Is community college GPA not included as the net GPA on the resume?

I'll assume this is the US. Most places will want the average over the four years, just as if you had switched from one four year program to another.

You can list the two separately if you like, unless you are filling out an online form that only permits one number. But if you need to report a single number you should provide the most honest weighted average you can come up with over the four years.

Normally courses are "weighted" by credit hours or some equivalent. Normally a 4 credit course meets more often than a 3 credit course. The other variable is the "quality points" of a grade.

Complications arise when one school is on a system where an A counts as 4.0 quality points but another uses a different scale, perhaps including A+ which is above A, perhaps 4.5.

But also note that the GPA isn't the only consideration in applying for jobs or for further education. The actual grades in "important" courses might be more important (and often is). There are many other factors that let a committee make a somewhat valid prediction of a person's likelihood of success.

But don't just report the final four semesters without any comment. That will give an incorrect picture, and, in your case, seems to be a disadvantageous one.


Does considering someone's work regarding a piece of literature constitute plagiarism if you knowingly derive/spark ideas from it and don't cite it?

Why not cite things clearly if you know where your own idea 'derives/sparks from'? Laziness? Shyness?

Citing somebody else's work won't diminish the quality or significance of your own contribution, on the contrary.

And readers will be able to understand your foundations and line of thought better as a result.

And ultimately it saves you a lot of headaches, as you don't have to worry if you should - have - cite(d) other people's work that stimulated your thought.


Is research output determined by your type of institution more than your skill?

Almost definitely. It doesn't matter how much skill you have if you do not actually use the skill. There, however, are people at R1s who do not have the needed skills to be successful researchers.

Your comments like

  Consequently, people who look at Scholar B's academic record ten or twenty years after his Ph.D. confidently conclude that he is a mediocre scholar, who would never have been fit for an R1 that hires top scholars.

and

  But Scholar B ends up being deemed "not very smart" because he produces little research.

are not universally true. I don't know many people who judge intelligence (i.e., smartness) based on research output. In my field we often have to evaluate how people who chose to work in industry will be able to fit into an R1 environment.


How to associate an arxiv paper on Google Scholar with the rest of my account?

ArXiv papers take a few days to get indexed by Google scholar. It should show up eventually. The procedure to add it your profile is no different than with any other paper from any other database.


Is it a self plagiarism to reuse a section of my previous paper in a new paper?

Technically, it is not self-plagiarism if you were to cite the relevant material, even if it's your own. It would be advisable if to rephrase the section. If considerable amount of detail is repeated from thee pervious paper, it would be better to have consent from your publisher before hand.

I notice this many times among authors. Those who make a minor improvement over their own research tend to have major portions of their old papers rephrased (some even repeated, but again, that's not encouraged). As long the overall concept is novel this won't be a problem.


Citation for a processor instruction set?

Cite their manual

The links to the manuals seem to appear at the reference sections of the respective Wikipedia pages.


I would also agree with your gut feeling in this particular case. I can, however, think of a scenario where a declined award/scholarship should be included on your CV. In countries where you pay to study at a university, you can apply for scholarships/postgraduate awards/student funding. There is often a limit on how much funding an individual can accept. So, say for example you applied for funding from A and B and that these Funding Agents only give funding to high achievers. If you are awarded X from Funding Agent A and Y from Funding Agent B, and you can only accept the funding from Funding Agent A, I would say it is still acceptable to list that you were awarded funding from Funding Agent B but that you were unable to accept it. In cases where the award implies certain personality characteristics/strengths (but doesn't directly compare to the place to which you are applying as in your example), it can be advantageous. I hope that this makes sense.


Does one need to be affiliated with a university to publish papers?

Absolutely not. Affiliations do not matter; what matters is the value and the fit of the contribution to the journal or the conference to which you are submitting.


Zotero: referencing multi-word organisations like "World Bank" so that it's not, "Bank, World"

Found the answer:

https://forums.zotero.org/discussion/3275/entering-corporate-authors

There's a tiny box to the right of the author names, that if you click on, you can change the setting to a full name.


Transitioning from experimental to theoretical research after masters

This depends strongly on the branch of physics. For theoretical PhD work in high energy physics you need a very profound theoretical and mathematical background. A purely experimental master work would make me suspicious if you can catch up the lost time to learn by yourself this necessary background.

In branches like nano and quantum physics due to the size and nature of the investigated objects, a strong collaboration of theorists and experimentalists is very common and practiced and even within a master or PhD work project these systems/objects can be and are often modeled/simulated/calculated additionally to experimental measurements by single students.

Your question is very valid, for PhD positions in top universities and groups the group leader will take an in-depth look on your background. Switching form theoretical nanophysics in the master work to theoretical high-energy physics PhD is much less troublesome than from applied physics, but also not easy. The likelihood for tenure is in the bigger branches like condensed matter physics much higher than in small niche branches. The smaller and more competitive your aimed branch is, the earlier you should work towards it. And in addition to computer science or math, even if you decide to become a pure theoretical physicist, you still have to have a good overview and understanding of experimental methods.

Many physics students know before starting to study that they want to work later in hep or astrophysics or ... and specialize over their studies by attending special lectures and seminars ("Sheldon-Nerd-syndrome"). Promising that you will catch up this content will not help you a lot, as it can take years to understand, apply and further develop some physical theories.

Speak to professors in the field you are interested in or look simply on some faculty homepages, if the field is split up into experimental/theoretical/computational groups. As said, for some fields experimentalists and theorists work within one group, for other both types rather and only interact in big collaborative projects or over publications and the single research groups are purely theory/experiment oriented.


How to write an email to request a dataset to a professor

Professors are just normal humans, even at MIT. Be friendly and brief. How about this:

Subject:

  Request for dataset used in [article name]

Body:

  Dear Professor [last name],

  on page [page number] of the article "[article name]" you are referring to a dataset consisting of [elements of dataset]. I am currently working on _____ and would like to ask if you could send me this dataset for further analysis as it would help me [benefit for you, e.g. "verify your results"].

  Thank you,

  [your first name] [your last name]


How is employment experience considered in PhD funding decisions in the United Kingdom?

I help to run admissions for a DPhil (doctoral programme) in the social sciences at Oxford. Professional experience is of very minor importance during the admissions process (except where it has some truly central role in the research project). The four important things we give significant weight to are

academic transcript,
quality of research proposal/statement,
admissions interview.
academic reference letters.

These will typically also be the main factors for funding allocated by the university (e.g. Clarendon, DTC). In particular, the panels that award these scholarships will have access to the same application material as the admissions coordinator, along with notes from the interviewer.

My suspicion is that a more vocational area might give more weight to practical experience. For example, someone with legal practice experience, or work as a laboratory intern might respectively have a bit of an advantage for a law/lab science DPhil. But the general understanding at Oxford is that academic excellent trumps all other considerations.


Question on rationale behind doubled "Int. Math. Res. Not. IMRN" journal name

This is just speculation, but the reason could be because of the slightly complicated history of the IMRN journal.

Throughout you should remember that MathSciNet grew out of what originally was a print publication called Mathematical Reviews. It was extremely important that they have a uniform house style for referring to journals.

Originally there was a journal called International Mathematics Research Notices published by Duke Univ. Press from 1991-2001. On MathSciNet its abbreviation was Internat. Math. Res. Notices. When the journal moved publishers to Hindawi in 2002, the abbreviation became Int. Math. Res. Not. on MathSciNet. In 2005 Hindawi started a new journal called International Mathematics Research Papers, which was indexed by MathSciNet under the abbreviation IMRP Int. Math. Res. Pap.

In 2006/7, the two journals were both transferred to Oxford Univ. Press. There was some relationship between the two journals (I remember seeing it in an old author submission guideline) and the two are treated as sort of a pair. Probably in an effort to clearly distinguish the two journals, either OUP or MathSciNet decided to list the two journals as, respectively, International Mathematics Research Notices. IMRN and International Mathematics Research Papers. IMRP with abbreviations Int. Math. Res. Not. IMRN and Int. Math. Res. Pap. IMRP.

In 2009 or thereabouts, OUP merged IMRP into IMRN.

I would surmise that the "duplication" appeared in an effort to add some redundancy for better disambiguation of two journals with extremely similar titles. Now it survives as a vestigial testament to the journal's history.


Wireless microphone system for giving lectures

I had the same problem.  To make me quit complaining, the department chair bought a RevoLabs USB wireless microphone.  I kept it in my office, plugged in to a USB charger wall wart, and took it to classes with me.

I'm still teaching a bit, even though I've retired, but the RevoLabs mic somehow "became lost" after I turned it in.  A new one is too pricey for me to buy at over $200, so I bought a "Fifine" USB wireless mic from Amazon.  It's neither as high quality nor as unobtrusive as the RevoLabs mic, but it's also $40 and works fine.

My use case is recording my lectures with PowerPoint; I then post a "narrated slides" video for students who missed the lecture.


Putting a scholarship received for upcoming summer school in CV

Sure. Just make clear the scholarship it is for a date/summer school in the future. You could also add sth. like planned/forthcoming/... or the like, to make this point clear.


Why is my paper "under review" if it contains no results?

There's a good chance the journal is getting confirmation that it is indeed a new problem. The fact that it's new to you does not mean it's actually new - perhaps you've simply not seen the paper(s) that stated and maybe even solved the problem.

The journal could also be confirming if the problem is actually interesting. It's not so difficult to come up with a new problem, but coming up with an interesting new problem would be something else.


Can I choose the initials I want to use when publishing a paper?

I have two middle names, and have faced a similar dilemma, since there is a great deal of inconsistency not just with journals and citations but in how pretty much all bureaucratic systems choose to handle names.

In making your decision, there are three main cases to consider about how your name will be used:

How your name appears on your own papers: With pretty much any reasonable publication, you should be able to specify your name precisely as you wish it to appear.  Just be consistent from publication to publication.
How you are identified in databases: This is important because this helps guide other people's discovery of your related works, but you are at the mercy of whoever coded up the database and how many bad assumptions they made about names.  Fortunately, this is why ORCID was created, because names aren't very good unique identifiers in the first place.  An ORCID, however, provides an easy hook for programmers to organize your publications correctly.
How people write your name in citations: This is (hopefully) the most common usage, but also the one you have least control over, since people and style guides may mutilate your name in any number of creative ways, especially if your name contains non-English characters.  Even closely related languages like French, Spanish, and German often get mangled in transliteration (e.g., losing their diacritics).  Fortunately, it matters somewhat less in this case, as the citation is really just a pointer to your own paper.

My personal solution has been to simply use no middle names, since I did not want to end up with one being picked over the other.  That works for me partly because my name is relatively unusual to begin with---somebody with more common first and last names might be much more motivated to include one or both of their initials.


Could a second masters hurt my PhD application because expectations will be higher?

In the parts of academia I'm most familiar with (mathematics, US), even one master's degree is not a necessary prerequisite for a PhD program.  Some students do improve their application and chances by doing a separate master's degree, but (when a master's degree is not a necessary prerequisite) I would advise any student to also apply for PhD programs and see what they get into.

In your case, having completed one master's degree in your field and having the desire to go on to a PhD program, I think you should certainly apply to PhD programs.  If there is a second master's program that you are extremely excited about -- in particular that you think is prestigious, would improve your academic record and offer you critical new skills that you would not necessarily pick up in the PhD program -- then you should apply to it as well.

If you get into a solid PhD program with funding, I advise you to take that over any master's program.  This is your life, and at some point you will want to have your student days behind you while you are still somewhat spry.  However, if you get in only to PhD programs that are substandard and you get into a very good master's program, then yes, taking that is probably a good investment for the future.

All this is definitely something to discuss with your current thesis advisor, by the way.


What to do when meeting your expected professor even before the interview?

Just for reference to others who might have the same question. The meeting was amazing, we communicated at Dinner, I asked many questions as well as she did the same to me.

In the end, I got questions if I am really interested to join her group..and my answer was yes since I saw she is ambitious, relaxed, open-minded, and collaborative. At the same time, I got semi-confirmation that she will do her best to make me the first option among candidates.

Therefore, my answers would be:

This type of meetings can really push the candidate acceptance and support forward.
following up Roland recommendation, be yourself and relaxed.
Ask your questions, try to see if your future supervisor is collaborative and motivating.

Best


Is it ethical/acceptable to take courses for the sole purpose of getting a reference letter?

Students have lots of reasons for taking courses and I don't think I want to be in the business of telling students that there are right and wrong reasons to take a class. I certainly think it's a good idea for prospective PhD students to think about who might be good letter writers early on in their program and to make sure they work with some of them — not doing so can make the academic job market very difficult. I don't see this as being substantively different. If you take the class, do well, and then ask for a letter, you might get a good one. Or you might not. So I'd say go ahead.

That said, there is something very mercenary about the way you have phrased your question that makes me skeptical. Do you really think that working with faculty wouldn't teach you anything? If it's true that the only reason you want to take a class is because of the letter you might get, something seems off. Maybe your interests are different enough from the professor's that I'm skeptical that this person would be such a great letter writer for what you want to do.

Being able to excel in a Masters program means not resenting the idea that you may have to learn from professors when you could "just read the book." I think it's OK to take a class for a recommendation but you should use this as opportunity to learn something you are passionate about in ways you could not with just the textbook.

Talk to the professor. Let them know you are an advanced and passionate student. Get feedback on your work. Go beyond what is just in the book. If you do that, you will get more than you would otherwise. In the process, you will also earn a much stronger letter. If you can't get over that hump, I suspect that your recommendations — and your experience in grad school — will underwhelm.


Structuring Dissertation as Thesis Rather than "Standard" Bachelor's Structure

LaTex is irrelevant for the question. But there is no reason not to do it your way provided that there aren't rules that prevent it. But your advisor is the best guide here.

In fact, since you intend to move to doctoral studies the experience would probably be worth any additional effort.

But you need to get some assurance that you won't get late push-back on it from anyone. Again, your advisor, or other faculty should be able to give the best advice.


Should I secretly record a meeting to prove I'm being discriminated against?

No.

Such action should be the very, very last resort, and only undertaken if you have taken legal advice on whether it is advisable to do so.

As a UK student, you should have support available to you from the Student Union, which will almost certainly include disability representation.

The Student Union will be able to advise you on how to proceed on this matter, and possible provide you with a third party representative to join you at any meetings you have.

Also, you mention emails that exist 'about you.'  You are within your rights to request these to see what they say by making a freedom of information request.  Again, seek advice first before undertaking this action.


Denying offer of admission from graduate school after accepting

Presumably the school you heard from was not your first choice.

I'd just be as upfront as possible, with everyone. Next step is probably to contact the schools and/or professors you haven't heard from, say that you have another offer, and ask if they can give an update on the timing of their decisions.

Depending on what those schools say, contact the school you were accepted to and request another extension until the specific dates that the other schools gave you.


Letters of recommendation: what information to give to a recommender

You won't find a better or more complete answer to this question than the one given here, by Professor David E. Keyes.  Here is the key paragraph:

Likely reference writers (for instance, well-known professors of core courses) are sought out by many well-qualified candidates. To ensure that such a writer is well primed to execute your reference efficiently, you should create a self-contained packet containing all the information the author will need to dispatch the reference in one sitting: (1) contact information for the recipient of the letter, (2) a description of the position and application closing date, (3) your own application essays and cover letter, (4) a resume, (5) relevant transcripts and scores, and (6) an explanation of the niche of the writer! It is very useful, as a reference writer, to receive a reminder along the following lines: "Professor Keyes, your letter will be the one that comments most authoritatively about my analytical ability, my promptness in completing projects, and my reasons for wanting to pursue X next fall. Remember that you gave me an A– in partial differential equations two years ago and it was your suggestion that led to my summer at Los Alamos with Y." You should provide this packet in both hard and soft copy. Writers of lots of references maintain files that may be hard or soft, or both, and you should make it easy for those writers to locate your files quickly for subsequent updating and future requests.
Some faculty write many dozens of letters of reference during peak months, and they may even ask candidates for sample text to be incorporated into letters, to ensure that they capture their niches. You should not be flustered at such a request, and should not be modest in complying. You should be aware, though, that your words will not pass directly into the delivered product; they will be used simply to get the author's juices flowing following the formulaic paragraphs of the letter.


Trust issues with my PhD advisor, is it worth fixing or can I get out?

Faculty are human beings. We might be given only one slot a year for a doctoral student to work with us and we thus invest (or we feel we invest) an incredible amount of time into the students in our lab. We aren't paid extra for this, which perhaps exacerbates the feeling of ownership.

While I don't know you or your advisor, I would find it easy to believe that his feelings were hurt by your desire to shift PhD programs. You are basically taking his investment in you (which you may feel is minimal, but he may feel is considerable) and throwing it in the trash.

Managing people's feelings are part of being a professional academic. You might as well practice being good at it.  Some day you'll be on the other end of the equation -- being told by a student that you had high hopes for that they no longer value working with you and that they want to move to a different program altogether. It's all part of the karmic cycle of being faculty.

Now, with that preamble out of the way. You need to let your advisor know that your shifting programs isn't seen as any rejection at all of his lab or his style of mentoring you, etc. etc. (even if part of this might be true); but rather that you are seeking something different at the other program. It's the stereotypical "It's not you, it's me" form of a break up.


How do I improve a paper if they haven't published any code?

Even though journals encourage authors to publish their code and make their research easily reproducible, in some fields most authors do not publish their code.

In many cases, publishing code is plenty of extra work with little immediate benefit, as one would have to comment it/improve readability and check all licensing requirements of possibly reused snippets. There is often little motivation to do all this extra work on code that is anyway evolving in the middle of a project. In addition, publishing your code takes away your head start and enables the whole world to beat you to your own "future work" plans, so people might tend to only publish code when a project is finished.

This unfortunately means that you often have to implement state-of-the-art algorithms to be able to improve them or prove that you can beat them. Ideally, the algorithm is completely and unambiguously explained in the paper, so you should be able to implement it. Practically, this is not always the case, but you can always contact the corresponding author of the paper and ask for clarification. There is a reason why most articles include contact information of the corresponding author.


How to apply for Habilitation positions in Germany - Physics/Chemistry

The following is about habilitation and junior professorships in general, not particularly about physical chemistry.
A few things about junior professorships first:

Depending on the field, a habilitation is no longer a strict necessity. Having done a successful junior professorship is formally sufficient for a professor position as well. You of course don't know in advance if the hiring committee for the position you will be interested in at some point isn't preferring candidates with a habilitation, though.
There are nowadays also tenure-track junior professorships. They ensure that if you do good work, you get a permanent professorship afterwards, without the need to have a habilitation. Once you showed that you can do a good job on a permanent professorship, the habilitation should then cease to be important if you apply elsewhere later.

But more importantly:

There are no designated "habilitation positions" in Germany. Rather, there are positions as "wissenschaftlicher Mitarbeiter" (scientific employee) that you can hold while working towards your habilitation. The possibility to write a habilitation thesis while holding the position may be mentioned in the job advertisement, but is also often not. If you see a position that may be suitable offered somewhere, you will have to ask (the respective professor) if he/she thinks if you should apply as someone interested in working towards a habilitation.
The important part for writing a habilitation thesis is that you have a position with a perspective to stay for a longer period of time, as necessary for this purpose. A position in a newly started EU starting/consolidator/advanced grant would be suitable, for instance. A "Landesstelle" (not directly attached to a third-party funded project) is suitable, too - but you will have to convince the professor having such a position that giving it to you is a wise investment for him/her.
Sometimes you see a position for an "Akademischer Rat", which is a permanent somewhat glorified postdoc position and should be suitable for writing a habilitation thesis. These are very rare, though.

Note that positions suitable for habilitation are not always publicly announced, and it's not uncommon to have your current professor/advisor phone up a few colleagues in the area you want to move to in order to check if there are any suitable not yet announced free positions upcoming in their research groups.


How can one come to conclusion regarding topic for PHD

Unfortunately, narrowing your research plan actually requires, well, research. This is why commenters have noted that it might take a year to come up with a problem suitable for the dissertation. Not knowing your specific academic culture (country, university, ...) it is hard to give precise advice here. However, it is possible that you are thinking that you must do more, now, than is actually being asked of you.

I think that it is pretty rare for a beginning PhD candidate to actually have a worked out plan. It certainly happens in some cases where a person has worked in an industrial lab and has already found an interesting but unanswered question. It might also be true of some exceptional graduate of an exceptional Master's program. Most, I think, new doctoral students, however, come as seekers, initially.

Let me suggest two things. First, talk to other students who have been in this situation in your new program to see what they did and what was actually expected of them. What sorts of questions were asked in the interview? This will give you more realistic expectations of the requirements.

Second, assuming that you are not actually expected to have a fully formed research plan already in hand, be prepared to discuss both what you know in the field and what specific things interest you the most. Why do you want to study Machine Learning? What makes it interesting to you? What has clearly been solved and what (in general) still needs to be done? What sorts of real world problems would be solved if advances were made in a particular direction? ...

That may be all that is asked for at this stage. Perhaps the faculty is interested to know your deep interests so that they can help you find the correct advisor. It may be no more than that.

But ask other students first so that you are more sure about it. If it is as I describe you can be more comfortable. I can't guarantee that they don't want more, of course, but I think that would be unusual and expected only at an exceptional institution.

I often tell students that "You aren't here to prove that you don't need to be here."


What to do if my GRE is too low but application deadline close?

This is entirely dependent on the program you are applying to.

Some programs are flexible with deadlines, particularly so if applicants are domestic students. Others, as pointed out are very strict. There may be some of both types of programs within the same university or even college.

You can always try and the worst that can happen is you're told no.  For example, a few options:

Call or Email the admissions staff or the director of graduate programs and let them know you're taking the exam on DD-MM-YYYY.  Ask if they will consider you for a provisional admission that's conditional on you obtaining a competitive score.
Just apply anyway with what you have. Incomplete applications rarely move into the decision process. Execute #1 as well.

Again, this is very program and personality-dependent so your chances of success will vary greatly depending on the situation.* Some programs consider your best GRE score. Some super score (take best from each category).

* And how far "off the mark" your GRE scores are currently.


Why are some PhD holders unable to become professors?

[Thanks for the clarification, it turns out to be an easy question]

  What the reasons are that some people get STEM PhDs, want a research job in academia, but end up not getting it.

Because the ratio between the number of candidates and the number of available jobs in academia makes it mathematically impossible for every candidate to get a job.

Many candidates don't even lack anything to be a good academic, it's just a very competitive job market.

[Edit to answer comments (and the last version of the question)]

  are there PhD candidates that are just not qualified to be professors (why?)?

Of course there are:

a PhD is not a diploma which makes you qualified to be an academic professor anymore, it only validates the fact that you are capable of doing research. Basically you received the training, but it doesn't automatically mean that you're good at it, let alone in the top N%* best where you get a real chance to become a professor.
even being good at doing research is by far not the only skill required to be a professor. Of course there are teaching requirements (not everybody with a PhD is interested in teaching), but there's also a range of soft skills which are recommended: social skills, public engagement, performing administrative duties, and maybe more importantly nowadays being able to attract funding.

It's also worth noticing that very few people become professors just after the PhD, postdocs are part of the career process because that's where one can demonstrate the other skills I just mentioned. But the same applies to postdocs: even somebody who has  all the skills might not be good enough, it's a tough competition.

* "N" varies depending on many factors: discipline, country, etc.


applying after bachelor's degree which factor is the most important for top 10

I think it's useful for this question to step back and think about it from first principles.

What a top graduate program wants in a graduate student is high likelihood of becoming a leading researcher in the field.  There are some exceptions, but for most applicants at most leading departments, this is the only consideration.

The problem with putting this forward as a criterion is that no one can predict the future.  You really don't know whether you're going to become a leading researcher, and neither do the people reading your application.  Everyone is trying to make their best guess based on the information available.

At this point, someone is going to ask for a data-based solution, but the problem is that there really isn't that much data.  There aren't that many leading researchers, the factors that make leading researchers likely change quite a bit over time, so the kinds of people that did well twenty years ago might not do so well now, and the variables probably interact with each other in complicated, nonlinear ways that are hard to tease apart statistically without large amounts of data.

This means graduate admissions boils down to a committee of people reading applications and making their best judgement as to who is most likely to become a leading researcher.  You can now ask the psychological (or maybe sociological) question about what factors professors on admissions committees think correlate with probability of becoming a leading researcher, but there seems to be quite high variability between individuals, and you don't know who is sitting on admissions committees that year.

Given how difficult it is to determine how all these proxy measures work, I think it's best to believe that admissions committees will get it right and look at what they're really trying to measure - your probability of becoming a leading researcher - with the caveats that you should consider the judgement of other people you trust to have an informed opinion (your current professors) and that your own judgement is highly likely to be biased by imposter syndrome and or the Dunning-Kruger effect.


How do MIT OpenCourseware and real MIT courses compare?

MIT OCW doesn't offer "courses".  It offers "courseware" — basically textbooks with videos.

Real MIT courses have live instructional staff who answer questions, run recitation sections, and offer feedback (in particular, grades) on your solutions to the homework and exam problems.  Real MIT courses have deadlines that force (well, encourage) you to actually work on the course material regularly.  Real MIT courses also have a community of other students, all following the same lock-step schedule, that can work together to develop ideas, internal feedback, social outlets, and later professional contacts.  Real MIT courses give you an official record from MIT of your performance in the class.


What is the proper way to cite a mathematical theorem in a paper?

On the one hand, you sort of don't need to worry about it, but it's best to make your advisor happy (especially if they are a co-author).  Here are my thoughts.

Your advisor ought to have experience with this sort of thing in general.  So as a rule, it's good to take their opinion into consideration.
The journal you ultimately submit to will have people whose job is to make sure you use any nuanced writing rules like this correctly.  And the formatting and such that you choose will probably be changed by the journal any way.
I've never heard of any rule like you mention, and I don't think there's any expectation in the community about this.  Citations in math papers are always weird.  They have no standard format (the journal will do the format they like for you), and you don't have to worry so much about exactly quoting somebody per se.
My rule of thumb is that when I cite something, I always try to credit previous literature for everything I can.  I ask myself "is what I'm writing obviously equivalent to or implied by the theorem they wrote?"  If so, I would simply phrase the result in my own words and credit them for the theorem.  You can do this easily, and you don't have to mention a proof at all unless it's unclear how their result implies your statement.

For example, I would write something like:

  We recall the following theorem due to Smith [4].

  Theorem 3: All objects have property.

And the theorem number is just whatever number would be next in your paper.  Or you could do

  The problem was originally asked by Smith [4], who addressed the situation when things are nice.  In particular, she proved.

  Theorem 3 (Smith [4]): All objects have property.

Or if it's very hard to find where in [4] Smith wrote that theorem, you could say

  Smith proved the following, which appears as theorem 13.b of [4]

  Theorem 3: All objects have property.

Or if you want to emphasize that what you're stating is easily implied by Smith, I might say something like

  We now use a special case of a theorem of Smith [4] recalling here only what we need.

  Theorem 3: The objects I like have property.

Note that in all of the above cases, it wouldn't be appropriate to cite a proof or anything after the theorem statement.  The result should either be very obviously the same as the paper you cite, or it should be very obviously implied by it.  If you want to use something similar to Smith's theorem, but it's not obviously the same or implied, then I suggest something like the following.

  We now appeal to a general theorem of Smith [4], which states

  Theorem 3: All objects have property.

  By regarding her (thing) in (our setting), we obtain (by this hint of a proof sketch)

  Corollary 4: The things we care about do the thing we care about.

If needed, then say more about why this follows from Smith's result.  If this connection (and stating Smith's result in the first place) is too much, then you might want to consider putting that part in an appendix and just saying something like "the following is obtained from a theorem of Smith [4], but for ease of reading this connection is discussed in appendix A."

One final piece of advice would be to simply read a lot of well-written papers and see what they do.  Look in places that have good exposition even if it's not in your area.  It's not important to understand the math in those articles so much as how they write and how they handle these nuances.

You have a lot of freedom, and any choice you make is likely going to be fine as long as you thoroughly credit previous authors and you make your paper easy to read.


With the caveat that I don't speak for my department or institution (although my experience informs my opinion):

My inclination is to say that in practice the cutoff can be softer than the official advertisements or instructions, but this isn't guaranteed, and may even vary between departments at the same university.

The cut-off is usually there as a first-pass filter for applicants who got their Bachelor's or Master's degree at a UK university. Conversion of grades from other systems, such as US GPA, is done according to some University-determined scale, but depending on the volume of applications at any given university there may be scope for some ad hoc decisions on edge cases.

It's also the case that the relevant admissions committee/team will probably look at the awarding institution, even if GPA is supposed to be standard. A 3.4 from an institution which is known to have a strong undergraduate program, or which has a positive reputation among the academics reading the application, will get treated more favourably than a 3.4 from somewhere that is "less esteemed" in some sense.

(I think one reason the cut-off is higher in the UK is because our PhD programmes are usually shorter than the US and have a less comprehensive training period in the initial stages - so we need to get people in who are better prepared, rather than take a risk on someone with patchy background but some signs of potential. But this is just my experience/opinion from mathematics, and it could be way off-base for other disciplines.)

Even within the UK it's not clear to me that the cutoff is as strict as official statements imply. To take a not entirely hypothetical scenario: an institution might say applicants in mathematics should have a 1st class degree or equivalent. Yet if they get an applicant who has a 2:1 Bachelor's from, erm, certain UK institutions, with good references and with some positive predictions about the Master's program on which they are currently involved... I think that such an applicant has a decent chance of being considered seriously by the departmental admissions team, provided that the application material has made it through the centralized university pipeline.


How harmful is it to submit side-results that are not new?

Your impulse to try to find out whether your "mathematical side results" are new and/or publishable is a great one, but I think you need to go about it in a different way. If you are not a mathematician and working without the guidance / mentorship of an experienced mathematician, trying to get your results published in math journals will be somewhere between difficult and quixotic.

Have you tried making use of the site mathoverflow.net? Asking whether a result exists in the literature should be on-topic for that site providing the result is viewed to be a sufficiently contentful piece of mathematics.  (Yes, there is a certain amount of elitism / snootiness here, which most people seem to agree is necessary in order to keep a research level math Q&A site afloat).  Anyway, you can certainly try: what is great about MO (and in fact most SE sites) is that it is very likely that whatever happens will happen with almost magical quickness: with high probability, if within a few hours no one comes along to answer your question, then the answer is not "well known" by the mathematical community.

Here are some specific issues with the float-it-to-the-journals plan that you propose.  (It is not an exhaustive list: probably that is not necessary.)

  What if I just submit a side-result to a medium-class journal, e.g. American Mathematical Monthly?

The American Mathematical Monthly is not a "medium-class journal".  It occupies a specific niche, and within that (small) niche it is one of the top journals.  For instance, I have submitted four papers to the AMM.  Two of them were rejected.  One of these rejected papers was easy to publish in a more "mainstream" journal; the other was not.  The other two papers got accepted...eventually.  But I turned in a larger number of revisions on these two papers (I believe they were 3 and 7 pages long) than on most of my other papers.  Most of these revisions were made after the mathematics was agreed upon to be correct and of the sort they wanted to publish.

After my first four submissions, many years of close reading and half a dozen referee reports, I think I have a pretty good idea of what the AMM wants to publish (not necessarily the same good idea as everyone on the editorial board).  I now sometimes advise other people as to whether their manuscripts ought to be submitted there.  Even so I have just written an article that I had at first thought I wanted to submit to the AMM, but now I am leaning towards submitting elsewhere, and I am not sure.  It's complicated!

  If the results are new, they will be published and this may help other people.

No, just because the results are new does not mean they will be published by any reputable mathematical journal.  I have a few manuscripts that I tried to publish at several different places but did not succeed.  Eventually I stopped.  I agree that in theory they could be published somewhere, but in practice this can be a lot of trouble.

(I agree that the results may help other people!  Consider making them available in some other form, e.g. in a manuscript on your webpage and on the arxiv.  You can put things on the arxiv that you do not have plans to publish, so long as you are reasonable about it.)

  If the results are not new, the paper will just be rejected. This is not a big deal for me since these are only side-results.

Hard no.  Results get republished all the time.  The refereeing process for math journals is that the editors seek opinions from one or two people.  If those one or two people have not seen the results before -- maybe they made a reasonable attempt to search the literature, or maybe they didn't; both occur frequently --
then the paper will likely not be rejected for that reason.  There are some notorious examples in the mathematical community of papers that were published containing content this is not only "not new" but is well known material from undergraduate courses, or is actually at a lower level than that.  This is actually a pretty bad way to be sure that the results are not new.

  My only concern is that the editor and reviewers will be angry at me for having wasted their time on results that are not new. This may be harmful to my reputation.

I think that is a legitimate but rather minor concern.  The mathematical community is vast, and although we talk about people in some ways, gossiping about poor submissions (that never appeared) is very rare (in my experience, obviously).  If you are willing to "take no for an answer" and spread out your submissions among multiple journals, I don't think this will be very harmful to your reputation.  Yes, you might be wasting people's time and that is worth thinking about, although the less appropriate the paper is, the quicker and easier it should be for a qualified party to see that.  I think the main consideration here is wasting your own time.  Are you aware that if you submit a paper to a math journal you should expect to wait at least six months for a referee report, and that delays of a year or more are not uncommon?  That's way too long to wait to find out whether some lemmas should be put in your game theory paper or not, isn't it?

In summary: I urge you not to use the journal refereeing process the way you suggest, but more for your own good than for the sake of your reputation.  I hope you know that even if you don't have any mathematical connections, you could still make some.  Universities have multiple departments for a reason: have you tried to make contact with anyone in the math department of your university?  If your colleagues there do not have the specific expertise to help you, they are still your colleagues so some of them should be willing to take a little time to direct you to the people who do.  I encourage you to take advantage of this.


3 - 4 years since I graduated, how should I time asking for recommendations?

My recommendation is similar to those posted in comments. I worked for several years before applying to graduate school and did not stay in touch with my professors during that time. Approximately 4 months before I applied to graduate school, I sent each professor a brief (1 paragraph) email explaining my graduate education plans and career interests, and asking if they would be willing to write letters of recommendation, which would be due in November. I also indicated that if they were willing, I would send them my CV and a summary sheet of my college activities for their reference. I contacted them via email, as I lived in a different state than the college, and face-to-face meetings were impractical.

When they agreed to write the letters I sent them:

A summary sheet listing each program I was applying to. For each program I listed the address and contact person (so the letter could be properly addressed), 1 line about why the program interested me, the names of faculty I was interested in, the application deadline, and specific application letter forms or links to online applications, if relevant.
My CV
A summary sheet highlighting specific grades in major-related courses; research projects and activities I engaged in during college; a 1 paragraph narrative explaining what I had done since graduating and why I was interested in pursuing another degree; and a list of courses I took with that particular professor/letter writer, along with the grade for the course and any special projects completed in those courses. Try to keep this to 1 page.

Although this sounds like a lot of information, work to keep it as brief as possible, while ensuring the professor has the information they need to write a strong letter.

You may choose to time this differently, but the four month window ensured that I had committed to applying and gave me time to identify alternative writers if they had declined. I'm not sure it would be useful to ask your professors a year in advance, as 1) your plans may change, and 2) they may not recall a commitment they make that far in advance. That said, I would make initial contact in the summer before you apply; if you wait until the school year kicks into full gear, your email might get lost in the shuffle. When I was applying I was advised by multiple people to provide all materials to my letter-writers a minimum of 2 months prior to the deadline. Many schools require letters to be written on specific forms, have surveys your letter writers are asked to complete, or even ask the letters be submitted online; it's unlikely the most recent application will be available more than a few months prior to the application deadline.

A few final notes:

Be sure to ask if they feel they can write you a strong letter, not just a letter of recommendation. Most faculty will be honest about this.
Send your letter writers an email two weeks prior to the application deadline to thank them and remind them of the approaching deadline. Many online applications will indicate when your letters of recommendation have been uploaded.
Be sure to thank them, both when they agree to write the letter and when the letter is submitted. Consider writing and mailing a formal thank you note, once the application is submitted. Also, contact them once you're accepted and have decided on a school; they like to know how it's worked out!


As always, one needs to look within oneself. Ask yourself the following questions:

How broadly interesting is your oeuvre? In my experience, difficulty in finding a referee often indicates that the field is very narrow, and the editors are looking for a referee to check whether a paper is a breakthrough in the narrow field. Otherwise, the paper is rejected.
How well-written are the papers? Especially the introduction - if the prospective referee's eyes glaze over when s/he reads it, s/he probably won't want to referee the paper. I realize that the author is not the best judge for this, but show the paper to a friend.
You can usually get papers published quicker if you submit to a lesser journal (and I assume that it is ALREADY published on arxiv.org). The optimization problem (quality vs speed) is for you to solve. From a careerist standpoint, the journal weighting is very nonlinear: a single paper in Annals of Math is worth essentially an infinite number in, say, PAMS (no insult meant). If you are already established, then you might not care. If not, you might.

Just one man's opinion (though I am active on several editorial boards, so the opinion is somewhat informed).


Not ticking boxes in recommendation forms

It can definitely hurt the students.  Having worked on master's and doctoral admissions in my own department (physics and astronomy) and occasionally been consulted by faculty in closely related departments (chemisty and applied math) about unusual applicants, I can attest that there are some faculty members that do pay attention to those checkbox rankings.  They are not numerous in my department, but they do exist.

In most cases, the students' test scores, grades, and recommendation letters speak for themselves.  For a strong applicant, those checkboxes are probably never going to cost them an admissions slot.  However, when there are some questions about the strength of a recommender's letter, some people of the committee do turn to the numerical ratings to try to get a clearer idea of the applicant's abilities.  So if you write a student a compelling recommendation letter, those boxes will likely never matter; however, if your letter is short or expresses possible reservations about a student, you may be further hurting the student by leaving the boxes blank.


What are the boundaries between draft, manuscript, preprint, paper, and article?

paper = article: In the academic meaning of the words, papers and articles refer to the same thing: a published piece of writing. The term is used for journal papers or journal articles, which means they have been published by a journal, but also for less traditional publications, including self-publication (“Dr. Who just published a great paper on the intricacies of time travel on his webpage”) and e-print repositories such as arXiv (“check out the latest paper by Galileo on arXiv, that guy has mad ideas!”).

Some journals have different categories of “articles”, and differentiate between letters, communications, reports, reviews, and full papers (sometimes abbreviated as just “papers”). In usage I have seen, paper (or article) used as a generic term covers all of those: you would say, for example, that “letters and full papers are two types of articles”.
A preprint (more commonly used without the hyphen) refers to the distribution, in advance of formal publication, of something that will be published in print. The preprint may differ from the final publication.

Preprint status does not always indicate that the work has been formally accepted for publication. It just means the authors intend to publish it in a more formal venue (journal, book, etc.) but wanted to distribute by other means beforehand (preprints used to be distributed to colleagues as photocopies, but are now mostly circulated by email or repositories).
A manuscript is, in the New Oxford American Dictionary's words, “an author's text that has not yet been published”. Any piece of writing that you have not published in any way (but intend to) is a manuscript.
A draft is the same as a manuscript, except that it insists on the unfinished state of the manuscript.

Summarizing, I could say:

  Here's the draft I've been working on, please amend it with your corrections. Once we have done this final round of revision, I will upload the manuscript to the editor's website, and we can start circulating it as a preprint to colleagues whom you think may be interested. Once it is accepted and published, we'll just send them the published version of the paper for their records.


Retroactively turning down an accepted offer to a professional program from one school in favour of an offer from another school?

The first school won't like it, but there would be nothing to stop your brother from backing out of the first offer and accepting the second offer, unless the schools work closely together to prevent this from occurring, which seems highly unlikely, especially because their notification dates differ so greatly.

If your brother is accepted to the second program, the most courteous way to inform the first program would be:

as quickly as possible, so they can accept someone from their waiting list or otherwise make use of the information.
without insulting the first program.

For example, he might write something like:

  I realize that, as grateful as I am for admission into your program, pursuing it would not be the right thing for me to do at this time and that I should not have accepted your offer.  I am very sorry that I have to withdraw my acceptance.  I hope it is not too late for you to offer the place to a student who is a better fit for your program.


The cover letter should probably state:

The title and authors of the article you have reviewed (short list of authors "X et al." is fine)
Your recommendation for the disposition of the article (accept as is, reject, recommend major changes, etc.)
Any other important information that you wish to note. This could be anything exceptional, whether that be good (perhaps the article should be considered for "cover" status) or bad (for example, if you suspect something dishonest).

All other points can be addressed by referring the editor to the referee report.


What makes a publication (or a publishing forum) academically acceptable for inclusion in a literature review?

I am afraid this is an impossible question to get right: An "acceptable academic publishing forum" would be one that is accepted by "acceptable academics" - and "acceptable academics" would be identified by publishing in "acceptable academic publishing fora"...

Peer-reviewed is not a bad criterion, but it falls short: There are peer-reviewed journals for creationists and homeopaths - so the value of peer-review depends crucially on who the peers are. It doesn't even work as a necessary criterion, as missing the arXiv for math-y fields or books for humanities would mean that a literature review is very incomplete.

"Acceptance by funding bodies" gets the question backwards: Funding bodies try to approximate what the academic community considers good publication venues, they don't define it.

If formal inclusion/exclusion criteria are important for you (maybe because you do some meta-statistics?), you will need to look for field-specific standards. In medical subjects, I could imagine that "listed on pubmed" would be an acceptable one. In this case, looking are published meta-studies and their criteria would be useful.


How do you find interdisciplinary collaborators for your research?

If you really want them local, the best social network is actually being social.

You can either attend conferences and university events in your city, attend seminars at other departments (some are announced in their webpages), or just send a series of polite emails to researchers working in thins you want. Just list the departments that may be doing something you like, browse their personnel, and skim their last publications to see if your research interests may be aligned.


Are non-computer science PhD students using ML/AI techniques expected to publish in top CS conferences like NIPS/ICML?

Most conferences in any field are looking to present advances in that field. This is usually called novelty. If you are using standard techniques in AI/ML in your work then it may not be seen as very interesting to CS folk, unless the application is, itself, somehow, novel. The standard for that will be fairly high.

So, ask yourself where is the novelty in your work and publish/present in journals/conferences in that field.

But the bar for submission is low and it will be reviewers who make the judgement about suitability. So, if you want to do a trial submission, to see how your work is judged, you are free to do so, making your advisor happy. But, I agree that your general research trajectory is more important.


Fast way to find out the ISSN number of Publications

To get the ISSN of a paper by using the paper's DOI, try CrossRef's API. Specifically, use the URL https://api.crossref.org/works/ and add the DOI to it.

For example, if the DOI is 10.1177/0047117819856397,
then use the URL https://api.crossref.org/works/10.1177/0047117819856397

There is a branch called "ISSN" in that JSON-file. If the output looks confusing to you, copy-paste it into a 'JSON beautifier'.

(However, note that you cannot find the Impact Factor of the journal using this approach; as far as I know, there is no API for accessing an Impact Factor by using the ISSN as a key. Also see "Where can I find the Impact Factor for a given journal?")


Realistic expectations from a postdoc in terms of publications

One per year may appear unambitious. I suggest framing them in terms of 1/year 'sure bet' publications and additional 'reach goal' publications, to show a balance of ambition and realism.


Is this customary? What would be the most polite way to ask? What is the best way to go about this?

Don't overthink this: Just email your advisor, it is normal.


How do I come up with a "thesisy" thesis title?

You may not actually want your thesis title to sound "thesisy" - many academic manuscripts have ambiguous, wordy, or borderline nonsensical titles. That being said, a thesis is generally the result of substantial work, so the title should reflect that, right?

One way to do that is to identify exactly what is unique about the efforts. If it ends up on someone's bookshelf (or, more realistically, listed in digital format) then a title clearly stating what is novel about the work it represents will help to distinguish that document.

It should also be as short as reasonably possible while still being direct - does the thesis have a single, major conclusion? If it's more ambiguous, can multiple conclusions be summarized into one? It may help to phrase the conclusion as an action, e.g. "X does something to Y" or "X shows that Y is Z" rather than "On the nature of X: an exploration of the Y of X using the Z method". Avoiding jargon is also ideal, though standards may vary by field.

Your institution likely has a dedicated collection of previous theses. They may not all provide great examples of titles, but they're worth learning from.


what to do when someone has same name as yours and in IEEE search they show both peoples paper?

Yes, this is a very common problem.

You should publish with the most complete version of your name possible (e.g. use your middle name.)  Think very carefully before changing your name (e.g. if you get married.)
You should establish profiles with services that keep track of publications by author (including Google Scholar, Thompson's MyResearcherID, and ORCID)  and then "claim" your publications using these ID's.


How to obtain US Bachelor degree based on my old university credentials?

No real US university will award a degree to a student who has not taken any courses at that university.  What you want is not possible.
To award a degree, you must earn credits from the university.  Typically, this is at least half the total credits required for the degree.


The best ways to cite a theorem whose assumptions/conditions are written earlier in the source?

There are a number of ways to handle situations like this, depending on how much prominence you want to give to the result you are citing.
If the cited theorem is quite important to your work, and you think the reader will benefit from seeing it written out, then you can include a complete statement:

Theorem 1.2 [Smith 1953].  Suppose $X$ is compact, Artinian, and hyperfinite, and $\sqrt{Q(X)-57} > \pi/4$.  Then $U(X) \sim \gamma$.

[Oh right, we don't have MathJax here. :( ]
Then elsewhere in your paper you can say "By Theorem 1.2, ..."
If the hypotheses of the theorem are particularly complicated and you don't feel it's helpful to include them in your paper, you could write:

Theorem 1.2 [Smith 1953].  If $X$ satisfies the assumptions of Section 5 of [Smith 1953], then  $U(X) \sim \gamma$.

Then you can write elsewhere "We can easily check that $Y$ satisfies the conditions in [Smith 1953], so by Theorem 1.2., $U(Y) \sim \gamma$".
If you don't care to say much about Smith's result (perhaps it's well known, or you're just using it as a black box), you can just cite it, perhaps with a brief comment about its assumptions:

Since $X$ is hyperfinite, by Theorem 5.6.7 of [Smith 1967], ...
By Theorem 5.6.7 of [Smith 1967] (which requires $X$ to be hyperfinite)...


"Awaiting AE recommendation" before first notification of acceptance or rejection

AE stands for Associate Editor. According to the process described in IEEE Transactions, "Awaiting AE recommendation" status means that the AE has collected all reviews from the reviewers who were assigned to review your manuscript and that the AE's decision for acceptance is pending.

After this phase, the AE would send her/his report to the EiC (Editor in Cheif), for the final decision on accepting the manuscript for publication in the journal based on the review results and the report from the AE.

You would find more detail of the process here.


A negative graduate class experience and maybe some factors in cultural differences

I'm sorry. What happened to you should be very rare, but it does happen sometimes. In US higher education I have seen otherwise good professors embarrass someone by accident (not realizing the effect of their words on the student, or saying something more extreme than they had thought through), and some extremely blunt professors who say this sort of thing on purpose (this group is mixed in whether they are otherwise kind people).

I highly doubt that what the professor did was "justified," but this may depend on the tone they used. In my opinion, intending to embarrass you for this would not be justified.

As for coping, I suggest you think about whether the professor has done this sort of thing to other people. If so, then other people know what you feel like. If not, then it is unlikely that the professor considered how his words would make you feel.

It may feel empowering to go to the professor with direct feedback that this was very embarrassing to you. I think that directness might help the professor learn but would even better free you from some of this shame. However, that's expert-level self-confidence and emotional intelligence, and not at all what I did when I was in a similar situation (grad student giving final presentation on my work, and the professor said a few slides in that my approach didn't make sense/wouldn't work; that sort of deflated me and I ended the presentation there--I was the last student to present, the class had already gone over time, and the prof was complaining before my presentation that he needed to leave.). In my case, I never brought it up, there was no direct feedback on the presentation, and I continued going to next term's class with the same prof even when I felt like I was going to cry. I felt embarrassed for a while when I ran into my fellow students from that class. But eventually I figured out my feelings, realized that professor is extremely direct (to put it kindly), and the pain dulled over time.

To prepare for your remaining classes, really be kind to yourself. If you have a friend in this class, try to arrange to come to this class with them so you're not alone at the beginning or end or class. Bring a comforting hot drink with you to class. (Or ice cold drink, depending on weather. :) ) Wear jewelry or put something in your pocket that reminds you of home & loved ones or a meaningful accomplishment. And try to remain engaged with the ideas right in front of you in the class, rather than replaying that class in your mind. If possible, finish a draft of what you need to do for the rest of the class as soon as you can, so you can mentally close the door on this class.

You are almost done with your program! I am sorry that there was this awful experience at the end, but please try to celebrate what you have done!


Can I use the same paper topic for two different classes?

The best way to cover this is to cite the earlier paper in the new one. A citation can be to an "unpublished" work as well as to a published one.
Submitting the old paper in the new course would be a violation unless done with explicit permission, but you aren't suggesting that. You are planning to extend the earlier work in a different direction which is a perfectly good thing to do in any research or scholarly writing.
Many scholars cover "the same topic" in separate papers so long as they have new things to say and also cite the earlier work.
If you want to be really clear, cite the old work and also include a copy of it with the new paper when you submit it. It can be hard to find "unpublished work" as well as citations of "private communications" and such other things that require citation. No one can make any claim of improper behavior as long as you are completely transparent, as you have been so far.


Are Ph.D. dissertations always required to include new discoveries?

What distinguishes a PhD from all other academic degrees is the requirement of a novel, sufficiently substantial intellectual contribution.  In practice, what "novel" and "sufficiently substantial" mean are handled on a case-by-case basis.

The word "discovery" does not appear in the above description and would not be appropriate in certain academic fields, but in mathematics a PhD thesis is  required to contain new theorems or new proofs.  It is often contrasted (e.g. in various programmatic descriptions and graduate handbooks) with a master's thesis, which may contain only novelties of exposition.

So if you go around mathematics departments asking "Can I write a PhD thesis in which the novelties are all expository?" I would expect the answer to be a quite consistent no.

However:

1) "Inventing new things is not my strength." I too was once extremely daunted by the prospect of inventing/discovering significant new mathematics...so much so that I spent five years as a PhD student learning how to do it.  (I got it now.)  My point being: if you are otherwise talented and interested in mathematics, there is no good reason to think that you will not become good at this.

2) If you are otherwise talented and interested in mathematics, you will very likely become good enough at discovering new mathematics to write and defend a PhD thesis.  The requirements of a PhD thesis are partly aspirational: in reality, we settle for a bit less much of the time.  I have seen some PhD theses where I was confident that there was nothing really new in them.  To be a bit specific, I know a thesis in which a student attained the main result through five pages of calculation, whereas a more conceptual framework would yield it in about a paragraph.  The result was of the form "For all n, there is a [mathematical object of type X] for which the [parameter value associated to any mathematical object of type X] is n."  It had not been stated before in the literature, but when I searched further I found that the theorem could have been proven simply by citing extant examples in the literature.  And by the way, this was not the worst PhD thesis I've seen -- on the contrary, the theorem was natural and interesting, and I rather liked it.  It resulted in a paper published in a reputable journal.

3) You write

  In some cases, I think that this activity might even be more valuable than discovering new things,

Yes, I agree most heartily.  I suspect that the number of theorems proved in 2016 lies in the interval [10^5,10^6].  Without smart people taking time to reorganize, simplify and expose these results, we're all going to get carried away in the flood.

  and I find it be just as satisfying.

I do a lot of expository work, and I find it more satisfying in some ways and less satisfying in others than discovery-oriented research.  It is an unfortunate professional reality that its perceived value by the overall mathematical community is lower.

However, really good exposition is rare enough so that people who are good enough at it can make academic careers out of it.  Michael Spivak is a legendary figure for his lifetime of mathematical exposition.  Keith Conrad, a mathematician of my generation (and a friendly colleague of mine) is well on his way to the same achievement.  Both of these people can do discovery-oriented research and have the papers to show for it.  However it seems to be the case that they are more interested in exposition and have spent more of their time on that.  To become the Spivak or Conrad of your generation would be a worthy goal.

4) There are doctoral degrees that are not so heavily focused on discovery-oriented research.  In comparison to the PhD they are much fewer and they are not very widely known, but they exist.  Let me quote from my UGA colleague Michael Klipper's website:

  Before being hired by UGA, I received a Doctorate of Arts (D.A.) degree from Carnegie Mellon University in 2011. Instead of doing research, I wrote a textbook draft for an analysis course.

I know nothing about this degree program other than what I just said, but I know Dr. Klipper and the value he brings to my department.  Based on that alone I recommend that you give it serious consideration and search for similar programs if you feel that this is where your interests lie.

Good luck.


Verbal warning based on student complaints without evidence and investigation

Your question does not specify where in the world you are, but the behaviour you are describing from the students and staff sounds extreme.  It also sounds like your boss perceives you to be the cause of the problem and it sounds like they are not treating you well.  In such a case, your future at this institution might not be a good one, and it might be a good idea to consider looking for a position elsewhere.  Before you get to that point, I will make a couple of suggestions for what you might do here.
As a starting point, it might be useful to invite another academic to attend your lectures to observe what is going on.  Choose someone you respect as a good lecturer who has a good relationship with you, and ask them if they wouldn't mind coming along to a few of your lectures to observe.  This would have three purposes: (1) to see if you are doing anything wrong that would provoke such extreme behaviour; (2) in the event that you are not doing anything wrong, to act as a witness of what is occurring from the students; and (3) to give you advice on how you can improve your class (either by improving your own methods, or improving student discipline, or both).  The presence of another lecturer might alter the behaviour being observed, which is unfortunate, but even in that case the observer will be able to give you feedback on what you are doing.
Once you have had another lecturer observe your class you will be in a better position to determine whether you are contributing to the problems from your students, or whether these are just unruly students who are behaving badly without provocation.  You might also be in a better position to engage with your boss in relation to the problem.  (For example, you might now have another lecturer who can come along to meetings and give their observations of your class.)  Depending on what country you are in, there may be some rules for unfair disciplinary action or unfair dismissal.
Your proposal to write a minute and send it back to your boss might be okay, but only if the minute is written in an objective manner.  If the minute is just your characterisation of the way you were treated then it is unlikely that your boss will consider it an accurate statement of the meeting, and it might just further inflame the situation.


Improving work conditions of student assistants, PhDs, Postdocs etc

As mentioned in my comment, I am in full agreement that working conditions for young scientists tend to be somewhere between precarious to downright terrible, but I do not share your impression that this is an Austrian, or even a European, problem. Still, I agree that the situation is dire and needs improvement, independently of whether it is the same or worse than elsewhere.

I have by now moved to Sweden and my impression is that working conditions for young scientists here are quite good, much better than in most countries. What seems to help are the following:

Flat management structures and a fairly consequent implementation of the "many eyes" principle. Unlike in Austria, where people tend to be at the mercy of a single chair or full professor, a young scientist in Sweden tends to work with many different faculty members, both in research and teaching. PhD committees have multiple internal members, all of which meet regularly with the student, providing realistic ways to escalate issues with the main supervisor.
Part of this are also yearly one-on-one meetings of all students with the head of the PhD school as well as with the head of the division, where problems can be raised (really, it is expected that issues are raised here, and this is not seen as an attack against the main supervisor, as it may be in Austria).
Fairly generous paid vacations on all levels, and an expectation that this vacation is indeed taken yearly.
Clear rules for hiring. There are no vague promises of jobs - all positions need to be announced and run through a hiring process in which HR is involved. This is quite transparent, and internal hires are rare to start with.
Explicit support for mental health. Our university has a contract with a mental healthcare provider, which all employees can consult if they feel stressed or depressed. Usage of this provider is anonymous and encouraged by senior faculty.

It helps that the faculty/student ratio here is much lower than what I have seen in Austria (about 1:2 in my division, versus about 1:20 in the group where I did my PhD), and that the Scandinavian culture tends to de-emphasize hierarchy to begin with.

  what can we do as young researchers/academics against an oppressive system when we are not even being represented in works' councils? Who to turn to for help and support? Are there pan-European research associations that we can become involved in to take up these issues?

Realistically, what will be needed to substantially improve working conditions will be to break up the chair structure. As long as a single professor is the sole authority over a student or postdoc, mistreatment will happen and continue to happen.

I am afraid, neither external associations nor students can do much to make this change happen - it will need to come from within. Short-term, the only thing that students and employees can and should do is vote with their feet - don't go to universities and groups that have a history of treating their employees badly, and warn others from going there if you feel you have been mistreated.


Collaboration is generally seen as a major strength in computer science and computational science, not a weakness.  One of the biggest questions we ask about any faculty candidate in my department is "Who in the department/college will they work with?"  We do occasionally hire faculty that work alone in their cave and occasionally emit theorems, but they're rare exceptions (and even they still work with their students).

The most important thing is to establish a reputation as a leader in your collaborations, rather than a follower.  You need to establish your own research agenda, instead of just following someone else's.  More importantly, you need to be seen to have your own research agenda, instead of just following someone else's.  Your agenda must be visible in your publication record, in your recommendation letters, and (eventually) in your funding record.  To this end, it is very important to do a few things:

Limit your collaborations with more senior researchers, especially your advisor, especially between getting your PhD and getting tenure.  As I've suggested elsewhere, publishing at least one paper without your advisor before you graduate is a strong signal of independence, even if you have other coauthors.  Once you have your PhD, DO NOT publish with your advisor for at least a few years.
Do not always publish with the same set of coauthors.  It's fine to have two or three different groups of people that you always work with, as long as you can wind a consistent story that ties most of your work in those different groups together.
(Once you have a permanent job:) Get at least one grant as a principal investigator, not just as a co-PI.  Definitely join other grants as a co-PI, too, but you must have at least one grant with your name on top to get tenure.


I have to mention that about 6 weeks after the submission, its "status
  date" has been changed but its status not!

The status date changed because, either the editor sent the paper for review or any of the reviewer accepted to review the manuscript. Either case is possible. The status changes/date changes occur when some step has been taken by the editorial side or reviewer side.

  May you please tell me how long I have to wait for the decision about
  my paper?

I guess, nobody can give you a numeric estimate of this duration. It is completely dependent on the reviewer and their response to the editor's reminders. As a reviewer, we get around 4 weeks to review an article. However, they may remind us once or twice or sometimes give us an extension to do so. If the reviewer is very popular (bigshot), the editors sometimes don't care much about the timing rather focus on getting a strong and bias-free review from such reviewers. That takes time.

  I've checked the paper status in journalinsight.elsevier.com. For the
  journal, the first decision speed time is about 7.2 weeks. But my
  paper is still under review after about 3 months.

I have been waiting for last 6 months (and counting) to get the very first review on my paper; not in this journal, but something similar. If you are so curious to know, you should send a very gentle email to the editor asking about it or just a hint to remind him about your article. Because, in a pile of many articles under review, the editors sometimes may not look into your article. Probably something like this:

  Dear Editor

  Could I ask you about the present status of the review of my following: submitted manuscript?
  Title: Knowledge-Based Analysis of Review period of the Journal X (ID: KBS-16-xxxxx)?

  Sincerely

  You

Remember, editors are busy persons; he many not respond to your email too. And, Computer Science/Mathematics journals often take a lot of time for review purpose -- This is well-observed fact. No proof of this hypothesis is required!


I can only speak for germany and only my own experience as a researcher:
I don't know exactly what you mean by "kick-start leading to PhD program", but if you mean "will a masters help me get a PhD?" Then the answer is definitely yes. This should apply anywhere on the globe where bachelor/master is established. Where in general it is possible to do a PhD with "only" a bachelor degree, it is pretty rare and I personally know not a single case.

As for tips: If you want a PhD, do the masters program. Get in touch with people, professors and lecturers. In my group, a lot of people are hired after completing their master thesis here.

So the best tips I can give you are:

Enroll into topics which you are truly interested in
Make a good impression in exercises(talk to the lecturer after the session, don't slack off, get good grades...)
Get a position as research assistant in a working group
Do your master thesis in the group where you are most interested in(and here is the hard part: during this time you should work very hard, make good impressions, try to get good results... since you want to work there later)

Those tips are pretty much the route I took and I guess there are many more tips and life experiences out there to help you.


Can a university claim patent rights for inventions performed on my own time?

Note that a detailed response to your question, as well as any answer tailored to your specific case, will need to be given to you by a lawyer. And, if you think of doing anything that could even remotely be considered borderline or controversial… just ask a lawyer. And even if you don't do anything borderline, better safe than sorry!
Now, I want to explain some of the background of that answer: I have acquired some experience of my own, though not in the US, on dealing with being employed as a full-time researcher and professor, yet maintaining a certain level of activity outside of my employer. I actually produce intellectual property on my leisure time (both copyrightable materials and patent rights), and have consulted with law professionals on how to effectively keep control of my own IP (as opposed to that which I create for my employer).
The main conclusion is: you actually have to be very careful to be able to fend off any potential claim of your employer on the IP created. Of course, it's a risk of the “if it comes to that” variety. If your university is not interested in pursuing any claim to such IP, you may never have a problem, even if you did not clearly separate your own IP from that created for your employer. But… you never know what may happen in the future (e.g., your current understanding with the dean may not hold in a few years), so you should take maximal precautions.
In short, you should assume the following:

Everything you do on company time is owned by the company. I'm pretty sure that this includes your “20% time”: if it's 20% of the time the company pays you, it may mean that they leave you free to do research in a direction you choose for yourself, but it is still research you performed as their employee.
You certainly can't expect to be paid 40 hours a week, work 32 hours for your employer and then spend the remaining 8 hours for someone else, can you?! (in this case, the “someone else” is yourself as a freelancer)

Don't use resources from your university. This is also very typical of contracts and, at least the few European countries I know, the legal status quo: use of company resources means the company has rights on your production. This includes every resource you list, even smaller things you may not think of, like email account, FTP/web/ssh hosting, internet connection, …

Everything you create while inside the company is not yours. Walls, internet connection, desktop, electricity… are company resources. While courts in some jurisdictions have recognized that certain limited activities done inside the company, such as reading email during lunch break, may fall within the personal sphere (and not the professional sphere), it is not likely to be the case for any larger activity.

Finally, if you think of doing on your spare time anything that is thematically closed to your day job, take care: it becomes hard to claim that your own activities are not linked to your university position and resources, and do not in any way interfere with it, if you are a computer science researcher by day and patent new sorting algorithms by night :)

And, did I mention? Get help from a professional, aka lawyer.


What do you suggest to keep track of new published papers?

Just follow all the people in your subfield on twitter. At this point that's easier than google or pubmed alerts, plus you can see when they're hiring too.
That + conferences (if conferences ever come back) is how I stay up to date.


Is it correct to use citations as nouns for scientific papers, such as dissertations of articles?

There’s no unique answer to this as citation styles (in text or in bibliography) are somewhat personal or institutional.  Some good ways of getting guidance include

Get one or more previous theses on the same topic and follow those models,
Look up established journals in the field and use their models (if they have a common one).

I personally prefer your second alternative but would then use numbered referencing to avoid name repetition, v.g. “In his dissertation [1], Mintgen ...”


An invitation from Frontiers (Frontiers Research Topics)

As far as I can tell, a "Research Topic" is a collection of papers on a specialized topic.  It's basically a special issue of one of their journals, although it's presented slightly differently, and they charge publication fees for the papers.

What really turns me off is the publisher's spamming practices.  I've had exactly the same experience you have: they send what's pretty obviously a form letter (populated with your name and one publication title/journal, seemingly randomly selected) and then some months later send a passive-aggressive reminder asking for a reply.  Maybe this is a coincidence, but I also got a follow-up message from them on February 12, so perhaps they sent out a whole wave of them on that day.  In any case, the fact that they feel they have to advertise by spamming makes me suspicious, and the reminder messages are irritating.


In my experience a major point is to engage with other's research. The most common occasion is to attend regularly seminars, and go to conferences. By listening to research talks, you will learn about tools which might apply to some of your questions, and about questions for which you might have the right tools.

Another possibility is simply to read other's research, but it is quite difficult to decide in what direction to read, while when you have a weekly seminar to attend you get in touch with ideas regularly without having to be proactive.

Maybe there is a subfield, with connexion with what you already know, where you heard things are happening and someone wrote a nice survey? Then read that and see if it leads you somewhere.


How to find collaborators for just writing and formatting manuscripts

Writing the manuscript is a significant scientific contribution. Is your research so trivial that anybody can interpret the data that you give them and write to a high scientific caliber on them, with no further inputs from you? Most likely, you'd need to also provide them with a rigorous analysis of that data, probably in writing form, since they might no share an office with you, and also for record keeping. That explanation becomes the crux of a paper that you could write yourself in the first place. The time spent explaining the data to someone not involved in an experiment will be greater than just writing the thing yourself. You'd be only saving time on tiny matters of sentence formulation, if you'd even save time at all.

Formatting a paper in my experience doesn't take that much time, so I'm not sure where you're coming from in on that point. Most journals provide you with a template that you can literally copy paste into. If something is straightforward as you say, it shouldn't take that much time at all. If by "getting bibliography", you mean compiling the bibliography, that will also be something that only you, being familiar with the experiment, can provide. A bibliography should be something that arises naturally from the need to reference previous methods/works for your analysis, not a chunk that you copy paste between papers without thoughts.

If you mean that they also do the data analysis, then they just become a regular scientific collaborator, with full authorship rights.


Doctorate with no affiliation submitting to a publication with an undergrad co-author

Your affiliation could be "Independent Researcher" or similar, though blank might be allowed.
The other person may require permission from the company to name them, even though permission to publish has been given. It is best to check.
But your listing seems to imply that you both are affiliated with XYZ, which is not the case. You probably need to clarify that.
And yes, her degree can, and probably should, be listed. Use whatever the diploma shows: BS, BSc, ...


How to react to this editor response after a long fruitless review phase?

Actually, you don't need their permission to withdraw the paper until you give them the copyright after final acceptance. The paper is yours to do with as you please.

The answer you got is hard to decipher. It makes me question their competence, as does the long time "in review".

Just tell them that you are withdrawing, though you might want to wait out the month that you offered.

Find a better publisher.


Should I offer to give a presentation in a postdoc interview if not requested in the invitation?

It would probably be worth it to develop such a thing as a backup, but I wouldn't offer it unasked.
If they already have an idea of the things they need to know and have questions ready, then I doubt that it would help and, unless it is "just right" (whatever that means), it could hurt.
Give them what they ask for.
But preparing a presentation will probably help you prepare and give you a bit of practice in presenting yourself. If nothing else, it gives you sentences and phrases to drop in as needed in the interview.


Correlation between GRE Scores and Profile

It will really depend on the university. Some universities look closely at the GRE score, others, like the one I teach at, require the GRE but only use it for borderline admission cases. There's a growing trend among universities to ignore the GRE altogether, since it doesn't correlate well with success in postgrad.


Applying for MS in CS - what are the programming languages I must know before starting graduate school?

You don´t need any specific languages.

Try to get your "basic" skills in (some of) the languages you already know to an "advanced" or "expert" level. Doing this you will automatically understand and internalize the concepts behind the programming languages.

All the rest is just syntax and you will be able to pretty much learn many other languages "on the fly" if needed.


Should a paper be reviewed in entirety, if the introduction contains plagiarized passages?

I think you've pretty much done your review.  You found a whole bunch of plagiarism up front, and that's enough to recommend rejection of the article.  Document your findings and report to the editor.  Even if the rest of the article turned out to be brilliant and original, there is no way it can be anything other than rejected and possibly even formal proceedings against the authors.


Can my supervisor steal my theoretical achievements, and publish a paper without me

Collaborating with someone you don't trust is no fun.  I do not speak from direct experience -- I have certainly trusted and remained on positive terms with all of my collaborators.  Yet even under these favorable conditions there are (most) often some conflicts with one's collaborators: e.g. (i) they are dragging their feet / pushing you forward impatiently, (ii) including sloppy and inaccurate / pedantically correct and overly lengthy text, (iii) pushing for publication of a modest partial result / never being satisfied with what has already been obtained, (iv) shooting way too low / way too high in the choice of journal...and so forth.  If I thought that my collaborators truly did not have my best interests at heart...yikes.  This goes doubly when there is a significant differential of power / seniority among collaborators: there can be a fine line between giving your junior collaborator the benefit of your additional experience and insisting that they do things your way.

I'm very sorry to hear that you are worried that your advisor may try to steal your joint work.  If your question is really whether it is in any way ethically acceptable or appropriate for him to do so, the answer is easy: of course not.  However, that you ask shows either great inexperience / mild paranoia on your part or is a sign that the collaboration is dangerously in the "no fun" range.  I looked at your profile and saw that you are a PhD student at a quite reputable research university in the US.  Moreover based on your username I suspect that you are either one of two students with that name in a certain department (not the math department) at that university, each with the same advisor, a young faculty member with an impressive CV.  Obviously I can't promise anything, but in all of my experience a faculty member with a CAREER grant is not someone who would want or need to steal their student's work: not even close, and not on their worst day.  (As an aside, the fact that I suspect that I have identified your advisor whom you are one step away from accusing of stealing your joint work is not great, and you should think about being a bit more circumspect.)

I advise you to concentrate on improving the interpersonal aspects of your collaboration: try to understand your advisor better and vice versa, and try to shore up trust.  If you really can't do that, it's time to find a new advisor.  Though I don't know the situation, based on the fact that you've given no convincing evidence for your suspicions and some other clues, my guess is that you are rather new to research (at least of this kind or at this level) and that as you "learn the ropes" your suspicions will be assuaged.  If you have made a significant mathematical (note: not "mathematic"!) breakthrough, then indeed you should proceed carefully and patiently and not rush into publication.  If the paper is not well written -- according to standards that are difficult to meet or even fully grasp for most graduate students -- that can affect its reception and jeopardize its suitability for publication in a top journal.

Good luck.


Advisor says I shouldn't expect to finish thesis soon, but won't offer specific feedback on what is missing; how to react?

My PhD advisor once told me that one aspect he considers when rating a thesis is how much the candidate did try to go beyond the initial idea or goal. If they are like "I solved the initial problem, here's the thesis, I just want to finish a fast as possible" then they will earn an intermediate grade at the end. Only if they try to go beyond the initial problem, try to at least estimate the further implications or steps or apply the outcome of the initial problem to further problems, they really can earn a top grade.

To my experience, to successfully finish a physics PhD within roughly a year, you have to have had really great luck to find something really excitingly new that provided a huge progress to your specific field. In most cases after one year you can't even tell for sure what the final focus of the thesis will be. Those applications of the theory to some example cases can easily take up more time than the whole development of the theory as there might come up issues and flaws that you were not expecting. Also their importance is not necessarily reflected in the number of pages they make up in the final thesis.

Therefore it seems to me, that you are somewhat belonging to the first type of people mentioned above who are just heading to leave before really having understood the implications of what they were working on.