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How to cope with life changes and burnout after PhD thesis submission?
The last year has been ridiculously difficult. I can easily say it has been 90h weeks 12 months in a row, with the hours taken of rest being vastly overshadowed by intense guilt (over not using that time to work) and inadequacy. I produced a lot of research, published 5 new papers, and produced a thesis which is now submitted for evaluation. On the day I submitted it (about a month ago), I couldn't even read a single sentence and maintain focus - that's how severe my burnout was. My sense of not being good enough permeated every aspect of my being.
I'm finding myself now getting better, slowly and surely. But the brain fog is ridiculously severe. I don't think I have lost intelligence, but the lack of care I feel for my current position as a research assistant eclipses all output I know I'm otherwise capable of producing (or used to be, anyway). On top of that, I feel more tired than usual. I easily need 1-2 more sleep in a day. Normally, I'd be exceptionally motivated to work out, and now I really could not care less. I adopted this "You don't have to do anything you don't want to do." attitude, in hopes to be kinder and gentler to myself as opposed to the whoo-tshh (whipping sounds) dictator I had employed to stay on track in my madness PhD.
I cannot fathom a job in this field anymore, I cannot stand the endless thinking up of made-up projects to pursue research grants. I want out of academia, and this both excites and terrifies me. I feel largely inadequate as a computer scientist joining industry post-PhD because I just spent 3 years of my life not getting industry experience.
I feel lost. Like there's a daily existential crisis. I don't know what to do with my life, and what's worse, I don't even know if I'll recover from this. I mean, what even is this? PTSD? Burnout? Needing a break after excruciating intense labour and emotional distress?
How can I deal with the life changes and the drop in motivation after having submitted my PhD? How do I deal with the remaining burnout?

Are you seeing a counselor, or similar professional?

Nope. It's hard to afford that when my life is in complete flux with needing to choose where to go next (job, country). I suppose I can speak to my PhD counselor, if that is still an option. Why do you suggest this?

I suggest it because I think it would help.  Almost all of your post is about mental/emotional health issues ("intense guilt", "inadequacy", "burnout", "brain fog", "more tired than usual", "excites and terrifies", "existential crisis", "PTSD", "emotional distress") that are certainly not uncommon in academia, but for which a mental health professional will IMHO be better able to help with. Certainly better than someone who only knows you from four paragraphs you posted on the internet.

Not common? I should hope so. However every single PhD student I have spoken with has talked to me about all those things, and on a few occasions I've witnessed colleagues breaking down. :(

I said these issues are "not uncommon", i.e. they are pretty common.

Ah! Sorry. Misread.

I don't find a question here, just a plea. But, let me, at least, give some perspective. You've just won a marathon. It was especially difficult at the end but you pushed through to success. Your body gave out after you passed the finish and you collapsed, hopefully into the arms of loved-ones. At the moment, you don't even want to think about ever running, or even moving, again. Your coach and medical advisors will help you back into a normal state in which you can plan your next steps. But it is too early to think of that now. You just need to recover. Life isn't always like that last mile.

Thank you for the reassurance, @Buffy. I understand and even agree with your suggestions to take a step back. But I must ask, in the real world, how can people just take a break "to recover"? Who handles their job, their paychecks, their lives? Isn't checking out like that a luxury we can't always afford? :/

Continuing my analogy, I have a friend who blew out his knees running marathons. He now rides a bicycle and does much better with the more measured and less punishing pace it affords. You don't need to give up everything or move into a cave. Find some professional help to help you decompress, as others have suggested.

"I want out of academia, and this both excites and terrifies me." I felt similarly for the same reasons (but not as intensely) when I finished my master's degree. I left to work in industry and am very happy with where I am now. Leaving academia is definitely an option worth considering. (Just don't decide one way or the other until your head and emotions have cleared.)

I've made what I believe to be your questions more explicit, so your post can be reopened. Feel free to revert or amend my edits, of course.

The first thing to do is to get rid of the 90 hour weeks, and resolve never to get back into that trap. There is a lot of experience suggesting that the maximum weekly output for intellectual jobs is produced at around 40 hours a week. Going beyond that reduces actual production, because of more mistakes and less creative thought. Your mileage may vary, but it would be very unusual for 90 hours to be optimal.
You need to accept that sleep, exercise, relaxation, and social life are all essential to achieving maximum productivity when working, and to general mental and physical health. If you feel intense guilt when not working, and cannot change that by yourself, you may need some sort of counseling to help you get a healthier attitude.
The mental issues you describe could just be because you got into a bad habit of working too long and relaxing too little. On the other hand, there could be an underlying problem that needs a professional. I am not qualified to evaluate that, and agree with the suggestion in comments that you should consider counseling.

Thank you for your answer. I've stopped working so hard after I submitted the thesis. It's been 1 month now (2 weeks of holiday and 2 weeks of working 40h) but I'm still experiencing a lot of lethargy. :/

@User293727 So you've had two weeks of rest after a stressful year of working 225% time and you wonder why you haven't recharged yet? I admit I'm not sure how long it's "supposed" to take, but two weeks of holiday (no, work doesn't really count) sounds awfully short compared to what you've put yourself through.

@Anyon you know, when you put it in perspective like that, it does seem silly of me to expect such rapid improvements... I suppose I was hoping to exert the same discipline and willpower onto recovery. But alas, seems I've run out of it.

Personally I can recommend hiking in the mountains for a week or two. It eliminates the feeling of being guilty of not working (enough), because one simply CANNOT work or actively prepare your „life after PhD“ while doing this, while presenting a different rewarding challenge at the same time. Good for your mind.

Discipline and willpower are not what one needs for effective relaxation. You need to turn them off, and just relax. If you enjoy hiking, go hike. If there is some TV show you like that you have not had time to watch, binge watch...

@User293727 After I finished all my classes and thesis defense for my master's degree, I didn't start working or work on any research for more than 3 months. I am very glad I took my sweet time finding a job and resting up.

I sometimes relax by watching fiendishly difficult TV quiz shows like Only Connect, @PatriciaShanahan. I'm not sure that's good relaxation, but I enjoy it.

Hello @PatriciaShanahan. I wanted to ask you what constitutes working hours. Like I work for 8 hours during week and after that play chess for 2 hours straight. But there can be a chess professional who does 8 hours week of chess but 2 hours of coding (just for learning purpose maybe). Is that 2 hours also counted as work since I'm actively involved? Thanks.

@LaschetJain Only you can decide which activities constitute relaxation and a change from work for you.

Thanks @PatriciaShanahan. I would also like to take advise from you on the following. I've begun to realise that anything done professionally can be only be relaxing for us to a certain extent. Like when I was younger I thought research is all about searching for crazy ideas but now after joining my masters I've realised it's more of a process and has to be done professionally and in a disciplined manner. I guess if I want to do research process as a crazy idea thingy it would be better for me to take up a job (thus manage finances) and do it as a hobby. Is my perception of the system , right?

Your first sentence describes diminishing and, eventually, negative returns.

First of all: congratulations on submitting your thesis and on publishing 5 papers! That's a tremendous effort!
I was in a somewhat similar situation to you in that the last 9 months or so of my PhD involved ridiculous hours and a lot of uncertainty around getting results and having access to equipment etc. It can be hugely stressful, and for months one builds up this expectation that with submitting the thesis all of this stress will just magically disappear and be replaced by elation, happiness, and fulfillment. Unfortunately in reality submitting my thesis (and later passing my viva) were two hugely anti-climactic experiences.
I was suddenly without a purpose, and without a plan (with respect to my career). Ever since I was a child I wanted to be a scientist, and later this had morphed into more tangible goals like "getting a PhD" and "working in academia". After my PhD I had achieved the first goal, but I didn't really want to work in "the real" academia anymore.
After my viva I soon wanted to get back into reading non-scientific books, as that's something that was very much on the back-burner during the PhD, but I found my attention span to be extremely short and my motivation to keep reading was very low. It took me about 3 months before my hunger for reading and new knowledge came back.
Figuring out what I wanted to do career-wise took a lot longer for me, and involved many hours of often somewhat circular conversations with friends and family (plus probably hundreds of hours of soul-searching on my own) over many months.
I realise that none of this really answers your questions, but I think they're also going to be fairly individual answers for everyone. However, I found the following to be hugely helpful:

If you can, take some time off from academia/work to spend time with friends/family and/or do something you love but you had to compromise on a lot during the PhD (for me that was travelling and spending time in the outdoors).
Without putting too much pressure on yourself with regards to timeframes and the like, start doing some research into options that could be attractive to you (through reading interesting books, lots of long articles, etc on a huge variety of topics I stumbled across a lot of interesting options, started following interesting companies, joined FB groups, observed, thought about what it would really be like to work in these areas, etc.). I went through lots of iterations of wildly different career paths before I arrived where I am today (actually surprisingly close to my PhD, but in industry).
Regarding the lack of industry experience: everyone was in the same boat once. I think this is about finding a company that values the experience and the knowledge you gained throughout your PhD and is willing to invest in you as a person (intelligent, educated, hard-working, willing to learn, quick at grasping new concepts, self-sufficient but able to work in a team, able to achieve long-term goals, etc.) rather than hiring an employee who can hit the ground running (i.e. a company worth investing your time and effort into). In my experience there's companies who are looking for people like us, and they're great, and there's companies that are looking for something else, and they'd probably not be a good match for us either.

Probably a bit of a rambly post, but maybe the two big take home messages from this should be:

You're definitely not the only one who feels like this!
It will work out! It'll take different amounts of time for everyone, but there are lots of options and lots of different paths!

Although a mental health professional may certainly be able to help, a time-honored cure for your problem, that I think is almost guaranteed to be of some help, is to take a vacation. Two-three weeks in a nice, relaxed setting, preferably in a warm, exotic locale, will do wonders for your state of mind and help you look at your situation more clearly and think about your future, which, by the sound of it, is much rosier than you seem to think it is.
Congratulations on handing in your CS dissertation. It’s a fantastic achievement that would make most people (including those who spent the last three years in industry, I assure you) green with envy.

OP mentioned in a comment that they have already taken two weeks of vacation.

@NateEldredge then I’d suggest taking more vacation, since the first time clearly wasn’t enough to recover from the period of overwork.

I adopted this "You don't have to do anything you don't want to do." attitude, in hopes to be kinder and gentler to myself...

So it was all worthwhile then. The value of an experience isn't always what you expect it to be.

I want out of academia, and this both excites and terrifies me.
  I feel largely inadequate as a computer scientist joining industry post-PhD because I just spent 3 years of my life not getting industry experience.

You had your experience, and learned something from it, and now you'll try something new with the benefit of that knowledge. This is life.
If "computer science" and "industry" are in reference to programming, then you can get some more experience based on your own interests by finding an open-source project to contribute to at your own pace.

I don't know what to do with my life...

Instead of struggling to find something to do with your life (for something new), you can focus on maintenance and preparedness. Do you have a bunch of junk to get rid of? Is your non-junk well organized? Do you have any health issues you need to address? Is your bathroom clean?
Are you prepared to receive what you only dare to dream of?

it sounds like you're depressed. I've felt very much like this. In my case it was triggered by reaching a point where I thought I had achieved my major life goals, and had no new goals to work towards. You'll get better but it may take some time and some help from a medical professional.
I suggest you explore opportunities for new creative or artistic endeavours, spend time with friends, make new friends etc. In my case I took up music (writing, learning, performing, playing in a band). You may not even have to make any big professional/academic changes, but it could help to do something fresh or different professionally for a while.

I'm finding myself now getting better, slowly and surely.

Well, from your description - not quite. That is, not surely, and in some respects you're now experiencing the repercussions of working yourself to the bone.

the lack of care I feel for my current position as a research assistant eclipses all

After you come back from your vacation, see if you still feel the same. If you do, it's time to remind yourself, or perhaps ask yourself "Why did I do this in the first place?" - and then re-assess whether you've achieved that goal; whether you want to continue following it (not in 90h work-weeks, nor in 50h work-weeks either); whether you want to try something else (for now or permanently).
Remember, though! You've not "lost" or "wasted" anything - except your peace-of-mind and physical health perhaps.

output I know I'm otherwise capable of producing (or used to be, anyway).

You're not a paper mill, you're a person. Stop thinking about imaginary theoretically-producible "output".

On top of that, I feel more tired than usual. I easily need 1-2 more sleep in a day.

When you're stressed out, in an anxiety spell, and/or depressed - your sleep suffers too. You don't sleep as well. That's why you feel you need more sleep, and at the same time - even that sleep is not enough. Consult your physician. He may or may not prescribe some sort of super-mild anti-anxiety medication if your sleep trouble is serious. In parallel, consider an appropriate physical/meditative activity; I have found Yoga to be helpful, but YMMV.

Normally, I'd be exceptionally motivated to work out, and now I really could not care less.

"work out" sounds like something very intensive and not very relaxing, which gets your adrenaline pumping. Like I said above, perhaps something with less "grrr!"

I adopted this "You don't have to do anything you don't want to do."

... but it seems like you're beating yourself up about it. Remember this is not a binary thing; and it's not permanent. So: "For a while, you don't have  to do all those things you don't want to."
Also, I'm guessing this doesn't help with the fact that you're not really sure what it is that you want.

I cannot fathom a job in this field anymore, I cannot stand the endless thinking up of made-up projects to pursue research grants.

... which is why - after your vacation - think of what it is that you actually want to do as an academic. And if there's no such thing - then your job search should probably focus, at least partially, on out-of-academia positions. This is not "failing" - because your goals have changed.

I feel largely inadequate as a computer scientist joining industry post-PhD because I just spent 3 years of my life not getting industry experience.

You're quite adequate - believe you me (and I'm a CSer who entered industry after academia, then back again, then back again).
Most industry experience is bad industry experience.
Industry needs people with academic experience.
If you worked 90h weeks, you got the industry experience of some places in industry...
When you leave academia you'll understand what "inadequate" really means.
Forget about adequacy - and think about finding something interesting to do in industry.

I feel lost.

Many, including myself, have been in your shoes - and worse. Hope this answer helps a bit. Don't try to snap yourself back to full working condition at once. It's a process.

I feel lost. Like there's a daily existential crisis. I don't know what to do with my life, and what's worse, I don't even know if I'll recover from this.

You need to keep in contact with people - not online, but physically. Visit friends and family. You don't have to repeat everything to every one of them, but try to be open to letting them cheer you up a bit about life.

It's post coital tristesse.  You shot your wad.  Seriously, though. As grim as the battle is, it can be sad when the combat is over.  Those 90 hour weeks had a sort of joy of the struggle to them.
Can't help you on academia.  There are a lot of twidgety aspects to it.  Can't say industry is perfect either, though.  But these issues exist whether you are just done with thesis or not.
Take some industry job interviews.  Don't even worry (too much) about getting the offer...although that would be nice.  But get yourself on the market.  It will change your mindset to be going after something.  And it will force you to get out of your own head...because of the person on the other end.
Go for some bike rides.  Doesn't have to be in "cardio mode".  But just get out and move a little and breath the vitamin D-shine.


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Is it possible to edit name in a paper at the stage of pre-proof correction after acceptance?
I am a part of a collaboration in an article. The paper is accepted in a journal and we are asked to check the pre-proof version. Now I see initial part of my name is missing. For, example if my name is "St. Stephen Bas", in that case, "St." is missing. I didn't submit the paper, my corresponding author submitted.
Can we edit the name before sending the pre-proof to journal?

Yes, editing mis-spellings and other obvious mistakes is possible at this stage. Contact the editor, journal staff, or the person with whom you have communicated about the proofs as soon as you can, and ask to have that change made.

@FerventHippo Yes, fixed.

Yes, if the problem is just the misspelling of your full name, you can edit it. If the problem is to add an extra author, then it's usually not possible.
See comments for details

"If the problem is to add an extra author, then it's not possible." I would not be so absolute about this. You might have some explaining to do, and sometimes it might really be impossible. However, if there is a good reason to add an author, quite some journals/editors will accept.

At the stage of pre-proof? I don't think so. Maybe in predatory journals.

It's definitely possible. It's unethical to leave out an author. If a legitimate author is missed, misspelled, or mis-affiliated, then a separate correction has to be published. It's far better to have the author added before publication than to fix it otherwise.

You can even add an author after publication. Journals have a process in place for it.

It's very rare and confined to cases where the authorship is disputed. It's absolutely not the norm and it shouldn't be. This practice is seen with suspicion since it's used to sell authorship of papers that have already been accepted. If you look in the Retraction watch blog you can read some articles about this. Of course I clarified in my comment that corrections of authors' names are possible.

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How to remove co-author from a reference of paper under review?
I am a PhD student in mathematics.
One of my article (say, paper A) is under review in a journal (say, journal J), where I have mentioned my next article (say, paper B) as a reference (which is completed but yet to be submitted in arxiv). The problem is that the reference or paper B has a co-author with me. But the co-author is not collaborating anymore, as of now. Moreover, not responding my emails, not looking at the paper B. So it might happen that he can let me know that he is not interested anymore in the paper B, so before submitting it to arxiv or journal, I have to remove his name from paper B.
Now suppose my paper A gets accepted from the journal J, in which it is under review, in that case I have to adjust the reference by removing the co-author.
In that situation, how would the editor or referee of the journal would react?

It is very unlikely that the editor and/or referees of the journal will react at all if you modify the reference by removing the co-author from your unpublished work. This is because they almost certainly won't notice.
Just change it the next time you modify the paper (either when the editor asks for revision, or when they ask for the final version after acceptance).
If they do, somehow, notice the change, that shouldn't really matter. Paper B is currently unpublished, so it is perfectly possible for its list of authors to change.
(I should add, however, that it is worrying that you want to remove a co-author from a paper that is "completed butyet to be submitted". Either the co-author contributed to the paper, in which case you can't just remove them from the list of authors, or they did not contribute, in which case they should not have been on that list in the first place.)

Thanks for the answer. The reason that forced me to think about to remove the co-author name is discussed in my questions here. I have been suffering for almost a year. My co-author is not helping. His only contribution is that he read the complete paper and raised some errors which I fixed on my own. But I offered him authorship and asked to give a final look at the paper and submit it. But in vain

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What does it mean for a Mathematics journal reviewed by AMS Mathematical Reviews?
In the indexing section of a Mathematics journal, out of several indexing (e.g., Scopus, MathSciNet etc), it is mentioned that the journal is reviewed by AMS Mathematical Reviews.
What does mean it ?
Google says Mathematical Reviews itself a journal published by AMS, but I am not sure it is a journal.
But in any case what does mean a particular is reviewed by AMS Mathematical Reviews ?
Is it a good criteria for a journal?
Any information please...

Mathematical Reviews is now better known as MathSciNet.  It's a subcription-based online database of mathematics research papers and books, produced by the American Mathematical Society.  Before the online era, it existed as a paper periodical called Mathematical Reviews that was sent out to libraries and subscribers, but it was never really a "journal"; it only included metadata and not original articles.
An entry in the MathSciNet database contains the bibliographic information for the book or article.  For selected items, there may also be a review: a summary of the article written by an independent expert who was recruited by the MathSciNet editors.  Despite the name, the "review" doesn't usually evaluate the paper as "good" or "bad" but instead summarizes the contents in the reviewer's own words, sometimes including more background information, context, sources, etc.  If there is no review (e.g. the paper wasn't selected for a review, or a reviewer couldn't be found, or the reviewer decided that they had nothing to say) then the database entry includes the article's original abstract instead.
When a journal is indexed by MathSciNet, it means that articles published in that journal are entered into the database.  Usually this is cover-to-cover, i.e. including all articles in the journal, but in some cases it could be more selective.  MathSciNet has pretty broad coverage and will generally index any journal that seems to be of interest to the community, so being indexed by MathSciNet is a pretty low bar.  If a journal is not indexed, it's likely either very new, very obscure, or of such low quality that the MathSciNet editors don't think it is of any significant interest at all.
I don't think it's accurate to speak of a journal being reviewed, since as I understand it, the decision to seek a review is per-article.  Even in top journals, not all articles receive reviews (though it's not necessarily clear whether the editors tried to solicit one).  Still, presumably papers in strong journals are more likely to be reviewed, as this is some indication that the paper is interesting.  In obscure or lower-quality journals, it could happen that none of the articles are reviewed.
So in short, if the publishers say their journal is "reviewed" by Mathematical Reviews, they probably just mean that it is indexed, and that at least some of the papers receive reviews.  I would take this as a signal that the journal is probably not complete garbage, but I wouldn't read into it much more than that.  As I said, it is a very low bar.

Thank you very much for all the valuable informations. I am more convinced now with you.

Math Reviews was a paper journal back in the day, but at some point it transitioned to being online-only.  Mathscinet is the web interface to search Math Reviews, and the brief reviews of papers it gives you are exactly the content of Math Reviews.
The goal of Math Reviews is to index the entire mathematical literature, so being indexed there is not really a meaningful signal as to how good a given journal is.

Thank you for the answer

Actually, it is a meaningful signal in the sense that, if a journal is NOT reviewed, then (assuming it is a math journal) it is not a reputable one at all and you should not publish math papers there.

@AlexanderWoo: That’s a good point, but from what the OP wrote it sounded like they thought being indexed might be a positive signal, and I think that is a mistake.

@AndyPutman, Are all mathematics journals reviewed by AMS Mathematical Review, by default?

@learner: I’m not sure exactly what you mean when you say “by default”.  They have an editorial board that manages things and decides when to start/stop indexing journals, so some judgement is performed (eg here is a recent statement about what they are looking for: https://www.ams.org/publications/math-reviews/mrpolidxjl), but they aim for broad coverage and don’t try to distinguish between “good” and “bad” journals.

@AndyPutman, I meant whether AMS Mathematical Reviews covers all math journals or not. And  I think your last comment answered it. By the way, my purpose is having some concept regarding such matters, I am not very interested in distinguishing good or bad journals. But I see journals in the persepectives of good editorial boards with established mathematicians( good publications), and which follows strict peer review process along ethical line,  should be reputable  journal, or at least meaningful journal.

To give you an idea of how little filtering MR does, during its brief existence they did index papers from the Antarctica Journal of Mathematics, which was most famous for being the butt of various internet jokes back in the day (google can find plenty about it).  Similarly, it now indexes plenty of pretty sketchy/predatory journals, but I don’t want to get into fights so I won’t mention any current ones by name.

@AndyPutman, ok thank you for the information. I got it


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How to react to colleague publishing my idea
Many months ago I informally explained to another PhD student of my chair the main idea I was working on. Today, 6 months after, I discovered that he submitted it to a minor conference, got it accepted and published. In the meantime, I have submitted a long paper to a major journal, where this idea is one of the key components. The paper has gone through the main revision and is expected to be published in around 3 months.
In the conversation with this person it was only the two of us, and from the deadlines of the conference he applied to, I can see that his submission was before mine. In any case, I have mails with the co-authors of my paper during our work on it, that show that this idea was already fully developed many months before submission. To be exact, I have drafts of this method as early as 6 months before the conversation between the other PhD student and I.
I am worried that since I cannot prove that he took the idea from me, this could backfire in case that is a "him versus me" situation and we look at the proven facts (this is, the submissions dates). My first questions is if the e-mails of my draft are a solid enough proof for avoiding me being accused of actual plagiarism if the situation scales. Also, does anyone has ideas of what is the best approach here for finding a fair solution?

Step one: never discuss work with them again.

If I have to think of a worst-case scenario, where it is your word against his word, better to harden up the timeline: when was the conference announced? when did you start your PhD? when did he start his PhD? do you share a common advisor? who are his co-authors at the conference?

We do have a common supervisor, who barely goes through the papers we publish, so he most likely didn't notice the issue. I'm 2.5 years into my PhD, and he's 3.5 years, about to finish his. Not sure when the conference was announced, is a very low quality one, and it's hard for me to get much information about it

Common supervisor, affiliated to the same department, common research area, you have a good publication on the research and he has a contribution to a minor conference ... I suggest you to let it run. If he will ever attack you for plagiarizing his research, the advisor is on both sides, so the attack it is extremely unlikely to be succesful.

First and above all: congratulations on your paper being accepted! Let's look at the half-full glass: it is such a relevant progress in your field that one peer of you found it so relevant that he decided to work on the same topic/approach on its own.
Regarding your question, first the malicious thinking, that your peer stole the idea from you. From an external observer, both of you are innocent until proven guilty, but the same facts you expose here can be easily turned the other way around.
If I were your malicious colleague, I would claim that I planned and submitted the work to the conference as soon as it was announced (way before conferences submission deadline, usually even minor conferences are announced one year before), and that I had informal discussions with you during our day-to-day interaction and that you stole the idea from me.
How to protect yourself?
You have a solid trace of your work, which is the mail discussing the work with your co-authors dating before the discussion with your colleague. The colleague of yours can claim they started working on that idea many months before your discussion, and either one of the following:

the idea sharing with you never took place;
he presented the idea to you and you stole the idea from him.

To protect yourself from such an occurence, you should signal to your co-authors that unfortunately someone from your group took inspiration on the main idea of your paper, because you discussed informally with them during day-to-day interactions and presented it at a minor conference. Forward them the contribution to the conference of your colleagues and give them an estimate of the time schedule. Plagiarism is (luckily) taken more and more seriously, better to prepare all of you from such an occurence.
Please also signal the situation to your PhD advisor (in person, not via email, this is a confidential topic and you do not want to put yourself in trouble because a misunderstood sentence or an ambiguous sentence that you wrote). You must have had some internal presentation and discussion on the topic before submitting the paper, before discussing the topic, has your fellow PhD similar records of his interest/involvement on the topic?
I unfortunately foresee the chances of your PhD advisor thinking it would be a good idea you start to work with your PhD peer on a follow-up paper on the topic: prepare yourself to defend your ground, stating that such a thing must be obviously discussed with the other co-authors.
However, I would not discount the possibility that your peer was stuck in a rut, thinking about problems to be solved in your field and he found the discussion with you so inspirational that he started using your approach, discussing it with other colleagues in your department (who are his co-authors?) and by affinity in sources, he ended up with a very similar research process and conclusions to the one you reached, along the process forgetting the casual discussion he had with you.
In short: I unfortunately see no good outcomes from this situation. Try to avoid as much as possible interactions with this PhD student.


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What tense to use in arts and humanities papers?
How to Write and Publish a Scientific Paper advises writers to use the past tense when they write about unpublished research (including the research their paper reports), and to use the present tense to write about research previously published in a primary journal. So, presumably, writers should use the past tense to refer within their paper.
However, in a reply to this question, a user commented that he uses the present tense when he references within his paper.

What tense should writers use when they refer within their paper?
Do arts and humanities papers use tense differently than science papers do?

Verb tense often distinguishes a paper in the humanities from one in the
natural and social sciences.
Generally you would write in the present tense in the humanities (e.g. John Doe explains) and you would use the past tense in a humanities paper only for reporting historical events.
The UNC Writing Centre have a good webpage with examples that explain the three types of verb tenses (present simple, past simple, and present perfect) that they say account for approximately 80% of the verb tense use in academic writing.

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Is it acceptable to apply for two different postdoc positions in the same institution at the same time
It is discussed here that it is generally okay to apply for multiple jobs in different ranks at the same university, but I want to know is it acceptable to apply two different postdoc positions in the same institution at the same time. I think I remembered seeing somewhere that you are not advised to do so because these two professors may talk to each other and find that you apply to both of them. Suppose I have sent an application to Prof. A but did not hear back, is it okay to send another application to Prof. B even if they are in the same institution or should I wait for a definite yes/no from Prof. A before moving on?

It's worth specifying the context (e.g., which field and country you are in).  In mathematics in the U.S., I can't see any reason why applying to two postdocs at the same institution would be a problem.  In particular, I don't think applying to another position at the same university would be more like to upset someone than applying to another university.  However, maybe this varies between fields.

@AnonymousMathematician I'm applying for theoretical physics postdoc U.S. and Asian universities. I agree that if you change the wording of your cover letter a bit and do not call both professors they are the 'best' you've known you possibly won't upset them but I've never applied before so help from someone who's experienced maybe beneficial to me and others who may have the same question.

I did exactly that and got offered a position at both places.

Are you assuming professor from different universities do not talk to each other?

Is it really necessary and effective in a cover letter to say a professor is the best?

It is entirely reasonable to apply for multiple postions at any one time, even at the same institution, provided you do it appropriately. There are a number of considerations to digest, but pretty well most of what is discussed in your linked question is relevant.
The most important thing to consider is that the application you make is tailored for the position you are applying for. You need to be able to highlight what amazing skills and abilities you will be bringing to this partnership, and how it will benefit the project. You need to avoid a cold call approach, otherwise your applications will sound like spam. This means you need to change your cover letter a lot. It is likely, though, that the skills you bring to any project will be very similar. You are, after all, a product of your previous experiences. If you were to apply for two different positions, highlighting two very different sets of skills and abilities, I believe this could be to your detriment if this information was shared between prospective employers.
You need to weigh up the relative value of each position. If they are both about equal, then I would apply to both simultaneously. If, however, one was far more cherished than the other - one was your dream position with a triple Nobel Laureate with access to the best research facilities and guaranteed ongoing funding opportunities and endless publications and the other was with an also-ran professor (do they exist?) who publishes once in a blue moon, I'd probably hold back on the application for the latter, just in case.
However, if there are two positions being offered in the same institution that you are qualified and suitable for, I believe you'd be crazy to let the opportunity slip.
There is an added consideration in that if your two professors discuss your applications, they may realise the potential to be able to share your expertise. And let's face it - professors do discuss applicants.
No professor/academic/employer is going to be that precious to believe that they are the only person in the world that you are willing to work for. No, I take that back - I've met a couple who are like that, but you wouldn't want to work for them!

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How do teachers learn to grade?
I teach math with about two years of experience now. In general I have found that all the cliches about graduate school teaching you "how to research but not how to teach" are true. But I have also found many great resources (at my institution, online, in print, etc.) that are helping me, over time, work through my teaching deficits.
...in all things but grading.
I struggle with many grading decisions: from small things, like grading individual homework problems, all the way up to life-changing things like evaluating master's degree defenses.  What I lack is a coherent philosophy of grading that might motivate my various grading policies/strategies/choices.
Interestingly, I have not found good resources for this.  Yes, my institution provides a tiny bit of guidance, but it is very broad.  This forum contains a hundred or so questions tagged with "grading", which is a good start, but I wonder if there are resources that provide a more cohesive treatment of the subject.
I want to hear about theories of grading.  I want principles which flow naturally from the theories.  I want applications and strategies which build on the principles.  I want to hear different viewpoints on the issues so I can evaluate their relative strengths and weaknesses as I come to understand my own thoughts better.  In short, I want it all.
Do any such resources exist?  Can anyone point me in the right direction?  If these don't exist, why not?

Are you asking about specifically the act of assigning a grade to a piece of work, deciding on the relative quality of work, or providing feedback?

To the first option, yes.  To the second, no, except insofar as addressing the first option spills over into it.  To the third, no, but that would make for another good discussion.

Practice!  I think it varies widely and is very subjective.  I heard one teacher say "Before coffee: F's!  After coffee: A's."  On the other side you have teachers who grade like machines.  My practice has always been how much progress did the student make compared to how much progress the student could have made, but that plays to my pretentious nature of feeling I understand humanity.  TLDR: There is no guide.  Do what feels right and communicate it clearly so your students understand.

Does your university offer tuition waivers for faculty? One option would be to take/audit an assessment theory class. At my university, we also have a teaching resource center designed to help with specific things like assessment.

Your question title does not match your actual questions.

I think the answer to your title question is something like "trial and error", and the reason why is related to the fact that you have to develop your own grading style because there's no single right way to grade. The only semi-objective aspects of a grading system I can think of are fairness and transparency, but there are different ways to acheive those two goals, and other valid goals besides those two.

I'd like to add one thing one Proffesor I had was good at. We had the last class before an exam solving exercises. He'd frequently exemplify an error and ask us what % of the points an exercise with that specific error should have. It really helped us understand what we valued most, and then he said more or less how much they would take away. Overall, it helped us out a lot because we didn't need to worry about changing notation (In logic AB = A.B), and instead could focus more on what actually mattered. Great teaching right there.

One principle is that the instructor should aspire to grade in a way that results in the grade being most closely correlated with those aspects of the knowledge and skills being assessed that the instructor considers important.
As an example, it is a common belief among instructors of university level mathematics courses that exam questions should test conceptual knowledge rather than facility with arithmetic and other low-level calculations. For this reason, most instructors would take off only a very small number of points, or not take off any points, for a small error of arithmetic in an otherwise conceptually correct answer. However, some instructors might consider accuracy to be an important skill to test in and of itself, and may impose a heavy penalty of points for even small arithmetic errors. So you see, the grading function chosen by the instructor reflects that instructor's view of what's important. Decide in advance what's important to you, and grade accordingly.

I'd add that it's then important to clearly communicate your philosophy of what's important to you, perhaps on your syllabus and/or during the first class session. Since different instructors consider different elements to be more or less important, it's only fair to make sure students know where you stand, so nobody is surprised later.

I would change the word instructors view to course objective. This is because math dept. teaches the courses from Basic Math 1 for Fresh Biz Studs to the Information Theory for Math PhD. The same lecturer, but two totally different objectives.

I am not sure whether this answer answers the question "How do teachers learn to grade?", or rather the question "How should teachers grade?"

@O.R.Mapper OP said "I want it all". My answer is a subset of "all".

This answer doesn't seem to answer the question at all. The question is "How do teachers learn to grade?" and then "Do any such resources exist? Can anyone point me in the right direction [implicit: to these resources]? If these don't exist, why not?". This is about the process of learning how to grade, not about the process of grading in itself. I'm just commenting this here since it is the highest-voted answer at the moment, not because it is particularly bad or something like that.

@AnoE to elaborate on my sarcastic comment above, my answer does not purport to be anything other than a humble attempt to satisfy at least some of OP's many requests. Among other things OP asked for "principles". I gave a principle. Anyway thanks, I welcome your feedback, and your vote (whether negative or positive) should you wish to cast one.

@DanRomik, I did not vote (I'm not on a crusade here :) ), I was just wondering why the answer has received so many upvotes. The irony is that the OP asks "(why) are there no formal methods/resources for this" and a answer that basically reinforms this problem (by giving a very subjective, non-formal hint on how to grade) is the highest voted. There seems to be something going on here. ;)

@AnoE I agree, clearly there's something going on.

There are a couple of restrictions:

Everyone must be graded equally.
A better answer should get a more points.

These two do leave one with quite many degrees of freedom, but satisfying even these two is not trivial.
My methodology is as follows:

Solve the problem I am about to grade.
Start reading the answers. Try to understand them.
After I feel that I understand most of the answers (there are no more surprising answers), start using the red pen. Mark errors, problems and omissions; maybe write comments to the extent warranted by the context. Give the obvious zero points or full points as well.
Come up with criteria for giving points.
After having marked several answers with errors etc., and maybe only after going through all the answers with a red pen, I start grading them. I postpone any difficult answers and put them to the bottom of the pile. I keep track of all ad hoc scoring criteria I come up with (known as a rubric).
Done.

Grade one problem at a time for all students; then tackle the next one. This helps with consistency.
This algorithm tries to make the scores as consistent as possible.
For the scoring criteria, I try to divide the question into separate and distinct components, so that it is possible for a student to fail any of them while succeeding at the others. This is not always possible.
Depending on the answers, I give out criteria which are worth a point (6 points for a complete answer are common hereabouts) and then simply calculate how many the student got. Sometimes, this takes the form of assuming full score and giving negative points for missed portions of proof or for misunderstood concepts.
I usually do not give out penalties for writing complete nonsense in the answer, but sometimes I do give a maximum; say, a maximum of 5 out of 6 points if the response equals a false claim about continuity.
This all is mostly based on folklore (discussion with more experienced lecturers) and on own thinking.

My approach is similar to yours. I'd like to add one step: Sometimes, at the end, I'll grab a subset at random, and sort them according to the number of points received. I then check to make sure I think the quality of the answers align with the number of points given. It's just a sanity check to make sure I'm being consistent, particularly when I'm grading a relatively large number of students.

Having taught in both the US and the UK there are different philosophies associated with assigning grades. In the UK work is compared to a fixed set of marking criteria. This means that everyone could get A's or no one could get A's. In the US most grading is done on a curve such that a predetermined distribution is achieved.
In the UK some portion of the work is double (and in some cases tripled, quadrupled, ...) marked. This means that someone else independently marks the work and the two markers meet to discuss any discrepancies. This provides direct feedback on your marking and the learning is rapid. That said, the process is time consuming since it doubles the work load (plus the time to resolve discrepancies).
In the US, assigning grades is really a two step process. The first is dividing the work into groups of roughly equal quality. To me this is the hardest aspect and requires the grader to understand what is important in terms of learning outcomes. Once the groups are made one then needs to decide how much variation from the desired distribution is acceptable. Sometimes there are clear break points and a bimodal (or trimodal) distribution more than a continuous normal distribution.

"In the US most grading is done on a curve" [citation needed].  I can't recall any of my classes being norm-referenced, they all had criterion-referenced assessments.   I had heard of strict curves being used in engineering and MIS courses, but I have to admit, I'd be pretty peeved if a professor tried to give me a lower grade than someone in a different section/semester even though my quality of work was better just because I was with a different cohort of students.

@guifa: As a U.S. person, I am likewise amazed/appalled that anyone grades to a curve (and never had that in my schooling). But I do get lots of signals that's the custom. Krantz, How to Teach Mathematics (American Mathematical Society), 3rd ed., sec 2.15 (on training TA's): "Likewise, the TAs can be allowed to set the curve for grading (under supervision) and to perform the other ordinary functions of the instructor."

Or: Richard Francis, "Common Errors in Calculating Final Grades", Thought & Action, Fall 2006, concluding section: "Teachers have an obligation to use good judgment and the option to draw the cutoff point for each grade level [after standardizing to a curve], as they deem appropriate." (http://www.nea.org/home/33194.htm)

Most of my college classes were graded on a curve, but usually not in the sense that grades were adjusted after the fact to fit a predetermined distribution. Instead, it was more like the difficulty of work and the grading standards were calibrated to the skill level of typical students such that, over the long term, the grade distribution should turn out to fit certain constraints (e.g. average C, <50% A-range, or whatever). I mention this because I suspect there's some disagreement about what is meant by a "curve".

I abhor "grading on a curve."  I've seen it happen far too often.

The variation in the difficulty of a test is likely to be as large or larger than the variation in the ability of a class, and this probability increases as the size of the class increases. Therefore grading to a curve is likely fairer than grading to a pre-determined script.

@JackAidley: That depends on what you mean by "fairer". It can be by-design that out of a total of four tests on a given subject, two are easier than the other two, even though each test grade weighs the same in the end. At least to me, the issue with grading on a curve is two-fold: On the one hand, the student cannot usually influence whether they take a given exam alone, or together with n other students, so it should not have any influence on their grade. On the other hand, I consider it fundamentally wrong to provide an incentive to negatively influence the grade of other exam-takers.

@O.R.Mapper: When I say variation in difficulty of the test I mean between cohorts or locations. This variation cannot be by design.

@Daniel - I'm not sure those quotes you've cited are encouraging instructors to grade to a "predetermined distribution." That said, I know some professors who would view some distributions as "too strict" and others as "too lenient," so they would curve to get a result they are more comfortable with. I suppose you could call that a "predetermined distribution," but, in my experience, that acceptable range generally covers a pretty wide swath, and can vary quite a bit from offering to offering.

@MattSamuel I regularly teach two sections of the same course (size=20-30 students) in a semester, and the level of sections differs a lot.  If I assigned grades saying top 20% = A, next 40% = B, next 20% = C, next 10% = D, next 10% = F (or something similar), then a generally mediocre student would quite easily get an A in one section and a D or F in another.  That's not hypothetical either, I've had sections I've given all but 1 or 2 students C/D/F, and others where I had almost all A/B.  The only way for a consistent grade regardless of cohort is going criterion-referenced.

@MattSamuel I teach foreign language.  For us, in intro level courses, an A-C are representative of particular levels of proficiency (defined for each course), and a D or F represents levels inadequate for mastering (or really even keeping up with) subsequent courses.

Rubrics
When developing an assignment, I always want a rubric to go with it. A rubric tells how you to grade the different results you would expect to see from a student.
Rubrics also help keep you on-topic for grading, to ensure that appropriate weights are applied to each of the areas. For example, a paper assigned in a literature class should demonstrate, with good grammar, that a student has read and understands the work, and is able to provide an analysis of the work at the appropriate level. A rubric here might assign point values to each of those areas: grammar, writing level, demonstration of content in the work, and literary analysis. An algebra assignment might use a rubric to allow an instructor to weight between using the right formula or procedure vs getting the arithmetic right. An assignment for a programming 101 course might weigh between stylistic concerns like comments and naming choices, correctness (does the program do what it's supposed to), and higher-level concepts targeted by the assignment (did they use an array with 10 elements like you told them, or did they declare 10 separate variables?).1
Rubrics keep you objective. They help you defend against charges that you prefer some students over others. A good rubric will allow you to objectively demonstrate why a particular assignment received the grade it received.
When I first started building my own rubrics for assignments, I quickly figured out that I'm kind of bad at it. A rubric tries to anticipate the kinds of things a students will do, to assign the appropriate results, and a new instructor just can't anticipate everything. I eventually learned NOT to build the full rubric in advance. You should know enough to have the category areas for the rubric done ahead, but how things break down within those categories isn't always clear at the outset, especially the first time through an assignment for a new instructor. Instead, I will rough grade a few or several assignments, and then use my findings from those first few attempts to flesh out my rubric. At this point, I always go back and re-check those assignments using the rubric, once it's written.
Sometimes I'll find something unexpected late in the grading such that I need to revise a rubric. This means going back and re-checking papers with the updated rubric, because, again, objectivity is the goal. In spite of this, I view building the rubrics as a time-saving measure. It lets me grade by looking for more specific things in the assignment, rather than subjectively evaluate quality. The specificity really helps with being fast.
Eventually, you want to be confident enough in your rubrics that you can publish them to students (though not everyone agrees this is a good idea), so that students can also have a clearer idea of what you expect. In some subject areas, I've seen rubrics given to students to use as peer-review guides. Good students, with good rubrics, can produce the same grade that would be assigned by the instructor in a peer-review situation.

1 As an aside, I remember being told in my own first programming class that a full half of the grade was dedicated to stylistic concerns, rather than correctness or assignment objective. Today I better understand some of the reasons for this: force students to develop good habits early, have some easier "soft" points to buffer the grades (see this Erno de Weerd's answer for why that's a good thing), force students to spend time in design instead of just jumping into code, and because naming and style really is that important to programmers.

@sdg238 You should be writing the rubric when you create a test. How can you grade a piece of assessment if you do not know what it has  been specifically designed to assess? And yes you should give the students the rubric so they know how best to succeed and will question your marking far far less. It saves everyone so much time in the long run.

My experience as a grader (TA): Let's say there are four problems in the homework set.  The professor has established how many points each problem is worth.  First, I work the problems myself, consulting the solution key if necessary.  Next, I start looking at some student work for Problem 1.  When I encounter a solution that is completely off base, that's easy -- the score is 0.  I try to find a couple of representative solutions of "not quite right" and "deserves some partial credit."  I use those as reference points and come back to them as needed, to make sure my calibration is remaining constant -- especially if I get interrupted or if I get tired.  It's easy to get tired if you're grading 50 to 100 submissions.
To check my calibration, I would go back and check the first 5 to 10 that I did, to make sure I hadn't slid in one direction or another as I went along.
Once in a while someone would use a completely different approach than what I used, and then I would have to put on my thinking cap to make sure it held water.
Similarly with exams.
In conclusion, if the problem is worth 3 points, it's helpful to hold onto a sample one-pointer and a sample two-pointer to use as reference points.
In terms of feedback written on the papers... I often wished I had some rubber stamps, such as "Does not follow," and "How is this germane?"
If there was an extensive calculation such as matrix manipulations, I would circle the first value that was in error.  Then I would assume it was correct and check if the subsequent calculations, and logical conclusions, followed.  If so, I would take off a bit but not a whole lot.
If there were multiple errors in one problem, I would look at the paper from the opposite point of view.  Instead of looking for meaningful errors for which to subtract points, I would ask myself, is there anything of value in this paper?  If so, partial credit.
If the student was struggling in general, I would make a point of looking for something on his paper that I could fairly praise.  It is so discouraging to get back an assignment with nothing but negative feedback on it.
I learned most of this by grading alongside more experienced TAs.  The rest, by doing.
When I was grading technical writing papers, I would provide feedback on drafts and ask the student to make some improvements and hand it in again.  Then in the final version I would mainly pick out some aspects to provide positive feedback on.  I figured, this would help the student have a clear idea of what I was looking for, in preparation for the next assignment.
I was looking for growth in writing, ability to write a good outline (which I required that they hand in), ability to self-edit, ability to respond to developmental guidance.  I didn't see it as my job to separate the A's from the B's or the C's.
Perhaps this is not as theory-based as you were requesting.  But it worked for me.

My mother wrote up a true story about a professor or hers who looked for succinct essay answers.  He said he graded by tossing the projects (each of which was neatly stapled) down a staircase.  In other words, he gave the best grades to the shortest papers (assuming they all addressed the question to a reasonable extent, which they did, since it was a graduate level course).

I like the anecdote at the end. Gives new meaning to "grading on a curve".

I have some experience in this. My view is that grading should be chiefly about fairness and consistency.
By fairness, I mean the exam should have enough questions to be marked out of 100. It should also be constructed so that the results will form a bell curve around 60, for arguments sake, with the first standard deviation at 12.5
In this way, students can be compared against each other. The actual marks can then yield a "z score". This might look like 58 ± 10, meaning the test was actually harder than normal, but quite bunched. On the other hand It might look like 70 ± 15 which would indicate too easy a test, on average, but too many found it too easy.
In both cases, this z-score can be used to "standardise" the results.
so in the hard case (58 ± 10), someone who got 63 (above average), would get:
(60) + (63 - 58)*12.5/10 = 66
in the easy test, someone who got 63 would get:
60 + (63 - 70)*12.5/15 = 53.
This also helps fairly align groups of students from one school compared with another, provided they all sit one common exam - once.
The last point is about consistency. Was last years test harder than this years ? This is important to keep standards consistent across years, so that dilution or excessive rigour is also protected against. This is more political, but interestingly tends to be the case in more communist countries.
In cases where i've marked lab work for 20 students at university, I will get the books and spend considerable time making a rough ordered list from best to worst. I will start with the best work, and assign that the top mark, then work my way down, using the best one as the benchmark. The mark will be pencilled in, just in case I need to move things around as I work through. Then I'll make a final run through to assign final scores.
One final thought - I always give full marks for the correct answer (in maths), regardless of showing the "working".
However it is in the students interest to show working, because marks can be awarded in this case, depending on how far through mistakes were made.

This answer is about resources for understanding grading philosophies and how those can be practically enacted. This was my interpretion of the OPs main question.

Do any such resources exist? Can anyone point me in the right
  direction? If these don't exist, why not?

One book that came highly recommended to me was McKeachie's Teaching Tips (http://www.cengage.com/c/mckeachie-s-teaching-tips-14e-mckeachie
) It includes three chapters on assessments and grading:
"Assessing, Testing, and Evaluating: Grading is Not the Most Important Function", "Good Designs for Written Feedback for Students", and "The ABCs of Assigning Grades".
The book stresses that the choice of assessment and non-grade feedback are just as important as the grading strategy. The philosophy and practice of these items should be complementary.
Other potential resources (which I have not read personally) are: the chapter "Grading Practices" in Tools for Teaching by Barbara Davis and the book Effective Grading: A Tool for Learning and Assessment by Walvoord and Anderson.
In addition, you may want to google "grading strategy for teaching and learning", since many major universities have centers for teaching and leaning which include grading ideas and resources for faculty.

When I was teaching maths in secondary school, I ran into an interesting issue: I was too precise in calculating grades. (our grades range from 1 to 10)
This might have been be due to the fact that I was a math teacher. I would have a very precise weighing of the individual part of the tests and the end grade would be rounded from an indefinite number of decimals to the nearest first decimal.
Until the moment I sat in a meeting to discuss the grades per student by all teachers. A PE teacher would adjust his grade by a full point on the fly to allow a student to have a nicer list... The contrast with my precision made me rethink my grading.
I ended up with giving whole grades and not going below 4. My reasoning:

Any weak student receiving less than a 4 would hardly be able to compensate a 1, 2 or 3 and a 4 would already fail them. A strong student would be able to compensate a 4 (a 7 or 8 would be sufficient).
I graded the exercises separately, assigning points to each exercise in ratio to the other exercises. Calculated the sum of all the points and made grade 'buckets'. E.g.: 0-20 points => 4, 20-30 points => 5, 30-40 points => 6 ... 80-90 point => 10

The effects

Students never felt locked into a bad year grade due to one or two low (<4) grades
Less 'living on the edge' by students: "If I can get a 5.75 or higher, my year's average will be 5.5 so I will pass"
A 10 was reachable even if you made a couple of mistakes
No fake precision; I didn't feel comfortable with comparing a student's skills in geometry to the student's skills in algebra and expressing the difference in one decimal.
Less discussions with students about their grades, in most cases getting a few more points for an answer would not change their grade.

Multiple interesting comments (including content in answers) on this one.  e.g., I liked this part from Dave Kaye's comment:

There is no guide. Do what feels right and communicate it clearly so your students understand.

The "question" section asked these questions:

Do any such resources exist? Can anyone point me in the right direction? If these don't exist, why not?

Those are excellent questions to which I am not directly answering.  However, I do address the topic of the title question, "How do teachers learn to grade?"
Growing up, I heard that before a person becomes a teacher, they go through a process of being a "student teacher" where they learn things like this.
Well, let me tell you my experience.  (I imagine this will raise some eyebrows.)
A college reached out to me and asked me to become an instructor.  I agreed.  I don't recall ever being taught how to assign grades.  So I did things by trial and error.
It turns out that the college department I joined was failing in multiple ways.  The drop-out rate was high.  For those that didn't drop out, the department chair taught courses and gave students solid As, but they obtained degrees without sufficient skill/knowledge.  I decided to do something about this, and I gave lower grades when I determined they were deserved.
Sometimes, grades would end up being too low.  A student once said that I took the Gandalf approach to making tests.  ("You shall not pass!")  I recall the time in my second set of classes where the top grades on the midterm were something like an 82, a 76, and a 58.  Clearly I didn't want to flunk the vast majority of the class (which might have triggered numerous more drop-outs).  My tests were not too hard: The intent of this department was to train people well enough to take industry certifications, and those were slightly harder than what I gave.  So I had to be stern and have them rise to the challenge.
At the end of every quarter, after final exams were collected and graded, I looked at the grade of every student.  Then I would make adjustments to the value of assignments and tests, as needed, so that the final grades made sense to me.  I had some students who were clearly trying the hardest, succeeding at tests the best, and learning the most.  I figured they ought to get an A, and any deviation from that would be a failure of the assessment system, not a failure of the student.  So I made sure the people who deserved top marks got them, and I looked at the grades of every other student and thought about what their grade looked like and how well they were learning the material.  I made sure that nobody got a lower grade than I thought they deserved, and the vast majority of the students got exactly what grade I thought they deserved.  If that wasn't true, then I adjusted some assignment/test weights equally across the board.
In the end, I was usually satisfied with every student's grade, but sometimes a couple of students would end up with a grade that was a notch (or maybe two) higher than I intended, and I couldn't adjust their grade without making someone else look wrong (giving someone else a grade lower than deserved).  In those cases, I just figured that the student, whom I thought was performing a bit low, must've actually done a bit better than I thought, and so I finalized things with them getting a slightly higher grade than I would have thought.  (I figured that even if a student got answers right due to luck, I had no grounds to penalize them.)
There was some grumbling about people not getting solid A's as easily, and the increased workload I may have been expecting, and tests being much harder.  Nobody ever actually challenged a grade of mine, or asked me why they got the grade that they did.
I view the results of my efforts as entirely positive.  Grades were doing a better job of reflecting reality.  I feel like I improved things as much as possible without causing so much student frustration as to skyrocket the dropout rate.  Actually, as my involvement increased (particularly as I led the department, since the department chair left within 90 days of my start), drop-outs happened less.  More accuracy, stronger resulting students, and better critical numbers all seemed like good things.
I do recall the college president speaking to the instructors, showing that too many As were being given out.  In the entire college, over half of all grades were As, and most of the rest were Bs.  He told us to make such good grades harder to get.  (I happily thought about how I was doing exactly that.)  Besides that one point of instruction, I don't recall other teaching about how to assign the final grades.  There were some guidelines that had to be followed (relative weights documented on the syllabus, rubrics for some specific college-wide assignments), but we still had some flexibility (which I definitely utilized) and ultimately it was up to the instructor's authority to determine what made sense.
So, in my case, the answer was largely trial-and-error (but fixing the errors before the finalized grades got posted).  I'm sure that at another university I've been a part of, graders had specific rubrics about everything and they had to follow those very closely, and be able to justify how every grade fit within the rubric they were assigned to, with much less flexibility.
Like another answer of mine, the ultimate conclusion is that specifics vary A LOT between different organizations (including different institutions, and possibly between different departments.  Different instructors are very likely to have significantly different experiences.  Although I'm sure people have written books on the subject (as well as all kinds of other subjects on the planet), that doesn't mean that instructors actually go through any sort of centralized/standardized training in practice.  I know that the state I live in has some standardized test for teachers of Kindergarten through 12th grade, but ironically, there can be a lot more variance in the higher education.

There are some great answers here so i'll try and be more direct about the question "how do teachers learn to grade?".
We learn to grade from observation, implementation, and feedback.  It's crucial to see how others have marked in your subject area to get an idea of what is top level, mid level, etc.  From there you can mark work and ask another teacher to take a look at some items and give you feedback which you can use when you mark the rest.
If this isn't an option and you're really flying by wire, then grouping work into piles based on a quick look "Good", "Average", "Improvement required" and then from there you can make each group into 3 piles of "top level, mid level, low level" and assign grades A*- Ungraded (or however it is you do it at your end!).  SHOW THE STUDENTS EXEMPLAR WORK.  I cannot stress this enough!  If they don't know what amazing work looks like, how will they know where they are?  If you show them "This is a grade A item from a similar question last year!" then they can understand your expectations.

I had some students who were clearly trying the hardest, succeeding at tests the best, and learning the most. I figured they ought to get an A

This part of another answer deserves to be highlighted. While I'm strongly for objective grading, we must realize that most educational institutes and societal expectations compare grades between courses, and some teachers close more eyes to serious conceptual errors than others, so I think fairness requires us to ultimately assign grades that convey to others the level of mastery of the course content that we feel the students have.
This has two implications. I personally feel it is necessary to give raw scores for assignments and tests that reflect objectively how much the students grasp the course content. However, I equally gladly adjust the final grades (maintaining the relative order) that would end up in their academic records so as to give others the right impression. For example, if we teach a course that involves much more difficult concepts than the average course, then it makes no sense to give a B to some student who normally achieves A+ in ordinary courses and has put in the same hard effort into this course, just because the raw score says so, since this would only give other people the incorrect impression due to not knowing the relative difficulty of such a course.
Ultimately, I think that one should give a grade that one can defend as being exactly what the student deserves to get on his/her academic record, but at the same time give detailed feedback totally apart from the grade, so that the students know precisely what they know and what they do not know. That pedagogical component of grading is far too often lacking, especially in mathematics, because a lot of graders faced with an incoherent answer try their best to figure out what the student means and even attempt to patch a fundamentally flawed answer, giving more credit than is usually due. This results in the students rarely aware of their mistakes, and worse still some of them realize (and tell others) that they can get away with handwaving.

Incidentally, and not surprisingly, good students like this approach to grading.


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If a paper or software is released to the public, can the university still file a patent?
It is my understanding that patents can be invalidated if there is prior art to the technique at hand; DJB has a piece that would suggest that this way authors can inadvertently invalidate their own patents, if not being careful with information disclosure.
http://cr.yp.to/patents/us/4200770.html

Diffie disclosed the idea of public-key cryptography at a conference
  in June 1976. Diffie and Hellman also distributed preprints of their
  ``New Directions in Cryptography'' paper, which disclosed the
  Diffie-Hellman system, at that conference and by mail. For example,
  Mike Matyas received a copy in August 1976. The patent was filed in
  September 1977.
Under United States case law, a document has been published if it
  ``has been disseminated or otherwise made available to the extent that
  persons interested and ordinarily skilled in the subject matter or
  art, exercising reasonable diligence, can locate it.'' A patent is
  automatically invalid if the patented invention was published more
  than a year before the patent's filing date.
It appears, therefore, that the Diffie-Hellman-Merkle patent was
  invalid. In the subsequent court case MIT v. Fortia, another patent
  was invalidated for the same reason: the inventor handed out six
  copies of a preprint at a conference fourteen months before applying
  for the patent.

How does this work in the general case?  Is it important that in both examples a whole year has passed between the publishing and the patent application?
Is it necessary for a significant amount of time to pass between the publishing of a paper, and the patent application, for the patent to be subsequently declared invalid?
Specifically, if one's university explicitly claims that it has no interest in one's copyrighted work (whether books, articles or software), and no interest in any part of any revenue from such copyrights, but that patent revenue sharing and disclosure to the university of the patentable ideas is mandatory (IU), can one get around of any future claims for patents by simply releasing everything open-source and publishing all pre-prints before the university's patent office can get their hand on any of the research?

You need to talk to a lawyer, not just Random People on the Internet.

"A patent is automatically invalid if the patented invention was published more than a year before the patent's filing date." So yes, the year is important.

Yes, in most cases, dissemination of a patentable invention by academic publication (papers, talks, code) constitutes prior art and will result in a later patent application being rejected. That is why people and institutions who intend to patent their discoveries are very careful about what they publish, and when. (Basically, publish after the patent application is filed.)
Regarding your patent evasion scheme, it would probably work in practice, but could lead to severe retaliation from your institution. You said yourself that the policy is to report all patentable inventions. By not doing so, and publishing without first enquiring whether your employer wants to patent the invention, you violate the policy... And, given your question, you would be doing so willingly and in bad faith. This sort of thing could get you fired. And, it could get the papers retracted (look at some of the examples of this on Retraction Watch).
Finally, one piece of advice: if you're so afraid that your employer owns the IP you create, enough to look for strategies to remove from them some of the IP they pay you to create, you should consider quitting. It doesn't look like you have a healthy relationship with your employer.

Your suggestion for unconditional quitting is misguided, and your presumption that everyone in universities is compensated for their time, on the merit of what their time is worth, is misinformed.

@cnst my point exactly! If you strongly feel you are not compensated for what you're worth, quit and find another job... But feeling that you are underappreciated definitely doesn't qualify as a reason to violate a contract you signed

F'x you are assuming full employment.

Actually, if you're employed by the university and publish in violation of university policy, you're not only opening yourself up to being terminated, but to lawsuits. This is particularly true in this case where you're violating the policy in bad faith (e.g. with the intent to deprive them IP owned by them.) And, no, this does not assume full employment.

In response to your specific questions, yes, it is significant that the disclosure occurred more than a year before the patent was filed. In the U.S., there is a one-year "bar-date" after public disclosure of the invention covered by a patent. Most of the rest of the world does not allow any period between disclosure and patenting; once you've disclosed, the invention is no longer patentable in those countries (though it may still be patented in the U.S. for up to a year.)
As noted by F'x, sabotaging your employer's patent claims is a sure way to make a lot of trouble for yourself.


text:
Graduate math student migrating to engineering?
I don't know how to start, truly, but lately I've been involved with some projects in pure mathematics and I've grown frustrated and disappointed. I don't think that pure mathematics is so inspiring; my intent is to move on to study some applied math but most teachers in my department aren't that dedicated to it. All I see are theoretical approaches to problems "that applied sciences may be interested some day".
By talking to a colleague of mine who is seriously considering moving on from Math to Physics, he told me of some engineering departments who might accept someone with a master's degree in their Phd programs. There are some areas I like that might have a connection with what is studied in some Engineering Phd programs, like applied ODE and Dynamical systems and I'd love to put some programming on what I do.
But every teacher I talked about this so far tells me to avoid this kind of migration, since it brings a loss of academic focus and it might be hard for me to find a job later as a teacher. There is no strong tradition in Mathematical Engineering as there is in other countries (I know that such courses exists in Italy and some other European contries).
So I'd like to know some thoughts from more seasoned students and researchers out there. Any advice is welcome.

There's not much difference between modern physics and pure mathematics.

@DonAntonio, mathematical engineering, as I said, is not to be taken lightly. Take a look: http://www.polinternational.polimi.it/index.php?id=184

I might like to program but that doesn't mean that I want to make a living out of it. Though I admit that there would be so much easier to find a good paying job, wouldn't it be better just to graduate again in CS?

Yes, but if I had to choose between a MS or PhD or a bachelor's in CS the second option (in Brazil) would be better. I could get a better job that way (since PhD and the CS would both take 4 years).

Math-Physics-Applied Physics-Engineering...  Sure, you can go/from from most Science, Engineering, Math programs and careers.  There's also blends, like Engineering Physics, Architectural Engineering.  If you want to apply math, then there are many ways in STEMA (STEAM?) to apply math.

The only problem with switching to a particular field of engineering is that you'll be missing a core set of knowledge particular to that discipline that will hinder your progress for a while.  For instance, you would probably do great in many electrical engineering sub-diciplines, but if you've never taken a circuits or signals course, you're going to be lost for a while before you can learn that material.
If you already have research experience, that will count for a lot, but I would suggest finding an engineering program that would allow you to take a few undergraduate courses during your first year or two in order to get up to speed.  If you find a professor that is looking for a mathematics-savvy graduate student to fill in the gaps in his/her lab, that might be the best way to get your foot in the door.  You've got skills that could be very valuable to the right lab, and if you use those as leverage to join a particular lab/research team, you'll be able to fill in the missing pieces to your new field and move forward with your own degree.

The most likely domain of interface for a mathematician with engineering would be in the realm of "computational engineering," in which numerical algorithms are used to study physical and engineering systems. This work is highly interdisciplinary, and requires close collaboration among all of the different researchers involved, as very few are experts in all of the areas with which they are concerned.
However, there is a certain amount of logic to the idea of staying in one's "home" discipline. It makes it easier to figure out "who you are," which can make starting your career a bit easier. One possibility might be to pursue a degree in applied mathematics, in which you study problems relevant to engineering, rather than remaining in "pure" mathematics. This might be a reasonable compromise that keeps you in the mathematics field, while still allowing you to pursue topics in areas that interest you more.

I second this. Applied math is the way to go. I would look for schools where the two departments (math and applied math) would be separate and then apply for applied math. It will make good use of your pure math background while giving you full opportunity to work with physical/engineering sciences. You get a little bit of taste of everything including plenty of coding.

I have been in your shoes, as I migrated from mathematics to computational engineering.  While my math background gave me some advantage, I remember it was difficult to make the transition because I was very unfamiliar with a lot of the key concepts in engineering.  What really helped me was watching online courses (MIT, IIT, etc...) in the material I was missing... Of course, I had an entire year to prepare for it.  If you have a lot of time to make the transition, by all means do so and you shouldn't have "too much" trouble.  But if you're pressed for time to make up for a lack of engineering background, it can be quite overwhelming.  It's best to hit the ground running in graduate school.

Most CS graduate programs would be quite happy to admit a math major. It might be tricky early on if you have zero programming experience, but depending on the kind of work you're interested in, you could be in a strong position.


text:
Resource for learning about research funding system in the UK/Europe
I am currently considering to take up a tenure-track job in computer science at a UK university. I have little (i.e. no) experience with the research funding situation in Europe.
Is there any resource where I can start reading up on the research funding opportunities and the general system in place in Europe/UK?

There are databases that the unis subscribe to. A basic starting point would be to look up the reseach councils (EPSRC is my one).

For the UK, you'd be immediately interested in EPSRC and the European Union opportunities (Horizon 2020 being the main agency). Coming to the UK from abroad, you'd also be eligible for a Marie Curie Incoming grant.

Without any experience, and without knowing your nationality (from EU or not) and your publication track; I would recommend to ask from the institute you will be working for any available fundings. Most UK universities do provide some fundings for various projects they are involved in. The best way to do this is to ask your research group manager for any recommendation.