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A senior colleague that belittles my contributions, expertise and won't acknowledge a published error that I identified
I am a PhD student and the most junior person on our small team (me, a lab manager, a statistical analyst, a wet-bench scientist, a senior statistician, and our PI). The statistical analyst has been on this team for over 15 years--we'll call her Emily. Emily trained me in some areas when I started, but I've learned a lot and I have become very independent in the 5 years I’ve been a trainee.
Some Context
Emily and I have been working closely on a project lately.  Because we work so closely, I often ask her for documents related to relevant analyses that she has previously done. I have come to realize that Emily is very error-prone, which I believe our PI already knows. Lately, many of these errors have been discovered when I say something like "that estimate doesn't seem quite right to me" in a lab meeting. I nearly always turn out to be correct and Emily is livid with me for pointing it out. She is typically very defensive and it's very difficult to persuade her to re-check her work. She is dismissive of pretty much everything I say to her directly.
When we went to publish a paper for which I wrote the entire first draft, contributed half of the figures/table, and designed ~90% of the experimental approach, my PI said that Emily and I should be "co-first" author. I agreed because Emily had done ~80% of the experimental work (she wrote most of the code). When my boss made the suggestion that we equally share first-authorship, Emily was so upset that she wasn't the sole first author that she literally screamed in my PI's office about it and then didn't come into lab for 3 days after. These things have set up a poor working relationship between me and Emily.
The Problem
That paper was published, and I'm currently working on several papers that build on those published findings. In working on these new projects, I've discovered an important error that Emily made in the published paper that we are co-first author on.
I made the decision to go to Emily about the error first so that she had a chance to address it with our PI. She denies that there is a mistake and tells me that I'm "too confident about myself" when I say that I'm 100% certain that there is a mistake and lay out all of the evidence that definitively proves it. Unfortunately, I lost my cool a little bit and some of my responses to her were harsh and less-than-professional.
So, I have an email thread that documents Emily's mistake, that I approached her about it directly, and that she actually doesn’t understand what she was doing and therefore denies that the mistake is real; however, we both made some statements that were unprofessional.
The mistake needs to be corrected in order for me to continue with publishing my recent projects (but fortunately does not change the main takeaway of the paper). Emily plans on telling our PI that I’m just a trainee and that I don't know what I'm talking about and that she did not make a mistake (again, I can definitively prove that she did with the email chain). She also has some clout with our PI because she's been there much longer than I have and is more experienced.
How should I proceed?

Isn't your PI capable of looking at what Emily did, looking at your explanation of why it's wrong, and determining whether it's actually wrong (perhaps after talking with both of you)?

Yes. I'm not concerned that I can demonstrate that the mistake is real to my PI, but I feel that this issue goes beyond just correcting this single mistake. I feel like the way that Emily treats me is inappropriate and unprofessional, and furthermore, I have a hard time trusting a lot of her work due to the magnitude of errors that I find. I'm not sure if I should only discuss the mistake or if I should discuss some of the broader issues exemplified by this situation.

In your position, I'd be inclined to get the immediate problem, this single mistake, solved so that you can proceed with your recent projects. Afterward, you could mention the larger problem to your PI. Make sure you have documentation about whatever mistakes you mention.

Fair enough. Thanks for your advice @AndreasBlass!!  I do appreciate it.

The statistical analyst has been on this team for over 15 years, yet is very error-prone. Why is the statistical analyst still on the team? Is there something that you're missing?

@user2768 , I know.  It does feel crazy.  But I am not the first to discover that she is quite error-prone.  And I know that we all make mistakes sometimes, but the rate of errors from Emily is remarkable.

You told her that she made a mistake in front of everyone else in a lab meeting?
As for the co-authorship, in most fields "doing experiments and coding" would be 80% of all work. You've got at co-first for writing up a draft and, adding "half of the figures" (why no all of them?) and "designing the experimental approach".
All too often the latter means throwing in some half-thought through ideas while the PI was in the room, and leaving actually bringing them to fruition up to someone else.
Did you ever have the thought that you could be the problem in this whole story?

When we went to publish a paper ... my boss made the suggestion that we equally share first-authorship, Emily was so upset that she wasn't the sole first author that she literally screamed in my PI's office about it and then didn't come into lab for 3 days after.

If possible, it is always a good idea to negotiate contributions and authorship of a paper prior to conducting the relevant research and drafting of the paper.  This kind of dispute can best be avoided by having all the researchers sit down prior to the research project and agree on the roles of each of the researchers, and how the authorship will be allocated (i.e., who is a co-author vs an acknowledgement, order of authors, etc.).  In some cases the actual contributions may end up differing from the initial plan, and so a renegotiation of the authorship could occur, but in many cases you can avoid disputes by having a clear set of expectations at the start of the project.  Once a dispute arises, there is going to have to be some negotiation and decision made about the dispute, but in the future it would be best to avoid these problems by agreeing on authorship details in advance.

... I'm currently working on several papers that build on those published findings.  In working on these new projects, I've discovered an important error that Emily made in the published paper that we are co-first author on.  She denies that there is a mistake...  The mistake needs to be corrected in order for me to continue with publishing my recent projects (but fortunately does not change the main takeaway of the paper).  Emily plans on telling our PI that I’m just a trainee and that I don't know what I'm talking about and that she did not make a mistake (again, I can definitively prove that she did with the email chain).  She also has some clout with our PI because she's been there much longer than I have and is more experienced.

Firstly, you should do everything possible to see if you, Emily, and your PI, can reach an agreement on whether or not there is an error in the published paper.  I would suggest making a meeting with your PI where all of you can look over the details of the claimed error, check your working and discuss the matter, and see if you can come to agreement about whether or not there is actually an error.  If you can get your co-authors to agree with your view, then you could all submit an erratum to the previous paper correcting the error.  If your co-authors can convince you that there is no error, the matter is also resolved.
It sounds like this might not be possible, and so if you try all this and exhaust all possibility of agreement, then here is what I would suggest.  You are the author of your new papers, so it is up to you what to write in them.  It is perfectly acceptable for you to claim in your new papers that you have identified an error in the previous published paper.  For full disclosure to your reader, you should make your claim in the paper, but also note that the claim of the error is disputed by your co-author.  (You can give relevant details in a footnote, but keep it succinct and professional.  Do not bog the reader down with excessive detail or a big shit-fight.)  Re-run the previous analysis without the error, note the new results, and proceed with your new papers on that basis.  Emily will be just as entitled to submit new papers claiming that she is correct and there is no error.  (Both sets of papers would be vetted by referees, but it might be difficult for them to tell who is right, so you might find that some referees will be reluctant to recommend publication.)
If you are unable to come to an agreement on the alleged error with your co-authors, ultimately that is going to mean that you end up claiming one thing and she ends up claiming another.  If these are your papers, and you have tried and failed to reach agreement on the matter, I see no reason why this issue would require any further intervention of your PI, so her greater "clout" with the PI should not make any difference.  You are entitled to submit research to journals making claims you believe in good-faith to be true.  (If you want to, it would also be legitimate for your to submit an erratum for the previous paper to the original journal, notifying your co-authors, and noting clearly in your erratum that your claim of an error is disputed by your co-authors.  I suspect that the journal might not accept this, but you could submit it if you wanted to.)

Unfortunately, I lost my cool a little bit and some of my responses to her were harsh and less-than-professional. ...  we both made some statements that were unprofessional.

That is a problem, and you are both going to need to cool it.  (And it is probably worth apologising for any comments that were unprofessional.)  Keep your focus on the work, and the correctness or incorrectness of the methods and results.  If you cannot engage with Emily without making unprofessional comments, you should disengage communication with her.

From what I read in your communications, you have a very serious communication problem with your co-workers.

Lately, many of these errors have been discovered when I say something like "that estimate doesn't seem quite right to me" in a lab meeting.
  I nearly always turn out to be correct and Emily is livid with me for pointing it out.
In working on these new projects, I've discovered an important error
  that Emily made in the published paper that we are co-first author on.

And some of your other sentences...
Paper writing with a group is a TEAM project. You are not playing as a team player. That error you found does not belong to Emily only. That error belong to all of you as a team, all of the authors. You have no right to say it is Emily's error only. If you insist on this attitude, this means that you want all the positives from the paper but no negatives. Since you are able to find the error now, this means that you did not check it yourself good enough before.
Of course you should point out errors and fix them going forward but to err is human. This problem is not about you finding errors of your co-workers but more about how you communicate with them about this errors.
Lets consider that you become a team leader yourself, in academia or in a company, and a co-worker find your errors, this means nothing. See following wikipedia page about David Hilbert.

His collected works (Gesammelte Abhandlungen) have been published several times.
  The original versions of his papers contained "many technical errors of varying degree";...

But if a person informs rudely you about your mistakes, anyone will become defensive regardless of their position. And this is more about perceived rudeness. You need to think about your communications and talk with some other people so that they can give you feedback.
Take a lesson from this problem. This type of relationship problems will exists everywhere. It will not be different in professional domain also.

I have to disagree. Teamwork does not repeal the notion of personal areas of responsibility. A team member is primarily responsible for their own contribution, and only then for checking the work of others. Sometimes there is only one member with knowledge of e.g. stats or experiment work. Their errors remain their own. They can compromise the work of the team, though.

I think, you can only assume this to be true for some journals where they explicitly state personal contributions. But those journals are rare.

No, this is true also for areas where people do not publish at all. Example: Two people serving a cafe are a team. But if one of them is personally responsible for keeping cash safe, and cash gone missing, it's not the team failure, it's individual under-performance. BTW, why are you spell team in ALL CAPITALS?

In this case, I disagree with you, though I see your point. In this case, I have 4 different email threads with our team PRIOR to submission where I bring up 4 different concerns about the analysis in which I found the error. I suspected that there was a problem months before we submitted, but Emily was dismissive of those concerns, and our PI followed-suit with hardly any further investigation into my concerns. I only found the error after I went through her log files, which I did not have access to before publishing. I couldn't be 100% certain of the error before I had the logs.

Also, this was published in a journal where specific author contributions are listed, and this error is not under my "jursidiction."

Then you are in a very good position, but I still think that you need to find a middle way by communication.

For the current project: Focus on what the scientific error is.  Stop focusing on whose fault it is.  You may need to get the error fixed to continue with the followup work, but presumably the followup doesn’t depend on anyone admitting fault.  All the issues about digging up email trails to show whose fault it was are a massive distraction — things like that serve no scientific purpose, and will make Emily more defensive, and make it look to other people like you’re (at best) mean-spirited and intolerant of other people’s fallibility, and (at worst) like you have a vendetta against Emily.
If, instead, you point out a mistake and its content without finger-pointing about the blame, people are much more likely to be willing to admit the mistake and help fix it (and to try to avoid such mistakes going forward).
Even though the water has been muddied, it’s hopefully not too late for damage control.  Apologise to Emily, either privately or in the group setting, for anything unprofessional you said.  Hopefully she’ll then apologise in turn, but if don’t try to make her — that won’t help anything.  Maybe also apologise, if you can bring yourself to, for having focused too much on finger-pointing.  Emphasise that you just want to make sure this scientific point is correct, going forward.  And then if she disputes the issue further, be ready to explain again what you think the mistake is — purely the scientific error, nothing personal, no finger-pointing, describing things as “we wrote X…” rather than as “Emily wrote X…”, and being genuinely open-minded to the possibility you might be mistaken (even though you’re sure you’re not).
On this possibility: bear in mind that happens to all of us sometimes, even when we’re pretty sure about something.  If you are phrasing the problem as “Hey, I’m worried we have a mistake in that pervious … could someone else check this with me?”, and it turns out there’s no error after all, then it’s still no big deal — you’ve not lost much face.  If on the other hand you phrase it as “Look, Emily made an error here!” and it turns out she didn’t, then that really looks bad for you.  Being diplomatic, tactful, and a team player isn’t just about being nice to others (though that is important) — it’s also much better for you in many ways.

You say "Stop focusing on whose fault it is" & "point out a mistake without finger-pointing", but there's no indication whatsoever in the question that the asker ever openly attributed blame to Emily in his communications with her or others. It's Emily, in this story, who is refusing to allow errors to be fixed because she knows she was the one who made them. This entire answer basically consists of making up a load of behaviour that there's no indication the OP has ever engaged in and then telling them to stop doing it.

@MarkAmery: Agreed, I’m reading between the lines a little — the OP doesn’t explicitly say much about how they described it to their colleagues.  However, in their description of it here, they frame it very much in language of personalised fault and blame.  Perhaps they didn’t show any of the same framing in their discussions with their colleagues, in which case sure, this answer isn’t the right one.  But if they’re thinking of it the way they describe it here, it seems quite likely to me that this is also part of how they have raised it in the group, in which case this answer is relevant.

Part of the problem here is that Emily is often dismissive of me when I say anything that even might be construed as critical of her work. I did actually use the "I'm a little concerned about X because I know Y, and X & Y don't seem to jive, can we have a second look?"  approach. Unfortunately, that approach didn't work.  And others on the team didn't feel my argument was strong enough to look into then. Now I am 100% sure that there is an error, and I am frustrated because I did, in fact, try to address it prior to submission with basically no success.


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Publishing phd work after joining another institute for job
I recently submitted my phd thesis and immediately joined as a faculty member in another institute. My final phd viva will be in around 3 months time. Now, I need to publish some of my thesis work which I haven't published yet. Do I need to give my affiliation from both my institutes? Can I give both??  I will be the corresponding author.

I'm surprised this is a question, in my field i would have just done the new institute, however I'm not familiar with systems where you can be faculty before finishing your phd.

I had the same thing recently and was advised to include both if you have used any resources (including time) while working at the new institute on the paper. I chatted with my advisor at the new institute and we agreed that as any work I had done on my PhD paper was done in my spare time, not during time my new institute was paying me for, I didn't need to include them as an affiliation.
But if you're taking significant chunks of the working day to work on this paper (including during review response) and the institute is paying you for that time, I would include them, as they have then been funding the time you're spending to work on it. Also in my case, I totally switched fields to one my new institute doesn't do any work in so they didn't really want their name on my old work.

How you list your affiliation is field dependent. You could probably ask your advisor what is best for you. I assume you can list them both.
See this answer to a meta post for part of the discussion on variability in academia.
If your doctoral institution funded you in any way they probably want an acknowledgement, at least. Maybe so even when they don't. But your readers will also want to be able to find you if they have questions, etc.

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Pursuing a master's in mathematics with eyes on a PhD: Will a D or C in graduate Analysis 2 ruin my chances?
I'm a master's student currently, with a focus in pure mathematics. I would like to  apply to PhD programs this fall at other universities (as well as the program at my current university).
Last semester I got an A in graduate Topology and graduate Analysis, but a C in graduate Algebra. I am going to retake the Algebra class this fall (required to get a B for my concentration.)
This semester has been rough. The second half of the graduate Topology sequence is going well, but I'm struggling in Analysis. Right now I'm feeling like I'll be lucky to get a D, but I'm holding out hope that if I throw myself into it I can squeeze out a C.
My undergraduate transcripts are good, but not stellar. They got me admittance and funding here. I might look into some research next year, but probably not before my applications go in.
Will I still be able to get into a PhD program? I'm not looking to go to a top school, but I was looking at some that are bit nicer - UVA, UMD, etc.

Sorry, I think I have to be blunter than the other answers.
Unless there are extenuating personal circumstances that have led to your poor performance, a C or D in one core graduate course combined with a C in another core graduate course (even if you will retake the course, presumably with a better grade) should make you seriously question your goal of getting a PhD.  Keep in mind many lower-ranked programs admit students in part so that they can have cheap labor to teach classes, while hoping rather than expecting that the student will be able to earn a PhD and get a job using their degree afterwards.  This means you could easily be admitted to some programs without necessarily having a high expectation of success.
Most PhD programs in (pure) math will require you to take comprehensive exams in analysis and in algebra.  Generally speaking, the problems on these exams will be like the most difficult problems in the final exams for your courses, although you will not be expected to solve all of them to pass.  Unless your current professors are exceptionally tough graders, or you have something else going on that indicates your performance this year is not indicative of your mathematical abilities, or you have some sudden gain of insight that significantly improves your ability to solve math problems, you will likely have great difficulty passing these exams.
Moreover, while there are quite a few exceptions, generally speaking, your ability to learn graduate level mathematics is correlated with your ability to do research.  Therefore, difficulties with your courses suggests that you are likely (but not certain) to have difficulties writing a dissertation.  (Since you might be doing a research project next year, you might have more information about this then, so I wouldn't give up yet, but keep this in mind.)
Finally, the job market in pure mathematics is quite dismal and likely to remain so for the foreseeable future.  Someone graduating with an average or mediocre dissertation will not get a postdoc.  If you are a good teacher (and you presumably have some idea by now of whether you could become one or not), you can get a teaching-oriented position, but you can (in reality, not just theory) get most community college positions and many lecturer positions with a Masters degree.  There are almost zero industry positions that you can get with a PhD in pure math that you could not have gotten with a Bachelor's degree (and an undergraduate record that can get you into graduate school).

Well, a D certainly isn't going to help. But then, a C won't either. That doesn't necessarily make it impossible, but certainly harder. In any admissions (or job, actually) application you need to give a lot of evidence that you will be successful and your grades aren't pointing toward that now. You will also face competition from people with better grades.
I wonder if you are doing well enough that you can continue to a doctorate at your current institution. That might be an option if it is available.
But, at a minimum, you will need some outstanding letters of recommendation and even, perhaps, a personal touch to get over the wire. If your professors know people at doctoral institutions and can give you a push, it might help.
On the other hand, a PhD in mathematics is awfully specialized. If you want to work in Topology and are good enough in a small area, someone might be willing to overlook the other issues. But just getting a good mark in one class won't be sufficient.

I know nothing about how PhDs in mathematics work, so I’ll just speak generally. I got a first class degree at undergraduate level and As and Bs in all my modules during my Masters but because of circumstances out of my control I got a C- in my dissertation. This pulled down my grade from a distinction to a merit. This was two years ago, and I have been trying to get a PhD position ever since and so far have been unsuccessful. I have great references and have been working as a research assistant where I’ve published two articles and a book chapter, but some universities have been kind enough to tell me that although my proposals and supplementary documents are impressive, my applications are not competitive enough because of that one C- because understandably my dissertation was significant.
However, I keep on trying because I know of people who have substantially worse grades than I have who got into PhD programs with funding attached. I know as academics we hate to admit it, but sometimes it just comes down to luck. You need to apply to the right supervisor at the right university at the right time, but also work hard to prove that you can conduct independent research.

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Minor(?) error introduced during typesetting
I recently had a paper accepted by a journal which doesn't provide author proofs. Unfortunately, a typographical error was introduced during typesetting, but I had no way to know this until the paper went in print. I'm trying to determine what is the line between a minor typo and an error which requires issuing a correction.
To get into some more specifics, a constant was left out of an equation. Although that sounds really bad on its face, the equation is very standard and everyone in the field already knows the correct form of the equation. I can't realistically conceive of anyone being misled by the error. In fact, I doubt most readers will even notice. But it's technically incorrect as it stands.
This is one of those instances where I feel damned if I do and damned if I don't. Issuing a correction looks bad, but leaving the mistake looks bad as well. I double checked the revised manuscript we submitted and confirmed the error was definitely introduced by the journal staff. What do I do here?

This is definitely dependent on the culture of your field and of your subfield.  You will get much better answers by asking a range of senior people in your field than by asking people who have no idea about your field and its norms.  If you don't know enough senior people to ask, the editors of the journal are good choices - the editors have nothing to do with the actual production and printing of your paper (it's handed off to the publisher) and will be just as annoyed by the misprint (if not more, especially if it's a common issue) as you are.

When you say that issuing a correction looks bad, I imagine that you mean issuing an Erratum/Corrigendum. Now, these really don't reflect that badly on you and your career in the first place, but the error honestly sounds so minor that an erratum would be rather overkill. Actually, I imagine many journals might even decline publishing an erratum for such a trivial case.
However, especially if the publication was quite recent, it might be possible to correct it anyway. At least some journals are willing to make small corrections to published articles, sometimes with a small notice, sometimes accompanied by something like a Publisher's note. In such cases it's quite common to see the journal accept responsibility for errors they've introduced in the notice. It might be worth checking if the journal would be willing to do that.

The "small correction" option sounds ideal, if available. I'll contact the editor. I wasn't aware that this could be done without a formal erratum. You're correct, a erratum feels like overkill which essentially was the basis of my original question. I will think twice about publishing in a journal which doesn't provide author proofs in the future.

You should inform the editor of the error just to get it on the record. Ask that a correction be issued if possible. There are probably people who will in fact misinterpret it. It is a simple thing. Just let them know.
Maybe they will improve their process in the future.
I don't understand why you suggest issuing a correction looks bad. Leaving it untended seems worse.

I'm suggesting a correction looks bad, it's because I'm putting up a huge sign right up front saying, "we made a sloppy mistake"--in my mind that's a negative connotation before the reader even reads a word of the paper. Is that a silly concern? Perhaps, but people can be judgmental towards sloppiness. If a serious error was made, this is justified--obviously, scientific integrity comes first. Fundamentally, I'm asking where is the line between a stylistic error (which can be overlooked) and a content error (which must be corrected).

Your call, of course, but the uncorrected error is also sloppy.

@pww024 Ideally, the journal would admit, in a correction, that the error was the fault of the typesetter, not the author. So it's not "we made a sloppy mistake" but "the typesetter made a sloppy mistake". Even if the journal won't admit that it's their error, I'd rather have people think I made a sloppy mistake, noticed it, and corrected it than have people think I made a sloppy mistake and didn't notice it (or noticed it and chose to ignore it).


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How to learn math independently as a biologist/bioinformatician
I am in the same boat as many bioinformaticians, where I got my degrees in biology and taught myself computer science, and that's gotten me pretty far. But unlike those lovely physicists-turned-bioinformaticians, I only took the required maths courses ten years ago and wish I'd payed more attention.
As far as I can tell it's currently for me more of a problem of concepts, and familiarity with symbols. For example with the latter, when I get to a part of a paper with equations, my eyes just gloss over... I'm not used to reading equations, so it's difficult for me to parse them or understand them in context- everything from 'what is that greek letter pronounced as?' to understanding the general form of the specific equation.
What is a good way to get up to speed on the important mathematics in my field? Most of the stuff I come across is either too high level (academic texts) or too low level (Khan Academy, for example). I feel that this lack of knowledge is really limiting the directions I could take my research and tools I could use, but I'm not sure how to go about improving it.

If you are a bioinformatician (i.e., working on computer science/programming/software engineering applications for biology), then academic texts should not be "too high level", no? As you are finding out, the math involved simply is advanced, so any method of coming to grips with it will involve advanced material, whether this is courses or textbooks.

Related: How to build bridges between mathematicians, computer scientists and biologists? AND Start studying mathematical biology from basics AND Books on mathematical biology. Useful, I think, is A Mathematical Nature Walk by John Anthony Adam, but it's written for someone with roughly a 2-semester calculus background (U.S. calculus), so it doesn't get into more advanced stuff that you might want.

There's no end to statistical analysis in bioinformatics with varying degrees of mathematical sophistication. Maybe an interesting analysis in a paper is a good place to start. What sort of mathematics underlies ANOVA? You could always work backwards. There's no replacing lots of experience, just pick a place to start and go, one thing leads to another.

The way to learn mathematics is to do mathematics. Trying to understand by merely reading equations will get you nowhere. You've got to get out your pencil and paper and work problems.

A key point of information missing is what do you want to learn the maths for/which subfield of mathematics do you want to know. Most of the answers here assume you want to learn statistics (or mathematical biology in the answer above), but there is a lot of different maths that can be applied to biology: do you want statistics or the biophysics of animals or statistical mechanics that underlies sub cell level behaviour, or optimisation (for conservation efforts/animal energy conservation), or even group theory. Knowing the level you are aiming for will help provide better answers for you.

Agreeing and adding to @Matt : learning how to code and simulate/plotting the math can help immensely at bringing the math to life. Knowing the specific field of bio you are in can help narrow down the starting point. Either way, becoming proficient in the math will likely enable meaningful insights on your work!

I would recommend that you search the internet for courses of study in the specific field you need to catch up on - here, bioinformatics. For instance, here is a list of universities in Germany that offer programs in bioinformatics (in German).
Then check the relevant classes that are mandatory or recommended in those programs and that check your boxes - in your case, any introductory math course for this particular program.
Finally, find out whether you can audit this course if it is nearby or streamed on the internet (or recorded on YouTube). Or find out which textbook is used. If this is not indicated on the course homepage, you can always simply send an email to the instructor, you may (or may not) get an answer.
After that, you will indeed need to invest some time. Math is hard, which is why you did not pay a lot of attention that last time. Ideally, try to work your way through a few papers of the kind you are struggling with, until you understand 90% of the math. And yes, this can mean multiple days to understand just one paper. You will need practice, but it will get easier.

As a mathematician - I want to echo that math is hard.  If I really want to understand in detail a paper in my specific area of research, I am in for 20-40 hours of reading and working to understand the paper.  If you're used to spending an hour or two to understand a paper, you might be wondering what you are missing when in fact you're just used to a different concept of how much in the way of new ideas there is in a paper.

I'd echo the comment to the main question - I'd start by learning some statistiscs, and the math important to it. Everyone one has their favourite textbook, but personally I like
"Modern statistics for modern biologists" by Susan Holmes and Wolfgang Huber. Its available free online or you can buy a paper copy.
Also recommended are some online courses, such as Raffeal Izzary's EdX courses. In particular, take a look at the courses on Matrix Algebra and linear models.
Finally, if you are really committed, I recommend the Open University. You can take any number of first or second year undergraduate modules in Math or statisitcs, which is probably about the right level for someone wanting to do what you are doing. I learnt a lot of my statistics this way (I am a Bioinformatics PI and senior lecturer).

I suggest you check out MIT ocw courses. Particularly check single variable and multivariable calculus. You also need probability and stats, check out Probability and Statistics 131a and 131b on youtube. Try to follow the textbook while watching the videos. I think these should give you the foundation that you need.

Are you certain you aren't more interested in biostatistics than in bioinformatics? I'm just saying.
For starters that's Experimental Design,  Analysis of Variance. Analysis of Covariance and Multivariate Analysis. Then there's more than that. And probably... today, Machine Learning.  Biostatistics is the background a pharmaceutical statistician has to have to get
drugs approved at the FDA.
A VERY GOOD read are the first two chapters of Albert Bourla's book: MOONSHOT.  You'll be impressed with how much Bourla understands experimental design. Bourla might enjoy having a woke staff. But he's a hella statistician!
Read that book to get a feel of how knowledge of advanced biostatistics could result in a job in a leadership position at a pharmaceutical company.
On the other hand. You can self teach yourself all the statistics. But - since there is a lot of competition - you'll need a Masters to get in line for a dream job. As to how to teach yourself... Go to the bookstore at UCLA and peruse the shelf of biostatistics books. You might get lucky and discover the books have a "teachers edition" with answers to all the questions. Look on Ebay for that.


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Accepted by European university, rejected by all American ones I applied to? Possible reasons?
I've been wondering this for a while.
I'm currently doing the first year of my PhD in Frankfurt. Originally from New Zealand.
I'm not complaining about my situation but if anyone asks me I'll honestly say I would have preferred an English-speaking country.
I'd actually applied to about 9 PhD programs in the US and all rejected me. Yet I was accepted to a (supposedly far more competitive) fully funded European PhD, and rather quickly - accepted late last year and already working now.
It has me wonder. I had very strong letters of recommendation from professors that are well known in my field. I had also published a paper (which has now been cited in Nature) out of the fruits of my research Master's.
My GPA is about 2.8-2.9 by US standards (hard to convert, my school was a "we grade harshly, rarely give out As and we'll make you sweat for a B" style system). Professors at home told me my grades were irrelevant with the strong letters.
People say that I was likely discounted because I had a research master's already and I'd probably see doing more course load as beneath me? That doesn't seem to hold water.
I really don't know. Any thoughts?

Did you include General and Subject GRE scores with the US applications? Even programs that say these are optional often put a lot of weight on them when making admissions decisions.

I'm not sure what you expect us to say. We don't know your CV, and your situation already clearly shows the (somewhat unsurprising) fact that different universities look for different things.

The programs I applied to said GRE was not just optional, but unnecessary, since I'm in a very young and interdisciplinary field.
I guess it's troubling me because I'm worried that I only got the post on account of academic nepotism - current supervisor is a former student of my MS supervisor - even if the letters were anonymized before anyone saw them. Good old impostor effect.

2.8-2.9 would easily get an American student rejected, perhaps without even reading the letters. If those grades are typical for NZ, I would expect the conversion formula would take this into account (otherwise no one from NZ would ever be accepted). but if your institution grades very harshly by NZ standards, that could easily explain it.

By the way, (I'm in the U.S., in mathematics) I know of no situation in which letters of recommendation are anonymized at all. And for better or for worse, "academic nepotism" is often decisive... Unclear whether or not it really means "inappropriate influence", or, perhaps, "detailed knowledge of the viewpoint of the letter writer".

The other thing that is really hard to say is what the relative "competitiveness" of the schools were that you applied to vs the ones you applied to in the US. It is not at all hard to get rejected from 9 institutions in the US, even if there is nothing wrong with your application - especially if these were 9 of the ones that have large international name recognition, simply because so very many people apply to them every year, especially internationally. Its a weird system.

Germany is an English-speaking country. U Frankfurt has a decent world ranking.

Looking up a 2.8 in my New Zealand institution's international GPA conversion guide, the equivalent local grades would be well below what we would consider for doctoral admission for domestic students. I don't know where you were, but it would have needed a lot of explanation even though we would certainly know the institution. Do you think that explanation was covered in your application materials or letters? What was the original GPA?

How is this question not going to be primarily opinion based? All any answer is going to do is speculate because there are a bunch of things we don't know about the OP, including the schools he applied to, test scores, possible grudges with his advisor, conference presentations, course-load, etc.

For the record, this is very similar to my (also anecdotal) experience. I'm Brazilian and applied to 4 American and 3 European MBA's. I didn't even get called for an interview by any of the Americans, but was accepted by all the Europeans (some of which were higher-ranked than the Americans). I just assumed there's some difference in the desired student profile on each side of the Atlantic.

2.8 is a downright terrible GPA in the US. Really, anything under a 3.5 is not going to look good. Maybe you converted wrong? If not, then that's probably why. GPA might matter more in the US than in other countries.

Funds available to cover tuition, fees and provide a stipend may be available only to US citizens. I know that on doctoral admissions committees one of the things we consider is how students will be funded. I would also note that grads are very much considered (along with letters of recommendation): we take a broad look at grades, curriculum, test scores, publications, recommendations, the resume, and the personal statement. That said: congratulations!

What level of universities did you apply to in the US? Top tier schools would almost certainly reject the application based on the B– GPA without bothering to look at the recommendations, as cag51 says. Mid-to-lower tier programs might look at them, but I suspect the recommendations alone would not be enough to counter the grades, so unless you have (near) perfect GREs I wouldn't expect you'd get into those either.

Anecdotally I've been told that recommendation letters targeted to US institutions need to be much more glowing than the ones targeted to European institutions to have the same effect. I don't know if that makes a difference in this case.

It is sometimes difficult for admissions committees to evaluate applicants coming from universities or university systems that they don't have direct experience with.  This is especially true if they also don't know your letter writers.  It can help to apply to universities where someone in the dept. has some connection to the country you're applying from.  Since someone at Frankfurt knew one of your letter writers, that person may be better informed about your letter writers, the quality of your school, and the meaning of your grades.

Many Universities have GPA cut-offs where they don't look at applications below a particular GPA threshold. The cut-off is generally much lower than the average admitted applicant, but can still be quite high. Universities vary on this, some don't do it at all, some have strict transparent GPA requirements, and some do this in practice but don't say so in writing. Most programs that use these sorts of GPA cut-offs would probably have a cut-off of 3.0 (or even higher for elite institutions). So your application may have not even been read if your official GPA conversion translated to 2.8 - 2.9!
If you want to avoid getting your application thrown away before it is even looked at, one strategy is to contact a professor in the department that you want to work with. If you convince them that you would be a great student under their supervision they can often contact the admissions committee and ask them to look out for your application. In this scenario, you still might not get admitted, as the committee does usually have the final say, but your letters of reference will at least be looked at, and the professor at the university you are applying to can send the committee a note about how tough your university is and how well respected your letter writers are in your field.
Your friend's explanation about your research masters is almost certainly wrong. I doubt many programs would reject you just because you already had a research masters.

From my experience, a 3.0 might be even a low cutoff. I have seen higher (e.g. 3.3)

Grade inflation is real and damaging!

The grade cutoff was my first thought as well.  Even the company I work for has a 3.0 grade cutoff for new graduate hires, and I'd expect that to have much less restrictive requirements than an internationally well-known PhD program.

Also I presume submitting a GRE (with very high scores) is almost mandatory when you want to claim 'its not me, its my school grading harshly".

@bremen_matt usually 3.0 (or even as low as 2.7) is the type of official requirement that might be written on a University website. But you are right, in practice, the admission committee might operate using a much higher threshold, 3.3 or even as high as 3.5 would not be uncommon for the most elite programs.

To be fair to myself, my in-topic GPA is over 3.5. I was the only person in my class to land an A+ in the courses closest to my specialty.
I was dragged down by my very... interesting... decision to simultaneously minor in Physics and Mathematics.
It seems I made the erroneous decision of thinking my letters and my extremely high in-topic grades would speak louder than the other stuff.

@CountessIsolde Please note that your letters & high in topic grades would definitely speak louder than that stuff if your application was actually seen. But I doubt anyone even looked at your application. A 2.8 GPA at a US institution is worse than the average undergrad student (median undergrad has a GPA between 3 - 3.3). It is not uncommon for the best PhD programs to get 500 applications competing over only a few spots! No one is going to read 500 applications, they have to cull some in an automated way just to make their job manageable. I'm sorry you fell victim to this system.

Your existing related master's does make a significant difference in most US schools. Somebody that already has a master's will usually skip coursework and go directly to research because the school cannot grant a second master's in the same or related field.
This means you bypass the stage where you're being a TA and taking classes and consequently, there's no opportunity for you to get to know professors and their labs. On the flip side, there is no period for groups to assess your work before they invite you in.
Practically, in the departments I've been in, this means a student with a master's needs to contact professors prior to application review and find a group that is willing to accept them. From that point, the application is a mere formality.
As you have found out, there is little chance if somebody goes through the normal application route. Those applications tend to get stuck in a pile that PIs don't read.
The strongest way to do this is having your existing professors send an e-mail, especially to somebody they have a working relationship with. In any case, good recommendations are required with research background. Courses and grades aren't really that important.

While perhaps true for some fields of study at some particular universities, this is simply not true in general. For example, in mathematics, you'd likely still take coursework even if you got a masters elsewhere. You might be able to take different classes though. And at my university, you were allowed to get a second masters in mathematics.

In other places, you do not TA while you are still taking courses (the first year or two) but rather after that (the last, say, 3 years).

Hmm, this certainly isn't true in the fields I'm familiar with.

@RichardHardy Some schools, including my current institution, incentivize TAing with classes. After somebody is done with classes and qualifies, the tuition drops to a lower level. Because TAing comes with a tuition waiver, it's best to do this early. (There's a minimum 1 course TA requirement, so this is $30k+ of guaranteed money, the difference is something approaching $10k after overhead)


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Using paper figure for public talk
I’m giving a public talk (to laypeople in a sci-com event) and wanted to showcase some figures from research papers that weren’t mine. I wanted to know:

If putting citations (Author, Year) followed by a final slide of references was acceptable, or;
Do I need to have “Copyright [journal name]”, or;
Do I need to get permission from author/publisher, or;
ls such a thing even allowed outside of academic conferences

Do the answers to the above questions change if the journal is open access or behind a paywall?
Thanks.

You can use all this information in a public talk. You should tell your audience where it comes from, but the details don't need to be part of the ongoing presentation. Consider a handout so that they can go look for themselves if they are curious.
The fact that some of the information is behind a paywall does not prevent you from referring to it, as long as you obtained it legally and do not quote large parts of it.
You do not need any permissions. It might be nice to write the authors to tell them that you used their work in your talk.
+1 for sci-com.

Doesn't this depend on the country?  "Full-figure citations" are not covered under Germany's laws w.r.t the allowed re-use of materials. There are exceptions for classroom use, but in a public talk, I think that they don't apply. So a permission from the publisher would be necessary for a public talk, as far as I know.

@DCTLib I assumed US, perhaps mistakenly. In any case I doubt that a full figure on a slide in a public talk would require the kind of permission necessary to republish. But this isn't a legal opinion, just my experience of common ethical academic practice.


text:
Advice needed--reaching out to a potential advisor
I have applied to a Canadian university for a math PhD starting this fall. I was very keen on working with Prof. A and he in fact, had encouraged me to apply. Few days earlier, I reached out to him for an update on my application status and he replied saying sorry that his funds for this fall are already committed. However, he finished by saying that I may find another advisor to begin my graduate studies.
Now I know this does not mean that I am admitted. But can I reach out to other potential advisors now? As a matter of fact, I have been independently reading some new topics and been finding them much intriguing. Now there is a Prof. B who has similar interests and I like his profile too. Will it be worthwhile to write to him now? If yes, how should I broach this subject? Should I mention Prof. A? I don't want to look pushy, but at this time now, I really want an opportunity to start my graduate studies and Prof. B's interests are very similar to what I've been reading recently.
I am looking forward to your suggestions. Thanks in advance!

Of course you should contact him.  There is no harm in that.  But I wouldn’t mention professor A.  Write a simple and short email stating the you have already applied in the department and you are looking for a supervisor for your PhD. Then also mention that you have been reading papers on topic X and you find them interesting. And since his research interests are similar to what you want to do, would he be interested in serving as your supervisor?  And then end your email by asking him to review your application and contact you in case of any question or query.
Good luck!

Thank you for your answer and valuable suggestions. I made some careful edits to my draft and have sent the email now. Hope for the best!

In the US it is common to begin doctoral studies without a dissertation advisor. One then has a chance to learn more about the options. I know the Canadian system is similar in some ways to the US, but differs in others. What I say below may be helpful or not.
If the available profs are getting busy it is probably a good idea to make contact as soon as feasible. Look at their specialties as you have done. Especially, try to determine if there is an ongoing faculty/student seminar that is also attended/led by your first choice. You could start with another member of that seminar, perhaps, but I'd advise against an extremely junior member if possible. They may be more devoted to obtaining tenure than helping students.
Again, in the US one normally starts with course work for a while and it is possible here to choose your preferred advisor later if an opening comes up. This might be less possible in a lab science, but in math it could work out.

Yes, Profs. A and B are both members of the Analysis, Geometry and Topology group. What does obtaining tenure mean, though? And yes, it is true that the ideology of getting a supervisor prior to admission is a bit unsettling. I hope one can work around that after actually getting in there.

New faculty members normally go through a period of probationary employment. In the US it is normally seven years. During that time it is necessary for them to make the case that they are a good candidate for permanent employment, called tenure. In many places getting tenure is an arduous process and something like shooting craps. It can be very stressful for a young academic.

That is certainly something that I did not know! Thanks a lot.

Thank you for your suggestions. I have sent an email after drafting it rather carefully. Fingers crossed now.

I have a problem: this Prof. B has two email addresses mentioned on the website. I sent the email on one of those addresses. Now what if he doesn't use that one often? Should I send it to the other id too? Will it be annoying of me to do so?

It is hard to say. It is best to use the "official" email if that can be determined, but many people forward emails from one to the other in any case. Wait a bit to see if you get a reply, then try the other if you think it has been missed.

Both addresses carry the university's domain name, so I am guessing one might be an old one. The thing is, I am running against time and I don't know how long to wait for sending a reminder. I am stressed.

One option is to send it again with "apologies if this is the second time this has arrived" or similar language.

Update: I did not receive a response from the concerned professor. Instead, I received a rejection email from the Office of Graduate Admissions. Oh well.


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An ex-student of my future supervisor is accusing the lab of fraud. How does this affect me?
I start my master's degree in this lab in September. After accepting my offer I found out that an ex-PhD student has been spreading rumors that the supervisor is publishing fraudulent data, going back many years, basically suggesting her whole field of research is a lie. The ex-student was very insistent to let me know about this and encourage me to not go into that lab. I think he is even trying to get an official investigation into her research to get the paper(s) retracted.
I'm worried that this will affect my career in academia, especially if the research for my master's thesis is based on falsified data. The ex-student apparently got his career ruined as well by the supervisor because he refused to put his name on the paper(s) and she made some calls that resulted in him not getting a post-doc. But I am only hearing one side of the story and I'm not sure what to believe. She is pretty well-known in her field for her research and from my personal interactions seemed nice. I'm scared if I ask her or her other students about it directly it could ruin our relationship before I even begin working there.
From my understanding my acceptance into the master's program is to the department and I could request another supervisor, though this would definitely make things awkward and there's probably limited options at this point for profs that can accept me. I'm not sure how I should proceed.

With no further information available, this seems like a situation to avoid. If you have time, and if the resolution of the case seems imminent, then you could wait, but otherwise you would be good to protect yourself. Protect yourself from the turmoil that seems inevitable to come as well.
One way to proceed is to go to the head/chair for a sit down and ask for advice. If the advice is to stay with this professor, you want some assurance that you will be allowed to succeed even in the worst case for the professor.
The charges might be false, of course, though the professor sabotaging another student would be equally serious, if that is what actually happened. But make sure that you aren't just being driven by rumor here. Make sure you have accurate information.
The head or another senior professor is likely to have better information.

"if the resolution of the case seems imminent" There is no way an investigation will take less than a year.

"The charges might be false, of course, though the professor sabotaging another student would be equally serious." - that statement is misleading, without that, I would have upvoted. Namely, if ex-student brings up false charges on the falsification issue, is is quite possible that they are equally mendacious on the sabotage by the professor (or the professor quite justifiably warned off his colleagues from a dangerous candidate). I agree that trying to get a second opinion is a good idea. Everything exists, from The Superviser from H*ll to the disgruntled research group poisoner.

@CaptainEmacs, I guess that's why I also recommend not acting on rumor. Sometimes the truth is hard to get at.

@Buffy Yes, that's what I wanted to give the upvote for. I find the aforementioned statement simply confusing/misleading, not wrong. In my experience, people who lie drastically on one thing do not much hesitate to lie on its consequences. The truth value of their statements is not statistically independent ;-)

Generally is it acceptable to go straight to the head/administrator and ask to talk confidentially?

It is the head's job to know and manage such issues. Even such issues as rumors.

Find a new supervisor.  Even if the ex-student is dishonest or mentally ill, this seems like a bad situation.
I think you should be quite open about your problem.  The more people know you have changed supervisor because of "future supervisor's" reputation, the more scrutiny will be cast on the situation, and the sooner the truth will get out.  Make it clear you do not know who to believe, and that you are just avoiding the situation.  Then nobody will blame you.
Also, contact some other ex-students and ask them for advice too.

What's a good way to find other ex-students?

Ask the supervisor for a list of their previous students.


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Accepted to PhD program but declined, but now want to return 3 years later
I got accepted to a PhD program at a university 3 years ago, sent an offer and everything but declined. Now I have secided I want to return. Is there any possibility of being admitted again without reapplying if I went and spoke with members of the department and graduate division?
Has anyone done this before? 3 years is a long time for sure but im curious if anyone was readdmitted without a defferal of admissions after 1 year.
Going back through old correspondance the faculty in the department were fond of me and hoped I would attend.
Any thoughts or insight appreciated thanks!

I don't think we can tell you anything you don't already know -- the normal process would not allow this, but there is a small chance that one of the professors you mention could arrange for an exception. Even estimating how often this happens is difficult, since your school may be totally different.

If you do reapply make sure you explain very convincingly why you have changed your mind and what you have been doing. Depending on the details this could be a huge red flag or a strong point of your application!

I did something similar (2 years).  I just went ahead and reapplied.  5 of the 6 schools that accepted me previously did so over again.
Didn't even think about not doing the applications.  What's the big deal.  You should know how.  Let them run their process.
I recommend to apply to several schools.  Always good advice but in this case to hedge your bets in case "A" doesn't like how they were cold shouldered earlier.
I would try to put a positive spin on things but not dwell on the previous decline (no mea culpa).  'Have had 3 productive years doing X, but now see more than ever that my skills would better fit in a Ph.D. level position.'  Hopefully they still want you.  Of course for any schools that you didn't decline earlier, you don't need to mention it as much.  Just say you worked a while and decided you belong in Ph.D.

Some programs will explicitly say that once given an offer, you can accept, defer for a year, or decline, with declining requiring reapplying if you want to be admitted again. Your offer may say something along those lines if you can fetch it.
If you'd like to check with the department and are uncomfortable reaching out to the professors, see if the department has a staff directory on its website. If there is an office coordinator or a graduate program specialist, they may be able to tell you if you have to formally apply again.

Most likely you will need to reapply. However, reaching out to some of the faculty who were fond of you couldn't hurt, to let them know you are reapplying and tell them you are looking forward to meeting with them again.

Thanks for the responses. Ive fallen out of touch with some of my old references is one of the reasons I was hoping I wouldnt have to reapply. I think that was the main thing holding me back, or hoping that I wouldn’t have to. Also I havent really been involved in the field these past couple years, not at all accually


text:
Putting class ranking in CV, but against dept guidelines
I graduated last year from a master's course where I was fortunate enough to graduate top of my class. However I was told this in confidence by one of my referees to a PhD programme, and they informed me that under no circumstances was I to put this on academic applications, as it would be against 'department guidelines'.
I also tried to enquire with the department directly concerning class rankings, but as expected they were unwilling to reveal this information to me.
I'm now considering applying for a job, and believe that the class ranking would be a good thing for my CV. However I really ought not to know this fact, as it was revealed to me in confidence by my referee, and I risk jeopardising my relationship with him if the department found out.
Am I overthinking this, and should I just put it down, or is there a way to resolve this in a less risky way?

Does your transcript say anything about class rank?

I can not speak for others, but your "class rank" means nothing to me.  The lowest ranked student out of a highly selective program is more impressive than the top ranked student out of a very poor program.

@emory, not sure what your background is but that strikes me as an academia-centric viewpoint. In industry, I'm not sure if anyone cares about ranking or program after a certain point. I've hired many staff from low-ranked local colleges who outperformed hires from Ivy League programs. Further, it could be argued that class ranking in some programs correlates to work ethic - people who tested their way into a name brand program and then ended up low-ranked because they couldn't apply themselves might not have the sweat equity as someone who worked hard to get to the top of a lower program.

that strikes me as an academia-centric viewpoint — Well, yeah.
Consider where we are, @dwizum!

@JeffE well yes! But in the context of this question, the OP stated that they're looking for a job "in the real world" which I took as a sign that the industry viewpoint may be more applicable than the academic viewpoint. This question strikes me as being on the border between Academia and The Workplace.

@dwizum I am not a perfect person.  Maybe it should mean something to me, but it does not.  In general, you should try to figure out what the hiring manager cares about and build your CV around that.  If hiring managers are like me, then leave it out.  If they are like you, then put it in.

Luckily none of us are perfect! I agree very much with your "in general," sentence - if anything, rank and program are minor details compared to showing skills, experience, and the ability to solve problems in a way that's relevant for the specific position.

OP have you tried approaching your graduate advisor (the administrative staff member in charge of Masters’ students) and asking them a reasonable way to proceed in the matter ?

@emory your opinion regarding what you consider valuable on an application is quite beside the point and doesn't help OP.

But how did the person who told him know? Professors don't generally have enough free time, interest, or access to everyone's grades to compute class ranks themselves. Sure, professors can express their opinion that the student is very strong, but without the actual data (and the time and inclination to process it), any claim that a student "tops the cohort" just uninformed opinion.

If the answers here don’t thoroughly answer your question, you may think about posting a question on workplace.se.  They are the experts on CV creation and ethics

It depends on the individual institution (and its policy, or lack of) whether there are or are not official/unofficial class rankings, and whether they are published and available to be (externally) verified, often this is not the case. Where this is not the case, lecturers might (or might not answer) broader verification questions like "Was  in the top X% of their class?". Or they might not answer any such question.

It seems to me your dilemma is whether to violate someone's trust, not whether to violate departmental guidelines, which no longer matter to you after you have left.

So, you put it on your CV, the future employer does what employers do and phones the institution to check details of awards, years etc.
BOOM - the institution does not confirm you were "top of the class" as that is just not done.
Now the future employer is confused - what else may be wrong on your CV AND your referee is pissed at you as well.
Do you really want to go there?

The discussion about rhetorical questions has been moved to chat.

@Wrzlprmft , Is moving discussions about rhetorical questions to chat really where we want to go as a Q&A community? ;)

For many jobs, willingness to keep confidential information confidential is essential, far more important than class rank. If a potential employer finds out during a background check that you disclosed something you were told in confidence, you may lose the job regardless of how well you did in class.
Class rank is not something I would have cared much about when I was interviewing, because it is too dependent on how other students did. For recent graduates, I did care whether the candidate got a respectable GPA for a relevant degree. Once someone has a few years work behind them, experience becomes more important. I have known excellent programmers with no degrees at all.

Aside from the insightful advice given by Solar Mike, I'd like to emphasize the importance of maintaining a good professional relationship with that referee. You would be compromising a seemingly valuable relationship by doing something he explicitly advised you against, and he will most likely include that information in some form in the letter/recommendation anyway. It is quite common for academic referees to state in their reference letters that the student is among top students in the course/class/whatever, for example, along the lines of "This student was among top 1% of students in the class". They have different ways and means of saying that, and I would trust that they know how to provide an excellent reference for an excellent student (it's an integral part of their job, after all). He trusted you, why wouldn't you trust him?
An action you could do that might be less contentious is to state your GPA for the course, but then you might want to adjust your CV accordingly (e.g., you'd probably want to state that for other courses). You could ask your referee about what they think of stating the GPA.

This may not need to be a separate answer, but many people are pointing out that, if they were reviewing resumes, they would not be impressed with the placement because they don't know who you were competing against, etc.  If what they are saying is true, then it's possible that the value of putting it on your resume is zero, while the cost (in terms of causing a rift between you and your referee (and possibly causing the referee professional issues if the leak can be traced back), or having the department refuse to confirm it and make you look shady, or whatever) seems to be very likely non-zero.
So analyzing the risk/reward would make adding this to a resume a questionable decision at best.
[For the record/intellectual honesty of my argument, I personally think being able to say I was "top of my class" is going to have a positive psychological impression on pretty much anyone that reads the resume, and it's a shame you can't use it.  But it's knowledge you are not supposed to have, and it's good practice at the beginning of your career to learn not to be tempted to act on knowledge you aren't supposed to have.]

Honestly, if you have the skills and can prove to your potential employer that you are fit for the job, they will hire you even if you were an average student. I personally feel like it is an irrelevant thing to put on a CV. Employers really do not seem to care about this.

As suggested by your prof, this information is not appropriate on your CV or application. Even if there were no department guidelines or telling in confidence, you should not do what you suggest.
Your ranking will not matter when applying for a job in the "real world". You are not competing against your schoolmates. If you place it on the CV, you will just display that you don't understand irrelevance of the fact.
Regardin academic applications - if anyone cares there (doubt it) they will check it themselves instead of trusting your word. And you don't even know if this fact is true or the prof just said it out of mistake or to make you feel better. After all, you are the only person to whom your placing matters.

Most application rules require you to document any claim in your CV to be taken in account, and some of them may want to check those that can't be documented. Your claim that you ended on top of your class can't be backed by document or reference. As any unverifiable claim, yours is not worth much. At least, it isn't likely worth enough to overcome the drawbacks described in the other answers.
In summary: since any of your former classmates could make the same claim and the prospective employer couldn't tell it's false, don't expect any employer to value it.

Ordinarily, the way details of your performance in your program would be
passed from graduate department to potential employer would be in a letter of recommendation. In my own letters of recommendation, I have often used
phrases such as "one of our very best students" or "the best performance I have
seen in several years," backed up by specific, relevant reasons for saying so.
I hope your discussions about this issue haven't damaged your relationship with your
adviser and others who write such letters.


text:
Shall I quit academia or continue doing research without too much luck?
My first three year postdoc was almost over and no good publications came out. The thing is that my carefully crafted papers are getting rejected again and again by decent journals (not that good ones). Knowing how bad the academic job market is now, I have a feeling that I may not make it in academia. I could do another postdoc after my 3 year contract or probably choose to quit.
If I am bad at research, I would quit now for sure. It is just that somehow my mentor has been supportive of me staying in academia and she is very famous. She can't be too wrong, right? Also, I got many projects going well. I think I am pretty good at research. I hope one of those projects will end up in a good journal.  But, it has been three years after my phd.
I came to Europe to do a phd as a poor Chinese guy. At the time, I didn't know much about English and only learned my current major though a 3 year master program in China. I worked hard and learned fast to catch up. But, things just wouldn't click. I did my job but the journals just wont accept my papers. Bad luck? probably. Or, something wrong with my topic or approaches.
If I do another postdoc, I will be way over 30. My life already suffered from my research career. A lonely Chinese guy in a foreign country. No money. No nothing. Just my research. Another postdoc without much hope of making it in academia could cause damages to my life, from which I may never recover.
Shall I finish more projects and try my luck to do another postdoc ? Or just quit, even though people say i am good. Being good isn't very useful in academia I guess. Only papers count.

Sorry to hear of your difficulties. I'm not sure we can assess your situation better than you can -- obviously permanent positions are hard to come by, and papers do count for a lot, but a strong researcher does a non-zero chance of a faculty job. I do suggest you research other options before committing to another post-doc -- academia is not the only place where interesting research happens, and it is a huge weight off your shoulders once you have a permanent position and can move forward with your life. Good luck.

I hope you are on a continual job hunt, not just at the end of a post doc contract. It can take a lot of time to bring it to fruition. But it sounds like you have a lot of ideas that can be exploited. That is independent of the state of the job market.

You write "My life already suffered from my research career." This is worrying.
Think about this: what do you need the most for a satisfying life? Is it being close to home? Having a fulfilling relationsship? Having a garden? Living in China? Living near the sea? Being a researcher? Find out what it is for you and focus at first on that. Then find out what else you can do while realising your first priority.
Don't get too hung up on Academia. Being a researcher is not a higher calling from some God, at the end of the day it's just a job. There are many good and satisfying jobs out there. Find out what else the world has to offer.

There isn't really a question in your post we can answer -- you're having difficulties in your job and your life but what you should do is a very individual question: what is it that matters to you.
But I'll try to address one part of your post: Your papers are getting rejected. Most of the time, you will have gotten feedback of some sort on these papers. What do reviewers say? That the paper has a good idea but is poorly written? That the paper has a good idea, but that others have already done that and published a few years ago? That the paper does not have a good idea and that, while well executed, the question the paper tries to answer is simply not very interesting? In all of these cases, there is something to be learned from the feedback you get, and it should inform your future approach to both research and paper writing. I am a bit surprised that none of this feedback has found its way into your post.
So my suggestion is this: There is a saying in English that "insanity is doing the same thing over and over and expecting a different outcome". So sit down and think through what feedback you got on your manuscripts, and how you would have to change your approach to writing papers and, maybe more generally, doing research. For example:

If reviewers say your papers are poorly written, then start writing papers with co-authors who are good writers.
If reviewers say that your papers do not show anything new, then start reading more -- pick the newest issues of the journals in your area and just read random articles related to your work to see what others are doing.
If reviewers say that your ideas are just not interesting, then have more conversations with your adviser about whether something is worth pursing or not.

well, I got reviews saying the writing had problems for my first paper. But, the most recent experience was two reviewers saying the paper was well written. One reviewer said this was deadly wrong and the fourth one failed to understand the math behind it and was very negative about complicated analyses. Rejected ! Writing a paper now to me is quit fast and easy. This might be an illusion from an optimistic  non native  speaker. Anyway, I think it is the topic. I guess i have to admit it now. Anyway, many thanks for your reply. This is kinda a wakening call for me.

Take these papers and reviews to your adviser and let her talk you through what she sees in them. She will be able to place these reviews in context.

I'll note that even though I have 20 years of experience and 50+ peer reviewed publications, writing papers is not "fast and easy" for me. It is still a carefully executed and thought through art that requires me to find the best way to explain what I want to say. If your paper writing is fast and easy, you're probably doing something wrong.


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the paper status was back from "decision in process" to "under review"
I submitted a paper to Journal of comparative physiology-B. After major revision, two reviewers gave me minor revision (only change one word) and the editor was pleased to consider publication. After re-submission, the status changed from "under review" to "decision in process". However, the status was then back to "under review". What does it mean?

Possible duplicate https://academia.stackexchange.com/questions/55665/what-does-the-typical-workflow-of-a-journal-look-like

Not enough information to say. I suggest patience.

I assume by now you have more details: so what does it mean?

The question presupposes that the behavior of such an editorial system has a meaning. Granting that presupposition, my first guess is that the editor got the reviewers' reports and was about to make a decision ("decision in process") but then noticed that something was unclear in one of the reports and asked the reviewer for a clearer report ("under review").

But would it be potentially positive or negative? That is the point I suppose.

Yes, it wold be potentially positive or negative. Obviously, if my guess is right and the editor is asking a reviewer for a clearer reports, the decision would depend on that report.

From the perspective of a reviewer, it's just a button you press. Sometimes you accidentally press one button, even when you meant another. In your situation, the change it status might now mean anything and it's still under review.


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Research Paper Self Referrel
How would I refer to myself in a research paper? I know the use of 'I' is out of the question, so would it be 'this researcher'?

I personally use "we" for single-author papers, but have had reviewers point out I should use "I". In which cases I made an exception just for them.

Possible duplicate of Choice of personal pronoun in single-author papers and many others

The use of "I" had better not be out of the question; I've used it.

This is very field-dependent. In my field (engineering), it is typical for authors to use "we" even if there is only one author. (FWIW, I don't really like that convention, but it's what most authors do.) In other fields, such as in the humanities, it's usual for a single-authored paper to use "I". (It's not out of the question.) I've also seen "the author" or "the researcher" or phrases like that.


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Emailing professor about unexpected questions on exam
I'm taking a class where the professor has only provided power point slides, which are not even based off of the textbooks listed in the syllabus.
For our final exam, he just provided a generic list of topics. The final turned out to be a different format from our only other exam and some topics required calculations we had never given practice on.
Would it be appropriate to email the professor and voice these concerns? I want to but I'm afraid it might affect how he grades my exam.

Many schools have anonymous course evaluations.  You could express your concerns that way, and not have to worry about a possible effect on your grades.

@NateEldredge At least at my university, the period for student evaluations ends before the final exam period.

I had a final like that once.  To this very day I'd swear midterm and final were written by two different professors.  My reaction was to suck it up and hope for the best.  (It worked.)

I'm taking a class where the professor has only provided power point slides, which are not even based off of the textbooks listed in the syllabus.

Power-points slides are just a medium; there is wide variation in the quality of power-point slides, so this does not really tell us much about the quality of the material you were given.  Your concern here also depends on whether the syllabus sets the textbook as the primary material, or if this was just intended as a supplement.  Ideally the course slides and textbook should be of high quality, and should "mesh" well.  If you found that the material provided by the lecturer was not useful to you, that is something you should feel free to raise.  I would recommend being more specific about your concerns here.

For our final exam, he just provided a generic list of topics. The final turned out to be a different format from our only other exam and some topics required calculations we had never given practice on.

Academics have wide discretion in writing exams, including how to structure/format these exams, and how much detailed pre-exam guidance is given as to its contents.  It is not necessarily wrong for a professor to give you a final exam that is of a different format to past exams.  Material on the exam should be within the scope of what was taught in the course, but it might involve some new wrinkle on material, and might sometimes include questions or calculations that are in-scope, but sufficiently different from past questions that you have not had previous direct practice.  There is certainly no requirement that questions should involve repetition of calculations done in class.  Having said this, if you have concerns about the format/content of the exam, you should feel free to raise this and give your views on it.  Academics are human, and we sometimes write exams that miss the mark a bit, so it is useful to have student feedback to know what students found jarring.

Would it be appropriate to email the professor and voice these concerns?  I want to but I'm afraid it might affect how he grades my exam.

It is perfectly acceptable to give a (professional and polite) email raising concerns about an exam.  Most universities have systems in place to solicit formal anonymous course evaluations at the end of the session, and they usually also have "course reps" that can deliver anonymous feedback directly to the lecturer during the session.  You can also give feedback directly to your professor by email during the session if you wish.  Your professor should be sufficiently professional to grade all the exams fairly regardless of any concerns you raise.  No-one here can guarantee that your professor is not a vengeful and unprofessional person, but the odds are against it.  Just make sure your email is polite and reasonable (maybe have a friend read it before you send) and make sure you are clear about the things that are of concern to you.

I'd note that in my experience, the most common source of complaints about "new material" on exams regards content from prerequisites. We are usually quite careful to not actually ask anything we didn't cover in class, but have to draw the line at some point when it comes to reviewing things they are supposed to already know.


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Any suggestions for a rapid publish journal in material science?
I am looking for a rapid publish journal in material science, environmental science or electrochemical science, open access journals are OK.
This is so weired that my defense committee requires me 3~4 papers to pass the oral defense. Though I've already had one medium and one high impact factor papers.
There's no requirements for the journal. I have 2 low quality papers, I thought I could work with others to improve their quality for better publication after I graduate, followed my supervisors' advice .
However, I need to graduate ASAP since my scholarship had already been ended.
Just looking for a rapid and easy journal in material science, environmental science or electrochemical science to publish my paper ASAP, no specific requirement is needed, I can pay that money.
Thanks.

Sorry to hear you're in that situation, and really unfortunate that the requirement wasn't communicated earlier. However, these kind of "shopping questions" are considered off-topic here, so your question will likely be closed soon. You may want to have a look at SciRev instead, to get an idea of turnaround times for different journals.

This explains the demand for predatory publishers. But I hesitate to recommend them. Whatever you do, make sure that your supervisor) graduation committee is ok with the journal you choose.

It seems if there literally is no requirement about the journal then you can create your own journal and publish those papers yourself.


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Should I give a talk about an insignificant result?
I wrote a paper with some coauthors who are more senior than me (I am a grad student) and it got published although not in a top journal. I thought I understood it and followed the proof line by line but I have been asked to give a talk about it and now I realize that the paper is not very good. We claimed to improve a result of some other people and actually one of our main theorems that we spend lots of space proving is a trivial consequence of theirs just worded differently so I'm worried that giving a talk about this paper will make everyone in the audience just think I'm/we're stupid for not noticing this. I was specifically invited by someone interested in the topic so I can't even talk about anything else. What should I do? Pretending I don't know it's bad gives me more chance to get away with it but seems dishonest. Owning up to the problem sounds like career suicide. And I don't have a good reason to cancel the talk but I'm thinking of saying I'm sick and I can't make it because I really wish this paper doesn't exist.

I know about entire research communities getting away with not understanding/knowing the literature. As a grad student, you're allowed to make stupid mistakes.

I was specifically invited by someone interested in the topic so I can't even talk about anything else. - This is not at all true.  I have many times visited someone to discuss one thing, but I gave a talk about something else, e.g., if the project wanted to discuss was not in a suitable state of affairs for a talk.

Buffy's answer is quite good, but it's important to add:

Check with your coauthors that you're actually right in your assessment.

I've definitely had the experience of mistakenly thinking something I've proved is a trivial consequence of something else, when in actuality there was a slightly subtle reason the "something else" didn't actually apply. (And, yes, I've also had the experience of realizing correctly that something I did was a trivial consequence of existing work - or indeed simply trivial on its own.)
Another important aspect of the above is:

Don't surprise your coauthors with this observation.

Think of it form their point of view: how would you feel if one of your coauthors were to give a talk on your paper, and midway through unexpectedly announced that they'd discovered that one of your results was trivial?

I'm pretty sure you aren't alone here. People find surprising things all the time. Be thankful that you are the one who found it.
This may sound risky, but I don't believe it is. Give a technical description of the problem as you normally would and then give an historical tour through what you originally thought and what you now think and why.
Rather than being career suicide, you will, IMO, be thought refreshingly honest and open to the truth wherever it leads. If you "get away with it now" but don't later, things will be much worse. Much much worse is if a student in your talk raises his/her hand with ... well, you know.
Out with it my friend. Just take a deep breath and say it all. You can even say that you feel a bit silly now that you've gotten a deeper understanding. Noting wrong about a deep understanding, of course, even if it eludes you early.
And, of course, your more senior colleagues and the reviewers, if any, also missed the point. You are a hero, not a bum. The math is what it is.

Another option, of course, is to say that you have found an issue along with the consequence but then talk about another topic. But I think that would disappoint people. Seeing the flaw can, itself, be enlightening.

This sounds like good advice, but I am surprised that you do not even mention talking to the co-authors.

@penelope, you are correct to mention it asNoah Schweber was. I just focused on getting the OP over the fear of failure aspects.

In my discipline, part of the purpose in giving talks is to thrash-out ideas which might not be particularly brilliant, in order to get feedback from your audience, so that you can build on the ideas or find better ideas. Academia is supposed to be collegial, which means that we should give and receive robust yet constructive criticism on work-in-progress (and I think you should treat your paper as work-in-progress with potential for future development, even though it has already been published) in order to advance scholarship now and in the future. In other words, a talk need not be a perfect and earth-shattering result.

This is definitely not how this is done in mathematics.


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How to follow specific journal or conference in google scholar for new paper?
I want to follow few journal and conference. IS it possible to create alert for such specific item in google scholar? or is there any other system available for these kind of tasks?

Many conferences and journals have RSS feeds that you can aggregate with an RSS reader. Usually they are linked on the conference / journal website (though sometimes you need to search for "rss" in the page source because it is hidden somewhere).
Example: the arXiv math.AG site doesn't mention RSS anywhere, but the page source does.

There's also this page on RSS news feeds for arXiv updates from their help pages, which documents the naming scheme and some further options.

You can turn any Google Scholar search into a search alert that will send you periodic email updates. So if you have a search for a particular journal, something like:

source:Biogeosciences

You can enter that into the form for creating a new alert at https://scholar.google.com/scholar_alerts?view_op=create_alert_options&alert_params=hl%3Den&hl=en
For a journal or conference name with spaces you should enclose it in quotes like:

source:"ACS National Meeting"

You may not get the results you expect if the journal name is abbreviated or truncated in some way (or if it is not released in a way that is crawled by Google Scholar), but once you find the most common way that the name shows up in Google Scholar results, you should be good to go in most cases.


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How to change the affiliated authors?
I received an email from a journal to confirm my contribution to a manuscript that was submitted by my colleague, and I am the first author in that paper. In this email, there were two links; one for (yes, I am affiliated) and the other for (No, I am not affiliated), and I clicked by mistake on the second link, and my contribution to the manuscript was removed. What can I do to be affiliated to the manuscipt?
Thank you in advance.

You need to contact the editor as soon as possible and get your mistake rectified.
If you have waited too long then it may not be possible for the versions already made public.


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PhD interview - how to explain why I left a previous PhD?
I previously quit a STEM PhD program after 1 year. The reasons were complex but included burnout, mental health, pressure from the industrial sponsor, lack of support and loss of interest in the project.
Following some time out of education, I decided to reapply for PhDs. I have been invited to interview for a very competitive PhD program. It is stated in my application that I started a PhD previously, and I expect to be asked about this in the interview.
The answer is messy and difficult to talk about - how can I explain it in the best light possible?

What's changed since the last time you started a PhD?

It will depend on what they ask...

@BryanKrause thank you for your response. Many of the issues were specific to the group I was in - I started there straight after completing masters without enough consideration. The group had a very high PhD student drop-out rate which I think is indicative of what kind of environment it was - in this sense I do not expect the problems to be repeated. Regarding burnout and loss of interest, I have taken time out and thought very carefully whether to reapply, and to which groups. I also am changing area of study to one which I am very much more motivated to pursue.

@Alexandra Buffy's answer is similar enough to what I'd post that I won't make my own answer, but I'd reiterate the statement in that answer "Don't avoid the direct answer, but focus on what is now different." - quitting a PhD program looks bad. If I'm interviewing you, I'm worried you'll quit again. Focus more on what's changed in you rather than making excuses/blaming circumstances, and frame it as growth.

I'm not sure that explaining why you left is the most important thing. Questions might be phrased that way, but people really want to know what is different now so that they can predict that you will be a success this time. You can't avoid giving some direct response to the question, of course, but you also need to be able to point to things you have done since then that make your success more possible and more likely.
Perhaps "loss of interest" was a result of lack of support or burnout. Both of those are easier to account for than lack of interest, I think. You needn't give every reason you can think of, but reasons that are fairly common and that have obvious corrective actions are easier to account for than others.
Don't avoid the direct answer, but focus on what is now different.