other words, help them help you by showing exactly where you got to and what you're having trouble with, just as you should here. To give you more specific advice we'd need to see a specific example of the question you're asking and how you're asking it... in other words, you need to help US help you.

Talk to the TA instead of the professor, this professor might just have a bad personality.  If the TA can't understand either then you might have a problem.

@keshlam that should be an answer by itself.

Do any other students have the same experience with this prof? and I take it you don't have this experience with any other prof or TA?

Can you successfully get through the course by just interacting with the TA and ignoring the prof, or not?

@user28663, you never supplied those crucial missing parts, that's wasting people's time here, please don't do that. Also you got four decent answer nearly two whole years ago, and you neither accepted one nor at minimum commented on whether it was relevant.

It's possible that your professor just doesn't want to help you: in that case, obviously, you need to find somebody else.  Or it may be that she just has bad interpersonal skills and comes across as rude and patronizing when she's just trying to be efficient. In any case, I'll assume that she does want to help but genuinely can't understand your questions.
Most likely, it's because you're asking the "wrong" question.  A common phenomenon is the so-called "X-Y problem", where you're asking about the wrong thing. For example, you've tried to solve an exercise but you couldn't do it. There are two basic possibilities: either you used the wrong method, or you used the right method but got stuck somewhere in the implementation.  In the X-Y problem, you start asking detailed questions about how to fix your implementation of the method when, in fact, your problem is that you used the wrong method. There's a great post about recognizing and dealing with the X-Y problem on meta.stackexchange.com.
A related phenomenon is asking questions that only make sense to people who share a particular misunderstanding of some other topic. You don't understand X so, of course, you're asking about X.  However, the root cause of this is probably that you don't understand Y.  Because you don't understand Y, the way you think X works just doesn't make sense: your question only makes sense in the context of your misunderstanding of Y.
Random (and slightly silly) example.  Suppose a student of automotive design notices that the tyres are black and the steering wheel is black, too. He decides that all wheels have to be black so there must be a reason for this and builds up some elaborate theory in his head about how black things rotate better or something. And then he sees that his friend's car has a beige steering wheel. The next day, the student goes to his professor and asks what mechanisms the friend's car uses to compensate for the deficiencies of its beige steering wheel. This question makes perfect sense to the student but is total nonsense to anybody else.
The solution is to work backwards through your assumptions with your professor, to try to find the step where you misunderstood.
Student. What mechanisms does my friend's car use to compensate for the deficiencies of its beige steering wheel?
Prof. Er... I don't understand your question.
Student. Well, cars need to have black steering wheels because they rotate better. My friend's car seems to steer fine so it must have some way of dealing with the bad rotation of its beige steering wheel.
Prof. Why do you think that black steering wheels rotate better? [Note that slight differences of phrasing in this question can make the professor seem much more or less sympathetic. "What makes you think that..." can come across as being annoyed, for example.]
Student. I'm not sure but maybe it's because [whatever]. But the tyres and the steering wheel are both black so there must be reason.
Prof. Actually, that's just a coincidence. The tyres are black because they add carbon to the rubber to make it stronger, and the steering wheel is black because the designer thinks it looks nice.
Student. Ohhhhhh.  I get it, now.
It may be that your other professor is better at answering your questions because he's better at figuring out what the root cause of your misunderstanding is.

While I may be downvoted for this, you should also be aware of (the possibility of) your own subjective bias in regards to the gender of the professor. I noticed that you said the female professor was not helpful ("confused" and "annoyed") while you were much more generous to the male professor.
The analysis of RateMyProfessor (http://benschmidt.org/profGender/#) shows clear gendered variations between student ratings of professors along the lines of gender.
Using the keyword "confused" yields this chart:

and "annoyed" also shows a much stronger bias towards female faculty:

whereas the keyword "brilliant" shows that men are rated more highly for this attribute:

while this data from Ben Schmidt is not peer reviewed, there are peer reviewed articles that also note this:

Centra, John A. and Noreen B. Gaubatz. "Is There Gender Bias in Student Evaluations of Teaching?" The Journal of Higher Education. Vol. 71, No. 1 (Jan. - Feb., 2000), pp. 17-33
Bennett, Sheila K. Student perceptions of and expectations for male and female instructors: Evidence relating to the question of gender bias in teaching evaluation.
Journal of Educational Psychology, Vol 74(2), Apr 1982, 170-179. http://dx.doi.org/10.1037/0022-0663.74.2.170

I give you a +1 for this.  Downvotes don't seem very plausible to me: numbers don't lie.  (They can be a bit inscrutable at times, but they don't lie.)  You make quite a compelling case.

The OP may not like my insinuation that he suffers from perceptual or interactional bias...

I leave it as an exercise to the reader to look at the gender differences between "rude" and "condescending" as well. The latter is particularly interesting as it's one area where some disciplines including math have or approach gender equity.

This answer seems like a flimsy excuse to talk about some (admittedly very interesting) research that is only tangentially related to the question and seems very unlikely to solve the OP's problem.  The question strongly suggests that there is an actual difference between the female professor's response to questions and the male professor's response to questions, and that it is this difference that is causing the problem, rather than a difference in the OP's perceptions of the responses.  (I am not denying that there may also be differences in perception caused by bias.)

Also, I'm not sure that these particular charts have much relevance to the question.  The OP stated (1) he or she does not believe that the female professor was actually confused, whereas it seems to me that the "confused" chart would show some combination of the effects (2) female professors are more often perceived to be confused by their students, and (3) students report being confused more often in female professors' classes, effects that would both be quite different from (1).  The chart for "annoyed" may be relevant, but the chart for "brilliant" is not at all, as far as I can tell.

@WilliamKappler I do not see the word "causation" or any other related word in this post. The closest this post comes to such a notion is when they recommend the OP to be "aware of (their) own subjective bias", which could be rephrased as "aware of the possibility that they have a subjective bias", with which you would probably agree, I guess.

RoboKaren, this answer is VERY sketchy, as there are a number of possible explanations of the data you cite that have nothing to do with subjective bias when assessing confusion.  For example, the data would also be consistent with a hypothesis that "female candidates who are confused (by some objective measure) are more likely to be hired anyway than male candidates".  Real world causes could include "diversity" efforts, and the important of other factors, both unrelated to performance (physical appearance) and related (number of publications) in the hiring process.  Perhaps the studies you

mentioned did some analysis to try to rule this out, but your answer doesn't even refer to someone else's conclusion that biased assessment is at fault as opposed to actual differences in the faculty being assessed.  Without some sort of evidence, advising someone to be aware of subjective bias is premature.

FWIW, adding my voice to the comments of Pete Clark, Paul Garrett, and @Did

I disagree but these are interesting statistics.


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Tool for obtaining a BibTeX entry from a key, without creating it manually
I am looking for a tool, where I only need to write something like alessandroni2015bibtex (this very question) to obtain the BibTeX entry, without needing to rewrite it.
I am aware that Google Scholar always offers a BibTeX link and uses AuthorYearFirst_Word as a scheme, but I do not know how to use this key for searching, because Google uses an internal ID for each BibTeX. Thus, when I feed the data of my citation to Google Scholar, sometimes I do not find it. For example, in case of books, I find only new editions (maybe due to a wrong use of the tool).

If you have the DOI, you can retrieve it through the API. curl -LH "Accept: text/bibliography; style=bibtex" http://dx.doi.org/10.1021/pr100594k

Thank you @Davidmh, I have just tested your script... under Windows, and it runs. ;-)

In mathematics, MathSciNet has bibtex informations. You can just copy and paste into your Latex file.

Doesn't this question probably belong to TeX.SE?

Please don't vote to close->migrate to meta if you want to migrate a question to another site. Just close as off topic for "other" reason and leave a comment. The close->migrate to meta path actually migrates the question to meta, which is certainly undesirable here.

@EnthusiasticStudent As for whether it actually belongs on [TeX.se]; it's probably on-topic there. On the other hand, it's not a technical question about LaTeX (which would be off topic here), but a question asking for a software tool. So it's not any more or less on topic than any of the other [tag:tools] questions, just because it happens to be about bibtex.

I already had a partial answer (using the DOI). Of course a tool that gives me the BibTeX (or BibLaTeX, that I do not use, but someone yes) by the knowledge of Author, Year of publication and Title I think that is helpful for all. Of course, If is possible, I can ask to also tex.SE.

Don't cross-post to two SE sites at once, that's against the rules. Now that this is reopened, you can wait and see if it gets an answer, or you can flag and ask a moderator to migrate it to TeX (if you don't think you'll get an answer here)

I'm voting to close this question as off-topic because it's about BibTeX and APIs, not academia - might be on-topic at TeX.SE (certainly not on meta!).

Ok @StephanKolassa, tell me what I have to do.

I doubt it. In all but the most verbose or non-human friendly (e.g., DOI) key style, the problem is a one-to-many mapping in that each BibTeX key maps to many sources even though any single source has just a single BibTex key. Even in relatively small personal bib files, conflicting keys are common and need to be disambiguated (usually with an additional letter or number).  The bigger the database (and Goggle Scholar is a big database) means that there will be lots of collisions.

Ok, In also my opinion this question is close at off topic. Is interesting for all, but is important a deep knowledge of LaTeX for a good answer. And now: which it is the procedure for move it?

@GiacomoAlessandroni I don't see how knowing TeX is needed to answer this. Maybe software recs. I asked on chat to see if we can get an idea. I think it fits here.


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How to find out if a conference submission deadline is likely to be extended?
I am writing a paper for a conference. I have finished the paper, but I must review some experimental results and this requires some additional days.
How can I find out the probability that the submission deadline will be extended?

Why don't you try contacting them?

Why not? I try. Thanks @Compass.

Just look at past editions and see if there was indeed an extension. If they always do it, there will be another one; if they never extend, there is no reason to believe they will start this year.
If they don't, you could always give a shot to a polite email to the organizers and explain your situation. Perhaps you can submit a tentative proposal, with the uncertain data, and submit a refined version later (provided it doesn't change much).

More specifically, don't even bother writing them, just check past editions. If they always extend, they'll extend. If they never extend, they won't this time, either.

@xLeitix good point. I have now switched them around.

Yes, last year there was an extension from February 17 to March 6, and so three year ago. But is not clear if this practice repeats every year. Unfortunately, every year the site is different (is not like www.conference.com/year/), but you have answered my question. Thank you.


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Is there any way to avoid wasting a long time in review process for mathematics journals?
I sent two different articles to two different mathematics journal. The fist one review process is 6 months(accepted). The second one is still under review(14 months ago) and it may be rejected. A third one took 9 months and editor said
"... the topic/content of your study is outside our journal's area of interest, we regret to inform you that we are unable to consider your manuscript for publication"
My questions

Is there any way to avoid time wasting in review process?
Are there journals with fast reviewing process?

Long review process (an aside) I once heard a lecture by the Chinese number theorist Hua Luogeng.  At one point he discussed one of his results, then the slide showed the journal name, with date of submission and date of publication.  He paused while we looked at the 10-year gap between.  Then he explained that the intervening period was the "Cultural Revolution" in China.

There is an emerging trend in post-publication peer review but it doesn't seem to be a usual thing currently.

@GEdgar how can one avoid this? Do you think it is a good idea to search for fast publishing journals?

While the times you give are probably above average, I would say they are not wildly unusual for maths.

Are there journals with fast reviewing process?
The really quick ones are the "questionable" journals ... every paper is accepted, and published (for a hefty fee).
The Notices of the American Mathematical Society publishes a survey once a year, which includes information on mathematics journals, including statistics on time from submission to publication (when available).
added
"Backlog of Mathematics Research Journals"
Notices of the AMS, Volume 61, Number 10,
November 4, 2014, page 1268.

First, I am searching for journal with non-zero impact factor. Second I searched Notices of AMS and I did not find such statistics, kindly post a link if possible.

Do you think it is a good idea to search for a fast publishing journals?

Is there any way to avoid  wasting time in the review process?
Before submitted you can send the paper to the editor and ask whether s/he considers the paper to be in scope for the journal. This can be eased by providing a good, short overview of the paper, along with the paper itself.

I did this for the last one (14 months). The main problem is the review process time.

@Semsem: Ideally, asking the editor for his/her opinion should avoid the whole review process altogether, for papers out of scope.

You can send a pre-submission inquiry to the journal editor with a summary of your research. Make sure you cover the following areas in your summary as these are some of the things editors need to know about your study to be able to judge whether they would be interested in it:
1. the subject area of your research;
2. its significance to your field of study and to the scientific community in general;
3. some idea of the nature of evidence provided to support the findings;
4. a brief explanation of what previous work on the topic has shown and what significant contribution this study makes.
You can send pre-submission inquiries to multiple journals at a time, so you can save a lot of time this way.

It is a good idea and i did it before in the third article(14 months till now), but the main problem is the review process time. Do think it is a good idea to search for a fast publishing journals?

This is really not common in mathematics (I've never heard of anyone doing it).  If someone sent me a pre-submission inquiry, it wouldn't speed things up at all.  If the paper sounded totally inappropriate, I'd say so, but that's the same thing I'd do soon after submission.  In other cases, I couldn't say anything without seeing the actual submission.

@AnonymousMathematician what do you think about solving this issue?

Your part 3 suggests that this answer is not written about math journals, which is what the question is about.

I strongly agree with @AnonymousMathematician.  This strategy is likely to annoy an editor without accomplishing anything.

@Tobias Kildetoft I am not sure of the field of Mathematics, but it does work work in other fields. Sorry if my answer wasn't very specific.

I simply meant that your part 3 makes no sense for a mathematical paper.

One option would be Peerage of science, http://peerageofscience.com/, which is a service through which you can request peer reviews (which are also reviewed) for your articles and review the articles of others. There are, however, two problems, one of them significant:

The review criteria are not a good fit for mathematics articles. This is a minor issue, really, but annoying. See below for more details.
To my knowledge, the service is not popular among mathematicians.  This can be slowly changed by using the service, but there is no immediate solution. The service is free for scientists.

Quality indices at Peerage of science are: question, data, methods, inference, writing. Of these, data is not relevant for pure mathematics, and both methods and inference require interpretation.
The refereeing format is standardised and there is plenty of room for discussion, so one is in now way communicating only through the five indices.
Why it might become popular among mathematicians
The main users of Peerage are biologists (of certain subfields), but the benefits are common to all fields of science where one publishes articles: One can request a peer review and then, when submitting to a journal, tell that the article has already been peer reviewed, with a link to the review. The journal, of course, is free to do their own review, if that is what they would rather do. If the article is rejected, then one can send it to another journal and share the same review at Peerage.
This reduces the work load of referees and editors and speeds up the process for authors.
The peer reviews are reviewed, so their credibility is also measured.
The reviewers can get their work recognised. One can get credit as an excellent reviewer, for example.
There are further benefits with respect to some journals that are linked to the service, but I don't think this is relevant to mathematicians at this point.

I'm a mathematician, and I've not heard of this site before.  If you'll forgive two naive questions: 1) In what way are the review criteria not a good fit for mathematics articles?  2) Given 1), why would the service become popular among mathematicians?

@PeteL.Clark I expanded the answer.

Cell published an interesting article about PoS: http://www.sciencedirect.com/science/article/pii/S0169534712000249 and the answer of the authors: http://www.sciencedirect.com/science/article/pii/S0169534712000250

@DaveClarke I am not affiliated with Peerage (though my university is). I would like it to be used in mathematics and do believe it would be useful. Advertising in the sense of sharing something useful, but not in any negative sense, I hope. Is this in some way different from mentioning Notices of AMS, for example?

Thanks for the clarification Tommi. I'll retract my comment.

Thanks for the elaboration. I must say that I don't understand the downvotes here: I am not so optimistic that services like this will become popular among mathematicians, but nevertheless this is a relevant, informative answer.  +1

I have asked many colleagues about this side, they did not hear about it before?

@Semsem Yes, the site is most popular among biologists (of certain subfields).


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Paper status with Associate editor after Under review
I have a submitted manuscript to IEEE transactions. The paper was under review for 4 months. Then, it has been with associate editor" for 2 week now. How this status can be explained?

The editor has received the reviews and s/he is in the process of judging them (sometimes maybe s/he will decide on a new review, but not likely) and communicating the decision to you. Sometimes this can take few weeks for various personal reasons (for example heavy work load on the editor). I expect that very soon you will receive the answer.

@Frank If you think my answer is the one you were looking for, consider accepting it.

This status "With Associate Editor" means that the associate editor who is in charge of your manuscript has received the minimum number of reviews (usually 2) for your paper. This does not mean that he has received all the reviews he is expecting, some reviewers are invited or accept their invitations later than others (sometimes 2-3 weeks apart, even longer), or maybe the reviews he has received are conflicting and he is awaiting an additional review before making a decision.
The system in most Transactions lets you change the minimum number of reviews so that the status is "Under Review" rather than "with Associate Editor".
Also in most cases, the AE will receive an e-mail to notify him that the minimum number of reviews has been received and he must submit a decision within a couple of days / week.


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Parenthesis in paper title?
I am writing an academic paper with some co-authors and we are thinking of including a word in parentheses in the title. So the title would look something like

XXXX (YYYY?) XXXX

I have two questions:

Is there any style issue/argument against this? The fact that I need to ask this question in the first place leads me to believe that there is. But I thought I would ask since this may just be a rare occurrence and may not violate any writing/style rules.
In case it is okay, would it be okay for the title to start with the parentheses?

If the question mark is part of the title, it makes it more informal sounding. This is common in some fields (e.g. Computer Science security), but might not be in yours.

Thanks for the answer Ric, question marks and relatively informal titles are common and acceptable in my field (economics - I realized I forgot to mention it).

There are many papers out there with parentheses in my title. In particular, there are at least three articles (from different publishers) starting with a parenthesis:

(Patho)physiological Significance of the Serum- and Glucocorticoid-Inducible Kinase Isoforms
(Patho)physiological implications of chronic dietary sodium restriction during pregnancy; a longitudinal prospective randomized study
(Patho)physiological implications of the novel epithelial Ca2+ channels TRPV5 and TRPV6

Thus, there is at least some publishers who do not object to this.
On the other hand, this probably does not hold for all publishers, and there very likely is at least one out there, who objects against parentheses in titles.
Unless there is a clear rule in the publisher’s guidelines, it will be impossible to predict its opinion on this matter. Thus, I would suggest to just use the parentheses and let the publisher or the copy editor, respectively, worry about this.

Thank you very much for the answer, and for the examples. I am sure that some publishers will object to it. I mostly wanted to gauge whether this is an absolute no-no or if it could be deemed acceptable.

@mfariacastro In the worst case, the publisher will tell you to remove the parentheses, that is, you surely don't risk rejection for this. As Wrzlprmft suggests, use them and let the copy editor worry about that.

The definition of a good paper title is not "one that my publisher did not object to." Personally I think these titles are horrible (no offense - I know nothing about the field and haven't looked at the papers, which for all I know are Nobel-prize worthy). In addition to the clunky parenthesized adjective, the middle one actually contains a semicolon! Methinks these authors may be good scientists but could use more than a little polishing of their marketing skills.

@DanRomik: I am no expert on these very papers either, but the alternative to (patho)physiological is almost certainly physiological and pathophysiological (no, just physiological won’t do), which is more clunky in my opinion. I do not think debating the latter is any useful, as we are in pure opinion territory.

@Wrzlprmft (pseudo)okay.

The main stylistic argument against the use of parentheses in a paper title is that parentheses are an expository device that should be used very sparingly, even in the body of a paper or other text. I learned this the hard way: for many years I had a bad habit of injecting too many parenthetical clauses into my writing. At some point I became aware of this and started making a conscious effort to replace any use of parentheses with an equivalent non-parenthetical statement, and found that in 90% of the cases doing so made sense, was easy to achieve, and improved the presentation. Overall I feel that my writing has greatly improved thanks to this small change, and I would recommend to anybody to follow the same guideline that parentheses are like a strong spice, to be used in moderation and only when there is a very good reason to do so.
With that said, I have used parentheses in the title of one of my own papers (the idea of one of my coauthors, but not necessarily a bad one), and think that this is fine if it serves some clear purpose and done in good taste. As others have commented, it may be done to lend the title a slightly more informal feel, or to inject a pun or a bit of humor, or to add some important qualifier to the main statement of the title, e.g., "The infinite-dimensional halting problem is (almost) undecidable."
Finally, I do think using parentheses at the beginning of the title is almost certainly a very bad idea. Parentheses by their nature are just a little bit distracting, and the beginning of the title of your paper is the last place where you want to distract your reader's attention. The title should have a strong, punchy start that pushes the reader along and helps them to appreciate what your paper is about; see a related discussion here. Moreover, another small principle of good scientific writing is that sentences in general, and titles in particular, should not start with punctuation marks of any sort (or with mathematical symbols), so that's another reason why parentheses would be bad at the beginning of the title.

Thank you so much for your feedback. I am happy to use the parentheses at this stage, but am still not totally comfortable to use them to start the title, so I may just decide to rewrite it in a clever manner.

@mfariacastro - It does sound like a good idea to at least try to recast.  Even if you go back to the first version of the title, you may realize something interesting about your topic while trying.


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Is it unethical to hire a paper writer AFTER the assignment is done?
This is an intriguing scenario that came to my mind. I have not done this and am not planning on doing it, but I am curious about it. Of course, it’s well known that if you hire a paper writer to write your assignment for you, that’s cheating. But what about this situation?:
You have a difficult writing assignment. You follow all the rules, do it yourself, turn it in, and then you get your grade, and it’s a poor grade. But you want to learn what a really good paper for that assignment would look like, for the purposes of gaining knowledge, not grades. So you hire one of those paper writers people usually use to cheat, who is known for getting (dishonest, of course) As on all the papers they write, to nix it for you, so you’ll have an example of what an excellent paper would look like for your study pleasure.
So my question is: is this unethical, and if so, why, and what might be the consequences were it found out? The reason it seems interesting is because it’s being done after the assignment is turned in, so you’re not doing anything to deceive/defraud the teacher or get grades you did not merit – all transactions with the teacher were done by the book. But on the other hand you are going through the motions you’d go through to cheat, not to mention paying money to someone people pay to cheat. So where does this situation stand, ethically, and why?

See Is it considered cheating if I purchase an essay but then don't use it?. (Note that the answers there address both the case of "looked at the paper you bought before writing your own" and "didn't look at it until after you submitted your own")

Note that this sort of situation would typically be how paper-writing companies would justify that their product is not inherently unethical, and if you use it to cheat then that is your responsibility, not theirs.

Or, you could just ask a friend who got a good grade if you could look at theirs? ;-)

In your hypothetical situation, no cheating occurs, since you do not misrepresent your own efforts. Comparing your own to someone else's solution after corrections have been returned in order to better your understanding is a perfectly good study practice.
Let me also clarify one point: you say, "paper writers [...] known for getting (dishonest, of course) "A"s on all the papers they write". There is nothing dishonest about the A grade. If the teacher gives it an A grade, it's because it is an excellent paper. If it had been handed in with a different name on it, it would have received the same honest A grade. The only dishonest thing is the student's behavior in putting their own name on it and claiming it as their own work, and arguably the ghostwriter's in knowingly assisting in this deception. Absent this, everything is above-board.
The only point where questions could be raised is the influence of money in your hypothetical. There are two places where this could play a role:
1) Acquiring this solution is expensive, and therefore out of reach for poorer students. This kind of disparity seems to be more acceptable to some societies than others, as shown e.g. by the price of education in the US (lots) vs Germany (nothing).
2) You are contributing to the maintenance of an industry which is predominantly assisting others' dishonesty. On this question, which is similar to e.g. contributing to bittorrent development because you like to use it to download linux distributions, I think that society has not formed a uniform opinion, and it is left to the individual to decide their own comfort level.


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How to find universities helping commercialization of research
I have a PhD in computer science. I have done some successful applied projects. Now, I am looking for a postdoc position in the US. However, I prefer a university with more support for commercialization of projects.
As I tried to search, most universities have offices for university–industry liaisons, but I do not look for a collaboration with industry. I wish to find universities specifically have an office for helping student and staff to start their own business, i.e., if I complete an applied project, the university supports me to establish my company.
How can I find universities that actively have this service?

Welcome to Academia SE. I edited your titular question and removed another question to have your question contain only one question, which is no shopping question and actually answerable by us (as opposed to the university).

It is fairly common for universities to want to commericialize faculty research, and take a share. "Technology transfer" is a key-phrase to look for, and "Office of technology transfer" is the name of the office concerning such at my univ in the U.S.

@paulgarrett: That looks as if it should have been an answer

@Wrzlprmft, I don't really know that that phrase is typical in the U.S., so it'd be at best a very-partial answer... Also, it seems to be that faculty are expected to get external funding to do the research that results in start-ups, etc., so the univ may not really "help"...

All research universities in the United States have "technology transfer" or "commercialization" offices. They will help you patent your invention, license that patent to licensees, and/or help you set up your own company to commercialize the invention.
Of course, all of this is subject to an assessment that what you think is a commercializable idea is really worth the university's support.